Research Article On the Tapping Mode Measurement for Young s … · 2019. 7. 31. · plastic...

Hindawi Publishing CorporationJournal of NanotechnologyVolume 2013 Article ID 761031 10 pageshttpdxdoiorg1011552013761031

Research ArticleOn the Tapping Mode Measurement for Youngrsquos Modulus ofNanocrystalline Metal Coatings

H S Tanvir Ahmed Eric Brannigan and Alan F Jankowski

Edward E Whitacre Jr College of Engineering Mechanical Engineering Texas Tech University P O Box 41021Lubbock TX 79409-1021 USA

Correspondence should be addressed to Alan F Jankowski alanjankowskittuedu

Received 7 June 2013 Revised 26 July 2013 Accepted 27 July 2013

Academic Editor Carlos R Cabrera

Copyright copy 2013 H S Tanvir Ahmed et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Youngrsquos modulus of nanocrystalline metal coatings is measured using the oscillating that is tapping mode of a cantilever with adiamond tip The resonant frequency of the cantilever changes when the diamond tip comes in contact with a sample surface AHertz-contact-based model is further developed using higher-order terms in a Taylor series expansion to determine a relationshipbetween the reduced elastic modulus and the shift in the resonant frequency of the cantilever during elastic contact betweenthe diamond tip and sample surface The tapping mode technique can be used to accurately determine Youngrsquos modulus thatcorresponds with the crystalline orientation of the sample surface as demonstrated for nanocrystalline nickel vanadium andtantalum coatings

1 Introduction

A variety of indentation-based test methods are used to eval-uate strengthening effects [1ndash4] in materials at the nanoscaleNanoindentation normal to the surface is routinely usedto measure the hardness and Youngrsquos modulus Triboin-dentation tests are used [5ndash7] to measure both hardnessand shear strength as well as quantify strain-rate sensitivity[8 9] effects in the evaluation of deformation mechanismsin nanocrystalline alloys The standard approach [10ndash12]to determine the elastic modulus during nanoindentationevaluates the load (119875) versus displacement (ℎ) curve duringunloading after plastic deformation It remains difficult tocollect a sufficient quantity of 119875 versus ℎ data during elasticloading since elastic displacements (119911) are commonly limitedto depths of only a few nanometers or less in many hardmaterialsThe initial linear slope (119878) of the power-law-shapedunloading curve is used [11 12] to determine the reducedelastic modulus (119864lowast) as

119864lowast

=119878radic120587

2120573radic119860119888

(1)

The contact area (119860119888) equals the square of the contact

depth (ℎ2119888) multiplied by the tip area (119888

ℎ) coefficient and

the shape parameter 120573 equals 100 for flat punch 1034 forBerkovich and 1012 for Vickers indenter tips The reducedelastic modulus (119864lowast) of the indenter tip and sample surfacesystem is related to the elastic moduli of the indenter tip andsample surface as

1

119864lowast=1 minus ]2119905

119864119905

+1 minus ]2119904

119864119904

(2)

Here the subscripts 119905 and 119904 represent the probe tip andsample respectively for the Poisson ratio (]) and Youngrsquosmodulus (119864) values Indentation size effects (ISEs) arefound with the directional loading of the indenter tip Forexample beyond an indentation depth that is sim10 of thefilm thickness the use of a Meyer plot indicates [13 14]that the substrate material contributes to the elastic andplastic property measurements of the coating Also thesensitivity of the nanoindentationmeasurement to accuratelymeasure anisotropic elastic behavior is shown [15ndash17] tobe a function of the indenter tip shape For example atriangular indenter can give values that are much higherthan axisymmetric tips such as spheroconical but with lesssensitivity than that obtained using axisymmetric shapesNanoindentation measurements with Berkovich diamond

2 Journal of Nanotechnology

tips may not quantify the full effect of anisotropic behaviorthat is the anisotropic response can be underestimated inboth modeling and experimental efforts For example a 10difference from 125 to 140GPa is reported [15] betweenCu(100) and Cu(111) whereas the known elastic moduli119864(hkl) along different crystalline directions [hkl] vary by300 with values from 66 to 192GPa Similarly differenteffects are found [18 19] for the effect of tip shape on plasticflow wherein spheroconical shapes evidence work hardeningof material during indentation as opposed to well-definedpyramidal indentations that produce a near-perfect plasticresponse

The torsion-resonance mode of atomic force acousticmicroscope is used [20] to measure the elastic constants ofanisotropic materials A piezoelectric device is excited usingan alternating current voltage to induce vibrations in theatomic force microscopy (AFM) cantilever while the tip isin contact with the sample surface Indentation elastic mod-ulus is extracted from the tip-surface interaction assumingHertzian contact mechanics In a similar technique [21] thedeflection of the AFM cantilever is used to determine thelocalized modulus Vibrating reed measurements [22] havesimilarities to the AFM technique where the major differenceis that the sample along with the substrate in the vibratingreed method is exposed to piezoelectric vibrations whereasthe probe cantilever is vibrated in the AFM technique Theoscillating bubble method [23] is another technique formeasuring surface elasticity of liquids The tapping modeelastic modulus measurement technique [24ndash29] providesanother relatively new method for measuring the reducedelastic modulusThemeasurement is based on the oscillationfrequency of a probe that is in elastic contact with the surfaceThe tapping mode technique is nondestructive which pro-vides an advantage of measuring the elastic modulus prior toplastic deformation whereas nanoindentation measures theelastic-plastically deformed material

The tapping mode method is now pursued for evaluatingtheYoungrsquosmodulus of nanocrystallinemetal coatings Vapordeposited coatings of cubic metals can have a single-growthtexture that is of interest for assessing the sensitivity ofthe measurement technique to anisotropic elastic behaviorin nanocrystalline metals such as nickel For this purposepolycrystalline samples provide a basis for measurementcalibration along with single-crystal wafer specimens Fur-ther development of the classic Hertz-contact solution usinghigher-order terms of a Taylorrsquos series expansion showsa quadratic rather than a linear relationship between thereduced elastic modulus and the resonant frequency shiftThenew solution can be used to simulate themagnitude of theshift in the resonant frequency as a function of the reducedelastic modulus using the cantilever bending stiffness and theindenter tip radius of curvature

2 Materials and Methods

21 Materials The materials for the tapping mode measure-ment should have smooth surfaces If there is a high ampli-tude to short-wavelength surface roughness then multiple

point contact can occur which could appear to artificiallystiffen the mechanical response Smooth surfaces and ananocrystalline structure for tantalum (Ta) vanadium (V)and nickel (Ni) coatings are produced from the high-quenchrates (gt106 Ksdotsminus1) of the sputter deposition method [30ndash34] The metals are coated onto polished flats such assemiconductor-grade silicon and sapphire wafers In briefthe 03ndash06120583m thick coatings were synthesized by planar-magnetron sputter deposition in a vacuum chamber cryo-genically pumped to a 2 times 10minus5 Pa base pressure The nativeSi oxide on the substrate is not removed prior to depositionof the coating from target materials of gt0999 purity Thecathodes are operated in the DC mode with a typicaldischarge potential of 2 times 102 Volts The source-to-substrateseparation is 7ndash10 cm and the 1 Pa working-gas pressure ofargon ismaintainedwith a 35 cm3sdotsminus1 flow rateThemeasuredsurface temperature of the substrate remains below 473Kduring the deposition process The deposition rates andthickness accumulation during deposition are recorded usingcalibrated Au-coated quartz-crystal microbalances

Details of the structural characterization for the Ta V andNi sputter deposited coatings are reported elsewhere [30 35]The characterization methods consisted of X-ray diffraction(XRD) transmission electronmicroscopy (TEM) and atomicforce microscopy (AFM) The XRD measurements wereconducted in the 1205792120579mode to determine both the crystallinestructure and orientation The sputter deposited metal coat-ings have a single growth orientation of close-packed planesThe body-center-cubic (bcc) metals of Ta and V are (110) andthe face-center-cubic (fcc) Ni is (111) TEM imaging in brightfield in the electron-diffraction mode and the use of highresolution lattice imaging conditions [36 37] enable a closerlook at the grain size grain boundary structure and defectstructure Selected area diffraction patterns (SADPs) confirmthe (110) growth for the Ta and V coatings as well as the(111) growth for the Ni coating Also the SADPs indicate thatthe coatings are polycrystalline in plane that is randomlyoriented parallel to the surface The grain sizes determinedfrom the average width to the columnar growth as seen inthe bright field TEM images range from 14 to 20 nm for theTa and V coatings to less than 150 nm for the Ni coatingAFM images [35] of the Ta and V surfaces indicate a smoothsurface with less than a 1-2 nm variation in amplitude over1 120583m length scales that is a surface smooth for establishing aHertz-contact condition

Semiconductor-grade single-side polished wafers of sil-icon Si(100) Si(111) and sapphire Al

2O3(002) are used to

provide smooth single-crystal reference materials Also pol-ished polycrystalline samples of polycarbonate (pC) quartz(SiO2) hydroxyapatite (HA) and sapphire (Al

2O3) are used

as reference standards with known elastic constants for theestablishment of the calibration curve from the tappingmodemeasurements

22 Tapping Mode Experiment The tapping mode use [2426 28] of a nanoprobe in the configuration of a scan-ning force microscope provides a method for measuringelastic deformation A universal micro-nano-materials tester

Journal of Nanotechnology 3

(UMNT) as manufactured by Bruker-Nano CETR Inc isequipped with a NanoAnalyzer (NA)-II test module thatcontains a ceramic cantilever with a Berkovich diamond tipBoth the 14 kHz resonant frequency (119891

0) of the free-standing

cantilever with a spring constant (119896119888) of 22229 kNsdotmminus1 and

the initial 5 nm amplitude (119860119898) of motion are changed as the

probe is lowered so that contact is made with the specimensurface The frequency (119891) and amplitude (119860

119898) of the probe

oscillation are quantitatively measured as a function of thevertical displacement (119909) of the probe tip A frequencyfeedback system [29] moves the probe into the materialsurface until a predefined frequency shift (Δ119891) is achievedthat is typically less than 500ndash900Hz In the elastic regimethe net elastic displacement (119911) beyond the initial surfacecontact is only a few nanometers that is 1ndash6 nm for mostmetals that accompany a decrease in the vibration amplitudefrom 5 to less than 02 nm A series of frequency shift curvesoften a dozen or more are used to achieve accuracy Thelimited range of frequency shift (Δ119891) available for elasticdeformation from the free-standing resonant frequency (119891

0)

in the NA-II precludes access to an examination of higher-order harmonics

The Δ119891 versus 119911 variation of the tip-surface system canbe equated as a function of the reduced elastic modulus (119864lowast)The dynamic behavior of the indenter probe in contact withthe surface is derived from the equation of motion and theequation for the frequency of oscillation of the system Aformulation of the 120572-parameter is determined [24 25] from aTaylor series expansion of the equations to the Hertz-contactmodel for the variation of Δ119891 with 119911 as

1205722

=(Δ119891)2

119911 (3)

The relationship between the square of the resonant fre-quency shift (Δ119891)2 and the vertical displacement (119909) of thecantilever is seen in the schematic in Figure 1 that has fourdistinct regions where (1) the tip oscillates without surfacecontact (2) there is contact between the tip and a viscous(contamination) surface layer (3) direct interaction of the tipoccurs with atoms of the specimen surface and (4) dampingof the probe oscillation is seen due to plastic deformationRegion 3 has twoportionsThe amplitude of the tip oscillationis still large and the probe base is far from the surface in region31015840 that is the tip is bouncing off the surface As 119909 increasesthe tip and surface begin to oscillate in region 310158401015840 withoutseparation in a strict contact mode that is the elastic regimecorresponding with (3) In almost all cases the amplitudeof the oscillation can have a significant role in determiningthe extent of the linear regime in region 310158401015840 The length ofthe linear elastic regime is reduced when the amplitude ofoscillation is large with respect to the tip radius In generalthe amplitude-to-tip radius ratio is in the order of 5 orless An initial vibration amplitude of 5 nm works well for awide range of materials using a Berkovich-shaped diamondtip The material starts to plastically deform in region 4 ofFigure 1 as the probe is pressed further into the surface wherethe associated deformation imparts a damping action on thevibration of the probe The result is a sudden change in the

1 2 4

Displacement (x)

Slope = 1205722

Freq

uenc

y sh

ift (Δ

fr)2

3998400 998400

3998400

Figure 1 A plot of the characteristic regions observed for variationin the square of the resonant frequency shift (Δ119891

119903)2 with displace-

ment (119909)when the probe tipmounted to a vibrating cantilever comesin contact with a surface

frequency shift from the linear regime of region 310158401015840 as theamplitude fully diminishes This phenomenon is observedfor a wide range of materials such as metals and ceramicsThe series of frequency shift curves are aligned where theamplitude reduces to zero to define the upper limit to region310158401015840 As a visual confirmation the displacement 119909 for theregion 310158401015840 upper limit position should not proceed beyondthe square of the frequency shift where an indentation isobserved on the imaged surface that is plastic deformationTo determine the lower limit to region 310158401015840 that bounds theonset of the elastic response care must be taken to avoid thepreceding nonlinear section of the curve as shown by thevertical lines that bound region 310158401015840 in Figure 1 Once the linearregime is defined as for example by a correlation coefficient1198771198881198882 gt 098 the slope of region 310158401015840 is determined from (3)The calibrated measurement of the reduced elastic mod-

ulus (119864lowast) for an unknown material is accomplished fromtapping mode measurements of 120572

2 using the followinggeneralized expression

120572 = 119886(119864lowast

)119899

(4)

In (4) use is made of a power-law exponent (119899) and a scalingconstant (119886) This generalized expression can accommodatethe most basic form of a nonlinear relationship between 119864

lowast

and 120572 as is commonly found in experimental measurementsA two-term Taylor series expansion [24 25] for the solutionof the Hertz-contact condition between tip and surface yieldsan exponent 119899 value of one that is a linear relationshipIn the next section the more satisfactory formulation of ageneralized nonlinear relationship between 119864

lowast and 120572 willbe seen to require additional terms in the Taylor seriesexpansion For the calibration test method several uniquemeasurements of 120572

2 must be obtained for a variety of


known material standards from which a calibration curveis plotted using (4) In this way the basis is establishedfor an experimental calibration curve that corresponds withthe particular cantilever-tip configuration The calibrationcurve is made using materials with well-established elasticmoduli (119864) to cover a large 119864

lowast range from 3 to 400GPaThe determination of 119864lowast for the unknown material proceedswith (4) using an input of the measured 120572 value for thatmaterial The NanoAnalyzer NA-II is used as well to scan thesample surfaces to avoid defected regions and to confirm thesmoothness required for the tapping mode measurements

3 Results and Discussion

31 Tapping Mode Analytic Model An analytic method [38]is used to determine Youngrsquos modulus 119864 through derivationof exact expressions for 120572 and 119864

lowast as well as the final formof the elasticity equation from Hertz-contact mechanics Theformulations presented in (3) and (4) are justified using thedynamic equivalent of the cantilever with a probe tip Thisdynamic system can be represented [26] by a spring-masssystem where the equation of motion is given as

119898 + 119896119888119909 = 0 (5)

In (5) the mass is 119898 the displacement is 119909 and the springconstant of the cantilever 119896

119888is given by

119896119888=3119864119868

1198713 (6)

In (6) the cantileverrsquos moment of inertia is 119868 the elasticmodulus is 119864 and its length is 119871 Thus the natural oscillationfrequency of the system is described as

120596119899= radic

119896119888

119898= 2120587119891

0 (7)

When the probe is in contact with the surface the dynamicsystem is modeled such that for a displacement 119909 thefrequency of oscillation of the system 119891 is given as

2120587119891 = radic119896119888+ 119896119904

119898 (8)

In (8) 119896119904is the spring constant to the elastic response of the

surface Combining (7) and (8) and solving for 119891 yield theexpression

119891 = 1198910(radic1 +

119896119904

119896119888

) (9)

The change of frequency from the state of natural oscillationto the contact state with the surface is then given by

Δ119891 = 119891 minus 1198910= 1198910(radic1 +

119896119904

119896119888

minus 1) (10)

ATaylor series expansion of (9) using only the first two termscombined with (10) gives the previously well-known simpli-fied expression for Δ119891 as

Δ119891 = 1198910(119896119904

2119896119888

) (11)

From Hertz-contact mechanics it is known that after appli-cation of normal load (119875) the distance (119911) from the plane ofthe surface contact is given by

119911 = (3119875

4119864lowast)

23

(1

119877)

13

(12)

In (12) the hemispherical tip radius is 119877 The spring constantfor the surface (119896

119904) can be modeled using the relationship

119896119904=120597119875

120597119911 (13)

After inserting (12) into the operation for (13) an expressionfor 119896119904then results as

119896119904=120597119875

120597119911= 2radic119877119864

lowast

radic119911 (14)

Using (14) expression for 119896119904and inserting it into (11) yield an

expression for the frequency shift (Δ119891) as

Δ119891 =1198910radic119877

119896119888

119864lowast

radic119911 (15)

After taking a square of both sides to (15) a relationship isnow derived between (Δ119891)2 and the displacement (119911) as

(Δ119891)2

= 1205722

119911 (16)

where

120572 =1198910radic119877

119896119888

119864lowast

(17)

A plot of the square of frequency shift (Δ119891)2 versus the probetip-surface elastic displacement (119911) as first presented in thesimilar expression of (4) is used to experimentally measurethe slope 1205722 that corresponds with (16) The expression (17)that shows a linear relationship between 119864lowast and 120572 as derivedelsewhere [25 26] uses only the first two terms of the Taylorrsquosseries expansion for (10) Therefore in order to determine amore exact analytic expression for the relationship between120572 and 119864

lowast that accommodates a nonlinear relationship asexpressed in the generalized power-law expression of (4) athird term is now introduced into the Taylorrsquos series expan-sion This procedure provides an increase in accuracy incomparison to (11) for determining the relationship betweenthe frequency shift and elastic modulus using (14) The seriesexpansion used to derive (11) and (17) for 120572 now becomes thefollowing expression that is derived from (9) and (10)

120572 =1198910radic119877

119896119888

119864lowast

[1 minus1

2(radic119877119864

lowast

)radic119911

119896119888

] (18)


Table 1 Values for 120572 displacement (119911) Poissonrsquos ratio (]) and elastic modulus 119864lowast 119864(ℎ119896119897)

Sample 120572 (Hzsdotnmminus12) 119911 (nm) 119864lowast (GPa) ] 119864 (GPa) Cubic materials 119864(ℎ119896119897) (GPa)

(111) (110) (100)Polycarbonate pC 358 plusmn 14 508 4 037 35 mdash mdash mdashFused silica SiO2 145 plusmn 14 417 70 017 72 mdash mdash mdashFused quartz SiO2 149 plusmn 13 325 70 017 72 mdash mdash mdashHydroxyapatite HA 170 plusmn 15 146 86 027 85 mdash mdash mdashSilicon Si(100) 202 plusmn 16 118 127 027 130 188 169 130Vanadium V(110) 228 plusmn 22 163 130 037 125 119 125 147Silicon Si(111) 236 plusmn 23 274 176 027 188 188 169 130Tantalum Ta(110) 271 plusmn 23 162 187 034 192 216 192 144Nickel Ni(111) 325 plusmn 20 171 269 031 305 305 227 129Fused sapphire Al2O3 401 plusmn 26 098 367 027 470 mdash mdash mdashSapphire Al2O3(002) 392 plusmn 27 078 382 027 496 mdash mdash mdash

Equation (18) can be reduced to the form of (17) Formula(18) can be solved for 119864lowast as a function of 119891

0 120572 119911 119896

119888 and 119877 by

using a standard quadratic expression for 119864lowast as

119864lowast

=

1 plusmn radic1 minus (2120572radic1199111198910)

radic119877119911119896119888

(19)

Experimentally meaningful values are produced from (19)using the (1 minus radic ) term in the numerator Equations (3) and(4) become the basis for the calibration procedure to curve-fitthe coefficient (119886) and exponent (119899) values to the power-lawrelationship and to be used for the determination of unknown119864lowast values The nonlinear algebraic solution of (18) indicates

a quadratic relationship between 120572 and 119864lowast(as dependent onradic119877 and radic119911) to reveal that the corresponding value of theexponent 119899 for the power-law fit to (4) may be approximately12

The reduced elastic modulus (119864lowast) of the sample canbe computed from (19) provided that measurements arepossible for the free-standing oscillation frequency 119891

0of the

cantilever the cantilever bending stiffness 119896119888 the probe tip-

surface displacement 119911 and probe tip radius 119877 The calibra-tion method for measurement of reduced elastic modulus119864lowast is more frequently used since the probe tip values are

often determined with limited accuracy In the calibrationmethod the 120572 values are measured as described previouslyusing a particular probe tip for several materials with knownelastic modulus The 120572 values are then plotted as a functionof the corresponding known reduced modulus values inaccordance with (4) to fit the parameters for the coefficient119886 and power-law exponent 119899 The greater the number ofcalibrationmaterials is the better the power-law curve fit willbe for amore accurate calculation of unknown elasticmoduliUse of (19) will be made to simulate (4) curve fit results andto determine an approximate value for the indenter tip radius119877 as may be dependent upon 119911

32 Computation of Elastic Moduli The effect of crystallineanisotropy on the elastic moduli can be quantified using amathematical formulation [39] of the elastic moduli (119864) and

tabulated values [40ndash48] for the elastic constants (119862119894119895) and

compliances (119878119894119895) The equation for Youngrsquos modulus 119864(hkl)

for cubic systems along the lthklgt directions with respect tothe crystalline orientation using the unit vectors (119897

119894) such as

those designated by the Miller indices of lt100gt lt110gt andlt111gt is

1

119864= 11987811minus 2 (119878

11minus 11987812minus1

211987844) (1198972

11198972

2+ 1198972

21198972

3+ 1198972

31198972

1) (20)

For the crystal systems with 3m 32 and minus3m classes of sym-metry the expression for Youngrsquos modulus becomes

1

119864= (1 minus 119897

2

3)2

11987811+ 1198974

311987833

+ 1198972

3(1 minus 1198972

3) (211987813+ 11987844)

+ 21198972

11198972

3(31198972

1minus 1198972

2) 11987814

(21)

The 119864(hkl) values computed using (20) and (21) are listedin Table 1 for the comparison of anisotropy within each andall of the materials in the order of increasing stiffness Thelisted 119864lowast values are computed using (2) assuming a (1minus]2

119905)119864119905

value of 000075GPaminus1 for the probe tip as based upon ananoindentation calibration of the Berkovich diamond tip tothe known hardness value for silicon The (1minus]2

119905)119864119905value of

000075GPaminus1 is consistent with the typical ]119905values of 007ndash

010 and 119864119905values of 1150ndash1250GPa that are often reported

for diamond

33 TappingModeMeasurements The square of the resonantfrequency shift (Δ119891

119903)2 with probe displacement 119909 for the

nanocrystalline V(110) and Ni(111) coatings is shown in theplots of Figures 2(a) and 3(a) For the V(110) example anaverage value of 85 times 104Hz2 is computed for the changein (Δ119891

119903)2 that corresponds to the 163 nm portion of the

linear elastic displacement (119911) from region 310158401015840 in Figure 2(a)centered at a displacement (119909) of 287 nm The data plots ofFigures 2(b) and 3(b) show the simultaneous variation of theoscillation amplitude119860

119898with the probe tip displacement (119909)


0

10

20

30

10 15 20 25 30 35Displacment x (nm)

(104

Hz2

)Fr

eque

ncy

shift

(Δfr)2

(a)

0

1

2

3

4

5

6


Am

plitu

deAm

(nm

)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600

Am

plitu

deAm

(nm

)

Frequency fr (kHz)

(c)

Figure 2 (a) The square of the resonant frequency shift (Δ119891119903)2

variation with the probe tip displacement 119909 and the amplitude 119860119898

of the oscillation variation with (b) the probe tip displacement 119909and (c) resonant frequency119891

119903are shown for a nanocrystallineV(110)

coating deposited onto a Si substrate

0

10

20

30

40

50

10 15 20 25 30Displacment x (nm)

(104

Hz2

)Fr

eque

ncy

shift

( Δfr)2

(a)

0

1

2

3

4

5

6

10 15 20 25 30

Am

plitu

deAm

(nm

)

Displacment x (nm)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600 14800Frequency fr (kHz)

Am

plitu

deAm

(nm

)

(c)


variation with the probe tip displacement 119909 and the amplitude119860119898of

the oscillation variation with (b) the probe tip displacement 119909 and(c) resonant frequency 119891

119903are shown for a nanocrystalline Ni(111)



20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)

Figure 4 The amplitude 119860119898of the oscillation variation with the

resonant frequency (119891119903) for the free-standing cantilever

The magnitude of 119860119898decreases to only 02 nm in region 310158401015840

from its original region 1 value of 5 nm when free standingThe decrease in the amplitude 119860

119898for the V(110) and

Ni(111) samples with increasing resonant frequency (119891119903)

is shown in Figures 2(c) and 3(c) The vertical markerscorrespond with the changes in the square of the resonantfrequency shift indicated in Figures 2(a) and 3(a) for theV(110) and Ni(111) samples For comparison a forward andbackward scan through the resonant frequency of the free-standing cantilever is shown in Figure 4

The results for the calculations of the 120572 values for allof the samples that are determined from the tapping modemeasurements of the change in (Δ119891

119903)2 according to (3)

are listed in Table 1 The results for the reduced elasticmodulus 119864

lowast (GPa) calibration curve as plotted with themeasured 120572 (Hzsdotnmminus12) values are shown in Figure 5 bythe solid symbols The power-law curve fit to (4) gives avalue for 119899 equal to 0532 and value for 119886 equal to 162(Hzsdotnmminus12sdotGPaminus119899) where the correlation coefficient 119877

1198881198882 to

the curve fit equals 0994The computation of the Table 1 values for 119864lowast from the

known 119864 values is made using (2) The individual (open-symbol) data points for the elastic moduli of non-close-packed growth planes are plotted to evaluate the effect ofcrystalline orientation on the calibration curve fitting of themeasured elasticmodulus for the cubic nanocrystallinemetalcoatings The values that are computed for Ni(100) Ni(110)V(100) V(111) Ta(100) and Ta(111) using (20)-(21) are listedin Table 1 Clearly the modulus values for Ni(100) Ni(110)and Ta(100) cannot be considered as these values rest welloff (4) calibration curve In addition a poor curve fit to (4)results using averaged 119864(hkl) values for Ta Ni and V Themodulus that corresponds to the single growth orientationof the nanocrystalline metal coating is consistent with (4)curve fit of modulus values for the polycrystalline and single-crystal standards Therefore in general it appears that the

0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)

Reduced modulus Elowast (GPa)

Al2O3(002)

Figure 5Themeasured120572 value (119904) that correspondswith the squareroot of the slope in region 310158401015840 (of Figure 1) is plotted as function ofthe reduced modulus 119864lowast value for various sample materials wherethe crystalline orientation is indicated by the symbol shape in thelegend

measured Youngrsquos modulus values correspond to the actualgrowth orientation of the nanocrystalline metal coatings

These present results for the variation of 119864lowast with 120572 areconsistent with the polycrystalline calibration materials andthe elastic anisotropy of the single-crystal samples of Si(100)Si(111) and Al

2O3(002) as well as the elastically anisotropic

nanocrystalline Ta(110) V(110) and Ni(111) coatings Forcomparison similar elastic modulus values of 187GPa and141 GPa are reported [35] for the Ta(110) and V(110) coat-ings respectively as determined from nanoindentation testsHowever the nanoindentation values do appear to includesome contribution of a (100) component during elasticunloading of the coating subsequent to plastic deformation

The 119864lowast values that correspond with the actual crystallineorientation of the coatings are used in the (solid-line) curvefit to (4) A (dashed-line) curve that represents the analyticmodel approach is computed using (19) The analytic modelcurve overlays the calibration curve fit The analytic model(dashed-line) curve in (19) is formed by computing the 119864lowastand 120572 values using tip radius values (119877) that are fitted tothe corresponding elastic displacement condition for eachsample to reproduce the experimental (solid-line) calibrationcurve The tip radius (119877) variation with elastic displacementis reproduced as generally anticipated for diamond indentersAn 119877 value of 102 nm is modeled at the larger depths offull elastic displacement (119911) (Only a portion of the elasticdisplacement 119911 used in the 120572 value computations is listedin Table 1) In general the elastic displacement progressivelydecreases as the samples stiffen Whereas a very sharp tipradius and nanometer-scale elastic deformation could clearlypresent the need to consider modeling of near-atomic inter-actions the use of a classic modeling approach as presentedfor Hertzian tests is generally consistent with the actualdiamond tip condition where the contact radius is less than5 of the tip radius The utility of the classical model is


supported by the self-consistent experimental measurementsof the calibration materials with known elastic behavior

34 Discussion The sensitivity to potential elastic anisotropyis seen in themeasurement of theYoungrsquosmodulus values thatcorrespond with surface normal loading of the tapping modemethod The elastic response is measured in the directionof growth for the nanocrystalline coatings as well as thesingle-crystal wafer orientation seen in the different 120572 valuesmeasured for Si(100) and Si(111) The present result indicatesthat measurement of Youngrsquos modulus is directionally depen-dent on loading Modulus values determined with in-planeloading condition are not equivalent to the normal-incidentloading bymethods such as nanoindentation and the tappingmode

The tapping mode measurement of thin film coatingsusing the resonant frequency shift is useful for a widerange of materials with smooth surfaces The method iseasily applied when the indenter tip is much stiffer thanthe surface being measured The use of higher-order termsin the Taylor series expansion of the linear solution for 120572in (17) results in the more general nonlinear solution aspresented in (18) This extension can be advantageous inmodeling experimental data since it is difficult to meet theassumption of the first-order approximation that 119896

119904≪ 119896119888

for typical cantilevers where 119896119888

sim 104 kNsdotmminus1 and 119877 sim

102 nm However the analytic approach presented does notaccount for adverse effects of tip deformation a pull-off forceor surface adhesion Whereas the Hertz expression of (12)can hold true for large loads [49 50] an overestimationof the elastic modulus at low loads can occur when theeffect of surface energy (120574) is significant Here the Johnson-Kendall-Roberts (JKR)model can provide a better estimationof the contact radius Similarly an accurate expression canbe derived [51] from the Derjaguin-Muller-Toporov (DMT)model that involves a Taylor series expansion with morethan just the first two terms The amount of pull-off forcecan be determined by conducting future nanoindentationexperiments [52 53] The measurement of pull-off forcerequires careful chemical cleaning of the sample surfaces Atpresent the tapping mode measurements are made with thesurface-contamination layer intact which contains hydrocar-bons and appears to provide a natural lubrication alleviatingbackground adhesion effects

4 Conclusions

Youngrsquos modulus 119864 is measured using the tapping mode of acantilever-mounted diamond probeThe shift in the resonantfrequency 119891

0of the cantilever is recorded when the diamond

probe is in elastic contact with the sample surface The vari-ation in the square of the change in the resonant frequency(Δ119891119903)2 divided by the accompanying elastic displacement 119911 is

equated to an experimental 1205722 parameter that is 1205722 equals(Δ119891119903)2119911 A power-law relationship is used to equate 120572 with

the reduced elastic modulus119864lowast An analytic derivation usinghigher-order terms from a Taylor series expansion of thesolution to the Hertz condition for the probe and surface

indicates that the exponent to the power-law relationshipapproximates a quadratic expression between 120572 (Hzsdotnmminus12)and 119864

lowast (GPa) For the Berkovich tip of this study 120572 equals162sdot(119864lowast)0532

Tapping mode measurements are made of sputter depos-ited tantalum (Ta) vanadium (V) and nickel (Ni) coatingsthat have a close-packed plane and growth orientationPolycrystalline ceramics and single-crystal wafers of Si(100)Si(111) and Al

2O3(002) are used to establish the 120572 versus 119864lowast

calibration curve along with measurements of the nanocrys-talline metal coatings The tapping mode results indicatethat Youngrsquos modulus measurement corresponds with thecrystalline orientation that is normal to the sample surfaceand in the loading direction of the elastic displacement Forexample a measured 120572 value of 325Hzsdotnmminus12 correspondswith a 305GPa Youngrsquos modulus for a nanocrystalline Ni(111)coating The directional behavior reveals sensitivity to elasticanisotropy for a variety of knownmaterials over a 3ndash400GParange of elastic modulus using a diamond tip probe

Acknowledgments

This work was supported by the JW Wright and RegentsEndowments for Mechanical Engineering at Texas TechUniversity (TTU) The authors thank Dr Ilja Hermann forreviewing the paper and for his instructive comments

References

[1] T G Nieh and J Wadsworth ldquoHall-petch relation in nanocrys-talline solidsrdquo Scripta Metallurgica et Materiala vol 25 no 4pp 955ndash958 1991

[2] C A Schuh T G Nieh and H Iwasaki ldquoThe effect of solidsolutionWadditions on themechanical properties of nanocrys-talline Nirdquo Acta Materialia vol 51 no 2 pp 431ndash443 2003

[3] A F Jankowski C K Saw J F Harper B F Vallier J L Ferreiraand J P Hayes ldquoNanocrystalline growth and grain-size effectsin Au-Cu electrodepositsrdquoThin Solid Films vol 494 no 1-2 pp268ndash273 2006

[4] M Dao L Lu R J Asaro J T M De Hosson and E MaldquoToward a quantitative understanding of mechanical behaviorof nanocrystalline metalsrdquo Acta Materialia vol 55 no 12 pp4041ndash4065 2007

[5] N Tayebi T F Conry and A A Polycarpou ldquoDeterminationof hardness from nanoscratch experiments corrections forinterfacial shear stress and elastic recoveryrdquo Journal of MaterialsResearch vol 18 no 9 pp 2150ndash2162 2003

[6] C A Schuh T G Nieh and T Yamasaki ldquoHall-Petch break-down manifested in abrasive wear resistance of nanocrystallinenickelrdquo Scripta Materialia vol 46 no 10 pp 735ndash740 2002

[7] K M Lee C-D Yeo and A A Polycarpou ldquoNanomechanicalproperty and nanowear measurements for Sub-10-nm thickfilms in magnetic storagerdquo Experimental Mechanics vol 47 no1 pp 107ndash121 2007

[8] J Chen L Lu and K Lu ldquoHardness and strain rate sensitivity ofnanocrystalline Curdquo Scripta Materialia vol 54 no 11 pp 1913ndash1918 2006

[9] L O Nyakiti and A F Jankowski ldquoCharacterization of strain-rate sensitivity and grain boundary structure in nanocrystalline


gold-copper alloysrdquoMetallurgical andMaterials Transactions Avol 41 no 4 pp 838ndash847 2010

[10] M F Doerner and W D Nix ldquoA method for interpreting thedata from a depth sensing indentation instrumentrdquo Journal ofMaterials Research vol 1 no 4 pp 601ndash609 1986

[11] W C Oliver and G M Pharr ldquoImproved technique for deter-mining hardness and elastic modulus using load and displace-ment sensing indentation experimentsrdquo Journal of MaterialsResearch vol 7 no 6 pp 1564ndash1583 1992

[12] W C Oliver and G M Pharr ldquoMeasurement of hardnessand elastic modulus by instrumented indentation advancesin understanding and refinements to methodologyrdquo Journal ofMaterials Research vol 19 no 1 pp 3ndash20 2004

[13] E Z Meyer ldquoUntersuchungen uber Harteprufung und HarterdquoZeitschrift des Vereines Deutscher Ingenieure vol 52 pp 645ndash654 1908

[14] A F Jankowski ldquoSuperhardness effect in AuNi multilayersrdquoJournal of Magnetism and Magnetic Materials vol 126 no 1ndash3pp 185ndash191 1993

[15] J J Vlassak and W D Nix ldquoMeasuring the elastic propertiesof anisotropic materials by means of indentation experimentsrdquoJournal of the Mechanics and Physics of Solids vol 42 no 8 pp1223ndash1245 1994

[16] J G Swadener and G M Pharr ldquoIndentation of elasticallyanisotropic half-spaces by cones and parabolae of revolutionrdquoPhilosophical Magazine A vol 81 no 2 pp 447ndash466 2001

[17] A Delafargue and F-J Ulm ldquoExplicit approximations of theindentationmodulus of elastically orthotropic solids for conicalindentersrdquo International Journal of Solids and Structures vol 41no 26 pp 7351ndash7360 2004

[18] F A McClintock and A S Argon ldquoOther measures of plastichardnessrdquo in Mechanical Behavior of Materials vol 13 ofAddison-Wesley Series inMetallurgy andMaterials pp 450ndash458Addison-Wesley Reading 1966

[19] D Tabor ldquoThe hardness of solidsrdquo Review of Physics in Technol-ogy vol 1 no 3 pp 145ndash179 1970

[20] M Reinstadtler T Kasai U Rabe B Bhushan and W ArnoldldquoImaging and measurement of elasticity and friction using theTRmoderdquo Journal of Physics D vol 38 no 18 pp R269ndashR2822005

[21] D DeVecchio and B Bhushan ldquoLocalized surface elasticitymeasurements using an atomic force microscoperdquo Review ofScientific Instruments vol 68 no 12 pp 4498ndash4505 1997

[22] R Whiting and M A Angadi ldquoYoungrsquos modulus of thin filmsusing a simplified vibrating reedmethodrdquoMeasurement Scienceand Technology vol 1 no 7 article 024 pp 662ndash664 1990

[23] K-D Wantke H Fruhner J Fang and K LunkenheimerldquoMeasurements of the surface elasticity in medium frequencyrange using the oscillating bubble methodrdquo Journal of Colloidand Interface Science vol 208 no 1 pp 34ndash48 1998

[24] A S Useinov ldquoA nanoindentation method for measuring theYoung modulus of superhard materials using a NanoScanscanning probe microscoperdquo Instruments and ExperimentalTechniques vol 47 no 1 pp 119ndash123 2004

[25] K V Gogolinskiı Z Y Kosakovskaya A S Useinov and I AChaban ldquoMeasurement of the elastic moduli of dense layersof oriented carbon nanotubes by a scanning force microscoperdquoAcoustical Physics vol 50 no 6 pp 664ndash669 2004

[26] S I Lee SW Howell A Raman and R Reifenberger ldquoNonlin-ear dynamics of microcantilevers in tapping mode atomic forcemicroscopy a comparison between theory and experimentrdquo

Physical Review B vol 66 no 11 Article ID 115409 10 pages2002

[27] O Sahin and N Erina ldquoHigh-resolution and large dynamicrange nanomechanical mapping in tapping-mode atomic forcemicroscopyrdquo Nanotechnology vol 19 no 44 Article ID 4457172008

[28] D W Chun K S Hwang K Eom et al ldquoDetection of theAu thin-layer in the Hz per picogram regime based on themicrocantileversrdquo Sensors and Actuators A vol 135 no 2 pp857ndash862 2007

[29] N Gitis M Vinogradov I Hermann and S Kuiry ldquoCompre-hensive mechanical and tribological characterization of ultra-thin filmsrdquoMRS Proceedings vol 1049 2008

[30] A F Jankowski ldquoVapor deposition and characterization of na-nocrystalline nanolaminatesrdquo Surface and Coatings Technologyvol 203 no 5-7 pp 484ndash489 2008

[31] A F Jankowski ldquoOn eliminating deposition-induced amor-phization of interfaces in refractory metal multilayer systemsrdquoThin Solid Films vol 220 no 1-2 pp 166ndash171 1992

[32] A F Jankowski J P Hayes T E Felter C Evans and AJ Nelson ldquoSputter deposition of silicon-oxide coatingsrdquo ThinSolid Films vol 420-421 pp 43ndash46 2002

[33] A F JankowskiM AWall AW Van Buuren T G Nieh and JWadsworth ldquoFrom nanocrystalline to amorphous structure inberyllium-based coatingsrdquo Acta Materialia vol 50 no 19 pp4791ndash4800 2002

[34] A F Jankowski C K Saw C C Walton J P Hayes andJ Nilsen ldquoBoron-carbide barrier layers in scandium-siliconmultilayersrdquoThin Solid Films vol 469-470 pp 372ndash376 2004

[35] A F Jankowski J P Hayes and C K Saw ldquoDimensional attrib-utes in enhanced hardness of nanocrystalline Ta-V nanolam-inatesrdquo Philosophical Magazine vol 87 no 16 pp 2323ndash23342007

[36] A F Jankowski andM AWall ldquoTransmission electronmicros-copy ofNiTi neutronmirrorsrdquoThin Solid Films vol 181 no 1-2pp 305ndash312 1989

[37] A F Jankowski andM AWall ldquoSynthesis and characterizationof nanophase face-centered-cubic titaniumrdquo NanostructuredMaterials vol 7 no 1-2 pp 89ndash94 1996

[38] H S TAhmedUse of dynamic testmethods to revealmechanicalproperties of nanomaterials [PhD thesis] Texas TechUniversity2010

[39] J F Nye Physical Properties of Crystals Oxford Press OxfordUK 1960

[40] J R Neighbours and G A Alers ldquoElastic constants of silver andgoldrdquo Physical Review vol 111 no 3 pp 707ndash712 1958

[41] G A Alers ldquoElastic moduli of vanadiumrdquo Physical Review vol119 no 5 pp 1532ndash1535 1960

[42] F H Featherston and J R Neighbours ldquoElastic constants oftantalum tungsten and molybdenumrdquo Physical Review vol130 no 4 pp 1324ndash1333 1963

[43] B T Bernstein ldquoElastic constants of synthetic sapphire at 27∘rdquoJournal of Applied Physics vol 34 no 1 pp 169ndash172 1963

[44] H M Trent D E Stone and L A Beaubien ldquoElastic constantshardness strength elastic limits and diffusion coefficients ofsolidsrdquo inAmerican Institute of Physics Handbook Section 2 pp49ndash59 McGraw Hill New York NY USA 1972

[45] H P R Frederikse ldquoElastic Constants of Single Crystalsrdquo inHandbook of Chemistry and Physics D Lide Ed section 12 pp33ndash38 CRC Press Taylor and Francis Boca Raton Fla USA88th edition 2008


[46] J Hay Application Notes 5990-4853EN (Agilent Technology)2009

[47] Y Yamada-Takamura E Shimono and T Toshida ldquoNanoin-dentation characterization of cBN films deposited from vaporphaserdquo in Proceedings of the 14th International Symposium onPlasma Chemistry (ISPC rsquo14) M Hrabovsky Ed vol 3 pp1629ndash1634 Prague Czech Republic

[48] J Y Rho and G M Pharr ldquoNanoindentation testing of bonerdquoinMechanical Testing of Bone and the Bone-Implant Interface YH An and R A Draughn Eds chapter 17 pp 257ndash269 CRCPress New York NY USA 2000

[49] K L Johnson K Kendall and A D Roberts ldquoSurface energyand the contact of elastic solidsrdquo in Proceedings of the RoyalSociety A vol 324 pp 301ndash313 1971

[50] Y-P Zhao X Shi and W J Li ldquoEffect of work of adhesion onnanoindentationrdquo Reviews on Advanced Materials Science vol5 no 4 pp 348ndash353 2003

[51] B V Derjaguin V M Muller and Y P Toporov ldquoEffect ofcontact deformations on the adhesion of particlesrdquo Journal ofColloid And Interface Science vol 53 no 2 pp 314ndash326 1975

[52] J Drelich ldquoAdhesion forces measured between particles andsubstrates with nano-roughnessrdquo Minerals and MetallurgicalProcessing vol 23 no 4 pp 226ndash232 2006

[53] M M McCann Nanoindentation of gold single crystals [PhDthesis] Virginia Polytechnic Institute and StateUniversity 2004

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


tips may not quantify the full effect of anisotropic behaviorthat is the anisotropic response can be underestimated inboth modeling and experimental efforts For example a 10difference from 125 to 140GPa is reported [15] betweenCu(100) and Cu(111) whereas the known elastic moduli119864(hkl) along different crystalline directions [hkl] vary by300 with values from 66 to 192GPa Similarly differenteffects are found [18 19] for the effect of tip shape on plasticflow wherein spheroconical shapes evidence work hardeningof material during indentation as opposed to well-definedpyramidal indentations that produce a near-perfect plasticresponse

The torsion-resonance mode of atomic force acousticmicroscope is used [20] to measure the elastic constants ofanisotropic materials A piezoelectric device is excited usingan alternating current voltage to induce vibrations in theatomic force microscopy (AFM) cantilever while the tip isin contact with the sample surface Indentation elastic mod-ulus is extracted from the tip-surface interaction assumingHertzian contact mechanics In a similar technique [21] thedeflection of the AFM cantilever is used to determine thelocalized modulus Vibrating reed measurements [22] havesimilarities to the AFM technique where the major differenceis that the sample along with the substrate in the vibratingreed method is exposed to piezoelectric vibrations whereasthe probe cantilever is vibrated in the AFM technique Theoscillating bubble method [23] is another technique formeasuring surface elasticity of liquids The tapping modeelastic modulus measurement technique [24ndash29] providesanother relatively new method for measuring the reducedelastic modulusThemeasurement is based on the oscillationfrequency of a probe that is in elastic contact with the surfaceThe tapping mode technique is nondestructive which pro-vides an advantage of measuring the elastic modulus prior toplastic deformation whereas nanoindentation measures theelastic-plastically deformed material

The tapping mode method is now pursued for evaluatingtheYoungrsquosmodulus of nanocrystallinemetal coatings Vapordeposited coatings of cubic metals can have a single-growthtexture that is of interest for assessing the sensitivity ofthe measurement technique to anisotropic elastic behaviorin nanocrystalline metals such as nickel For this purposepolycrystalline samples provide a basis for measurementcalibration along with single-crystal wafer specimens Fur-ther development of the classic Hertz-contact solution usinghigher-order terms of a Taylorrsquos series expansion showsa quadratic rather than a linear relationship between thereduced elastic modulus and the resonant frequency shiftThenew solution can be used to simulate themagnitude of theshift in the resonant frequency as a function of the reducedelastic modulus using the cantilever bending stiffness and theindenter tip radius of curvature

2 Materials and Methods

21 Materials The materials for the tapping mode measure-ment should have smooth surfaces If there is a high ampli-tude to short-wavelength surface roughness then multiple

point contact can occur which could appear to artificiallystiffen the mechanical response Smooth surfaces and ananocrystalline structure for tantalum (Ta) vanadium (V)and nickel (Ni) coatings are produced from the high-quenchrates (gt106 Ksdotsminus1) of the sputter deposition method [30ndash34] The metals are coated onto polished flats such assemiconductor-grade silicon and sapphire wafers In briefthe 03ndash06120583m thick coatings were synthesized by planar-magnetron sputter deposition in a vacuum chamber cryo-genically pumped to a 2 times 10minus5 Pa base pressure The nativeSi oxide on the substrate is not removed prior to depositionof the coating from target materials of gt0999 purity Thecathodes are operated in the DC mode with a typicaldischarge potential of 2 times 102 Volts The source-to-substrateseparation is 7ndash10 cm and the 1 Pa working-gas pressure ofargon ismaintainedwith a 35 cm3sdotsminus1 flow rateThemeasuredsurface temperature of the substrate remains below 473Kduring the deposition process The deposition rates andthickness accumulation during deposition are recorded usingcalibrated Au-coated quartz-crystal microbalances

Details of the structural characterization for the Ta V andNi sputter deposited coatings are reported elsewhere [30 35]The characterization methods consisted of X-ray diffraction(XRD) transmission electronmicroscopy (TEM) and atomicforce microscopy (AFM) The XRD measurements wereconducted in the 1205792120579mode to determine both the crystallinestructure and orientation The sputter deposited metal coat-ings have a single growth orientation of close-packed planesThe body-center-cubic (bcc) metals of Ta and V are (110) andthe face-center-cubic (fcc) Ni is (111) TEM imaging in brightfield in the electron-diffraction mode and the use of highresolution lattice imaging conditions [36 37] enable a closerlook at the grain size grain boundary structure and defectstructure Selected area diffraction patterns (SADPs) confirmthe (110) growth for the Ta and V coatings as well as the(111) growth for the Ni coating Also the SADPs indicate thatthe coatings are polycrystalline in plane that is randomlyoriented parallel to the surface The grain sizes determinedfrom the average width to the columnar growth as seen inthe bright field TEM images range from 14 to 20 nm for theTa and V coatings to less than 150 nm for the Ni coatingAFM images [35] of the Ta and V surfaces indicate a smoothsurface with less than a 1-2 nm variation in amplitude over1 120583m length scales that is a surface smooth for establishing aHertz-contact condition

Semiconductor-grade single-side polished wafers of sil-icon Si(100) Si(111) and sapphire Al

2O3(002) are used to

provide smooth single-crystal reference materials Also pol-ished polycrystalline samples of polycarbonate (pC) quartz(SiO2) hydroxyapatite (HA) and sapphire (Al

2O3) are used

as reference standards with known elastic constants for theestablishment of the calibration curve from the tappingmodemeasurements

22 Tapping Mode Experiment The tapping mode use [2426 28] of a nanoprobe in the configuration of a scan-ning force microscope provides a method for measuringelastic deformation A universal micro-nano-materials tester









0)



1205722

=(Δ119891)2

119911 (3)


1 2 4

Displacement (x)

Slope = 1205722

Freq

uenc

y sh

ift (Δ

fr)2

3998400 998400

3998400







120572 = 119886(119864lowast

)119899

(4)


lowast










119898 + 119896119888119909 = 0 (5)


119888is given by

119896119888=3119864119868

1198713 (6)


120596119899= radic

119896119888

119898= 2120587119891

0 (7)


2120587119891 = radic119896119888+ 119896119904

119898 (8)



119891 = 1198910(radic1 +

119896119904

119896119888

) (9)


Δ119891 = 119891 minus 1198910= 1198910(radic1 +

119896119904

119896119888

minus 1) (10)


Δ119891 = 1198910(119896119904

2119896119888

) (11)


119911 = (3119875

4119864lowast)

23

(1

119877)

13

(12)



119896119904=120597119875

120597119911 (13)


119896119904=120597119875

120597119911= 2radic119877119864

lowast

radic119911 (14)



Δ119891 =1198910radic119877

119896119888

119864lowast

radic119911 (15)


(Δ119891)2

= 1205722

119911 (16)

where

120572 =1198910radic119877

119896119888

119864lowast

(17)



120572 =1198910radic119877

119896119888

119864lowast

[1 minus1

2(radic119877119864

lowast

)radic119911

119896119888

] (18)






0 120572 119911 119896

119888 and 119877 by


119864lowast

=


radic119877119911119896119888

(19)




0of the








119894) such as


1

119864= 11987811minus 2 (119878


211987844) (1198972

11198972

2+ 1198972

21198972

3+ 1198972

31198972

1) (20)


1

119864= (1 minus 119897

2

3)2

11987811+ 1198974

311987833

+ 1198972

3(1 minus 1198972

3) (211987813+ 11987844)

+ 21198972

11198972

3(31198972

1minus 1198972

2) 11987814

(21)


119905)119864119905


119905)119864119905value of



for diamond








0

10

20

30


(104

Hz2

)Fr

eque

ncy

shift

(Δfr)2

(a)

0

1

2

3

4

5

6


Am

plitu

deAm

(nm

)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600

Am

plitu

deAm

(nm

)

Frequency fr (kHz)

(c)






0

10

20

30

40

50


(104

Hz2

)Fr

eque

ncy

shift

( Δfr)2

(a)

0

1

2

3

4

5

6

10 15 20 25 30

Am

plitu

deAm

(nm

)

Displacment x (nm)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600 14800Frequency fr (kHz)

Am

plitu

deAm

(nm

)

(c)







20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)












1198881198882 to



0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)


Al2O3(002)











119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials











0)



1205722

=(Δ119891)2

119911 (3)


1 2 4

Displacement (x)

Slope = 1205722

Freq

uenc

y sh

ift (Δ

fr)2

3998400 998400

3998400







120572 = 119886(119864lowast

)119899

(4)


lowast










119898 + 119896119888119909 = 0 (5)


119888is given by

119896119888=3119864119868

1198713 (6)


120596119899= radic

119896119888

119898= 2120587119891

0 (7)


2120587119891 = radic119896119888+ 119896119904

119898 (8)



119891 = 1198910(radic1 +

119896119904

119896119888

) (9)


Δ119891 = 119891 minus 1198910= 1198910(radic1 +

119896119904

119896119888

minus 1) (10)


Δ119891 = 1198910(119896119904

2119896119888

) (11)


119911 = (3119875

4119864lowast)

23

(1

119877)

13

(12)



119896119904=120597119875

120597119911 (13)


119896119904=120597119875

120597119911= 2radic119877119864

lowast

radic119911 (14)



Δ119891 =1198910radic119877

119896119888

119864lowast

radic119911 (15)


(Δ119891)2

= 1205722

119911 (16)

where

120572 =1198910radic119877

119896119888

119864lowast

(17)



120572 =1198910radic119877

119896119888

119864lowast

[1 minus1

2(radic119877119864

lowast

)radic119911

119896119888

] (18)






0 120572 119911 119896

119888 and 119877 by


119864lowast

=


radic119877119911119896119888

(19)




0of the








119894) such as


1

119864= 11987811minus 2 (119878


211987844) (1198972

11198972

2+ 1198972

21198972

3+ 1198972

31198972

1) (20)


1

119864= (1 minus 119897

2

3)2

11987811+ 1198974

311987833

+ 1198972

3(1 minus 1198972

3) (211987813+ 11987844)

+ 21198972

11198972

3(31198972

1minus 1198972

2) 11987814

(21)


119905)119864119905


119905)119864119905value of



for diamond








0

10

20

30


(104

Hz2

)Fr

eque

ncy

shift

(Δfr)2

(a)

0

1

2

3

4

5

6


Am

plitu

deAm

(nm

)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600

Am

plitu

deAm

(nm

)

Frequency fr (kHz)

(c)






0

10

20

30

40

50


(104

Hz2

)Fr

eque

ncy

shift

( Δfr)2

(a)

0

1

2

3

4

5

6

10 15 20 25 30

Am

plitu

deAm

(nm

)

Displacment x (nm)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600 14800Frequency fr (kHz)

Am

plitu

deAm

(nm

)

(c)







20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)












1198881198882 to



0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)


Al2O3(002)











119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









119898 + 119896119888119909 = 0 (5)


119888is given by

119896119888=3119864119868

1198713 (6)


120596119899= radic

119896119888

119898= 2120587119891

0 (7)


2120587119891 = radic119896119888+ 119896119904

119898 (8)



119891 = 1198910(radic1 +

119896119904

119896119888

) (9)


Δ119891 = 119891 minus 1198910= 1198910(radic1 +

119896119904

119896119888

minus 1) (10)


Δ119891 = 1198910(119896119904

2119896119888

) (11)


119911 = (3119875

4119864lowast)

23

(1

119877)

13

(12)



119896119904=120597119875

120597119911 (13)


119896119904=120597119875

120597119911= 2radic119877119864

lowast

radic119911 (14)



Δ119891 =1198910radic119877

119896119888

119864lowast

radic119911 (15)


(Δ119891)2

= 1205722

119911 (16)

where

120572 =1198910radic119877

119896119888

119864lowast

(17)



120572 =1198910radic119877

119896119888

119864lowast

[1 minus1

2(radic119877119864

lowast

)radic119911

119896119888

] (18)






0 120572 119911 119896

119888 and 119877 by


119864lowast

=


radic119877119911119896119888

(19)




0of the








119894) such as


1

119864= 11987811minus 2 (119878


211987844) (1198972

11198972

2+ 1198972

21198972

3+ 1198972

31198972

1) (20)


1

119864= (1 minus 119897

2

3)2

11987811+ 1198974

311987833

+ 1198972

3(1 minus 1198972

3) (211987813+ 11987844)

+ 21198972

11198972

3(31198972

1minus 1198972

2) 11987814

(21)


119905)119864119905


119905)119864119905value of



for diamond








0

10

20

30


(104

Hz2

)Fr

eque

ncy

shift

(Δfr)2

(a)

0

1

2

3

4

5

6


Am

plitu

deAm

(nm

)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600

Am

plitu

deAm

(nm

)

Frequency fr (kHz)

(c)






0

10

20

30

40

50


(104

Hz2

)Fr

eque

ncy

shift

( Δfr)2

(a)

0

1

2

3

4

5

6

10 15 20 25 30

Am

plitu

deAm

(nm

)

Displacment x (nm)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600 14800Frequency fr (kHz)

Am

plitu

deAm

(nm

)

(c)







20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)












1198881198882 to



0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)


Al2O3(002)











119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








0 120572 119911 119896

119888 and 119877 by


119864lowast

=


radic119877119911119896119888

(19)




0of the








119894) such as


1

119864= 11987811minus 2 (119878


211987844) (1198972

11198972

2+ 1198972

21198972

3+ 1198972

31198972

1) (20)


1

119864= (1 minus 119897

2

3)2

11987811+ 1198974

311987833

+ 1198972

3(1 minus 1198972

3) (211987813+ 11987844)

+ 21198972

11198972

3(31198972

1minus 1198972

2) 11987814

(21)


119905)119864119905


119905)119864119905value of



for diamond








0

10

20

30


(104

Hz2

)Fr

eque

ncy

shift

(Δfr)2

(a)

0

1

2

3

4

5

6


Am

plitu

deAm

(nm

)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600

Am

plitu

deAm

(nm

)

Frequency fr (kHz)

(c)






0

10

20

30

40

50


(104

Hz2

)Fr

eque

ncy

shift

( Δfr)2

(a)

0

1

2

3

4

5

6

10 15 20 25 30

Am

plitu

deAm

(nm

)

Displacment x (nm)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600 14800Frequency fr (kHz)

Am

plitu

deAm

(nm

)

(c)







20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)












1198881198882 to



0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)


Al2O3(002)











119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

10

20

30


(104

Hz2

)Fr

eque

ncy

shift

(Δfr)2

(a)

0

1

2

3

4

5

6


Am

plitu

deAm

(nm

)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600

Am

plitu

deAm

(nm

)

Frequency fr (kHz)

(c)






0

10

20

30

40

50


(104

Hz2

)Fr

eque

ncy

shift

( Δfr)2

(a)

0

1

2

3

4

5

6

10 15 20 25 30

Am

plitu

deAm

(nm

)

Displacment x (nm)

(b)

0

1

2

3

4

5

6

14000 14200 14400 14600 14800Frequency fr (kHz)

Am

plitu

deAm

(nm

)

(c)







20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)












1198881198882 to



0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)


Al2O3(002)











119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




20

40

60

80

100

120

11000 12000 13000 14000 15000 16000 17000

ForwardBackward

0

Frequency fr (Hz)

Am

plitu

deAm

(nm

)












1198881198882 to



0

100

200

300

400

500

0 50 100 150 200 250 300 350 400 450

Ni

TaV

(111)(110)

(100)Poly(p)

p-carb

p-HAp-SiO2

Si(100)Si(111)

p-Al2O3

120572(H

zmiddotnmminus12)


Al2O3(002)











119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







119904≪ 119896119888




4 Conclusions











Acknowledgments


References

































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials


























































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Research Article On the Tapping Mode Measurement for Young s … · 2019. 7. 31. · plastic...

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Transcript of Research Article On the Tapping Mode Measurement for Young s … · 2019. 7. 31. · plastic...