ContentsArticles

EIA Class 1 dielectric 1EIA Class 2 dielectric 2Barium titanate 4Strontium titanate 7Curie temperature 11Piezoelectricity 13Permittivity 25Electric susceptibility 31Relative permittivity 32Permeability (electromagnetism) 36Sintering 40

ReferencesArticle Sources and Contributors 48Image Sources, Licenses and Contributors 49

Article LicensesLicense 50

EIA Class 1 dielectric 1

EIA Class 1 dielectricThe EIA Class 1 dielectric materials are ceramic dielectric materials used in ceramic capacitors of small values(typically <5 nF). The EIA Class 1 dielectrics in general are usually based on titanate formulas (usually titaniumdioxide with calcium titanate) with low or zero content of barium titanate; due to that low content, their susceptibilityto microphonics is low. (Cf. EIA Class 2 dielectric.) Their dependence on temperature is linear.C0G (EIA) or NP0 (industry spec) is the material with the lowest capacitance/temperature dependence(Negative-Positive zero). C0G/NP0 dielectrics have the lowest losses, and are used in filters, as timing elements, andfor balancing crystal oscillators.Ceramic capacitors tend to have low inductance because of their flat plate construction. Most other types of capacitorare wound and thus inductive. This makes ceramic capacitors well suited to high-frequency work, where they areoften used as a leadless disc or plate soldered inline with the PCB track.NP0 refers to the shape of the capacitor's temperature coefficient graph (how capacitance changes with temperature).NP0 means that the graph is flat and the device is not affected by temperature changes. The C0G/NP0 material canbe used up to gigahertz frequencies.Common materials are C0G/NP0, P350, N1000/M3K.The ceramic composition may involve one or more of dielectric electroceramics materials.There are two naming conventions. The EIA version relies on letter-digit-letter code for the slope of thetemperature-capacitance dependence. The industry version uses a N/P prefix (N for negative, P for positive) and theslope coefficient. See the comparison for some common materials:

EIA M7G C0G B2G U1G P2G R2G S2H T2H U2J P3K R3L

Industry P100 NP0 N030 N075 N150 N220 N330 N470 N750 N1500 N2200

The EIA three-character code for the material capacitance-temperature slope is derived from the low and hightemperature limit, and the range of capacitance change.

ppm/°C

C 0.0

B 0.3

L 0.8

A 0.9

M 1.0

P 1.5

R 2.2

S 3.3

T 4.7

V 5.6

U 7.5

Multiplier

0 -1

1 -10

2 -100

3 -1000

4 +1

6 +10

7 +100

8 +1000

Tolerance in ppm/°C (25-85 °C)

G ±30

H ±60

J ±120

K ±250

L ±500

M ±1000

N ±2500

EIA Class 2 dielectric 2

EIA Class 2 dielectricThe EIA Class 2 dielectric materials are ceramic dielectric materials used in ceramic capacitors.The EIA Class 2 dielectrics in general are usually based on formulas with high content of barium titanate (BT),possibly mixed with other dielectric electroceramics. Due to its piezoelectric properties, they are subject tomicrophonics. Other oxides added can be the same as used for Class 1 ceramics.

Comparison to Class 1 dielectricsIn comparison with the EIA Class 1 dielectrics they tend to have severe temperature drift, high dependence ofcapacitance on applied voltage, high voltage coefficient of dissipation factor, high frequency coefficient ofdissipation, and problems with aging due to gradual change of crystal structure. Aging causes gradual exponentialloss of capacitance and decrease of dissipation factor.

Marking codeThe EIA three-character code is derived from the minimum and maximum temperature limit, and the amount ofcapacitance change permitted within that range.

Minimumtemperature

X -55 °C

Y -30 °C

Z +10 °C

Maximumtemperature

4 +65 °C

5 +85 °C

6 +105 °C

7 +125 °C

8 +150 °C

9 +200 °C

Capacitancechange permitted

A ±1.0%

B ±1.5%

C ±2.2%

D ±3.3%

E ±4.7%

F ±7.5%

L +15% / -40%

P ±10%

R ±15%

S ±22%

T +22% / -33%

U +22% / -56%

V +22% / -82%[1]

EIA Class 2 dielectric 3

Common typesAlthough this code can describe a huge number of possible dielectrics, only a few are commonly manufactured.X5R performs better than other dielectrics, such as Y5V, and permits the construction of physically smallercapacitors than other dielectrics, such as NP0 and X7R. Typically its temperature variation of capacitance is +/-15%over a range of -55 to +85 degrees Celsius. The temperature variation is, however, non-linear.X7R is designed for capacitors with capacity ranging typically between 3.3 nF to 330 nF (SMT: 100 pF to 10 µF).Good for non-critical coupling, filtering, transient voltage suppression, and timing applications. Has high dielectricconstant. It is an EIA Class 2 dielectric. Its variation over a temperature range of −55 to +125 °C is ±15%.Y5P and Y5V are other such class 2 ceramics, with temperature range of −30 to +85 °C and wide capacitancechange with temperature of ±10% or +22/-82%.[1] Usually used for capacitances between 150 pF and 2 nF (SMT: 10nF to 10 µF). Y5P is equivalent to the IEC code 2B4.Z5U is commonly found from 2.2 nF to 2.2 µF, 20%. Good for bypass, coupling applications. Low price and smallsize, poor temperature stability. This is equivalent to the IEC code 2E6.

References[1] AVX. "Y5V Dielectric" (http:/ / download. siliconexpert. com/ pdfs/ Caps/ AVX/ Cy5v. pdf) (pdf). siliconexpert.com. . Retrieved 2011

October 31.

Barium titanate 4

Barium titanate

Barium titanate

Identifiers

CAS number 12047-27-7 [1] 

PubChem 6101006 [2]

ChemSpider 10605734 [3] 

RTECS number XR1437333

Jmol-3D images Image 1 [4]

Properties

Molecular formula BaTiO3

Molar mass 233.192 g/mol

Appearance white crystals

Odor odorless

Density 6.02 g/cm3, solid

Melting point 1625 °C

Solubility in water insoluble

Solubility slightly soluble in dilute mineral acids; dissolves in concentrated sulfuric acid and hydrofluoric acid

Band gap 3.2 eV (300 K, single crystal)[5]

Structure

Crystal structure Tetragonal, tP5

Space group P4mm, No. 99

Hazards

R-phrases R20/22

S-phrases S28A, S37, and S45

  (verify) [6] (what is:  / ?)Except where noted otherwise, data are given for materials in their standard state (at 25 °C, 100 kPa)

Infobox references

Barium titanate is the inorganic compound with the chemical formula BaTiO3. Barium titanate is a white powder and transparent as larger crystals. This titanate is a ferroelectric ceramic material, with a photorefractive effect and

Barium titanate 5

piezoelectric properties.

Structure

Structure of cubic BaTiO3. The red spheres areoxide centres, blue are Ti4+ cations, and the green

spheres are Ba2+.

The solid can exist in five phases, listing from high temperature to lowtemperature: hexagonal, cubic, tetragonal, orthorhombic, andrhombohedral crystal structure. All of the phases exhibit theferroelectric effect except the cubic phase. The high temperature cubicphase is easiest to describe, consisting of octahedral TiO6 centres thatdefine a cube with Ti vertices and Ti-O-Ti edges. In the cubic phase,Ba2+ is located at the center of the cube, with a nominal coordinationnumber of 12. Lower symmetry phases are stabilized at lowertemperatures, associated with the movement of the Ba2+ to off-centerposition. The remarkable properties of this material arise from thecooperative behavior of the Ba2+ centres.

Production and handling properties

Barium titanate can be manufactured by heating barium carbonate andtitanium dioxide. The reaction proceeds via liquid phase sintering. Single crystals can be grown around 1100 °Cfrom molten potassium fluoride.[7] Other materials are often added for doping, e.g. to give solid solutions withstrontium titanate. Reacts with nitrogen trichloride and produces a greenish or grey mixture, the ferroelectricproperties of the mixture are still present in this form.

Much work has been dedicated to its morphology. Fully dense nanocrystalline barium titanate has 40% higherpermittivity than the same material prepared in classic ways.[8] The addition of inclusions of barium titanate to tinhas been shown to produce a bulk material with a higher viscoelastic stiffness than that of diamonds. Barium titanategoes through two phase transitions that change the crystal shape and volume. This phase change leads to compositeswhere the barium titanates have a negative bulk modulus (Young's modulus), meaning that when a force acts on theinclusions, there is displacement in the opposite direction, further stiffening the composite.[9]

Like many oxides, barium titanate is insoluble in water but attacked by sulfuric acid. Its bulk room-temperaturebandgap is 3.2 eV, but it increases to ~3.5 eV when the particle size is reduced from about 15 to 7 nm.[5]

UsesBarium titanate is a dielectric ceramic used for capacitors. It is a piezoelectric material for microphones and othertransducers. The spontaneous polarization of barium titanate is about 0.15 C/m2 at room temperature and its Curiepoint is 120 °C.[10] As a piezoelectric material, it was largely replaced by lead zirconate titanate, also known as PZT.Polycrystalline barium titanate displays positive temperature coefficient, making it a useful material for thermistorsand self-regulating electric heating systems.Barium titanate crystals find use in nonlinear optics. The material has high beam-coupling gain, and can be operatedat visible and near-infrared wavelengths. It has the highest reflectivity of the materials used for self-pumped phaseconjugation (SPPC) applications. It can be used for continuous-wave four-wave mixing with milliwatt-range opticalpower. For photorefractive applications, barium titanate can be doped by various other elements, e.g. iron.[11]

Thin films of barium titanate display electrooptic modulation to frequencies over 40 GHz.[12]

The pyroelectric and ferroelectric properties of barium titanate are used in some types of uncooled sensors forthermal cameras.

Barium titanate 6

High purity barium titanate powder is reported to be a key component of new barium titanate capacitor energystorage systems for use in electric vehicles.[13]

Natural occurrenceBarioperovskite is a very rare natural analogue of BaTiO3, found as microinclusions in benitoite.

References[1] http:/ / www. commonchemistry. org/ ChemicalDetail. aspx?ref=12047-27-7[2] http:/ / pubchem. ncbi. nlm. nih. gov/ summary/ summary. cgi?cid=6101006[3] http:/ / www. chemspider. com/ 10605734[4] http:/ / chemapps. stolaf. edu/ jmol/ jmol. php?model=%5BBa%2B2%5D. %5BBa%2B2%5D.

%5BO-%5D%5BTi%5D%28%5BO-%5D%29%28%5BO-%5D%29%5BO-%5D[5] Keigo Suzuki and Kazunori Kijima (2005). "Optical Band Gap of Barium Titanate Nanoparticles Prepared by RF-plasma Chemical Vapor

Deposition". Jpn. J. Appl. Phys. 44: 2081–2082. doi:10.1143/JJAP.44.2081.[6] http:/ / en. wikipedia. org/ wiki/ Special%3Acomparepages?rev1=455377376& page2=%3ABarium+ titanate[7] Francis S. Galasso "Barium Titanate, BaTiO3" Inorganic Syntheses 1973, Volume 14, 142–143. doi:10.1002/9780470132456.ch28.[8] Nyutu, Edward K.; Chen, Chun-Hu; Dutta, Prabir K.; Suib, Steven L. (2008). "Effect of Microwave Frequency on Hydrothermal Synthesis of

Nanocrystalline Tetragonal Barium Titanate". The Journal of Physical Chemistry C 112 (26): 9659. doi:10.1021/jp7112818.[9] Jaglinski, T; Kochmann, D; Stone, D; Lakes, Rs (2007). "Composite materials with viscoelastic stiffness greater than diamond". Science 315

(5812): 620–2. doi:10.1126/science.1135837. PMID 17272714.[10] Wadhawan, Vinod K. (2000). Introduction to ferroic materials. CRC Press. p. 10. ISBN 9789056992866.[11] "Fe:LiNbO3 Crystal" (http:/ / www. redoptronics. com/ Fe-LiNbO3-crystal. html). . Retrieved 2009-06-06.[12] Tang, Pingsheng; Towner, D; Hamano, T; Meier, A; Wessels, B (2004). "Electrooptic modulation up to 40 GHz in a barium titanate thin

film waveguide modulator". Optics Express 12 (24): 5962–7. doi:10.1364/OPEX.12.005962. PMID 19488237.[13] "Nanoparticle Compatibility: New Nanocomposite Processing Technique Creates More Powerful Capacitors" (http:/ / gtresearchnews.

gatech. edu/ newsrelease/ barium-titanate. htm). . Retrieved 2009-06-06.

External links• Nanoparticle Compatibility: New Nanocomposite Processing Technique Creates More Powerful Capacitors (http:/

/ gtresearchnews. gatech. edu/ newsrelease/ barium-titanate. htm)• EEStor's "instant-charge" capacitor batteries (http:/ / blog. wired. com/ gadgets/ 2007/ 09/ instant-charge-. html)

Strontium titanate 7

Strontium titanate

Strontium titanate

Identifiers

CAS number 12060-59-2 [1] 

PubChem 82899 [2]

ChemSpider 74801 [3] 

EC number 235-044-1 [4]

MeSH Strontium+titanium+oxide [5]

Jmol-3D images Image 1 [6]

Image 2 [7]

Properties

Molecular formula SrTiO3

Molar mass 183.49 g mol−1

Exact mass 183.838305258 g mol−1

Appearance White, opaque crystals

Density 5.1 g cm−3[8]

Melting point 2080 °C (3740 °F)[8]

Refractive index (nD) 2.41

Structure

Crystal structure Simple cubic

  (verify) [9] (what is:  / ?)Except where noted otherwise, data are given for materials in their standard state (at 25 °C, 100 kPa)

Infobox references

Strontium titanate is an oxide of strontium and titanium with the chemical formula SrTiO3. At room temperature, it is a centrosymmetric paraelectric material with a perovskite structure. At low temperatures it approaches a ferroelectric phase transition with a very large dielectric constant ~104 but remains paraelectric down to the lowest temperatures measured as a result of quantum fluctuations.[10] It was long thought to be a wholly artificial material, until 1982 when its natural counterpart—discovered in Siberia and named tausonite—was recognised by the IMA. Tausonite remains an extremely rare mineral in nature, occurring as very tiny crystals. Its most important application

Strontium titanate 8

has been in its synthesized form wherein it is occasionally encountered as a diamond simulant, in precision optics, invaristors, and in advanced ceramics.The name tausonite was given in honour of Lev Vladimirovich Tauson (1917–1989), a Russian geochemist. Disusedtrade names for the synthetic product include strontium mesotitanate, Fabulite, Diagem, and Marvelite. Other thanits type locality of the Murun Massif in the Sakha Republic, natural tausonite is also found in Cerro Sarambi,Concepción department, Paraguay; and along the Kotaki River of Honshū, Japan.[11][12]

Properties

Atomic resolution image of SrTiO3. Brighteratoms are Sr and darker ones are Ti

Structure of SrTiO3. The red spheres are oxygens,blue are Ti4+ cations, and the green ones are Sr2+.

Strontium titanate is both much denser (specific gravity 4.88 fornatural, 5.13 for synthetic) and much softer (Mohs hardness 6–6.5 fornatural, 5.5 for synthetic) than diamond. Its crystal system is cubic andits refractive index (2.41—as measured by sodium light, 589.3 nm) isnearly identical to that of diamond, but the dispersion (the opticalproperty responsible for the "fire" of the cut stones) of strontiumtitanate is over four times higher, at 0.19 (B–G interval). This results inan excess of fire when compared to diamond.[11][12]

Synthetics are usually transparent and colourless, but can be dopedwith certain rare earth or transition metals to give reds, yellows,browns, and blues. Natural tausonite is usually translucent to opaque,in shades of reddish brown, dark red, or grey. Both have an adamantine(diamond-like) lustre. Strontium titanate is considered extremely brittlewith a conchoidal fracture; natural material is cubic or octahedral inhabit and streaks brown. Through a hand-held (direct vision)spectroscope, doped synthetics will exhibit a rich absorption spectrumtypical of doped stones. Synthetic material has a melting point of ca.2080 °C (3776 °F) and is readily attacked by hydrofluoric acid.[11][12]

The synthetic material has a very large dielectric constant (300) atroom temperature and low electric field. It is also used in high-voltagecapacitors. Strontium titanate becomes superconducting below 0.35 Kand was the first insulator and oxide discovered to be

superconductive.[13]

At temperatures lower than 105 K, its cubic structure transforms to tetragonal.[14] It is an excellent substrate forepitaxial growth of high-temperature superconductors and many oxide-based thin films. Its monocrystals can be usedas optical windows and high-quality sputter deposition targets.

SrTiO3 is a suitable material for electronics: niobium-doped strontium titanate, is electrically conductive.High-quality, epitaxial SrTiO3 layers can also be grown on silicon without forming silicon dioxide, thereby makingSrTiO3 an alternative gate dielectric material. This also enables the integration of other thin film perovskite oxidesonto silicon.[15]

Strontium titanate 9

Synthesis

A plate cut out of synthetic SrTiO3crystal

Synthetic strontium titanate was one of several titanates patented during the late1940s and early 1950s; other titanates included barium titanate and calciumtitanate. Research was conducted primarily at the National Lead Company (laterrenamed N. L. Industries, Inc.) in the United States, by Leon Merker and LangtryE. Lynd. Merker and Lynd first patented the growth process on February 10,1953; a number of refinements were subsequently patented over the next fouryears, such as modifications to the feed powder and additions of colouringdopants.

A modification to the basic Verneuil process (also known as flame-fusion) is thefavoured method of growth. An inverted oxy-hydrogen blowpipe is used, withfeed powder mixed with oxygen carefully fed through the blowpipe in the typical fashion, but with the addition of athird pipe to deliver oxygen—creating a tricone burner. The extra oxygen is required for successful formation ofstrontium titanate, which would otherwise fail to oxidize completely due to the titanium component. The ratio is ca.1.5 volumes of hydrogen for each volume of oxygen. The highly purified feed powder is derived by first producingtitanyl double oxalate salt (SrTiO(C2O4)2·2H2O) by reacting strontium chloride (SrCl2) and oxalic acid((COOH)2.2H2O) with titanium tetrachloride (TiCl4). The salt is washed to completely eliminate chloride, heated to1000 °C in order to produce a free-flowing granular powder of the required composition, and is then ground andsieved to ensure all particles are between 0.2–0.5 micrometres in size.[16]

The feed powder falls through the oxyhydrogen flame, melts, and lands on a rotating and slowly descending pedestalbelow. The height of the pedestal is constantly adjusted to keep its top at the optimal position below the flame, andover a number of hours the molten powder cools and crystallises to form a single pedunculated pear or boule crystal.This boule is usually no larger than 2.5 centimetres in diameter and 10 centimetres long; it is an opaque black tobegin with, requiring further annealing in an oxidizing atmosphere in order to make the crystal colourless and torelieve strain. This is done at over 1000 °C for 12 hours.[16]

Use as a diamond simulantIts cubic structure and high dispersion once made synthetic strontium titanate a prime candidate for simulatingdiamond. Beginning ca. 1955, large quantities of strontium titanate were manufactured for this sole purpose.Strontium titanate was in competition with synthetic rutile ("titania") at the time, and had the advantage of lackingthe unfortunate yellow tinge and strong birefringence inherent to the latter material. While it was softer, it wassignificantly closer to diamond in likeness. Eventually, however, both would fall into disuse, being eclipsed by thecreation of "better" simulants: first by yttrium aluminium garnet (YAG) and followed shortly after by gadoliniumgallium garnet (GGG); and finally by the (to date) ultimate simulant in terms of diamond-likeness andcost-effectiveness, cubic zirconia.[17]

Despite being outmoded, strontium titanate is still manufactured and periodically encountered in jewellery. It is oneof the most costly of diamond simulants, and due to its rarity collectors may pay a premium for large i.e. >2 carat(400 mg) specimens. As a diamond simulant, strontium titanate is most deceptive when mingled with melée i.e.<0.20 carat (40 mg) stones and when it is used as the base material for a composite or doublet stone (with, e.g.,synthetic corundum as the crown or top of the stone). Under the microscope, gemmologists distinguish strontiumtitanate from diamond by the former's softness—manifested by surface abrasions—and excess dispersion (to thetrained eye), and occasional gas bubbles which are remnants of synthesis. Doublets can be detected by a join line atthe girdle ("waist" of the stone) and flattened air bubbles or glue visible within the stone at the point ofbonding.[18][19][20]

Strontium titanate 10

References[1] http:/ / www. commonchemistry. org/ ChemicalDetail. aspx?ref=12060-59-2[2] http:/ / pubchem. ncbi. nlm. nih. gov/ summary/ summary. cgi?cid=82899[3] http:/ / www. chemspider. com/ 74801[4] http:/ / esis. jrc. ec. europa. eu/ index. php?GENRE=ECNO& ENTREE=235-044-1[5] http:/ / www. nlm. nih. gov/ cgi/ mesh/ 2007/ MB_cgi?mode=& term=Strontium+ titanium+ oxide[6] http:/ / chemapps. stolaf. edu/ jmol/ jmol. php?model=%5BSr%2B%2B%5D. %5BO-%5D%5BTi%5D%28%5BO-%5D%29%3DO[7] http:/ / chemapps. stolaf. edu/ jmol/ jmol. php?model=%5BSr%2B2%5D. %5BO-%5D%5BTi%5D%28%5BO-%5D%29%3DO[8] Lide, D. R., ed. (2005). CRC Handbook of Chemistry and Physics (86th ed.). Boca Raton (FL): CRC Press. p. 4.89. ISBN 0-8493-0486-5.[9] http:/ / en. wikipedia. org/ wiki/ Special%3Acomparepages?rev1=445096043& page2=%3AStrontium+ titanate[10] K. A. Muller and H. Burkard (1979). "SrTiO3: An intrinsic quantum paraelectric below 4 K". Phys. Rev. B 19 (7): 3593–3602.

doi:10.1103/PhysRevB.19.3593.[11] "Tausonite" (http:/ / webmineral. com/ data/ Tausonite. shtml). Webmineral.. . Retrieved 2009-06-06.[12] "Tausonite" (http:/ / www. mindat. org/ min-3895. html). Mindat. . Retrieved 2009-06-06.[13] Koonce, C. S.; Cohen, Marvin L. (1967). "Superconducting Transition Temperatures of Semiconducting SrTiO3". Phys. Rev. 163 (2): 380.

Bibcode 1967PhRv..163..380K. doi:10.1103/PhysRev.163.380.[14] L. Rimai and G. A. deMars (1962). "Electron Paramagnetic Resonance of Trivalent Gadolinium Ions in Strontium and Barium Titanates".

Phys. Rev. 127 (3): 702. doi:10.1103/PhysRev.127.702.[15] R. A. McKee, F. J. Walker, and M. F. Chisholm (1998). "Crystalline Oxides on Silicon: The First Five Monolayers". Phys. Rev. Lett. 81

(14): 3014. Bibcode 1998PhRvL..81.3014M. doi:10.1103/PhysRevLett.81.3014.[16] H. J. Scheel and P. Capper (2008). Crystal growth technology: from fundamentals and simulation to large-scale production. Wiley-VCH.

p. 431. ISBN 3527317627.[17] R. W. Hesse (2007). Jewelrymaking through history: an encyclopedia. Greenwood Publishing Group. p. 73. ISBN 0313335079.[18] Nassau, K. (1980). Gems made by man. Santa Monica, California: Gemological Institute of America. pp. 214–221. ISBN 0873110161.[19] O'Donoghue, M. (2002). Synthetic, imitation & treated gemstones. Great Britain: Elsevier Butterworth-Heinemann. pp. 34, 65.

ISBN 0750631732.[20] Read, P. G. (1999). Gemmology, second edition. Great Britain: Butterworth-Heinemann. pp. 173, 176, 177, 293. ISBN 0-7506-4411-7.

External links• An electron micrograph of strontium titanate, as artwork entitled "Strontium" at the DeYoung Museum in San

Francisco (http:/ / www. famsf. org/ deyoung/ about/ subpage. asp?subpagekey=731)

Curie temperature 11

Curie temperatureIn physics and materials science, the Curie temperature (T

c), or Curie point, is the temperature at which a

ferromagnetic or a ferrimagnetic material becomes paramagnetic on heating; the effect is reversible. A magnet willlose its magnetism if heated above the Curie temperature. The term is also used in piezoelectric materials to refer tothe temperature at which spontaneous polarization is lost on heating. An analogous temperature, the Néeltemperature, is defined for antiferromagnetic materials. The Curie temperature is named after Pierre Curie.Below the Curie temperature neighboring magnetic spins are aligned parallel within ferromagnetic materials andanti-parallel in ferrimagnetic materials. As the temperature is increased towards the Curie point, the alignment(magnetization) within each domain decreases. Above the Curie temperature, the material is paramagnetic so thatmagnetic moments are in a completely disordered state.The destruction of magnetization at the Curie temperature is a second-order phase transition and a critical pointwhere the magnetic susceptibility is theoretically infinite.A heat-induced ferromagnetic-paramagnetic transition is used in magneto-optical storage media, for erasing andwriting of new data. Famous examples include the Sony Minidisc format, as well as the now-obsolete CD-MOformat. Other uses include temperature control in soldering irons, and stabilizing the magnetic field of tachometergenerators against temperature variation.[1]

Below the Curie temperature, neighboringmagnetic spins align in a ferromagnet even if

there is no magnetic field.

Above the Curie temperature, the magnetic spinsare randomly aligned unless a magnetic field is

applied.

Curie temperature in ferromagnetic andferrimagnetic materials

Given below are various Curie temperatures for different substances.[2]

Curie temperature 12

Substance Curie temp °C

Iron (Fe) 770

Cobalt (Co) 1130

Nickel (Ni) 358

Iron Oxide (Fe2O3) 622

Gadolinium is ferromagnetic at temperatures below 19 °C (66 °F),[3] approximately room temperature, and stronglyparamagnetic above that temperature.

Curie temperature in piezoelectric materialsIn analogy to ferromagnetic materials, the Curie temperature is also used in piezoelectric materials to describe thetemperature above which the material loses its spontaneous polarization and piezoelectric characteristics. In leadzirconate titanate (PZT), the material is tetragonal below Tc and the unit cell contains a displaced central cation andhence a net dipole moment. Above Tc, the material is cubic and the central cation is no longer displaced from thecentre of the unit cell. Hence, there is no net dipole moment and no spontaneous polarization.

The Curie-Weiss lawA simple theory predicts that, above the Curie temperature, the magnetic susceptibility, χ, is given by theCurie-Weiss law:

where C is a material-specific Curie constant, T is absolute temperature, measured in kelvins, and Tc is the Curietemperature, measured in kelvins.Thus, the susceptibility approaches infinity as the temperature approaches Tc.

[4]

Notes[1] Pallàs-Areny & Webster 2001, pp. 262–263[2][2] Buschow 2001, page 5021, table 1[3] The Elements, Theodore Gray, Black Dog & Leventhal Publishers, 2009[4][4] Kittel 1986

References• Buschow, K. H. J. (2001). Encyclopedia of materials : science and technology. Elsevier. ISBN 0-08-043152-6.• Kittel, Charles (1986). Introduction to Solid State Physics (sixth ed.). John Wiley & Sons. ISBN 0-471-87474-4.• Pallàs-Areny, Ramon; Webster, John G (2001). Sensors and Signal Conditioning (2nd ed.). John Wiley & Sons.

pp. 262–263. ISBN 978-0-471-33232-9.

External links• Ferromagnetic Curie Point (http:/ / es. youtube. com/ watch?v=X8ZHQQUusGo). Video by Walter Lewin, M.I.T.

Piezoelectricity 13

PiezoelectricityPiezoelectricity (  /piˌeɪzoʊˌilɛkˈtrɪsɪti/) is the charge that accumulates in certain solid materials (notably crystals,certain ceramics, and biological matter such as bone, DNA and various proteins)[1] in response to applied mechanicalstress. The word piezoelectricity means electricity resulting from pressure. It is derived from the Greek piezo orpiezein (πιέζειν), which means to squeeze or press, and electric or electron (ήλεκτρον), which stands for amber, anancient source of electric charge.[2] Piezoelectricity is the direct result of the piezoelectric effect.The piezoelectric effect is understood as the linear electromechanical interaction between the mechanical and theelectrical state in crystalline materials with no inversion symmetry.[3] The piezoelectric effect is a reversible processin that materials exhibiting the direct piezoelectric effect (the internal generation of electrical charge resulting froman applied mechanical force) also exhibit the reverse piezoelectric effect (the internal generation of a mechanicalstrain resulting from an applied electrical field). For example, lead zirconate titanate crystals will generatemeasurable piezoelectricity when their static structure is deformed by about 0.1% of the original dimension.Conversely, those same crystals will change about 0.1% of their static dimension when an external electric field isapplied to the material.Piezoelectricity is found in useful applications such as the production and detection of sound, generation of highvoltages, electronic frequency generation, microbalances, and ultrafine focusing of optical assemblies. It is also thebasis of a number of scientific instrumental techniques with atomic resolution, the scanning probe microscopies suchas STM, AFM, MTA, SNOM, etc., and everyday uses such as acting as the ignition source for cigarette lighters andpush-start propane barbecues.

History

Discovery and early researchThe pyroelectric effect, by which a material generates an electric potential in response to a temperature change, wasstudied by Carl Linnaeus and Franz Aepinus in the mid-18th century. Drawing on this knowledge, both René JustHaüy and Antoine César Becquerel posited a relationship between mechanical stress and electric charge; however,experiments by both proved inconclusive.The first demonstration of the direct piezoelectric effect was in 1880 by the brothers Pierre Curie and Jacques Curie.They combined their knowledge of pyroelectricity with their understanding of the underlying crystal structures thatgave rise to pyroelectricity to predict crystal behavior, and demonstrated the effect using crystals of tourmaline,quartz, topaz, cane sugar, and Rochelle salt (sodium potassium tartrate tetrahydrate). Quartz and Rochelle saltexhibited the most piezoelectricity.

Piezoelectricity 14

A piezoelectric disk generates a voltage whendeformed (change in shape is greatly

exaggerated)

The Curies, however, did not predict the converse piezoelectric effect.The converse effect was mathematically deduced from fundamentalthermodynamic principles by Gabriel Lippmann in 1881.[4] The Curiesimmediately confirmed the existence of the converse effect, and wenton to obtain quantitative proof of the complete reversibility ofelectro-elasto-mechanical deformations in piezoelectric crystals.

For the next few decades, piezoelectricity remained something of alaboratory curiosity. More work was done to explore and define thecrystal structures that exhibited piezoelectricity. This culminated in1910 with the publication of Woldemar Voigt's Lehrbuch derKristallphysik (textbook on crystal physics), which described the 20natural crystal classes capable of piezoelectricity, and rigorouslydefined the piezoelectric constants using tensor analysis.

World War I and post-warThe first practical application for piezoelectric devices was sonar, first developed during World War I. In France in1917, Paul Langevin and his coworkers developed an ultrasonic submarine detector. The detector consisted of atransducer, made of thin quartz crystals carefully glued between two steel plates, and a hydrophone to detect thereturned echo. By emitting a high-frequency chirp from the transducer, and measuring the amount of time it takes tohear an echo from the sound waves bouncing off an object, one can calculate the distance to that object.The use of piezoelectricity in sonar, and the success of that project, created intense development interest inpiezoelectric devices. Over the next few decades, new piezoelectric materials and new applications for thosematerials were explored and developed.Piezoelectric devices found homes in many fields. Ceramic phonograph cartridges simplified player design, werecheap and accurate, and made record players cheaper to maintain and easier to build. The development of theultrasonic transducer allowed for easy measurement of viscosity and elasticity in fluids and solids, resulting in hugeadvances in materials research. Ultrasonic time-domain reflectometers (which send an ultrasonic pulse through amaterial and measure reflections from discontinuities) could find flaws inside cast metal and stone objects,improving structural safety.

World War II and post-warDuring World War II, independent research groups in the United States, Russia, and Japan discovered a new class ofman-made materials, called ferroelectrics, which exhibited piezoelectric constants many times higher than naturalmaterials. This led to intense research to develop barium titanate and later lead zirconate titanate materials withspecific properties for particular applications.One significant example of the use of piezoelectric crystals was developed by Bell Telephone Laboratories.Following World War I, Frederick R. Lack, working in radio telephony in the engineering department, developed the“AT cut” crystal, a crystal that operated through a wide range of temperatures. Lack's crystal didn't need the heavyaccessories previous crystal used, facilitating its use on aircraft. This development allowed Allied air forces toengage in coordinated mass attacks through the use of aviation radio.Development of piezoelectric devices and materials in the United States was kept within the companies doing the development, mostly due to the wartime beginnings of the field, and in the interests of securing profitable patents. New materials were the first to be developed — quartz crystals were the first commercially exploited piezoelectric

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material, but scientists searched for higher-performance materials. Despite the advances in materials and thematuration of manufacturing processes, the United States market had not grown as quickly. Without many newapplications, the growth of the United States' piezoelectric industry suffered.In contrast, Japanese manufacturers shared their information, quickly overcoming technical and manufacturingchallenges and creating new markets. Japanese efforts in materials research created piezoceramic materialscompetitive to the U.S. materials, but free of expensive patent restrictions. Major Japanese piezoelectricdevelopments include new designs of piezoceramic filters for radios and televisions, piezo buzzers and audiotransducers that can connect directly to electronic circuits, and the piezoelectric igniter, which generates sparks forsmall engine ignition systems (and gas-grill lighters) by compressing a ceramic disc. Ultrasonic transducers thattransmit sound waves through air had existed for quite some time, but first saw major commercial use in earlytelevision remote controls. These transducers now are mounted on several car models as an echolocation device,helping the driver determine the distance from the rear of the car to any objects that may be in its path.

Mechanism

Piezoelectric plate used to convert audio signal tosound waves

The nature of the piezoelectric effect is closely related to theoccurrence of electric dipole moments in solids. The latter may eitherbe induced for ions on crystal lattice sites with asymmetric chargesurroundings (as in BaTiO3 and PZTs) or may directly be carried bymolecular groups (as in cane sugar). The dipole density or polarization(dimensionality [Cm/m3] ) may easily be calculated for crystals bysumming up the dipole moments per volume of the crystallographic unit cell.[5] As every dipole is a vector, thedipole density P is also a vector or a directed quantity. Dipoles near each other tend to be aligned in regions calledWeiss domains. The domains are usually randomly oriented, but can be aligned using the process of poling (not thesame as magnetic poling), a process by which a strong electric field is applied across the material, usually at elevatedtemperatures. Not all piezoelectric materials can be poled.[6]

Of decisive importance for the piezoelectric effect is the change of polarization P when applying a mechanical stress.This might either be caused by a re-configuration of the dipole-inducing surrounding or by re-orientation ofmolecular dipole moments under the influence of the external stress. Piezoelectricity may then manifest in avariation of the polarization strength, its direction or both, with the details depending on 1. the orientation of Pwithin the crystal, 2. crystal symmetry and 3. the applied mechanical stress. The change in P appears as a variationof surface charge density upon the crystal faces, i.e. as a variation of the electrical field extending between the faces,since the units of surface charge density and polarization are the same, [C/m2] = [Cm/m3]. However, piezoelectricityis not caused by a change in charge density on the surface, but by dipole density in the bulk. For example, a 1 cm3

cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500 V.[7]

Piezoelectric materials also show the opposite effect, called converse piezoelectric effect, where the application ofan electrical field creates mechanical deformation in the crystal.

Piezoelectricity 16

Mathematical descriptionPiezoelectricity is the combined effect of the electrical behavior of the material:

where D is the electric charge density displacement (electric displacement), ε is permittivity and E is electric fieldstrength, andHooke's Law:

where S is strain, s is compliance and T is stress.These may be combined into so-called coupled equations, of which the strain-charge form is:

,

where is the matrix for the direct piezoelectric effect and is the matrix for the converse piezoelectric effect.The superscript E indicates a zero, or constant, electric field; the superscript T indicates a zero, or constant, stressfield; and the superscript t stands for transposition of a matrix.The strain-charge for a material of the 4mm (C4v) crystal class (such as a poled piezoelectric ceramic such astetragonal PZT or BaTiO3) as well as the 6mm crystal class may also be written as (ANSI IEEE 176):

where the first equation represents the relationship for the converse piezoelectric effect and the latter for the directpiezoelectric effect.[8]

Although the above equations are the most used form in literature, some comments about the notation are necessary.Generally D and E are vectors, that is, Cartesian tensor of rank-1; and permittivity ε is Cartesian tensor of rank 2.Strain and stress are, in principle, also rank-2 tensors. But conventionally, because strain and stress are all symmetrictensors, the subscript of strain and stress can be re-labeled in the following fashion: 11 → 1; 22 → 2; 33 → 3; 23 →4; 13 → 5; 12 → 6. (Different convention may be used by different authors in literature. Say, some use 12 → 4; 23→ 5; 31 → 6 instead.) That is why S and T appear to have the "vector form" of 6 components. Consequently, sappears to be a 6 by 6 matrix instead of rank-4 tensor. Such a re-labeled notation is often called Voigt notation.

In total, there are 4 piezoelectric coefficients, , , , and defined as follows:

Piezoelectricity 17

where the first set of 4 terms correspond to the direct piezoelectric effect and the second set of 4 terms correspond tothe converse piezoelectric effect.[9] A formalism has been worked out for those piezoelectric crystals, for which thepolarization is of the crystal-field induced type, that allows for the calculation of piezoelectrical coefficients from electrostatic lattice constants or higher-order Madelung constants.[5]

Crystal classes

Any spatially separated charge will result in anelectric field, and therefore an electric potential.

Shown here is a standard dielectric in a capacitor.In a piezoelectric device, mechanical stress,

instead of an externally applied voltage, causesthe charge separation in the individual atoms of

the material, .

Of the thirty-two crystal classes, twenty-one are non-centrosymmetric(not having a centre of symmetry), and of these, twenty exhibit directpiezoelectricity (the 21st is the cubic class 432). Ten of these representthe polar crystal classes, which show a spontaneous polarizationwithout mechanical stress due to a non-vanishing electric dipolemoment associated with their unit cell, and which exhibitpyroelectricity. If the dipole moment can be reversed by the applicationof an electric field, the material is said to be ferroelectric.

•• Polar crystal classes: 1, 2, m, mm2, 4, 4 mm, 3, 3m, 6, 6 mm.•• Piezoelectric crystal classes: 1, 2, m, 222, mm2, 4, 4, 422, 4 mm,

42m, 3, 32, 3m, 6, 6, 622, 6 mm, 62m, 23, 43m.For polar crystals, for which P ≠ 0 holds without applying amechanical load, the piezoelectric effect manifests itself by changingthe magnitude or the direction of P or both. For the non-polar, butpiezoelectric crystals, on the other hand, a polarization P different fromzero is only elicited by applying a mechanical load. For them the stresscan be imagined to transform the material from a non-polar crystalclass (P =0) to a polar one,[5] having P ≠ 0.

Materials

Many materials, both natural and man-made, exhibit piezoelectricity:

Naturally occurring crystals

• Berlinite (AlPO4), a rare phosphate mineral that is structurally identical to quartz• Sucrose (table sugar)•• Quartz•• Rochelle salt•• Topaz•• Tourmaline-group minerals

Piezoelectricity 18

Other natural materials• Bone: Dry bone exhibits some piezoelectric properties. Studies of Fukada et al. showed that these are not due to

the apatite crystals, which are centrosymmetric, thus non-piezoelectric, but due to collagen. Collagen exhibits thepolar uniaxial orientation of molecular dipoles in its structure and can be considered as bioelectret, a sort ofdielectric material exhibiting quasipermanent space charge and dipolar charge. Potentials are thought to occurwhen a number of collagen molecules are stressed in the same way displacing significant numbers of the chargecarriers from the inside to the surface of the specimen. Piezoelectricity of single individual collagen fibrils wasmeasured using piezoresponse force microscopy, and it was shown that collagen fibrils behave predominantly asshear piezoelectric materials.[10]

The piezoelectric effect is generally thought to act as a biological force sensor.[11][12] This effect was exploited byresearch conducted at the University of Pennsylvania in the late 1970s and early 1980s, which established thatsustained application of electrical potential could stimulate both resorption and growth (depending on the polarity) ofbone in-vivo.[13] Further studies in the 1990s provided the mathematical equation to confirm long bone wavepropagation as to that of hexagonal (Class 6) crystals.[14]

•• Tendon•• Silk• Wood due to piezoelectric texture•• Enamel•• Dentin

Man-made crystals• Gallium orthophosphate (GaPO4), a quartz analogic crystal• Langasite (La3Ga5SiO14), a quartz analogic crystal

Man-made ceramics

Tetragonal unit cell of lead titanate

The family of ceramics with perovskite or tungsten-bronze structuresexhibits piezoelectricity:

• Barium titanate (BaTiO3)—Barium titanate was the firstpiezoelectric ceramic discovered.

• Lead titanate (PbTiO3)• Lead zirconate titanate (Pb[ZrxTi1−x]O3 0≤x≤1)—more commonly

known as PZT, lead zirconate titanate is the most commonpiezoelectric ceramic in use today.

• Potassium niobate (KNbO3)• Lithium niobate (LiNbO3)• Lithium tantalate (LiTaO3)• Sodium tungstate (Na2WO3)• Zinc oxide (Zn2O3)• Ba2NaNb5O5• Pb2KNb5O15

Piezoelectricity 19

Lead-free piezoceramicsMore recently, there is growing concern regarding the toxicity in lead-containing devices driven by the result ofrestriction of hazardous substances directive regulations. To address this concern, there has been a resurgence in thecompositional development of lead-free piezoelectric materials.• Sodium potassium niobate ((K,Na)NbO3). In 2004, a group of Japanese researchers led by Yasuyoshi Saito

discovered a sodium potassium niobate composition with properties close to those of PZT, including a high .[15]

• Bismuth ferrite (BiFeO3) is also a promising candidate for the replacement of lead-based ceramics.• Sodium niobate NaNbO3• Bismuth titanate Bi4Ti3O12• Sodium bismuth titanate Na0.5Bi0.5TiO3So far, neither the environmental impact nor the stability of supplying these substances have been confirmed.

Polymers• Polyvinylidene fluoride (PVDF): PVDF exhibits piezoelectricity several times greater than quartz. Unlike

ceramics, where the crystal structure of the material creates the piezoelectric effect, in polymers the intertwinedlong-chain molecules attract and repel each other when an electric field is applied.

ApplicationsCurrently, industrial and manufacturing is the largest application market for piezoelectric devices, followed by theautomotive industry. Strong demand also comes from medical instruments as well as information andtelecommunications. The global demand for piezoelectric devices was valued at approximately US$14.8 billion in2010. The largest material group for piezoelectric devices is piezocrystal , and piezopolymer is experiencing thefastest growth due to its light weight and small size.[16]

Piezoelectric crystals are now used in numerous ways:

High voltage and power sourcesDirect piezoelectricity of some substances like quartz, as mentioned above, can generate potential differences ofthousands of volts.• The best-known application is the electric cigarette lighter: pressing the button causes a spring-loaded hammer to

hit a piezoelectric crystal, producing a sufficiently high voltage electric current that flows across a small sparkgap, thus heating and igniting the gas. The portable sparkers used to light gas grills or stoves work the same way,and many types of gas burners now have built-in piezo-based ignition systems.

• A similar idea is being researched by DARPA in the United States in a project called Energy Harvesting, whichincludes an attempt to power battlefield equipment by piezoelectric generators embedded in soldiers' boots.However, these energy harvesting sources by association have an impact on the body. DARPA's effort to harness1-2 watts from continuous shoe impact while walking were abandoned due to the impracticality and thediscomfort from the additional energy expended by a person wearing the shoes. Other energy harvesting ideasinclude harvesting the energy from human movements in train stations or other public places[17][18] andconverting a dance floor to generate electricity.[19] Vibrations from industrial machinery can also be harvested bypiezoeletric materials to charge batteries for backup supplies or to power low power microprocessors and wirelessradios.[20]

• A piezoelectric transformer is a type of AC voltage multiplier. Unlike a conventional transformer, which uses magnetic coupling between input and output, the piezoelectric transformer uses acoustic coupling. An input voltage is applied across a short length of a bar of piezoceramic material such as PZT, creating an alternating

Piezoelectricity 20

stress in the bar by the inverse piezoelectric effect and causing the whole bar to vibrate. The vibration frequencyis chosen to be the resonant frequency of the block, typically in the 100 kilohertz to 1 megahertz range. A higheroutput voltage is then generated across another section of the bar by the piezoelectric effect. Step-up ratios ofmore than 1000:1 have been demonstrated. An extra feature of this transformer is that, by operating it above itsresonant frequency, it can be made to appear as an inductive load, which is useful in circuits that require acontrolled soft start.[21] These devices can be used in DC-AC inverters to drive cold cathode fluorescent lamps.Piezo transformers are some of the most compact high voltage sources.

Sensors

Piezoelectric disk used as a guitar pickup

Many rocket-propelled grenades used apiezoelectric fuze. For example: RPG-7[22]

The principle of operation of a piezoelectric sensor is that a physicaldimension, transformed into a force, acts on two opposing faces of thesensing element. Depending on the design of a sensor, different"modes" to load the piezoelectric element can be used: longitudinal,transversal and shear.

Detection of pressure variations in the form of sound is the mostcommon sensor application, e.g. piezoelectric microphones (soundwaves bend the piezoelectric material, creating a changing voltage) andpiezoelectric pickups for Acoustic-electric guitars. A piezo sensorattached to the body of an instrument is known as a contactmicrophone.

Piezoelectric sensors especially are used with high frequency sound inultrasonic transducers for medical imaging and also industrialnondestructive testing (NDT).

For many sensing techniques, the sensor can act as both a sensor andan actuator – often the term transducer is preferred when the deviceacts in this dual capacity, but most piezo devices have this property ofreversibility whether it is used or not. Ultrasonic transducers, forexample, can inject ultrasound waves into the body, receive thereturned wave, and convert it to an electrical signal (a voltage). Mostmedical ultrasound transducers are piezoelectric.

In addition to those mentioned above, various sensor applications include:•• Piezoelectric elements are also used in the detection and generation of sonar waves.• Power monitoring in high power applications (e.g. medical treatment, sonochemistry and industrial processing).• Piezoelectric microbalances are used as very sensitive chemical and biological sensors.• Piezos are sometimes used in strain gauges.• Piezoelectric transducers are used in electronic drum pads to detect the impact of the drummer's sticks, and to

detect muscle movements in medical acceleromyography.• Automotive engine management systems use piezoelectric transducers to detect detonation by sampling the

vibrations of the engine block and also to detect the precise moment of fuel injection (needle lift sensors).• Ultrasonic piezo sensors are used in the detection of acoustic emissions in acoustic emission testing.• Crystal earpieces are sometimes used in old or low power radios

Piezoelectricity 21

Actuators

Metal disk with piezoelectric disk attached, usedin a buzzer

As very high electric fields correspond to only tiny changes in thewidth of the crystal, this width can be changed with better-than-µmprecision, making piezo crystals the most important tool forpositioning objects with extreme accuracy — thus their use inactuators. Multilayer ceramics, using layers thinner than 100 µm, allowreaching high electric fields with voltage lower than 150 V. Theseceramics are used within two kinds of actuators: direct piezo actuatorsand Amplified piezoelectric actuators. While direct actuator's stroke isgenerally lower than 100 µm, amplified piezo actuators can reachmillimeter strokes.

• Loudspeakers: Voltage is converted to mechanical movement of apiezoelectric polymer film.

• Piezoelectric motors: Piezoelectric elements apply a directional force to an axle, causing it to rotate. Due to theextremely small distances involved, the piezo motor is viewed as a high-precision replacement for the steppermotor.

• Piezoelectric elements can be used in laser mirror alignment, where their ability to move a large mass (the mirrormount) over microscopic distances is exploited to electronically align some laser mirrors. By precisely controllingthe distance between mirrors, the laser electronics can accurately maintain optical conditions inside the lasercavity to optimize the beam output.

• A related application is the acousto-optic modulator, a device that scatters light off of sound waves in a crystal,generated by piezoelectric elements. This is useful for fine-tuning a laser's frequency.

• Atomic force microscopes and scanning tunneling microscopes employ converse piezoelectricity to keep thesensing needle close to the probe.[23]

• Inkjet printers: On many inkjet printers, piezoelectric crystals are used to drive the ejection of ink from the inkjetprint head towards the paper.

• Diesel engines: High-performance common rail diesel engines use piezoelectric fuel injectors, first developed byRobert Bosch GmbH, instead of the more common solenoid valve devices.

•• Active vibration control using amplified actuators.• X-ray shutters.•• XY stages for micro scanning used in infrared cameras.• Moving the patient precisely inside active CT and MRI scanners where the strong radiation or magnetism

precludes electric motors.[24]

Frequency standardThe piezoelectrical properties of quartz are useful as standard of frequency.• Quartz clocks employ a crystal oscillator made from a quartz crystal that uses a combination of both direct and

converse piezoelectricity to generate a regularly timed series of electrical pulses that is used to mark time. Thequartz crystal (like any elastic material) has a precisely defined natural frequency (caused by its shape and size) atwhich it prefers to oscillate, and this is used to stabilize the frequency of a periodic voltage applied to the crystal.

• The same principle is critical in all radio transmitters and receivers, and in computers where it creates a clockpulse. Both of these usually use a frequency multiplier to reach gigahertz ranges.

Piezoelectricity 22

Piezoelectric motors

A slip-stick actuator.

Types of piezoelectric motor include:• The traveling-wave motor used for auto-focus in reflex cameras• Inchworm motors for linear motion• Rectangular four-quadrant motors with high power density (2.5

watt/cm3) and speed ranging from 10 nm/s to 800 mm/s.• Stepping piezo motor, using stick-slip effect.All these motors, except the stepping stick-slip motor work on thesame principle. Driven by dual orthogonal vibration modes with aphase difference of 90°, the contact point between two surfacesvibrates in an elliptical path, producing a frictional force between thesurfaces. Usually, one surface is fixed causing the other to move. Inmost piezoelectric motors the piezoelectric crystal is excited by a sinewave signal at the resonant frequency of the motor. Using theresonance effect, a much lower voltage can be used to produce a highvibration amplitude.

Stick-slip motor works using the inertia of a mass and the friction of a clamp. Such motors can be very small. Someare used for camera sensor displacement, allowing anti shake function.

Reduction of vibrations and noiseDifferent teams of researchers have been investigating ways to reduce vibrations in materials by attaching piezoelements to the material. When the material is bent by a vibration in one direction, the vibration-reduction systemresponds to the bend and sends electric power to the piezo element to bend in the other direction. Future applicationsof this technology are expected in cars and houses to reduce noise.In a demonstration at the Material Vision Fair in Frankfurt in November 2005, a team from TU Darmstadt inGermany showed several panels that were hit with a rubber mallet, and the panel with the piezo element immediatelystopped swinging.Piezoelectric ceramic fiber technology is being used as an electronic damping system on some HEAD tennisrackets.[25]

Infertility treatmentIn people with previous total fertilization failure, piezoelectric activation of oocytes together with intracytoplasmicsperm injection (ICSI) seems to improve fertilization outcome.[26]

SurgeryA recent application of piezoelectric ultrasound sources is piezoelectric surgery, also known as piezosurgery.[27]

Piezosurgery is a minimally invasive technique that aims to cut a target tissue with little damage to neighboringtissues. For example, Hoigne et al.[28] reported its use in hand surgery for the cutting of bone, using frequencies inthe range 25–29 kHz, causing microvibrations of 60–210 μm. It has the ability to cut mineralized tissue withoutcutting neurovascular tissue and other soft tissue, thereby maintaining a blood-free operating area, better visibilityand greater precision.[29]

Piezoelectricity 23

Further readingRao S and Sunar M (1994),[30] Fuduka E (2000),[31] Ballato A (1996),[32] Trainer M (2003),[33] as well as ManbachiA and Cobbold RSC (2011).[27]

References[1] Holler, F. James; Skoog, Douglas A; Crouch, Stanley R (2007). "Chapter 1". Principles of Instrumental Analysis (6th ed.). Cengage Learning.

p. 9. ISBN 9780495012016.[2] Harper, Douglas. "piezoelectric" (http:/ / www. etymonline. com/ index. php?term=piezoelectric). Online Etymology Dictionary. .[3] Gautschi, G (2002). Piezoelectric Sensorics: Force, Strain, Pressure, Acceleration and Acoustic Emission Sensors, Materials and Amplifiers..

Springer.[4] Lippman, G. (1881). "Principe de la conservation de l'électricité" (http:/ / gallica. bnf. fr/ ark:/ 12148/ bpt6k348640) (in French). Annales de

chimie et de physique 24: 145. .[5] M. Birkholz (1995). "Crystal-field induced dipoles in heteropolar crystals – II. physical significance" (http:/ / www. mariobirkholz. de/

ZPB1995b. pdf). Z. Phys. B 96 (3): 333–340. Bibcode 1995ZPhyB..96..333B. doi:10.1007/BF01313055. .[6] S. Trolier-McKinstry (2008). "Chapter3: Crystal Chemistry of Piezoelectric Materials". In A. Safari, E.K. Akdo˘gan. Piezoelectric and

Acoustic Materials for Transducer Applications. New York: Springer. ISBN 9780387765389.[7] Sensor Sense: Piezoelectric Force Sensors (http:/ / machinedesign. com/ article/ sensor-sense-piezoelectric-force-sensors-0207)[8] Damjanovic, Dragan (1998). "Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics". Reports on

Progress in Physics 61 (9): 1267–1324. Bibcode 1998RPPh...61.1267D. doi:10.1088/0034-4885/61/9/002.[9] Kochervinskii, V (July 2003). "Piezoelectricity in Crystallizing Ferroelectric Polymers". Crystallography Reports 48 (4): 649–675.

Bibcode 2003CryRp..48..649K. doi:10.1134/1.1595194.[10][10] M. Minary-Jolandan, and Min-Feng Yu, Nanotechnology 20 (2009) 085706 (6pp)[11] Lakes, Roderic. "Electrical Properties of Bone: A Review" (http:/ / silver. neep. wisc. edu/ ~lakes/ BoneElectr. html). University of

Wisconsin–Madison. .[12] Becker, Robert O; Marino, Andrew A (1982). "Chapter 4: Electrical Properties of Biological Tissue (Piezoelectricity)" (http:/ / www. ortho.

lsuhsc. edu/ Faculty/ Marino/ EL/ EL4/ Piezo. html). Electromagnetism & Life. Albany, New York: State University of New York Press.ISBN 0-87395-560-9. .

[13] Pollack, S.R; Korostoff, E., Starkebaum, W. y Lannicone, W (1979). ed. Brighton, C.T., Black, J. and Pollack, S.R.. ed. "Micro-electricalstudies of stress-generated potentials in bone". Electrical Properties of Bone and Cartilage (New York City: Grune & Stratton, Inc).

[14] Fotiadis, D.I; Foutsitzi, G., and Massalas, C.V (1999). "Wave propagation modeling in human long bones" (http:/ / www. springerlink. com/content/ tr43l7562581u4q8). Acta Mechanica 137: 65–81. doi:10.1007/BF01313145. .

[15] Saito, Yasuyoshi; Takao, Hisaaki; Tanil, Toshihiko; Nonoyama, Tatsuhiko; Takatoril Kazumasa; Homma, Takahiko; Nagaya, Toshiatsu;Nakamura, Masaya (2004-11-04). "Lead-free piezoceramics" (http:/ / www. nature. com/ nature/ journal/ v432/ n7013/ abs/ nature03028.html). Nature (Nature Publishing Group) 432 (7013): 81–87. Bibcode 2004Natur.432...84S. doi:10.1038/nature03028. PMID 15516921. .

[16] "Market Report: World Piezoelectric Device Market" (http:/ / www. acmite. com/ market-reports/ materials/world-piezoelectric-device-market-report. html). Acmite Market Intelligence (http:/ / www. acmite. com). .

[17] Richard, Michael Graham (2006-08-04). "Japan: Producing Electricity from Train Station Ticket Gates" (http:/ / www. treehugger. com/files/ 2006/ 08/ japan_ticket_gates. php). TreeHugger. Discovery Communications, LLC. .

[18] Wright, Sarah H (2007-07-25). "MIT duo sees people-powered "Crowd Farm"" (http:/ / web. mit. edu/ newsoffice/ 2007/ crowdfarm-0725.html). MIT news. Massachusetts Institute of Technology. .

[19] Kannampilly, Ammu (2008-07-11). "How to Save the World One Dance at a Time" (http:/ / abcnews. go. com/ International/story?id=5358214& page=1). ABC. ABC. .

[20] True Grid Independence: Robust Energy Harvesting System for Wireless Sensors Uses Piezoelectric Energy Harvesting Power Supply andLi-Poly Batteries with Shunt Charger (http:/ / www. linear. com/ docs/ 29984)

[21] Phillips, James R (2000-08-10). "Piezoelectric Technology: A Primer" (http:/ / www. techonline. com/ community/ ed_resource/feature_article/ 8277). eeProductCenter. TechInsights. .

[22] How Rocket-Propelled Grenades Work by Shane Speck (http:/ / science. howstuffworks. com/ rpg3. htm)[23] The scanning mechanism for ROSETTA/MIDAS from an engineering model to the flight model (http:/ / www. cedrat. com/ fileadmin/

user_upload/ cedrat_groupe/ Publications/ Publications/ 2001/ 09/ ESMATS9th_Scanning_piezo_mechanisms_Rosetta_Fligth_model. pdf)[24] Simonsen, Torben R. Piezo in space (http:/ / elektronikbranchen. dk/ nyhed/

dansk-elektronikvirksomhed-goer-klar-til-rumeventyr-efter-koeb-af-piezoteknologi) Electronics Business (in Danish), 27 September 2010.Retrieved: 28 September 2010.

[25] "Isn’t it amazing how one smart idea, one chip and an intelligent material has changed the world of tennis?" (http:/ / www. head. com/tennis/ technology. php?region=eu& tag=intelligence). HEAD. . Retrieved 2008-02-27.

[26] Baltaci V, Ayvaz OU, Unsal E, et al. (May 2009). "The effectiveness of intracytoplasmic sperm injection combined with piezoelectricstimulation in infertile couples with total fertilization failure". Fertil. Steril. 94 (3): 900–4. doi:10.1016/j.fertnstert.2009.03.107.PMID 19464000.

Piezoelectricity 24

[27] Manbachi, A. and Cobbold R.S.C. (November 2011). "Development and Application of Piezoelectric Materials for Ultrasound Generationand Detection" (http:/ / ult. rsmjournals. com/ content/ 19/ 4/ 187. full). Ultrasound 19 (4): 187–196. doi:10.1258/ult.2011.011027. .

[28] Hoigne DJ, Stubinger S, Von Kaenel O, Shamdasani S, Hasenboehler P. (May 2006). "Piezoelectic osteotomy in hand surgery: firstexperiences with a new technique." (http:/ / www. biomedcentral. com/ 1471-2474/ 7/ 36/ prepubyours). BMC Musculoskelet Disord 7: 36.doi:10.1186/1471-2474-7-36. .

[29] Labanca M, Azzola F, Vinci R, Rodella LF. (2008). "Piezoelectric surgery: twenty years of use." (http:/ / www. sciencedirect. com/ science/article/ pii/ S026643560800003X). Br J Oral Maxillofac Surg 46 (4): 265–9. doi:10.1016/j.bjoms.2007.12.007. PMID 18342999. .

[30] Rao S and Sunar M (1994). "Piezoelectricity and Its Use in Disturbance Sensing and Control of Flexible Structures: A Survey" (http:/ /scitation. aip. org/ getabs/ servlet/ GetabsServlet?prog=normal& id=AMREAD000047000004000113000001& idtype=cvips& gifs=yes&ref=no). Appl. Mech. Rev. 47 (4): 113. Bibcode 1994ApMRv..47..113R. doi:10.1115/1.3111074. .

[31] Fukuda E (2000). [ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=883516&tag=1 "History and recent progress in piezoelectric polymers"].Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on 47 (6): 1277–1290. doi:10.1109/58.883516.ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=883516&tag=1.

[32] Ballato A (1996). "Piezoelectricity: history and new thrusts" (http:/ / ieeexplore. ieee. org/ xpls/ abs_all. jsp?arnumber=584046). UltrasonicsSymposium, 1996. Proceedings., 1996 IEEE 1: 575–583. doi:10.1109/ULTSYM.1996.584046. .

[33] Trainer M (2003). "Kelvin and piezoelectricity" (http:/ / iopscience. iop. org/ 0143-0807/ 24/ 5/ 310). Eur. J. Phys. 24 (5): 535.Bibcode 2003EJPh...24..535T. doi:10.1088/0143-0807/24/5/310. .

International standards•• ANSI-IEEE 176 (1987) Standard on Piezoelectricity• IEEE 177 (1976) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators• IEC 444 (1973) Basic method for the measurement of resonance freq & equiv series resistance of quartz crystal

units by zero-phase technique in a pi-network• IEC 302 (1969) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators Operating over the

Freq Range up to 30 MHz

External links• Gautschi, Gustav H., 2002, Piezoelectric Sensorics, Springer, ISBN 3-540-42259-5,• Fundamentals of Piezoelectrics (http:/ / www. amazon. com/

Fundamentals-Piezoelectric-Sensorics-Mechanical-Thermodynamical/ dp/ 3540439668/ ref=sr_1_2?ie=UTF8&s=books& qid=1275053589& sr=1-2)

• Piezo motor based microdrive for neural signal recording (http:/ / www. ncbi. nlm. nih. gov/ pubmed/ 19163430)• History of Piezoelectricity (http:/ / www. piezoinstitute. com/ about/ piezohistory/ index. php)• Research on new Piezoelectric materials (http:/ / www. scientificblogging. com/ news_account/

research_new_piezoelectric_materials)• Piezo Equations (http:/ / www. techonline. com/ showArticle. jhtml?articleID=192201162& queryText=22)• Piezo in Medical Design (http:/ / medicaldesign. com/ motors-motion-control/ precision-via-piezo-20100501/ )• Video demonstration of Piezoelectricity (http:/ / vega. org. uk/ video/ programme/ 195)• DoITPoMS Teaching and Learning Package – Piezoelectric Materials (http:/ / www. doitpoms. ac. uk/ tlplib/

piezoelectrics/ index. php)• Piezo Motor Types (http:/ / commons. wikimedia. org/ wiki/ File:Piezomotor_type_inchworm. gif)

Permittivity 25

Permittivity

A dielectric medium showing orientation ofcharged particles creating polarization effects.

Such a medium can have a higher ratio of electricflux to charge (permittivity) than empty space

In electromagnetism, absolute permittivity is the measure of theresistance that is encountered when forming an electric field in amedium. In other words, permittivity is a measure of how an electricfield affects, and is affected by, a dielectric medium. The permittivityof a medium describes how much electric field (more correctly, flux) is'generated' per unit charge. Less electric flux exists in a medium with ahigh permittivity (per unit charge) due to polarization effects.Permittivity is directly related to electric susceptibility, which is ameasure of how easily a dielectric polarizes in response to an electricfield. Thus, permittivity relates to a material's ability to transmit (or"permit") an electric field.

In SI units, permittivity ε is measured in farads per meter (F/m);electric susceptibility χ is dimensionless. They are related to each otherthrough

where εr is the relative permittivity of the material, and = 8.85… × 10−12 F/m is the vacuum permittivity.

ExplanationIn electromagnetism, the electric displacement field D represents how an electric field E influences the organizationof electrical charges in a given medium, including charge migration and electric dipole reorientation. Its relation topermittivity in the very simple case of linear, homogeneous, isotropic materials with "instantaneous" response tochanges in electric field is

where the permittivity ε is a scalar. If the medium is anisotropic, the permittivity is a second rank tensor.In general, permittivity is not a constant, as it can vary with the position in the medium, the frequency of the fieldapplied, humidity, temperature, and other parameters. In a nonlinear medium, the permittivity can depend on thestrength of the electric field. Permittivity as a function of frequency can take on real or complex values.In SI units, permittivity is measured in farads per meter (F/m or A2·s4·kg−1·m−3). The displacement field D ismeasured in units of coulombs per square meter (C/m2), while the electric field E is measured in volts per meter(V/m). D and E describe the interaction between charged objects. D is related to the charge densities associated withthis interaction, while E is related to the forces and potential differences.

Vacuum permittivityThe vacuum permittivity ε0 (also called permittivity of free space or the electric constant) is the ratio D/E in freespace. It also appears in the Coulomb force constant 1/4πε0.Its value is[1]

wherec0 is the speed of light in free space,[2]

µ0 is the vacuum permeability.

Permittivity 26

Constants c0 and μ0 are defined in SI units to have exact numerical values, shifting responsibility of experiment tothe determination of the meter and the ampere.[3] (The approximation in the second value of ε0 above stems from πbeing an irrational number.)

Relative permittivityThe linear permittivity of a homogeneous material is usually given relative to that of free space, as a relativepermittivity εr (also called dielectric constant, although this sometimes only refers to the static, zero-frequencyrelative permittivity). In an anisotropic material, the relative permittivity may be a tensor, causing birefringence. Theactual permittivity is then calculated by multiplying the relative permittivity by ε0:

whereχ (frequently written χe) is the electric susceptibility of the material.

The susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field E tothe induced dielectric polarization density P such that

where is the electric permittivity of free space.The susceptibility of a medium is related to its relative permittivity by

So in the case of a vacuum,

The susceptibility is also related to the polarizability of individual particles in the medium by the Clausius-Mossottirelation.The electric displacement D is related to the polarization density P by

The permittivity ε and permeability µ of a medium together determine the phase velocity v = c/n of electromagneticradiation through that medium:

Dispersion and causalityIn general, a material cannot polarize instantaneously in response to an applied field, and so the more generalformulation as a function of time is

That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibilitygiven by . The upper limit of this integral can be extended to infinity as well if one defines for

. An instantaneous response corresponds to Dirac delta function susceptibility .It is more convenient in a linear system to take the Fourier transform and write this relationship as a function offrequency. Due to the convolution theorem, the integral becomes a simple product,

This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of thesusceptibility with respect to frequency characterizes the dispersion properties of the material.

Permittivity 27

Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. for), a consequence of causality, imposes Kramers–Kronig constraints on the susceptibility .

Complex permittivity

A dielectric permittivity spectrum over a wide range of frequencies. ε′ and ε″ denote thereal and the imaginary part of the permittivity, respectively. Various processes are labeledon the image: ionic and dipolar relaxation, and atomic and electronic resonances at higher

energies.[4]

As opposed to the response of avacuum, the response of normalmaterials to external fields generallydepends on the frequency of the field.This frequency dependence reflects thefact that a material's polarization doesnot respond instantaneously to anapplied field. The response mustalways be causal (arising after theapplied field) which can be representedby a phase difference. For this reasonpermittivity is often treated as acomplex function (since complexnumbers allow specification ofmagnitude and phase) of the (angular)frequency of the applied field ω,

. The definition ofpermittivity therefore becomes

whereD0 and E0 are the amplitudes ofthe displacement and electrical fields, respectively,

i is the imaginary unit, i 2 = −1.The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also calledthe static permittivity εs (also εDC ):

At the high-frequency limit, the complex permittivity is commonly referred to as ε∞. At the plasma frequency andabove, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximationfor alternating fields of low frequencies, and as the frequency increases a measurable phase difference δ emergesbetween D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the detailsof the medium. For moderate fields strength (E0), D and E remain proportional, and

Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural toseparate its real and imaginary parts, which is done by convention in the following way:

whereε" is the imaginary part of the permittivity, which is related to the dissipation (or loss) of energy within themedium.

Permittivity 28

ε' is the real part of the permittivity, which is related to the stored energy within the medium.

It is important to realize that the choice of sign for time-dependence, , dictates the sign convention forthe imaginary part of permittivity. The signs used here correspond to those commonly used in physics, whereas forthe engineering convention one should reverse all imaginary quantities.The complex permittivity is usually a complicated function of frequency ω, since it is a superimposed description ofdispersion phenomena occurring at multiple frequencies. The dielectric function ε(ω) must have poles only forfrequencies with positive imaginary parts, and therefore satisfies the Kramers–Kronig relations. However, in thenarrow frequency ranges that are often studied in practice, the permittivity can be approximated asfrequency-independent or by model functions.At a given frequency, the imaginary part of leads to absorption loss if it is positive (in the above sign convention)and gain if it is negative. More generally, the imaginary parts of the eigenvalues of the anisotropic dielectric tensorshould be considered.In the case of solids, the complex dielectric function is intimately connected to band structure. The primary quantitythat characterizes the electronic structure of any crystalline material is the probability of photon absorption, which isdirectly related to the imaginary part of the optical dielectric function ε(ω). The optical dielectric function is given bythe fundamental expression:[5]

In this expression, Wcv(E) represents the product of the Brillouin zone-averaged transition probability at the energy Ewith the joint density of states,[6][7] Jcv(E); is a broadening function, representing the role of scattering insmearing out the energy levels.[8] In general, the broadening is intermediate between Lorentzian and Gaussian;[9][10]

for an alloy it is somewhat closer to Gaussian because of strong scattering from statistical fluctuations in the localcomposition on a nanometer scale.

Classification of materialsMaterials can be classified according to their permittivity and conductivity, σ. Materials with a large amount of lossinhibit the propagation of electromagnetic waves. In this case, generally when σ/(ωε') >> 1, we consider the materialto be a good conductor. Dielectrics are associated with lossless or low-loss materials, where σ/(ωε') << 1. Those thatdo not fall under either limit are considered to be general media. A perfect dielectric is a material that has noconductivity, thus exhibiting only a displacement current. Therefore it stores and returns electrical energy as if itwere an ideal capacitor.

Lossy mediumIn the case of lossy medium, i.e. when the conduction current is not negligible, the total current density flowing is:

whereσ is the conductivity of the medium;ε' is the real part of the permittivity.

is the complex permittivityThe size of the displacement current is dependent on the frequency ω of the applied field E; there is no displacementcurrent in a constant field.In this formalism, the complex permittivity is defined as[11]:

Permittivity 29

In general, the absorption of electromagnetic energy by dielectrics is covered by a few different mechanisms thatinfluence the shape of the permittivity as a function of frequency:• First, are the relaxation effects associated with permanent and induced molecular dipoles. At low frequencies the

field changes slowly enough to allow dipoles to reach equilibrium before the field has measurably changed. Forfrequencies at which dipole orientations cannot follow the applied field due to the viscosity of the medium,absorption of the field's energy leads to energy dissipation. The mechanism of dipoles relaxing is called dielectricrelaxation and for ideal dipoles is described by classic Debye relaxation.

• Second are the resonance effects, which arise from the rotations or vibrations of atoms, ions, or electrons. Theseprocesses are observed in the neighborhood of their characteristic absorption frequencies.

The above effects often combine to cause non-linear effects within capacitors. For example, dielectric absorptionrefers to the inability of a capacitor that has been charged for a long time to completely discharge when brieflydischarged. Although an ideal capacitor would remain at zero volts after being discharged, real capacitors willdevelop a small voltage, a phenomenon that is also called soakage or battery action. For some dielectrics, such asmany polymer films, the resulting voltage may be less than 1-2% of the original voltage. However, it can be as muchas 15 - 25% in the case of electrolytic capacitors or supercapacitors.

Quantum-mechanical interpretationIn terms of quantum mechanics, permittivity is explained by atomic and molecular interactions.At low frequencies, molecules in polar dielectrics are polarized by an applied electric field, which induces periodicrotations. For example, at the microwave frequency, the microwave field causes the periodic rotation of watermolecules, sufficient to break hydrogen bonds. The field does work against the bonds and the energy is absorbed bythe material as heat. This is why microwave ovens work very well for materials containing water. There are twomaxima of the imaginary component (the absorptive index) of water, one at the microwave frequency, and the otherat far ultraviolet (UV) frequency. Both of these resonances are at higher frequencies than the operating frequency ofmicrowave ovens.At moderate frequencies, the energy is too high to cause rotation, yet too low to affect electrons directly, and isabsorbed in the form of resonant molecular vibrations. In water, this is where the absorptive index starts to dropsharply, and the minimum of the imaginary permittivity is at the frequency of blue light (optical regime).At high frequencies (such as UV and above), molecules cannot relax, and the energy is purely absorbed by atoms,exciting electron energy levels. Thus, these frequencies are classified as ionizing radiation.While carrying out a complete ab initio (that is, first-principles) modelling is now computationally possible, it hasnot been widely applied yet. Thus, a phenomenological model is accepted as being an adequate method of capturingexperimental behaviors. The Debye model and the Lorentz model use a 1st-order and 2nd-order (respectively)lumped system parameter linear representation (such as an RC and an LRC resonant circuit).

MeasurementThe dielectric constant of a material can be found by a variety of static electrical measurements. The complexpermittivity is evaluated over a wide range of frequencies by using different variants of dielectric spectroscopy,covering nearly 21 orders of magnitude from 10−6 to 1015 Hz. Also, by using cryostats and ovens, the dielectricproperties of a medium can be characterized over an array of temperatures. In order to study systems for such diverseexcitation fields, a number of measurement setups are used, each adequate for a special frequency range.Various microwave measurement techniques are outlined in Chen et al..[12] Typical errors for the Hakki-Colemanmethod employing a puck of material between conducting planes are about 0.3%.[13]

• Low-frequency time domain measurements (10−6-103 Hz)• Low-frequency frequency domain measurements (10−5-106 Hz)

Permittivity 30

• Reflective coaxial methods (106-1010 Hz)• Transmission coaxial method (108-1011 Hz)• Quasi-optical methods (109-1010 Hz)• Terahertz time-domain spectroscopy (1011-1013 Hz)• Fourier-transform methods (1011-1015 Hz)At infrared and optical frequencies, a common technique is ellipsometry. Dual polarisation interferometry is alsoused to measure the complex refractive index for very thin films at optical frequencies.

References[1] electric constant (http:/ / physics. nist. gov/ cgi-bin/ cuu/ Value?ep0)[2] Current practice of standards organizations such as NIST and BIPM is to use c0, rather than c, to denote the speed of light in vacuum

according to ISO 31. In the original Recommendation of 1983, the symbol c was used for this purpose. See NIST Special Publication 330,Appendix 2, p. 45 (http:/ / physics. nist. gov/ Pubs/ SP330/ sp330. pdf).

[3] Latest (2006) values of the constants (NIST) (http:/ / physics. nist. gov/ cuu/ Constants/ index. html)[4] Dielectric Spectroscopy (http:/ / www. psrc. usm. edu/ mauritz/ dilect. html)[5] Peter Y. Yu, Manuel Cardona (2001). Fundamentals of Semiconductors: Physics and Materials Properties (http:/ / books. google. com/

?id=W9pdJZoAeyEC& pg=PA261). Berlin: Springer. p. 261. ISBN 3540254706. .[6] José García Solé, Jose Solé, Luisa Bausa, (2001). An introduction to the optical spectroscopy of inorganic solids (http:/ / books. google. com/

?id=c6pkqC50QMgC& pg=PA263). Wiley. Appendix A1, pp, 263. ISBN 0470868856. .[7] John H. Moore, Nicholas D. Spencer (2001). Encyclopedia of chemical physics and physical chemistry (http:/ / books. google. com/

?id=Pn2edky6uJ8C& pg=PA108). Taylor and Francis. p. 105. ISBN 0750307986. .[8] Solé, José García; Bausá, Louisa E; Jaque, Daniel (2005-03-22). Solé and Bausa (http:/ / books. google. com/ ?id=c6pkqC50QMgC&

pg=PA10). p. 10. ISBN 3540254706. .[9] Hartmut Haug, Stephan W. Koch (1994). Quantum Theory of the Optical and Electronic Properties of Semiconductors (http:/ / books. google.

com/ ?id=Ab2WnFyGwhcC& pg=PA196). World Scientific. p. 196. ISBN 9810218648. .[10] Manijeh Razeghi (2006). Fundamentals of Solid State Engineering (http:/ / books. google. com/ ?id=6x07E9PSzr8C& pg=PA383).

Birkhauser. p. 383. ISBN 0387281525. .[11][11] John S. Seybold (2005) Introduction to RF propagation. 330 pp, eq.(2.6), p.22.[12] Linfeng Chen, V. V. Varadan, C. K. Ong, Chye Poh Neo (2004). "Microwave theory and techniques for materials characterization" (http:/ /

books. google. com/ ?id=2oA3po4coUoC& pg=PA37). Microwave electronics. Wiley. p. 37. ISBN 0470844922. .[13] Mailadil T. Sebastian (2008). Dielectric Materials foress Communication (http:/ / books. google. com/ ?id=eShDR4_YyM8C& pg=PA19).

Elsevier. p. 19. ISBN 0080453309. .

Further reading• Theory of Electric Polarization: Dielectric Polarization, C.J.F. Böttcher, ISBN 0-444-41579-3• Dielectrics and Waves edited by von Hippel, Arthur R., ISBN 0-89006-803-8• Dielectric Materials and Applications edited by Arthur von Hippel, ISBN 0-89006-805-4.

External links• Electromagnetism (http:/ / lightandmatter. com/ html_books/ 0sn/ ch11/ ch11. html), a chapter from an online

textbook• What's all this trapped charge stuff . . . (http:/ / keith-snook. info/ capacitor-soakage. html), A different approach

to some capacitor problems

Electric susceptibility 31

Electric susceptibilityIn electromagnetism, the electric susceptibility (latin: susceptibilis “receptiveness”) is a dimensionlessproportionality constant that indicates the degree of polarization of a dielectric material in response to an appliedelectric field. The greater the electric susceptibility, the greater the ability of a material to polarize in response to thefield, and thereby reduce the total electric field inside the material (and store energy). It is in this way that the electricsusceptibility influences the electric permittivity of the material and thus influences many other phenomena in thatmedium, from the capacitance of capacitors to the speed of light.[1][2]

Definition of Volume SusceptibilityElectric susceptibility is defined as the constant of proportionality (which may be a tensor) relating an electric field Eto the induced dielectric polarization density P such that:

Where:• is the Polarization Density• is the Electric Permittivity of Free Space• is the Electric Susceptibility• is the Electric FieldThe susceptibility is also related to the polarizability of individual particles in the medium by the Clausius-Mossottirelation. The susceptibility is related to its relative permittivity by:

So in the case of a vacuum:

At the same time, the electric displacement D is related to the polarization density P by:

Molecular PolarizabilityA similar parameter exists to relate the magnitude of the induced dipole moment p of an individual molecule to thelocal electric field E that induced the dipole. This parameter is the molecular polarizability and the dipole momentresulting from the local electric field is given by:

This introduces a complication however, as locally the field can differ significantly from the overall applied field.We have:

where P is the polarization per unit volume, and N is the number of molecules per unit volume contributing to thepolarization. Thus, if the local electric field is parallel to the ambient electric field, we have:

Thus only if the local field equals the ambient field can we write:

Electric susceptibility 32

Dispersion and causalityIn general, a material cannot polarize instantaneously in response to an applied field, and so the more generalformulation as a function of time is

That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibilitygiven by . The upper limit of this integral can be extended to infinity as well if one defines for . An instantaneous response corresponds to Dirac delta function susceptibility .It is more convenient in a linear system to take the Fourier transform and write this relationship as a function offrequency. Due to the convolution theorem, the integral becomes a simple product,

This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of thesusceptibility with respect to frequency characterizes the dispersion properties of the material.

Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. for), a consequence of causality, imposes Kramers–Kronig constraints on the susceptibility .

References[1] "Electric susceptibility". Encyclopædia Britannica.[2] Cardarelli, François (2000, 2008). Materials Handbook: A Concise Desktop Reference (http:/ / books. google. com/

books?id=PvU-qbQJq7IC& pg=PA524& dq=Electric+ susceptibility#v=onepage& q=Electric susceptibility& f=false) (2nd ed.). London:Springer-Verlag. pp. 524 (Section 8.1.16). doi:10.1007/978-1-84628-669-8. ISBN 9781846286681. .

Relative permittivity

Relative static permittivities of some materials at room temperature under 1 kHz [1] (corresponds to light with wavelength of 300 km)

Material εr

Vacuum 1 (by definition)

Air 1.00058986 ±0.00000050

(at STP, for 0.9 MHz),[2]

PTFE/Teflon 2.1

Polyethylene 2.25

Polyimide 3.4

Polypropylene 2.2–2.36

Polystyrene 2.4–2.7

Carbon disulfide 2.6

Paper 3.85

Electroactive polymers 2–12

Silicon dioxide 3.9 [3]

Concrete 4.5

Pyrex (Glass) 4.7 (3.7–10)

Relative permittivity 33

Rubber 7

Diamond 5.5–10

Salt 3–15

Graphite 10–15

Silicon 11.68

Ammonia 26, 22, 20, 17(−80, −40, 0, 20 °C)

Methanol 30

Ethylene Glycol 37

Furfural 42.0

Glycerol 41.2, 47, 42.5(0, 20, 25 °C)

Water 88, 80.1, 55.3, 34.5(0, 20, 100, 200 °C)for visible light: 1.77

Hydrofluoric acid 83.6 (0 °C)

Formamide 84.0 (20 °C)

Sulfuric acid 84–100(20–25 °C)

Hydrogen peroxide 128 aq–60(−30–25 °C)

Hydrocyanic acid 158.0–2.3(0–21 °C)

Titanium dioxide 86–173

Strontium titanate 310

Barium strontium titanate 500

Barium titanate 1250–10,000(20–120 °C)

Lead zirconate titanate 500–6000

Conjugated polymers 1.8-6 up to 100,000[4]

Calcium copper titanate >250,000[5]

Temperature dependence of the relative staticpermittivity of water

The relative permittivity of a material under given conditions reflectsthe extent to which it concentrates electrostatic lines of flux. Intechnical terms, it is the ratio of the amount of electrical energy storedin a material by an applied voltage, relative to that stored in a vacuum.Likewise, it is also the ratio of the capacitance of a capacitor using thatmaterial as a dielectric, compared to a similar capacitor that has avacuum as its dielectric.

Relative permittivity 34

TerminologyThe relative permittivity of a material for a frequency of zero is known as its static relative permittivity or as itsdielectric constant. Other terms used for the zero frequency relative permittivity include relative dielectricconstant and static dielectric constant. While they remain very common, these terms are ambiguous and have beendeprecated by some standards organizations.[6][7] The reason for the potential ambiguity is twofold. First, some olderauthors used "dielectric constant" or "absolute dielectric constant" for the absolute permittivity ε rather than therelative permittivity.[8] Second, while in most modern usage "dielectric constant" refers to a relative permittivity,[7][9]

it may be either the static or the frequency-dependent relative permittivity, depending on context.Relative permittivity is typically denoted as εr(ω) (sometimes κ or K) and is defined as

where ε(ω) is the complex frequency-dependent absolute permittivity of the material, and ε0 is the vacuumpermittivity.Relative permittivity is a dimensionless number that is in general complex. The imaginary portion of the permittivitycorresponds to a phase shift of the polarization P relative to E and leads to the attenuation of electromagnetic wavespassing through the medium. By definition, the linear relative permittivity of vacuum is equal to 1,[9] that is ε = ε0,although there are theoretical nonlinear quantum effects in vacuum that have been predicted at high field strengths(but not yet observed).[10]

The relative permittivity of a medium is related to its electric susceptibility, χe, as εr(ω) = 1 + χe.

MeasurementThe relative static permittivity, εr, can be measured for static electric fields as follows: first the capacitance of a testcapacitor, C0, is measured with vacuum between its plates. Then, using the same capacitor and distance between itsplates the capacitance Cx with a dielectric between the plates is measured. The relative dielectric constant can be thencalculated as

For time-variant electromagnetic fields, this quantity becomes frequency-dependent and in general is called relativepermittivity.

Practical relevanceThe dielectric constant is an essential piece of information when designing capacitors, and in other circumstanceswhere a material might be expected to introduce capacitance into a circuit. If a material with a high dielectricconstant is placed in an electric field, the magnitude of that field will be measurably reduced within the volume ofthe dielectric. This fact is commonly used to increase the capacitance of a particular capacitor design. The layersbeneath etched conductors in printed circuit boards (PCBs) also act as dielectrics.Dielectrics are used in RF transmission lines. In a coaxial cable, polyethylene can be used between the centerconductor and outside shield. It can also be placed inside waveguides to form filters. Optical fibers are examples ofdielectric waveguides. They consist of dielectric materials that are purposely doped with impurities so as to controlthe precise value of εr within the cross-section. This controls the refractive index of the material and therefore alsothe optical modes of transmission. However, in these cases it is technically the relative permittivity that matters, asthey are not operated in the electrostatic limit.

Relative permittivity 35

Chemical applicationsThe relative static permittivity of a solvent is a relative measure of its polarity. For example, water (very polar) has adielectric constant of 80.10 at 20 °C while n-hexane (very non-polar) has a dielectric constant of 1.89 at 20 °C.[11]

This information is of great value when designing separation, sample preparation and chromatography techniques inanalytical chemistry.The correlation should, however, be treated with caution. For instance, dichloromethane has a value of εr of 9.08 (20°C) and is rather poorly soluble in water (13 g/L or 9.8 mL/L at 20 °C); at the same time, tetrahydrofurane has its εr= 7.52 at 22 °C, but is completely miscible with the water.

Complex permittivitySimilar as for absolute permittivity, relative permittivity can be decomposed into real and imaginary parts:[12]

.

Lossy mediumAgain, similar as for absolute permittivity, relative permittivity for lossy materials can be formulated as:

in terms of a "dielectric conductivity" σ (units S/m, siemens per meter), which "sums over all the dissipative effectsof the material; it may represent an actual [electrical] conductivity caused by migrating charge carriers and it mayalso refer to an energy loss associated with the dispersion of ε' [the real-valued permittivity]" (,[12] p. 8). Expandingthe angular frequency ω = 2πc/λ and the electric constant ε0 = 1/(µ0c2), it reduces to:

where λ is the wavelength, c is the speed of light in vacuum and κ = µ0c/2π ≈ 60.0 S−1 is a newly-introducedconstant (units reciprocal of siemens, such that σλκ = εr" remains unitless).

MetalsAlthough permittivity is typically associated with dielectric materials, we may still speak of an effective permittivityof a metal, with real relative permittivity equal to one (,[13] eq.(4.6), p. 121). In the low-frequency region (whichextends from radiofrequencies to the far infrared region), the plasma frequency of the electron gas is much greaterthan the electromagnetic propagation frequency, so the complex permittivity ε of a metal is practically a purelyimaginary number, expressed in terms of the imaginary unit and a real-valued electrical conductivity (,[13]

eq.(4.8)-(4.9), p. 122).

References[1] Dielectric Constants of Materials (http:/ / www. clippercontrols. com/ pages/ Dielectric-Constant-Values. html) (2007). Clipper Controls.[2] L. G. Hector and H. L. Schultz (1936). The Dielectric Constant of Air at Radiofrequencies. 7. 133–136. doi:10.1063/1.1745374.[3] Paul R. Gray, Paul J. Hurst, Stephen H. Lewis, Robert G. Meyer (2009). Analysis and Design of Analog Integrated Circuits (Fifth ed.). New

York: Wiley. p. 40. ISBN 978-0-470-24599-6.[4] Pohl, Herbert A. (1986). "Giant polarization in high polymers". Journal of Electronic Materials 15: 201. Bibcode 1986JEMat..15..201P.

doi:10.1007/BF02659632.[5] http:/ / www. shef. ac. uk/ ccl/ research/ ccto. html[6] Braslavsky, S.E. (2007). "Glossary of terms used in photochemistry ([[IUPAC (http:/ / iupac. org/ publications/ pac/ 2007/ pdf/ 7903x0293.

pdf)] recommendations 2006)"]. Pure and Applied Chemistry 79: 293–465. doi:10.1351/pac200779030293. .[7] IEEE Standards Board (1997). "IEEE Standard Definitions of Terms for Radio Wave Propagation" (http:/ / ieeexplore. ieee. org/ servlet/

opac?punumber=5697). p. 6. .[8] King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover. p. 139.

Relative permittivity 36

[9] John David Jackson (1998). Classical Electrodynamics (Third ed.). New York: Wiley. p. 154. ISBN 047130932X.[10] Mourou, Gerard A. (2006). "Optics in the relativistic regime". Reviews of Modern Physics 78: 309. Bibcode 2006RvMP...78..309M.

doi:10.1103/RevModPhys.78.309.[11] Lide, D. R., ed. (2005). CRC Handbook of Chemistry and Physics (86th ed.). Boca Raton (FL): CRC Press. ISBN 0-8493-0486-5.[12] Linfeng Chen and Vijay K. Varadan (2004). Microwave electronics: measurement and materials characterization (http:/ / books. google. co.

jp/ books?id=2oA3po4coUoC& pg=PA8). John Wiley and Sons. p. 8, eq.(1.15). doi:10.1002/0470020466. ISBN 0470844922. .[13] Lourtioz, J.-M. et al. (2005). Photonic Crystals: Towards Nanoscale Photonic Devices (http:/ / books. google. com/

books?id=vSszZ2WuG_IC& pg=PA121). Springer. ISBN 354024431X. .

Permeability (electromagnetism)

Simplified comparison of permeabilities for:ferromagnets (μf), paramagnets(μp), free

space(μ0) and diamagnets (μd)

In electromagnetism, permeability is the measure of the ability of amaterial to support the formation of a magnetic field within itself. Inother words, it is the degree of magnetization that a material obtains inresponse to an applied magnetic field. Magnetic permeability istypically represented by the Greek letter μ. The term was coined inSeptember, 1885 by Oliver Heaviside. The reciprocal of magneticpermeability is magnetic reluctivity.

We can simplify it by saying, the more conductive a material is to amagnetic field, the higher its permeability.In SI units, permeability is measured in the henries per meter (H·m−1),or newtons per ampere squared (N·A−2). The permeability constant(μ0), also known as the magnetic constant or the permeability of freespace, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum.The magnetic constant has the exact (defined)[1] value µ0 = 4π×10−7 ≈ 1.2566370614…×10−6 H·m−1 or N·A−2).

ExplanationIn electromagnetism, the auxiliary magnetic field H represents how a magnetic field B influences the organization ofmagnetic dipoles in a given medium, including dipole migration and magnetic dipole reorientation. Its relation topermeability is

where the permeability μ is a scalar if the medium is isotropic or a second rank tensor for an anisotropic medium.In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the fieldapplied, humidity, temperature, and other parameters. In a nonlinear medium, the permeability can depend on thestrength of the magnetic field. Permeability as a function of frequency can take on real or complex values. Inferromagnetic materials, the relationship between B and H exhibits both non-linearity and hysteresis: B is not asingle-valued function of H,[2] but depends also on the history of the material. For these materials it is sometimesuseful to consider the incremental permeability defined as

.This definition is useful in local linearizations of non-linear material behavior, for example in a Newton-Raphsoniterative solution scheme that computes the changing saturation of a magnetic circuit.Permeability is the inductance per unit length. In SI units, permeability is measured in henries per metre (H·m−1 = J/(A2·m) = N A−2). The auxiliary magnetic field H has dimensions current per unit length and is measured in units of amperes per metre (A m−1). The product μH thus has dimensions inductance times current per unit area (H·A/m2). But inductance is magnetic flux per unit current, so the product has dimensions magnetic flux per unit area. This is

Permeability (electromagnetism) 37

just the magnetic field B, which is measured in webers (volt-seconds) per square-metre (V·s/m2), or teslas (T).B is related to the Lorentz force on a moving charge q:

.The charge q is given in coulombs (C), the velocity v in m/s, so that the force F is in newtons (N):

H is related to the magnetic dipole density. A magnetic dipole is a closed circulation of electric current. The dipolemoment has dimensions current times area, units ampere square-metre (A·m2), and magnitude equal to the currentaround the loop times the area of the loop.[3] The H field at a distance from a dipole has magnitude proportional tothe dipole moment divided by distance cubed,[4] which has dimensions current per unit length.

Relative permeabilityRelative permeability, sometimes denoted by the symbol μr, is the ratio of the permeability of a specific medium tothe permeability of free space given by the magnetic constant :

.

In terms of relative permeability, the magnetic susceptibility is:

.χm, a dimensionless quantity, is sometimes called volumetric or bulk susceptibility, to distinguish it from χp(magnetic mass or specific susceptibility) and χM (molar or molar mass susceptibility).

DiamagnetismDiamagnetism is the property of an object which causes it to create a magnetic field in opposition of an externallyapplied magnetic field, thus causing a repulsive effect. Specifically, an external magnetic field alters the orbitalvelocity of electrons around their nuclei, thus changing the magnetic dipole moment in the direction opposing theexternal field. Diamagnets are materials with a magnetic permeability less than (a relative permeability less than1).Consequently, diamagnetism is a form of magnetism that a substance exhibits only in the presence of an externallyapplied magnetic field. It is generally a quite weak effect in most materials, although superconductors exhibit astrong effect.

ParamagnetismParamagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field.Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic permeability greater than one(or, equivalently, a positive magnetic susceptibility). The magnetic moment induced by the applied field is linear inthe field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect. Unlikeferromagnets, paramagnets do not retain any magnetization in the absence of an externally applied magnetic field,because thermal motion causes the spins to become randomly oriented without it. Thus the total magnetization willdrop to zero when the applied field is removed. Even in the presence of the field there is only a small inducedmagnetization because only a small fraction of the spins will be oriented by the field. This fraction is proportional tothe field strength and this explains the linear dependency. The attraction experienced by ferromagnets is non-linearand much stronger, so that it is easily observed, for instance, in magnets on one's refrigerator.

Permeability (electromagnetism) 38

Values for some common materialsThe following table should be used with caution as the permeability of ferromagnetic materials varies greatly withfield strength. For example 4% Si steel has an initial relative permeability (at or near 0T) of 2,000 and a maximum of35,000[5] and, indeed, the relative permeability of any material at a sufficiently high field strength tends to 1.

Magnetic susceptibility and permeability data for selected materials

Medium Susceptibility χm

(volumetric SI)Permeability μ [H/m] Relative Permeability μ/μ

0Magnetic field Frequency max.

Metglas 1.25 × 10−1 1000000[6] at 0.5 T 100kHz

Nanoperm 10 × 10−2 80000[7] at 0.5 T 10kHz

Mu-metal 2.5 × 10−2 20000[8] at 0.002 T

Mu-metal 50000[9]

Permalloy 1.0 × 10−2 8000[8] at 0.002 T

Electrical steel 5.0 × 10−3 4000[8] at 0.002 T

Ferrite (nickel zinc) 2.0 × 10−5 – 8.0 × 10−4 16–640 100 kHz ~ 1 MHz

Ferrite (manganese zinc) >8.0 × 10−4 640 (or more) 100 kHz ~ 1 MHz

Steel 8.75 × 10−4 100[8] at 0.002 T

Nickel 1.25 × 10−4 100[8] – 600 at 0.002 T

Neodymium magnet 1.05[10]

Platinum 1.2569701 × 10−6 1.000265

Aluminum 2.22 × 10−5[11] 1.2566650 × 10−6 1.000022

Wood 1.00000043[11]

Air 1.00000037 [12]

Concrete 1[13]

Vacuum 0 1.2566371 × 10−6 (μ0) 1[14]

Hydrogen −2.2 × 10−9[11] 1.2566371 × 10−6 1.0000000

Teflon 1.2567 × 10−6[8] 1.0000

Sapphire −2.1 × 10−7 1.2566368 × 10−6 0.99999976

Copper −6.4 × 10−6

or −9.2 × 10−6[11]1.2566290 × 10−6 0.999994

Water −8.0 × 10−6 1.2566270 × 10−6 0.999992

Bismuth −1.66 × 10−4 0.999834

Superconductors −1 0 0

Permeability (electromagnetism) 39

Magnetisation curve for ferromagnets (andferrimagnets) and corresponding permeability

A good magnetic core material must have high permeability.[15]

For passive magnetic levitation a relative permeability below 1 isneeded (corresponding to a negative susceptibility).

Permeability varies with magnetic field. Values shown above areapproximate and valid only at the magnetic fields shown. Moreover,they are given for a zero frequency; in practice, the permeability isgenerally a function of the frequency. When frequency is consideredthe permeability can be complex, corresponding to the in phase and outof phase response.

Note that the magnetic constant has an exact value in SI units (thatis, there is no uncertainty in its value), because the definition of theampere fixes its value to 4π × 10−7 H/m exactly.

Complex permeabilityA useful tool for dealing with high frequency magnetic effects is the complex permeability. While at low frequenciesin a linear material the magnetic field and the auxiliary magnetic field are simply proportional to each other throughsome scalar permeability, at high frequencies these quantities will react to each other with some lag time.[16] Thesefields can be written as phasors, such that

where is the phase delay of from . Understanding permeability as the ratio of the magnetic field to theauxiliary magnetic field, the ratio of the phasors can be written and simplified as

,

so that the permeability becomes a complex number. By Euler's formula, the complex permeability can be translatedfrom polar to rectangular form,

.

The ratio of the imaginary to the real part of the complex permeability is called the loss tangent,

,

which provides a measure of how much power is lost in a material versus how much is stored.

References[1] "The NIST reference on fundamental physical constants" (http:/ / physics. nist. gov/ cuu/ Units/ ampere. html). Physics.nist.gov. . Retrieved

2011-11-08.[2][2] Jackson (1975), p. 190[3] Jackson, John David (1975). Classical Electrodynamics (2nd ed. ed.). New York: Wiley. ISBN 0-471-43132-X. p. 182 eqn. (5.57)[4][4] Jackson (1975) p. 182 eqn. (5.56)[5] G.W.C. Kaye & T.H. Laby, Table of Physical and Chemical Constants, 14th ed, Longman[6] ""Metglas Magnetic Alloy 2714A", ''Metglas''" (http:/ / www. metglas. com/ products/ page5_1_2_6. htm). Metglas.com. . Retrieved

2011-11-08.[7] ""Typical material properties of NANOPERM", ''Magnetec''" (http:/ / www. magnetec. de/ eng/ pdf/ werkstoffkennlinien_nano_e. pdf) (PDF).

. Retrieved 2011-11-08.[8] ""Relative Permeability", ''Hyperphysics''" (http:/ / hyperphysics. phy-astr. gsu. edu/ hbase/ solids/ ferro. html).

Hyperphysics.phy-astr.gsu.edu. . Retrieved 2011-11-08.[9] "Nickel Alloys-Stainless Steels, Nickel Copper Alloys, Nickel Chromium Alloys, Low Expansion Alloys" (http:/ / www. nickel-alloys. net/

nickelalloys. html). Nickel-alloys.net. . Retrieved 2011-11-08.

Permeability (electromagnetism) 40

[10] Juha Pyrhönen, Tapani Jokinen, Valéria Hrabovcová (2009). Design of Rotating Electrical Machines (http:/ / books. google. com/?id=_y3LSh1XTJYC& pg=PT232). John Wiley and Sons. p. 232. ISBN 0470695161. .

[11] Richard A. Clarke. "Clarke, R. ''Magnetic properties of materials'', surrey.ac.uk" (http:/ / www. ee. surrey. ac. uk/ Workshop/ advice/ coils/mu/ ). Ee.surrey.ac.uk. . Retrieved 2011-11-08.

[12][12] B. D. Cullity and C. D. Graham (2008), Introduction to Magnetic Materials, 2nd edition, 568 pp., p.16[13] NDT.net. "Determination of dielectric properties of insitu concrete at radar frequencies" (http:/ / www. ndt. net/ article/ ndtce03/ papers/

v078/ v078. htm). Ndt.net. . Retrieved 2011-11-08.[14][14] exactly, by definition[15] Dixon, L H (2001). "Magnetics Design 2 - Magnetic Core Characteristics" (http:/ / www. ti. com/ lit/ ml/ slup124/ slup124. pdf). Texas

Instruments. .[16] M. Getzlaff, Fundamentals of magnetism, Berlin: Springer-Verlag, 2008.

External links• Electromagnetism (http:/ / www. lightandmatter. com/ html_books/ 0sn/ ch11/ ch11. html) - a chapter from an

online textbook• Relative Permeability (http:/ / hyperphysics. phy-astr. gsu. edu/ hbase/ solids/ ferro. html)• Soil Permeability Test (http:/ / www. denichsoiltest. com)• Magnetic Properties of Materials (http:/ / www. ee. surrey. ac. uk/ Workshop/ advice/ coils/ mu/ )

SinteringSintering is a method used to create objects from powders. It is based on atomic diffusion. Diffusion occurs in anymaterial above absolute zero, but it occurs much faster at higher temperatures. In most sintering processes, thepowdered material is held in a mold and then heated to a temperature below the melting point. The atoms in thepowder particles diffuse across the boundaries of the particles, fusing the particles together and creating one solidpiece. Because the sintering temperature does not have to reach the melting point of the material, sintering is oftenchosen as the shaping process for materials with extremely high melting-points such as tungsten and molybdenum.Sintering is traditionally used for manufacturing ceramic objects, but finds applications in almost all field ofindustry. The study of sintering and of powder-related processes is known as powder metallurgy. A simple, intuitiveexample of sintering can be observed when ice cubes in a glass of water adhere to each other.The word "sinter" comes from the Middle High German Sinter, a cognate of English "cinder".

AdvantagesParticular advantages of the powder technology include:1. Very high levels of purity and uniformity in starting materials2. Preservation of purity, due to the simpler subsequent fabrication process (fewer steps) that it makes possible3. Stabilization of the details of repetitive operations, by control of grain size during the input stages4. Absence of binding contact between segregated powder particles – or "inclusions" (called stringering) – as often

occurs in melt processes5. No deformation needed to produce directional elongation of grains6.6. Capability to produce materials of controlled, uniform porosity.7.7. Capability to produce near net shape objects.8.8. Capability to produce materials which cannot be produced by any other technology.The literature contains many references on sintering dissimilar materials to produce solid/solid-phase compounds orsolid/melt mixtures at the processing stage. Almost any substance can be obtained in powder form, through eitherchemical, mechanical or physical processes, so basically any material can be obtained through sintering. When pureelements are sintered, the leftover powder is still pure, so it can be recycled.

Sintering 41

General sinteringSintering is effective when the process reduces the porosity and enhances properties such as strength, electricalconductivity, translucency and thermal conductivity; yet, in other cases, it may be useful to increase its strength butkeep its gas absorbency constant as in filters or catalysts. During the firing process, atomic diffusion drives powdersurface elimination in different stages, starting from the formation of necks between powders to final elimination ofsmall pores at the end of the process.The driving force for densification is the change in free energy from the decrease in surface area and lowering of thesurface free energy by the replacement of solid-vapor interfaces. It forms new but lower-energy solid-solid interfaceswith a total decrease in free energy occurring on sintering 1-micrometre particles a 1 cal/g decrease. On amicroscopic scale, material transfer is affected by the change in pressure and differences in free energy across thecurved surface. If the size of the particle is small (or if the radius of curvature is large), these effects become verylarge in magnitude. The change in energy is much higher when the radius of curvature is less than a fewmicrometres, which is one of the main reasons why much ceramic technology is based on the use of fine-particlematerials.[1]

For properties such as strength and conductivity, the bond area in relation to the particle size is the determiningfactor. The variables that can be controlled for any given material are the temperature and the initial grain size,because the vapor pressure depends upon temperature. Through time, the particle radius and the vapor pressure areproportional to (p0)2/3 and to (p0)1/3, respectively.[1]

The source of power for solid-state processes is the change in free or chemical potential energy between the neck andthe surface of the particle. This energy creates a transfer of material though the fastest means possible; if transferwere to take place from the particle volume or the grain boundary between particles, then there would be particlereduction and pore destruction. The pore elimination occurs faster for a trial with many pores of uniform size andhigher porosity where the boundary diffusion distance is smaller. For the latter portions of the process, boundary andlattice diffusion from the boundary become important.[1]

Control of temperature is very important to the sintering process, since grain-boundary diffusion and volumediffusion rely heavily upon temperature, the size and distribution of particles of the material, the materialscomposition, and often the sintering environment to be controlled.[1]

Ceramic sinteringSintering is part of the firing process used in the manufacture of pottery and other ceramic objects. Some ceramicraw materials have a lower affinity for water and a lower plasticity index than clay, requiring organic additives in thestages before sintering. The general procedure of creating ceramic objects via sintering of powders includes:• Mixing water, binder, deflocculant, and unfired ceramic powder to form a slurry;• Spray-drying the slurry;• Putting the spray dried powder into a mold and pressing it to form a green body (an unsintered ceramic item);•• Heating the green body at low temperature to burn off the binder;•• Sintering at a high temperature to fuse the ceramic particles together.All the characteristic temperatures associated to phases transformation, glass transitions and melting points,occurring during a sinterisation cycle of a particular ceramics formulation (i.e. tails and frits) can be easily obtainedby observing the expansion-temperature curves during optical dilatometer thermal analysis. In fact, sinterisation isassociated to a remarkable shrinkage of the material because glass phases flow, once their transition temperature isreached, and start consolidating the powdery structure and considerably reducing the porosity of the material.There are two types of sintering: with pressure (also known as hot pressing), and without pressure. Pressurelesssintering is possible with graded metal-ceramic composites, with a nanoparticle sintering aid and bulk moldingtechnology. A variant used for 3D shapes is called hot isostatic pressing.

Sintering 42

To allow efficient stacking of product in the furnace during sintering and prevent parts sticking together, manymanufacturers separate ware using Ceramic Powder Separator Sheets. These sheets are available in various materialssuch as alumina, zirconia and magnesia. They are also available in fine medium and coarse particle sizes. Bymatching the material and particle size to the ware being sintered, surface damage and contamination can be reducedwhile maximizing furnace loading.

Sintering of metallic powdersMost, if not all, metals can be sintered. This applies especially to pure metals produced in vacuum which suffer nosurface contamination. Sintering under atmospheric pressure requires the usage of a protective gas, quite oftenendothermic gas.[2] Many nonmetallic substances also sinter, such as glass, alumina, zirconia, silica, magnesia, lime,ice, beryllium oxide, ferric oxide, and various organic polymers. Sintering, with subsequent reworking, can producea great range of material properties. Changes in density, alloying, or heat treatments can alter the physicalcharacteristics of various products. For instance, the Young's Modulus En of sintered iron powders remainsinsensitive to sintering time, alloying, or particle size in the original powder, but depends upon the density of thefinal product:

where D is the density, E is Young's modulus and d is the maximum density of iron.Sintering is static when a metal powder under certain external conditions may exhibit coalescence, and yet reverts toits normal behavior when such conditions are removed. In most cases, the density of a collection of grains increasesas material flows into voids, causing a decrease in overall volume. Mass movements that occur during sinteringconsist of the reduction of total porosity by repacking, followed by material transport due to evaporation andcondensation from diffusion. In the final stages, metal atoms move along crystal boundaries to the walls of internalpores, redistributing mass from the internal bulk of the object and smoothing pore walls. Surface tension is thedriving force for this movement.A special form of sintering, still considered part of powder metallurgy, is liquid-state sintering. In liquid-statesintering, at least one but not all elements are in a liquid state. Liquid-state sintering is required for making cementedcarbide or tungsten carbide.Sintered bronze in particular is frequently used as a material for bearings, since its porosity allows lubricants to flowthrough it or remain captured within it. For materials that have high melting points such as molybdenum, tungsten,rhenium, tantalum, osmium and carbon, sintering is one of the few viable manufacturing processes. In these cases,very low porosity is desirable and can often be achieved.Sintered bronze and stainless steel are used as filter materials in applications requiring high temperature resistancewhile retaining the ability to regenerate the filter element. For example, sintered stainless steel elements are used forfiltering steam in food and pharmaceutical applications.Sintering of powders containing precious metals such as silver and gold is used to make small jewellery items.

Plastics sinteringPlastic materials are formed by sintering for applications that require materials of specific porosity. Sintered plasticporous components are used in filtration and to control fluid and gas flows. Sintered plastics are used in applicationsrequiring wicking properties, such as marking pen nibs. Sintered ultra high molecular weight polyethylene materialsare used as ski and snowboard base materials. The porous texture allows wax to be retained within the structure ofthe base material, thus providing a more durable wax coating.

Sintering 43

Liquid phase sinteringFor materials which are hard to sinter a process called liquid phase sintering is commonly used. Materials for whichliquid phase sintering is common are Si3N4, WC, SiC, and more. Liquid phase sintering is the process of adding anadditive to the powder which will melt before the matrix phase. The process of liquid phase sintering has threestages:• Rearrangement – As the liquid melts capillary action will pull the liquid into pores and also cause grains to

rearrange into a more favorable packing arrangement.• Solution-Precipitation – In areas where capillary pressures are high (particles are close together) atoms will

preferentially go into solution and then precipitate in areas of lower chemical potential where particles are nonclose or in contact. This is called "contact flattening" This densifies the system in a way similar to grain boundarydiffusion in solid state sintering. Ostwald ripening will also occur where smaller particles will go into solutionpreferentially and precipitate on larger particles leading to densification.

• Final Densification – densification of solid skeletal network, liquid movement from efficiently packed regionsinto pores.

For liquid phase sintering to be practical the major phase should be at least slightly soluble in the liquid phase andthe additive should melt before any major sintering of the solid particulate network occurs, otherwise rearrangementof grains will not occur.

Electric current assisted sinteringThese techniques employ electric currents to drive or enhance sintering.[3] English engineer A. G. Bloxam registeredin 1906 the first patent on sintering powders using direct current in vacuum. The primary purpose of his inventionswas the industrial scale production of filaments for incandescent lamps by compacting tungsten or molybdenumparticles. The applied current was particularly effective in reducing surface oxides that increased the emissivity ofthe filaments.[4]

In 1913, Weintraub and Rush patented a modified sintering method which combined electric current with pressure.The benefits of this method were proved for the sintering of refractory metals as well as conductive carbide or nitridepowders. The starting boron–carbon or silicon–carbon powders were placed in an electrically insulating tube andcompressed by two rods which also served as electrodes for the current. The estimated sintering temperature was2000 °C.[4]

In the US, sintering was first patented by Duval d’Adrian in 1922. His three-step process aimed at producingheat-resistant blocks from such oxide materials as zirconia, thoria or tantalia. The steps were: (i) molding thepowder; (ii) annealing it at about 2500 °C to make it conducting; (iii) applying current-pressure sintering as in themethod by Weintraub and Rush.[4]

Sintering which uses an arc produced via a capacitance discharge to eliminate oxides before direct current heating,was patented by G. F. Taylor in 1932. This originated sintering methods employing pulsed or alternating current,eventually superimposed to a direct current. Those techniques have been developed over many decades andsummarized in more than 640 patents.[4]

Of these technologies the most well known is resistance sintering (also called hot pressing) and spark plasmasintering, while capacitor discharge sintering is the latest advancement in this field.

Sintering 44

Spark plasma sinteringSpark plasma sintering (SPS) is a form of sintering where both external pressure and an electric field are appliedsimultaneously to enhance the densification of the metallic/ceramic powder compacts. This densification uses lowertemperatures and shorter amount of time than typical sintering.[5] The theory behind it is that there is ahigh-temperature or high-energy plasma that is generated between the gaps of the powder materials; materials can bemetals, inter-metallic, ceramics, composites and polymers. Using a DC pulse as the electrical current, spark plasma,spark impact pressure, joule heating, and an electrical field diffusion effect would be created.[6]

Certain ceramic materials have low density, chemical inertness, high strength, hardness and temperature capability;nanocrystalline ceramics have even greater strength and higher superplasticity.[6]

Many microcrystalline ceramics that were treated and had gained facture toughness lost their strength and hardness,with this many have created ceramic composites to offset the deterioration while increasing strength and hardness tothat of nanocrystalline materials. Through various experiments it has been found that in order to design themechanical properties of new material, controlling the grain size and its distribution, amount of distribution andother is pinnacle.[6]

Pressureless sinteringPressureless sintering is the sintering of a powder compact (sometimes at very high temperatures, depending on thepowder) without applied pressure. This avoids density variations in the final component, which occurs with moretraditional hot pressing methods.The powder compact (if a ceramic) can be created by slip casting into a plaster mould, then the final green compactcan be machined if necessary to final shape before being heated to sinter.

Densification, vitrification and grain growthSintering in practice is the control of both densification and grain growth. Densification is the act of reducingporosity in a sample thereby making it more dense. Grain growth is the process of grain boundary motion andOstwald ripening to increase the average grain size. Many properties (mechanical strength, electrical breakdownstrength, etc.) benefit from both a high relative density and a small grain size. Therefore, being able to control theseproperties during processing is of high technical importance. Since densification of powders requires hightemperatures, grain growth naturally occurs during sintering. Reduction of this process is key for many engineeringceramics.For densification to occur at a quick pace it is essential to have (1) an amount of liquid phase that is large in size, (2)a near complete solubility of the solid in the liquid, and (3) wetting of the solid by the liquid. The power behind thedensification is derived from the capillary pressure of the liquid phase located between the fine solid particles. Whenthe liquid phase wets the solid particles, each space between the particles becomes a capillary in which a substantialcapillary pressure is developed. For submicrometre particle sizes, capillaries with diameters in the range of 0.1 to 1micrometres develop pressures in the range of 175 pounds per square inch (unknown operator: u'strong' kPa) to1750 pounds per square inch (unknown operator: u'strong' kPa) for silicate liquids and in the range of 975 poundsper square inch (unknown operator: u'strong' kPa) to 9750 pounds per square inch (unknown operator: u'strong'kPa) for a metal such as liquid cobalt.[1]

Densification requires constant capillary pressure where just solution-precipitation material transfer would notproduce densification. For further densification, additional particle movement while the particle undergoesgrain-growth and grain-shape changes occurs. Shrinkage would result when the liquid slips between particles andincrease pressure at points of contact causing the material to move away from the contact areas forcing particlecenters to draw near each other.[1]

Sintering 45

The sintering of liquid-phase materials involve a fine-grained solid phase to create the needed capillary pressuresproportional to its diameter and the liquid concentration must also create the required capillary pressure within range,else the process ceases. The vitrification rate is dependent upon the pore size, the viscosity and amount of liquidphase present leading to the viscosity of the overall composition, and the surface tension. Temperature dependencefor densification controls the process because at higher temperatures viscosity decreases and increases liquid content.Therefore, when changes to the composition and processing are made, it will affect the vitrification process.[1]

Sintering mechanismsSintering occurs by diffusion of atoms through the microstructure. This diffusion is caused by a gradient of chemicalpotential – atoms move from an area of higher chemical potential to an area of lower chemical potential. Thedifferent paths the atoms take to get from one spot to another are the sintering mechanisms. The six commonmechanisms are:• Surface diffusion – Diffusion of atoms along the surface of a particle• Vapor transport – Evaporation of atoms which condense on a different surface• Lattice diffusion from surface – atoms from surface diffuse through lattice• Lattice diffusion from grain boundary – atom from grain boundary diffuses through lattice• Grain boundary diffusion – atoms diffuse along ground boundary• Plastic deformation – dislocation motion causes flow of matterAlso one must distinguish between densifying and non-densifying mechanisms. 1–3 above are non-densifying – theytake atoms from the surface and rearrange them onto another surface or part of the same surface. These mechanismssimply rearrange matter inside of porosity and do not cause pores to shrink. Mechanisms 4–6 are densifyingmechanisms – atoms are moved from the bulk to the surface of pores thereby eliminating porosity and increasing thedensity of the sample.

Grain growthGrain growth happens due to motion of atoms across a grain boundary. Convex surfaces have a higher chemicalpotential than concave surfaces therefore grain boundaries will move toward their center of curvature. As smallerparticles tend to have a higher radius of curvature and this results in smaller grains losing atoms to larger grains andshrinking. This is a process called Ostwald ripening. Large grains grow at the expense of small grains. Grain growthin a simple model is found to follow:

Here G is final average grain size, G0 is the initial average grain size, t is time, m is a factor between 2 and 4, and Kis a factor given by:

Here Q is the molar activation energy, R is the ideal gas constant, T is absolute temperature, and K0 is a materialdependent factor.

Reducing grain growthSolute ions

If a dopant is added to the material (example: Nd in BaTiO3) the impurity will tend to stick to the grain boundaries. As the grain boundary tries to move (as atoms jump from the convex to concave surface) the change in concentration of the dopant at the grain boundary will impose a drag on the boundary. The original concentration of solute around the grain boundary will be asymmetrical in most cases. As the grain boundary tries to move the concentration on the side opposite of motion will have a higher concentration and therefore have a higher chemical potential. This increased chemical potential will act as a backforce to the original chemical potential gradient that is the reason for

Sintering 46

grain boundary movement. This decrease in net chemical potential will decrease the grain boundary velocity andtherefore grain growth.Fine second phase particles

If particles of a second phase which are insoluble in the matrix phase are added to the powder in the form of a muchfiner powder than this will decrease grain boundary movement. When the grain boundary tries to move past theinclusion diffusion of atoms from one grain to the other will be hindered by the insoluble particle. More complicatedinteractions which slow grain boundary motion include interactions of the surface energies of the two grains and theinclusion and are discussed in detail by C.S. Smith[reference].

Natural sintering in geology

Petrifying spring in Réotier near Mont-Dauphin,France

In geology a natural sintering occurs when a mineral spring bringsabout a deposition of chemical sediment or crust, for example asof porous silica[7]

A sinter is a mineral deposit that presents a porous or vesiculartexture; Its structure shows small cavities. Two types of depositsare referenced : siliceous deposits, and calcareous deposits[8].

Siliceous sinter is a deposit of opaline or amorphous silica, thatshows as incrustations near hot springs and geysers. It sometimesforms conical mounds, called geyser cones, but can also shape as aterrace. The main agents responsible for the deposition of siliceoussinter are algae and other vegetation in the water. Altering of wallrocks can also form sinters near fumaroles and in the deeperchannels of hot springs. Examples of siliceous sinter are geyseriteand fiorite. They can be found in many places, including Iceland,New Zealand, U.S.A. (Yellowstone National Park - Wyo.,Steamboat Springs - Colo.),...

Calcareous sinter is also called tufa, calcareous tufa, or calc-tufa. Itis a deposit of calcium carbonate, as with travertine. Calledpetrifying springs, they are quite common in limestone districts.Their calcareous waters deposit a sintery incrustation onsurrounding objects. The precipitation being assisted with mosses and other vegetable structures, thus leavingcavities in the calcareous sinter after they have decayed.[8] Petrifying spring at Pamukkale, Turkey :

Sintering 47

References[1] Kingery, W. David; Bowen, H. K.; Uhlmann, Donald R. (April 1976). Introduction to Ceramics (2nd ed.). John Wiley & Sons, Academic

Press. ISBN 0-4714-7860-1.[2] "endo gas" (http:/ / www. crystec. com/ kllendoe. htm). .[3] "Materials Science and Engineering: R: Reports : Consolidation/synthesis of materials by electric current activated/assisted sintering" (http:/ /

www. sciencedirect. com/ science/ article/ pii/ S0927796X08000995). ScienceDirect. . Retrieved 2011-09-30.[4] Salvatore Grasso et al. (2009). "Electric current activated/assisted sintering (ECAS): a review of patents 1906–2008" (free download pdf).

Sci. Technol. Adv. Mater. 10 (5): 053001. doi:10.1088/1468-6996/10/5/053001.[5] Tuan, W.H.; Guo, J.K. (2004). Multiphased ceramic materials: processing and potential. Springer. ISBN 354040516X.[6] Palmer, R.E.; Wilde, G. (December 22, 2008). Mechanical Properties of Nanocomposite Materials. EBL Database: Elsevier Ltd..

ISBN 978-0-08-044965-4.[7] Sinter (http:/ / www. thefreedictionary. com/ sinter) in thefreedictionary.com.[8] sinter (http:/ / www. britannica. com/ EBchecked/ topic/ 546308/ sinter) in Encyclopedia Britanica.

Further reading• Chiang, Yet-Ming; Birnie, Dunbar P.; Kingery, W. David (May 1996). Physical Ceramics: Principles for

Ceramic Science and Engineering. John Wiley & Sons. ISBN 0-4715-9873-9.• Green, D.J.; Hannink, R.; Swain, M.V. (1989). Transformation Toughening of Ceramics. Boca Raton: CRC Press.

ISBN 0-8493-6594-5.• German, R.M. (1996). Sintering Theory and Practice. John Wiley & Sons, Inc. ISBN 0-471-05786-X.• Kang, Suk-Joong L. (2005). Sintering (1st ed.). Oxford: Elsevier, Butterworth Heinemann. ISBN 0-7506-6385-5.

External links• Particle-Particle-Sintering – a 3D lattice kinetic Monte Carlo simulation (http:/ / www. roentzsch. org/ SintPP/

index. html)• Sphere-Plate-Sintering – a 3D lattice kinetic Monte Carlo simulation (http:/ / www. roentzsch. org/ SintSP/ index.

html)• Thick Film Technologies- A Manufacturer of Ceramic Sintering Separator Sheets (http:/ / www. thickfilmtech.

com)

Article Sources and Contributors 48

Article Sources and ContributorsEIA Class 1 dielectric  Source: http://en.wikipedia.org/w/index.php?oldid=398839856  Contributors: Amalas, Fplay, Mellery, Mumiemonstret, Neilbeach, Saxbryn, Shaddack, Shrew, Tabby,Viking59, 4 anonymous edits

EIA Class 2 dielectric  Source: http://en.wikipedia.org/w/index.php?oldid=461898477  Contributors: Amalas, Fplay, Mellery, Pa2ees, Rogerbrent, Saxbryn, Shaddack, Tgabor, Trappist themonk, 27 anonymous edits

Barium titanate  Source: http://en.wikipedia.org/w/index.php?oldid=471410753  Contributors: Beetstra, Blank Frank, Burt Harris, Calaka, Chem-awb, Chris the speller, Dlhaq, Eudialytos,FelisSchrödingeris, Fplay, Jmurphee, Lucaskw, Mac, Magister Mathematicae, Materialscientist, Mathieu Perrin, Mlprater, Polonium, Puppy8800, RG2, Rycecube57, Sbyrnes321, Shaddack,Shanedidona, Smokefoot, Thricecube, Tizeff, TrygveFlathen, Twang, William Pietri, Zennwiki, 42 anonymous edits

Strontium titanate  Source: http://en.wikipedia.org/w/index.php?oldid=470523726  Contributors: Beetstra, Bendono, Bobblewik, Brian0918, Brockert, CSWarren, Choij, Chris the speller,Dcirovic, Difluoroethene, Ebe123, Flowerparty, Fplay, Freecat, George Burgess, Gil Gamesh, Hadal, Hmains, Jarekt, Javierpetrucci, Jeff G., John Vandenberg, Jonsinger, Ketiltrout, Ligulem,Materialscientist, Minesweeper, Netofcrystals, North Shoreman, Philip Trueman, Physchim62, Plasmic Physics, Polaron, Polonium, Rhanyeia, Rich Farmbrough, Rigel0, Rjwilmsi, Rod57, SamHocevar, SauliH, Sbyrnes321, Shaddack, Smack, Steve Hart, Svick, Thricecube, Tizeff, Vicarious, Vsmith, Zanimum, 霧 木 諒 二, 36 anonymous edits

Curie temperature  Source: http://en.wikipedia.org/w/index.php?oldid=477223078  Contributors: Ahoerstemeier, Algont, AlphaPyro, Archivist, Bdesham, CanadianLinuxUser, Canterbury Tail,Cruccone, Deeptrivia, Discospinster, Djr32, Eno-ja, EpiVictor, Fetofs, FirstPrinciples, FrYGuY, Fredrik, Giftlite, Greenguy1090, Gurubrahma, Guy Macon, Hamsterlopithecus, Headbomb,Herbee, Hgrobe, Humanist, Igoldste, Jasonbrotherton, Jaydeepsamant, Jcoffland, John of Reading, Kjkolb, LarryMorseDCOhio, Linas, Lophoole, Mani1, Marek69, Masher oz, Mentifisto,Monolith2, Nathaniel, NcSchu, Nirvanana, Peachypoh, Polyparadigm, Rjgibb, Roberpl, Robert Foley, Robofish, RockMagnetist, Roulianne, SCEhardt, Serrels, Shalom Yechiel, Skapur, So Godcreated Manchester, Spiritia, Steve Quinn, Stevenj, Tarquin, Thumperward, Trusilver, Wtshymanski, Ysyoon, Yungszen, 107 anonymous edits

Piezoelectricity  Source: http://en.wikipedia.org/w/index.php?oldid=479730345  Contributors: 16@r, 4e to 4e, 777sms, 7gb2, AIVIIR, Ahoerstemeier, Alansohn, Alexrudd, Alphax, Andreparis,Andrew Jameson, Angstorm, Antikon, Arteitle, Awknsl, AxelBoldt, Badseed, Bartholomeyczik, Barticus88, Beaufanamus, Beetstra, Belizefan, Bemoeial, Benbest, Billiewilliams, Binksternet,BjKa, Bluess76, Bobblewik, Brossow, Bryan Derksen, CBM, Carcharoth, Ceyockey, Charliecoe, Chefyingi, Choihei, Ciphers, Cjaegis, Clerlic, CommonsDelinker, Connecto, Conversion script,CorbinSimpson, CorreiaPM, CrazyTerabyte, Csblack, Cyberman, DabMachine, Dacxjo, Dancter, Daneshwiki, David Biddulph, David Haslam, Davidmide, Deflective, Deglr6328, Deineka, DeltaG, DerHexer, Dhollm, Diamonddavej, DigitalDrummer, Djupp, DocWatson42, Doulos Christos, Dulciana, Edcolins, Edison, Electron9, Ellywa, Eltonpan, Epbr123, Eras-mus, Erianna,Ericamick, Ericnutsch, Ewen, Ewlyahoocom, Extremist Moderate, Faturita, Foobar, Fortdj33, Freelance Intellectual, GRAHAMUK, Galwhaa, Gan0857, GeiwTeol, Gene Nygaard, GeorgeBurgess, German name, Gianluigi, Glane23, Glaurung, Glenn, Gmack1, Gnatbuzz, Gobonobo, Goffrie, GorillaWarfare, Green Energy is King, Grinning Fool, Guillom, Haianqutang,HarpooneerX, Hdt83, Hens48, Heron, Hooperbloob, Horsten, Icek, Icep, Inductiveload, IvanLanin, Ixfd64, J.delanoy, James.Denholm, Jamesyboyuk, Jcwf, Jdmartin86, Jivecat, Justinc, KarolLangner, Kenyon, Knowz, Kosebamse, Kragen, Ktsquare, Lanoitarus, Lantonov, Lbnoliac, Light current, Lightmouse, Linas, LittleWat, M jurrens, MBirkholz, MER-C, Madhurinagare, MalcolmFarmer, Mandarax, Marcmarroquin, Materialscientist, Matthias Buchmeier, Matthieu.berthome, Maxim, Mayalld, Mayur, Megacellist, Mejor Los Indios, Mfield, Mgiganteus1, Michaelbarnes,Michaelmas1957, Micru, Mikael Häggström, MikeCapone, Mikeblas, Mirv, Mishuletz, Mufka, Mxn, Nathaniel, Neparis, Nimur, Noliac Group, NoliacGroup, Non-dropframe, Nopetro, Norm,NuclearWinner, Oli Filth, Omegatron, Oneforlogic, OrgasGirl, PamD, Paolo.dL, Paul August, Paul White 511, Pege.founder, Piezoelectric, Piezotheory, Pinin, Plastikspork, Plugwash, Polaron,Prolog, Qdr, Qef, QorTek, RJB1, Radiojon, Ratherhaveaheart, Ravindra 20, Reddi, Richard D. LeCour, Rifleman 82, Rjwilmsi, Rupsyco, SDC, Sanders muc, Saxifrage, Sbason, Schneelocke,Scot.parker, Septegram, SeventyThree, Shaddack, Shadowolf, Shubinator, Sloughin, Someguy1221, Somenath.jalal, Srajan01, Srleffler, Ssomborac, Staffwaterboy, Stevemcl, Stevertigo, Stickee,Su92412055, Superpaul3000, Surfersteve 69, Sustainableyes, TDogg310, TGCP, Tarchon, Tarotcards, Tarquin, Tesspub, TexasAndroid, The Epopt, The wub, TheGoatTroll, TheSheepTroll,TheSlashTroll, Thedatastream, Thunderbird2, Tizeff, TopGun, Tordail, Towel401, Tritium6, Trojancowboy, Tulip19, Twilight Realm, Utcursch, VQuakr, ValRon, Van helsing, VegKilla,Versus22, Vigilant, VirgilsEgo, Vsmith, W.F.Galway, Wavelength, Waya sahoni, Wetman, Whitepaw, Wishy.kushagra, Wolfmankurd, Woodduck.mayne, Yifangao, Yomoyama20070729, Yyy,Zamphuor, ZooMom1321, Սահակ, 466 anonymous edits

Permittivity  Source: http://en.wikipedia.org/w/index.php?oldid=471018387  Contributors: Absinf, Adam410, Adams13, Alexrudd, Andres, Anthony, Archimerged, ArielGold, AvicAWB,AxelBoldt, Balcer, Bdesham, Bert Hickman, Born2bwire, Brews ohare, Brockert, Bryan Derksen, Bubba73, Cacycle, Carl Koch, Complexica, Crowsnest, DMacks, Dan, Darth Panda, Deepon,Djr32, Dougher, DrBob, Edward E. Hopkins, Edwinhubbel, Eequor, Emt409, Euc, FDT, Felipebm, FelisSchrödingeris, Femto, Fgnievinski, Fresheneesz, FrozenMan, Gazza1685, Gene Nygaard,Giftlite, Glmory, Gnowor, Heron, Humanist, Icairns, Ich42, Iridescent, Jaganath, Jauhienij, Jimp, Joriki, Jtslm, JunCTionS, Kaiserkarl13, Karol Langner, Keenan Pepper, Kidunye, Kjkolb, KyleP,Larryisgood, Light current, Lokozoid, Looxix, M.O.X, M1ss1ontomars2k4, Mak17f, Marie Poise, Materialscientist, Mckaysalisbury, Mfrosz, Michael Hardy, Michaelamiller, Mild Bill Hiccup,Mshuha, Mytomi, NeilTarrant, Numbo3, Osquar F, Out of Phase User, Paolo.dL, Patrick, Pfalstad, Pgan002, Pieter Kuiper, Polaron, QTCaptain, R6MaY89, Radagast83, Rdrosson,Ricardo.hein.h, Rwestafer, Salsb, Sam Hocevar, Sbyrnes321, Scheinwerfermann, Scollin, SeanTater, Selket, Sietse Snel, SimonP, Snaily, Someone42, Spike Wilbury, Srleffler, Stephen C.Carlson, Steve Quinn, Stevenj, Stikonas, Strykerhorse, Sverdrup, TDogg310, TheDeuce1123, Thurth, Tim Starling, Tobias Bergemann, Traxs7, Truffer, Twin Bird, UlmPhysiker, Unyoyega,Verrai, WhiteHatLurker, Wigie, Wood Thrush, Wtshymanski, Xezlec, Xtraneous, Zoicon5, 老 陳, 222 anonymous edits

Electric susceptibility  Source: http://en.wikipedia.org/w/index.php?oldid=467209571  Contributors: ABCD, Afri, Alzarian16, Barak Sh, Brews ohare, Crowsnest, Dodohjk, DrBob, FrozenMan,Gcm, Harold f, Headbomb, Karol Langner, KnightRider, Larryisgood, Light current, Mak17f, Marie Poise, Mathieu Perrin, Mattpickman, Maxim, Michael Hardy, Pfalstad, Radagast83,Rdrosson, Rich Farmbrough, Rjwilmsi, Siroxo, Steinsky, Steve Quinn, Stevenj, Ti-30X, Timwilson85, Ufim, Waggers, 老 陳, 13 anonymous edits

Relative permittivity  Source: http://en.wikipedia.org/w/index.php?oldid=476635251  Contributors: Adem.ibrahim89, Albedo, AndreiDukhin, Arkwatem, Astaroth5, Bassophile, Belovedfreak,Bert Hickman, Bhamer, Biblbroks, Brews ohare, Cacycle, Chaiken, Chowbok, Clipjoint, Crowsnest, CyrilB, Dan Austin, Dethme0w, Dr Zak, Drphilharmonic, Eequor, Eigenpirate,Email4mobile, Enix150, Esmu Igors, Fgnievinski, Fred Stober, FrstFrs, Gene Nygaard, Giftlite, Gioto, Greg L, Heron, Humanist, Icairns, Jaan513, Karol Langner, Ketil3, Kieff, Kostmo,Leifisme, Light current, M.O.X, Maarschalk, MagnInd, MangoChicken, Materialscientist, Matt.urq, Maximus Rex, Mherndon, Mikiemike, Modster, Mrtransient, NawlinWiki, Nicolaennio,Nono64, Ofey, Omegatron, Pgan002, Photonical, Pieter Kuiper, R'n'B, Rdrosson, Requestion, Rich Farmbrough, Richard Harvey, Rjwilmsi, Rmashhadi, Shoefly, Shoffsta, Skomorokh, Someoneelse, Ssd, Stan J Klimas, Starsong, Steven Zhang, Stevenj, Superdelocalizable, Svick, TStein, The Original Wildbear, ThorFreyaSaturn, Tttrung, Txomin, Unmitigated Success, Walkerma,Wikiwide, XJamRastafire, Xhienne, Zdilli, ら ん ふ ぉ き, 老 陳, 155 anonymous edits

Permeability (electromagnetism)  Source: http://en.wikipedia.org/w/index.php?oldid=475608905  Contributors: 2over0, Aami rony, Aimulti, Andre Engels, Antixt, Archimerged, Army1987,Arnero, Ashishbhatnagar72, Aulis Eskola, BD2412, Barkeep, BehzadAhmadi, Berserkerus, Bmk, Brews ohare, Brockert, Bubba73, Buggi22, Capricorn42, Cdmeyer, Complexica, Conscious,Crazymonkey1123, Cryptic C62, DMacks, Daniel,levine, Deepon, Donarreiskoffer, Draicone, Dxtrous, Ebyabe, Eequor, Electricmic, Evand, Ewilson2011, Ferengi, FrozenMan, Frungi,Fuhghettaboutit, Gene Nygaard, Giftlite, H2g2bob, Hasek is the best, Headbomb, Heron, Hippojazz, Hugo-cs, IanOfNorwich, Icairns, JLD, Jeltz, Jimmy, Jkthomps7, Joechuck, JohnOwens, Jtslm,Kanakukk, Katoa, Keenan Pepper, Keyur86, Kmarinas86, KoenDelaere, L-H, LMB, Lazulilasher, Lovecz, M.O.X, Manco Capac, Marie Poise, Materialscientist, Michael Hardy, Michi zh,MihaiLG, Mmortal03, Nakon, Omegatron, PNG, Pagw, Payakoff, Pearle, PlantTrees, Rdrosson, Rememberway, Rmashhadi, Rtdrury, Ryanrs, Salsb, Sam Hocevar, Sankalpdravid, Sceptre,Shadowlynk, Sibian, Skwa, Snowolf, SocJan, Srleffler, StevenVerstoep, Stevenj, Sundaryourfriend, Sverdrup, TDogg310, TStein, Teapeat, The Land, Thelb4, Tom.Reding, Trevor MacInnis,Verpies, Voidxor, WinstonSmith, Wolfkeeper, Xoder, Yoshigev, Z4ngetsu, Zhangzhe0101, Zureks, Zzedar, 143 anonymous edits

Sintering  Source: http://en.wikipedia.org/w/index.php?oldid=480381642  Contributors: A Doon, Alan Liefting, Alessandro.fais, Allenc28, Argento, Ayacop, Ayecee, Beach drifter,Belovedfreak, BenFrantzDale, BirgitteSB, Boredzo, Bryan Derksen, Caltrop, Cermet, Chiswick Chap, Cohesion, Danhicks, Danzaldi, Drecali, Edgar181, Everyking, Fabiform, Feťour,Firetrap9254, Firsfron, Fredvanner, Fuzheado, GargoyleMT, George Burgess, Giftlite, Heron, Hooperbloob, Hurmata, Interiot, JaGa, John, Jrankin, Julesd, Kaszeta, Keenan Pepper, Kgrad,Kinema, Knuffels, Krithin, L0b0t, L0ngpar1sh, Lacanx, Lightmouse, Llywrch, Logger9, LorenzoB, Lrreiche, Lupo, M dorothy, Madhero88, Mandarax, Marcusyoder, Materialscientist,Matthandlersux, Mav, MikeLynch, Mikiemike, Mythealias, Namazu-tron, Nekura, Nick Number, Njit0124, Nopetro, Pascalschreyer, Pedant17, Peterlewis, Phyzome, Polyparadigm, Propaniac,Rich Farmbrough, Romaioi, Roman Dawydkin, Romary, Sanjiv swarup, Shinkolobwe, SkazochNik97, Slashme, Slowking Man, Smith609, Speshuldusty, Syrthiss, TDogg310, The undertow,Theriac, Tmassey, Tom Duff, Tommy2010, Wizard191, YebisYa, Yellowpad, Yerpo, Zipspeed, 178 anonymous edits

Image Sources, Licenses and Contributors 49

Image Sources, Licenses and ContributorsImage:BaTiO3ceramics.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:BaTiO3ceramics.JPG  License: Creative Commons Attribution-Sharealike 3.0  Contributors:Materialscientist (talk). Original uploader was Materialscientist at en.wikipediaFile:Yes check.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Yes_check.svg  License: Public Domain  Contributors: AnomieImage:X mark.svg  Source: http://en.wikipedia.org/w/index.php?title=File:X_mark.svg  License: Public Domain  Contributors: User:GmaxwellImage:Perovskite.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Perovskite.jpg  License: Public Domain  Contributors: Original uploader was Cadmium at en.wikipediaImage:Tausonite.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tausonite.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: Materialscientist (talk).Original uploader was Materialscientist at en.wikipediaImage:Stohrem.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Stohrem.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: by MaterialscientistImage:Stocrystal.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Stocrystal.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: Materialscientist (talk)File:Ferromagnetic ordering.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Ferromagnetic_ordering.svg  License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: Michael SchmidFile:Paramagnetic probe without magnetic field.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Paramagnetic_probe_without_magnetic_field.svg  License: Public Domain Contributors: Jens Böning (Jensel)File:Loudspeaker.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Loudspeaker.svg  License: Public Domain  Contributors: Bayo, Gmaxwell, Husky, Iamunknown, Mirithing,Myself488, Nethac DIU, Omegatron, Rocket000, The Evil IP address, Wouterhagens, 18 anonymous editsImage:SchemaPiezo.gif  Source: http://en.wikipedia.org/w/index.php?title=File:SchemaPiezo.gif  License: Creative Commons Attribution-Sharealike 3.0,2.5,2.0,1.0  Contributors: MaelGuennou - TitzeffFile:Piezo bending principle.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Piezo_bending_principle.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors:Sonitron SupportImage:Capacitor schematic with dielectric.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Capacitor_schematic_with_dielectric.svg  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: Papa NovemberImage:Perovskite.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Perovskite.svg  License: Public Domain  Contributors: PininImage:Piezoelectric pickup1.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Piezoelectric_pickup1.jpg  License: GNU Free Documentation License  Contributors: Georg FeitscherFile:RPG-7 detached.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:RPG-7_detached.jpg  License: Creative Commons Attribution 2.5  Contributors: Michal Maňas (User:Snek01)Image:2007-07-24 Piezoelectric buzzer.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:2007-07-24_Piezoelectric_buzzer.jpg  License: Creative Commons Attribution-ShareAlike3.0 Unported  Contributors: GophiFile:Slip-stick actuator operation.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Slip-stick_actuator_operation.svg  License: Creative Commons Attribution 2.5  Contributors:InductiveloadFile:Diel.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Diel.gif  License: Public Domain  Contributors: hyperphysicsImage:Dielectric responses.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Dielectric_responses.svg  License: Attribution  Contributors: Original uploader was Archimerged aten.wikipediaFile:Water relative static permittivity.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Water_relative_static_permittivity.svg  License: Creative Commons Attribution 3.0 Contributors: Stan J KlimasFile:Permeability by Zureks.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Permeability_by_Zureks.svg  License: Public Domain  Contributors: ZureksFile:Permeability of ferromagnet by Zureks.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Permeability_of_ferromagnet_by_Zureks.svg  License: Public Domain  Contributors:ZureksImage:Source pétrifiante.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Source_pétrifiante.jpg  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors:SaphonImage:Pamukkale1.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Pamukkale1.jpg  License: GNU Free Documentation License  Contributors: Horvat, Traroth

License 50

LicenseCreative Commons Attribution-Share Alike 3.0 Unported//creativecommons.org/licenses/by-sa/3.0/