Lecture 3 - Structures of Metals and Ceramics

7/27/2019 Lecture 3 - Structures of Metals and Ceramics

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Chapter 3STRUCTURES OF METALS AND

CERAMICS


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The Next Level Into the Crystals

Discussed about atoms and how they bond Moving into the arrangements of atoms and how

they form a structure

Crystallinity and Non-Crystallinity
http://mac01.eps.pitt.edu/harbbook/c_ii/MINERALS/Msz0130.JPG


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Crystalline Materials

Crystal: A solid with atomsarranged in a repeating or periodicarray over large atomic distances

Long range order exists

Repetitive 3-D pattern Each atom is bonded to its

nearest-neighbor atoms

Simple arrangement for metals,

extremely complex for polymersand ceramics

Properties depend on the spatialatomic arrangement

Li3N
http://cst-www.nrl.navy.mil/lattice/struk.picts/Li3N.s.pnghttp://cst-www.nrl.navy.mil/lattice/struk.picts/Li3N.s.png


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Atomic Packing and Crystallinity

Local arrangement of atomsin a solid is usuallypredictable

This may be in long range

repeating structureCrystalline

This may be in shortirregular sections

Amorphous or Glassy

Arrangement depends onbond


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atoms pack in periodic, 3D arrays Crystalline materials

-metals

-many ceramics

-some polymers

atoms have no periodic packing

Non-Crystalline materials

-complex structures-rapid cooling

crystalline SiO2

noncrystalline SiO2"Amorphous" = NoncrystallineAdapted from Fig. 3.41(b),

Callister & Rethwisch 4e.

Adapted from Fig. 3.41(a),


Materials and Packing

Si Oxygen

typical of:

occurs for:


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Terminology

Atomic Hard Sphere Model: Atoms arethought of as hard spheres with well defineddiameters

Spheres representing the nearest neighboratoms touch one another

Stable materials want to stacktogether nicely


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Lattice and Unit Cell

Lattice: 3-D arrayof points coincidingwith the atompositions (spherecenters)

Unit Cell: Thesmallest repeating

entities in a crystalstructure


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Crystal Systems

A vast array of possible crystal structures Convenient to divide them into groups based on

cell configurations or atomic arrangements

Most common based on Unit Cell Geometry

Defining the unit cell geometry in terms of sixparameters3 edge lengths and 3 interaxialangles

Crystals having seven possible combinations ofedge lengths and interaxial angles


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3 Cubic Crystal Types

Simple Cubic Body-Centered

Cubic (BCC)

Face-Centered

Cubic (FCC)

Reduced Sphere Models


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More Terminology

Co-Ordination Number: The number of nearestneighbor, or touching atoms

Atomic Packing Factor (APF): Fraction of solidsphere volume in a unit cell (assuming the atomichard sphere model)

Volume of atoms in unit cell

Total volume of the unit cellAPF


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Simple Cubic Structure

Rare Poor packing

Co-ordination number - 6

APF = 0.52


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Body-Centered Cubic (BCC)

Atoms located at the eightcorners, and one at thecenter of the cube

Equivalent of one atom

from the eight corners,and one atom at thecenter2 atoms in aunit cell

Co-ordination number : 8

Hard-Sphere Model

4 1/8 s ahead4 1/8 s behindTotal 8 neighbors


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Body-Centered Cubic (BCC)

a

a2

a3


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BCC Atomic Packing Factor

aR

Unit cell c ontains:

1 + 8 x 1/8= 2 atoms/unit cell

APF = 0.68


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Face-Centered Cubic (FCC)

Atoms located at the eightcorners, and the centers ofall the cube faces

Corner atom is shared

among eight unit cells, face-centered atoms among twounit cells4 atoms in a unitcell

Co-ordination number : 12

a


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Face-Centered Cubic (FCC)


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FCC Atomic Packing Factor

a

Unit cell c ontains:

6 x 1/2 + 8 x 1/8

= 4 atoms/unit cell

APF = 0.74


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ABCABC... Stacking Sequence

2D Projection

FCC Unit Cell

FCC Stacking Sequence

A sites

B B

B

BB

B B

Csites

C C

CA

B

Bsites B B

B

BB

B B

BsitesC C

CA

C C

CA

AB

C

Hexagonal Close Packed Structure


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Hexagonal Close Packed Structure(HCP)

Atoms located at topand bottom hexagonalfaces, and at center ofthe faces

3 atoms provided by theplane between the twofaces

6 atoms in a unit cell

Ideal c/a ratio 1.633

Co-ordination number :12

APF : 0.74


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Coordination # = 12

ABAB... Stacking Sequence

APF = 0.74

3D Projection 2D Projection

Adapted from Fig. 3.3(a),


Hexagonal Close-Packed Structure(HCP)

6 atoms/unit cellex: Cd, Mg, Ti, Zn

c/a = 1.633

c

a

A sites

Bsites

A sites Bottom layer

Middle layer

Top layer


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Energy and Packing

Interatomic spacing

Inte

rparticle

Energy

r0

Interatomic spacing

Interparticle

Energy

r0

Typical bond length

Typical energy

Typical energy

Dense, regular-packedstructures tend to havelower energy


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Theoretical Density ()

Copper FCC Structure, A = 63.5 g/mol,

r=0.128 nm = 0.128 * 10-7 cm

n=4 (since FCC structure)

atoms/mol)(10*023.6*)cellunit/cm()10*128.0(*216

(g/mol)63.5*cell)atoms/unit(423337

3/89.8 cmg (Compare with 8.94 g/cm3 which is the experimental value)


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Common Densities for Materials

Why suchA change?


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Ceramic Crystal Structures

More complex than metals since two or moreelements present

Bonding can vary from purely ionic to purely

covalent, and many in between If dominantly ionic bonding, crystal structures

have electrically charged ions instead ofatoms

Cations positively charged (lost electrons)

Anions negatively charged (gained electrons)

F t th t D t i


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Factors that Determinethe Ceramic Crystal Structure

1.Relative sizes of ions Formation of stable structures:

--maximize the # of oppositely charged ion neighbors.

Adapted from Fig. 3.4,

Callister & Rethwisch 4e.- -

- -+

unstable

- -

- -+

stable

- -

- -+

stable

2.Maintenance of

Charge Neutrality:--Net charge in ceramic

should be zero.--Reflected in chemical

formula:

CaF2:Ca2+

cation

F-

F-

anions+

AmXp

m, p values to achieve charge neutrality

C di ti b d i i


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Co-ordination number and ion sizeratio

Co-ordination number increases with rcation/ ranion(c/a)

Computation of Minimum


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Computation of MinimumCation-Anion Radius Ratio

Determine minimum rcation/ranion for an octahedral site(C.N. = 6)

a 2ranion

2ranion +2rcation = 2 2ranion

ranion + rcation = 2ranion

rcation = ( 2 - 1)ranion

arr 222 cationanion =+

414.012anion

cation==

r

r


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Bond Hybridization

Bond Hybridization is possible when there is significantcovalent bonding

hybrid electron orbitals form

For example for SiC

XSi

= 1.8 and XC

= 2.5

% ionic character = 100 {1- exp[-0.25(XSi - XC)2]} =11.5%

~ 89% covalent bonding

Both Si and C prefersp3 hybridization

Therefore, for SiC, Si atoms occupy tetrahedral sites


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Common Ceramic Crystal Structures

StructureName

StructureType

AnionPacking

Cationco-ord

#

Anionco-ord

#

Examples

Rock salt(sodiumchloride)

AX FCC 6 6 NaCl, MgO,FeO

Cesiumchloride

AX Simplecubic

8 8 CsCl

Zinc blende AX FCC 4 4 ZnS, SiC

Flourite AX2 Simplecubic

8 4 CaF2, UO2

Perovskite ABX3 FCC 12, 6 6 BaTiO3

Spinel AB2X4 FCC 4,6 4 MgAl2O4

Example Problem: Predicting the Crystal


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On the basis of ionic radii, what crystal structure

would you predict for FeO?

Answer:

5500

1400

0770

anion

cation

.

.

.

r

r

=

=

based on this ratio,

-- coord # = 6 because

0.414 < 0.550 < 0.732

-- crystal structure is NaCl

Data from Table 3.4,


Example Problem: Predicting the CrystalStructure of FeO

Ionic radius (nm)

0.053

0.0770.069

0.100

0.140

0.181

0.133

Cation

Anion

Al3+

Fe2+

Fe3+

Ca2+

O2-

Cl-

F-


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Rock Salt Structure

Same concepts can be applied to ionic solids in general.

Example: NaCl (rock salt) structure

rNa = 0.102 nm

rNa/rCl = 0.564

cations (Na+) prefer octahedralsites



rCl = 0.181 nm


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AX Crystal Structures

939.0181.0

170.0

Cl

Cs==

-

+

r

r



Cesium Chloride structure:

Since 0.732 < 0.939 < 1.0,

cubicsites preferred

So each Cs+ has 8 neighbor Cl-

AXType Crystal Structures include NaCl, CsCl, and zinc blende


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ABX3 Crystal Structures



Perovskitestructure

Ex: complex oxide

BaTiO3


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Density computation - Ceramics

Theoretical density of a crystalline ceramic

n= number of formula units (all ions that are included inthe chemical formula) within the unit cell

AC= sum of atomic weights of all cations in the formulaunit

AA= sum of atomic weights of all anions in the formulaunit

Vc = unit cell volume

NA= avogadros number = 6.023 * 1023 formula units/mol

AC

AC

NV

AAn )('

Theoretical density of Sodium


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Theoretical density of Sodiumchloride

Compute theoretical density of NaCl ANa = 22.99 g/mol; ACl = 35.45 g/mol

Ionic radii of Na+ = 0.102 nm, that of Cl- =

0.181 nm a

Na+

Cl-

.See the solution in the text book


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Polymorphism and Allotropy

Polymorphism some metals and non metalshave more than one crystal structure

Prevailing crystal structure depends ontemperature and pressure

Polymorphism in elemental solids is calledAllotropy

Carbon polymorphs as Diamond and Graphite

Pure ion has a BCC crystal structure at roomtemperature and FCC at 912oC

Lecture 3 - Structures of Metals and Ceramics

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