Chapter 3: Structures of Metals & Ceramicsisdl.cau.ac.kr/education.data/mat.sci/ch03.pdfChapter 3:...

Chapter 3: Structures of Metals & Ceramics

Chapter 3 -

School of Mechanical EngineeringProfessor Choi, Hae-Jin

Materials Science - Prof. Choi, Hae-Jin 1

ISSUES TO ADDRESS...• How do atoms assemble into solid structures?

• How does the density of a material depend onits structure?

Chapter 3: Structures of Metals & Ceramics

Chapter 3 - 2

• How does the density of a material depend onits structure?

• When do material properties vary with thesample (i.e., part) orientation?

• How do the crystal structures of ceramic materials differ from those for metals?

Materials Science - Prof. Choi, Hae-Jin

• Non dense, random packing

• Dense, ordered packing

Energy and PackingEnergy

r

typical neighborbond length

typical neighborbond energy

Energy

Chapter 3 - 3

• Dense, ordered packing

Dense, ordered packed structures tend to havelower energies.

Energy

r

typical neighborbond length

typical neighborbond energy


• atoms pack in periodic, 3D arraysCrystalline materials...

-metals-many ceramics-some polymers crystalline SiO2

Adapted from Fig. 3.40(a),Callister & Rethwisch 3e.

Materials and Packing

Si Oxygen

• typical of:

Chapter 3 - 4

• atoms have no periodic packingNoncrystalline materials...

-complex structures-rapid cooling

noncrystalline SiO2"Amorphous" = NoncrystallineAdapted from Fig. 3.40(b),Callister & Rethwisch 3e.

Si Oxygen

• occurs for:


Metallic Crystal Structures • How can we stack metal atoms to minimize

empty space?2-dimensions

Chapter 3 - 5

vs.

Now stack these 2-D layers to make 3-D structures


• Tend to be densely packed.• Reasons for dense packing:

- Typically, only one element is present, so all atomicradii are the same.

- Metallic bonding is not directional.- Nearest neighbor distances tend to be small inorder to lower bond energy.

- Electron cloud shields cores from each other

Metallic Crystal Structures

Chapter 3 - 6

- Typically, only one element is present, so all atomicradii are the same.

- Metallic bonding is not directional.- Nearest neighbor distances tend to be small inorder to lower bond energy.

- Electron cloud shields cores from each other

• Have the simplest crystal structures.

We will examine three such structures...


• Coordination # = 8

• Atoms touch each other along cube diagonals.--Note: All atoms are identical; the center atom is shaded

differently only for ease of viewing.

Body Centered Cubic Structure (BCC)

ex: Cr, W, Fe (a), Tantalum, Molybdenum

Chapter 3 - 7

Adapted from Fig. 3.2,Callister & Rethwisch 3e.

2 atoms/unit cell: 1 center + 8 corners x 1/8


Atomic Packing Factor (APF)

APF = Volume of atoms in unit cell*

Volume of unit cell

Chapter 3 -

*assume hard spheres

Materials Science - Prof. Choi, Hae-Jin 8

Atomic Packing Factor: BCC

a

• APF for a body-centered cubic structure = 0.68

a2

a3

Chapter 3 - 9

APF =

43

p ( 3a/4)32atoms

unit cell atomvolume

a3unit cellvolume

length = 4R =Close-packed directions:

3 aaRAdapted from

Fig. 3.2(a), Callister & Rethwisch 3e.

2



• Atoms touch each other along face diagonals.--Note: All atoms are identical; the face-centered atoms are shaded

differently only for ease of viewing.

Face Centered Cubic Structure (FCC)

ex: Al, Cu, Au, Pb, Ni, Pt, Ag

Chapter 3 - 10

Adapted from Fig. 3.1, Callister & Rethwisch 3e.

4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8


• APF for a face-centered cubic structure = 0.74Atomic Packing Factor: FCC

maximum achievable APF

Close-packed directions: length = 4R = 2 a

Unit cell contains:6 x 1/2 + 8 x 1/8

2 a

Chapter 3 - 11

APF =

43

p ( 2a/4)34atoms

unit cell atomvolume

a3unit cellvolume

6 x 1/2 + 8 x 1/8 = 4 atoms/unit cella

Adapted fromFig. 3.1(a),Callister & Rethwisch 3e.


• ABAB... Stacking Sequence• 3D Projection • 2D Projection

Hexagonal Close-Packed Structure (HCP)

c

A sites

B sites Middle layer

Top layer

Chapter 3 - 12


• APF = 0.74

Adapted from Fig. 3.3(a),Callister & Rethwisch 3e.

6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

• c/a = 1.633

c

a

B sites

A sites Bottom layer

Middle layer


Hexagonal Close-Packed Structure (HCP)

Chapter 3 - 13Materials Science - Prof. Choi, Hae-Jin

Theoretical Density, r

Density = r =

VCNA

n Ar =

CellUnitofVolumeTotalCellUnitinAtomsofMass

Chapter 3 - 14

where n = number of atoms/unit cellA = atomic weight VC = Volume of unit cell = a3 for cubicNA = Avogadro’s number

= 6.022 x 1023 atoms/mol


• Ex: Cr (BCC) A = 52.00 g/molR = 0.125 nmn = 2 atoms/unit cell

R

Theoretical Density, r

Chapter 3 - 15

rtheoretical

a = 4R/ 3 = 0.2887 nm

ractual

aR

r = a3

52.002atoms

unit cell molg

unit cellvolume atoms

mol

6.022 x 1023

= 7.18 g/cm3

= 7.19 g/cm3

Adapted from Fig. 3.2(a), Callister & Rethwisch 3e.


• Bonding:-- Can be ionic and/or covalent in character.-- % ionic character increases with difference in

electronegativity of atoms.• Degree of ionic character may be large or small:

Atomic Bonding in Ceramics

SiC: smallCaF2: large

Chapter 3 - 16

Adapted from Fig. 2.7, Callister & Rethwisch 3e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

SiC: small


Ceramic Crystal Structures

Oxide structures– oxygen anions larger than metal cations– close packed oxygen in a lattice (usually FCC)– cations fit into interstitial sites among oxygen ions

Chapter 3 - 17Materials Science - Prof. Choi, Hae-Jin

Factors that Determine Crystal Structure1. Relative sizes of ions – Formation of stable structures:

--maximize the # of oppositely charged ion neighbors.


- -

- -+

unstable

- -

- -+

stable

- -

- -+

stable

Chapter 3 - 18

unstable stable stable2. Maintenance of

Charge Neutrality :--Net charge in ceramic

should be zero.--Reflected in chemical

formula:

CaF2: Ca2+cation

F-

F-

anions+

AmXpm, p values to achieve charge neutrality


• Coordination # increases with

Coordination # and Ionic Radii

2

rcationranion

Coord #

< 0.155 linearAdapted from Fig. 3.7, Callister & Rethwisch 3e.

ZnS (zinc sulfide)

rcationranion

To form a stable structure, how many anions cansurround around a cation?

Chapter 3 - 19

Adapted from Table 3.3, Callister & Rethwisch 3e.

2 < 0.155

0.155 - 0.225

0.225 - 0.414

0.414 - 0.732

0.732 - 1.0

3

4

6

8

linear

triangular

tetrahedral

octahedral

cubic




NaCl(sodium chloride)

CsCl(cesium chloride)


Computation of Minimum Cation-Anion Radius Ratio

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

a = 2ranion

arr 222 cationanion =+

Chapter 3 - 20

a = 2ranion

�

2ranion + 2rcation = 2 2ranion

�

ranion + rcation = 2ranion

�

rcation = ( 2 -1)ranion

414.012anion

cation =-=rr


• On the basis of ionic radii, what crystal structurewould you predict for FeO?

• Answer:

550014000770

anion

cation

...

rr

=

=

Example: Predicting the Crystal Structure of FeO

Ionic radius (nm)0.0530.0770.069

CationAl3+

Fe2+

Fe3+

Chapter 3 - 21

550014000770

anion

cation

...

rr

=

=

based on this ratio,-- coord # = 6 because

0.414 < 0.550 < 0.732

-- crystal structure is NaClData from Table 3.4, Callister & Rethwisch 3e.

0.0690.100

0.1400.1810.133

Anion

Fe3+

Ca2+

O2-

Cl-

F-Materials Science - Prof. Choi, Hae-Jin

Rock Salt StructureSame concepts can be applied to ionic solids in general. Example: NaCl (rock salt) structure

rNa = 0.102 nm

rCl = 0.181 nm

Chapter 3 - 22

rNa/rCl = 0.564

\ cations (Na+) prefer octahedral sites



MgO and FeO

O2- rO = 0.140 nm

Mg2+ rMg = 0.072 nm

rMg/rO = 0.514

\ cations prefer octahedral sites

MgO and FeO also have the NaCl structure

Chapter 3 - 23

rMg/rO = 0.514

\ cations prefer octahedral sites

So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms



AX Crystal Structures

939.0181.0170.0

Cl

Cs ==-

+

r

r

Cesium Chloride structure:

AX–Type Crystal Structures include NaCl, CsCl, and zinc blende

Chapter 3 - 24

939.0181.0170.0

Cl

Cs ==-

+

r

r


\ Since 0.732 < 0.939 < 1.0, cubic sites preferred

So each Cs+ has 8 neighbor Cl-


AX2 Crystal Structures

• Calcium Fluorite (CaF2)• Cations in cubic sites

• UO2, ThO2, ZrO2, CeO2

• Antifluorite structure –positions of cations and anions reversed

Fluorite structure

Chapter 3 - 25

• Calcium Fluorite (CaF2)• Cations in cubic sites

• UO2, ThO2, ZrO2, CeO2

• Antifluorite structure –positions of cations and anions reversed



ABX3 Crystal Structures• Perovskite structure

Ex: complex oxide BaTiO3

Chapter 3 - 26



Density Computations for Ceramics

A

AC )(NV

AAn

C

S+S¢=r

Number of formula units/unit cell

Avogadro’s number

Chapter 3 - 27

Volume of unit cell

= sum of atomic weights of all anions in formula unit

�

SAA

�

SAC = sum of atomic weights of all cations in formula unit


Densities of Material Classesrmetals > rceramics > rpolymers

Why?

(g/cm )3

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

20

30Based on data in Table B1, Callister

*GFRE, CFRE, & AFRE are Glass,Carbon, & Aramid Fiber-ReinforcedEpoxy composites (values based on60% volume fraction of aligned fibers

in an epoxy matrix).10

5

Steels

Titanium

Cu,NiTin, Zinc

Silver, Mo

TantalumGold, WPlatinum

Zirconia

Metals have...• close-packing

(metallic bonding)• often large atomic masses

Ceramics have...• less dense packing• often lighter elements

In general

Chapter 3 - 28

Data from Table B.1, Callister & Rethwisch, 3e.

r(g/cm )3

1

2

345

0.30.40.5

Magnesium

Aluminum

Titanium

GraphiteSiliconGlass -sodaConcrete

Si nitrideDiamondAl oxide

HDPE, PSPP, LDPEPC

PTFE

PETPVCSilicone

Wood

AFRE*CFRE*GFRE*Glass fibers

Carbon fibersAramid fibers

Ceramics have...• less dense packing• often lighter elements

Polymers have...• low packing density

(often amorphous)• lighter elements (C,H,O)

Composites have...• intermediate values


Silicate CeramicsMost common elements on earth are Si & O

• SiO2 (silica) polymorphic forms are quartz, crystobalite, & tridymite

• The strong Si-O bonds lead to a high melting temperature (1710ºC) for this material

Si4+

O2-

Chapter 3 - 29

Most common elements on earth are Si & O

• SiO2 (silica) polymorphic forms are quartz, crystobalite, & tridymite

• The strong Si-O bonds lead to a high melting temperature (1710ºC) for this material

Adapted from Figs. 3.10-11, Callister & Rethwisch 3e crystobalite


• Basic Unit: Glass is noncrystalline (amorphous)• Fused silica is SiO2 to which no

impurities have been added• Other common glasses contain

impurity ions such as Na+, Ca2+, Al3+, and B3+

Glass Structure

Si04 tetrahedron4-

Si4+

O2-

Chapter 3 - 30

• Quartz is crystallineSiO2:

(soda glass)Adapted from Fig. 3.41, Callister & Rethwisch 3e.

Si4+Na+

O2-


Polymorphic Forms of CarbonDiamond– tetrahedral bonding of

carbon• hardest material known• very high thermal

conductivity– large single crystals –

gem stones– small crystals – used to

grind/cut other materials – diamond thin films

• hard surface coatings –used for cutting tools, medical devices, etc.

Chapter 3 - 31

Diamond– tetrahedral bonding of

carbon• hardest material known• very high thermal

conductivity– large single crystals –

gem stones– small crystals – used to

grind/cut other materials – diamond thin films

• hard surface coatings –used for cutting tools, medical devices, etc.



Polymorphic Forms of Carbon (cont)Graphite– layered structure – parallel hexagonal arrays of

carbon atoms

– weak van der Waal’s forces between layers– planes slide easily over one another -- good

lubricant

Chapter 3 - 32

Graphite– layered structure – parallel hexagonal arrays of

carbon atoms

– weak van der Waal’s forces between layers– planes slide easily over one another -- good

lubricant



Polymorphic Forms of Carbon (cont)Fullerenes and Nanotubes

• Fullerenes – spherical cluster of 60 carbon atoms, C60

– Like a soccer ball • Carbon nanotubes – sheet of graphite rolled into a tube

– Ends capped with fullerene hemispheres

Chapter 3 - 33

Adapted from Figs. 3.18 & 3.19, Callister & Rethwisch 3e.


Crystal Systems

7 crystal systems

14 crystal lattices

Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal.

Chapter 3 - 34

Fig. 3.20, Callister & Rethwisch 3e.

7 crystal systems

14 crystal lattices

a, b, and c are the lattice constants


Point CoordinatesPoint coordinates for unit cell

center area/2, b/2, c/2 ½ ½ ½

Point coordinates for unit cell corner are 111

Translation: integer multiple of lattice constants à identical position in another unit cell

z

x

ya b

c

000

111

Chapter 3 - 35

Point coordinates for unit cell center area/2, b/2, c/2 ½ ½ ½

Point coordinates for unit cell corner are 111

Translation: integer multiple of lattice constants à identical position in another unit cell

x

y

z

·

2c

·

·

·

b

b


Crystallographic Directions

1. Vector repositioned (if necessary) to pass through origin.

2. Read off projections in terms of unit cell dimensions a, b, and c

3. Adjust to smallest integer values4. Enclose in square brackets, no commas

[uvw]

z Algorithm

y

Chapter 3 - 36


2. Read off projections in terms of unit cell dimensions a, b, and c


[uvw]

ex: 1, 0, ½ => 2, 0, 1 => [ 201 ]

-1, 1, 1

families of directions <uvw>

x

where overbar represents a negative index

[111 ]=>


ex: linear density of Al in [110] direction

a = 0.405 nm

Linear Density• Linear Density of Atoms º LD =

[110]

Unit length of direction vectorNumber of atoms

Chapter 3 - 37

ex: linear density of Al in [110] direction

a = 0.405 nm

a# atoms

length

13.5 nma2

2LD -==


HCP Crystallographic Directions


2. Read off projections in terms of unitcell dimensions a1, a2, a3, or c


[uvtw]-

a2

zAlgorithm

Chapter 3 - 38


2. Read off projections in terms of unitcell dimensions a1, a2, a3, or c


[uvtw]

[ 1120 ]ex: ½, ½, -1, 0 =>

Adapted from Fig. 3.24(a), Callister & Rethwisch 3e.

dashed red lines indicate projections onto a1 and a2 axes a1

a2

a3

-a32

a2

2a1

-a3

a1


HCP Crystallographic Directions• Hexagonal Crystals

– 4 parameter Miller-Bravais lattice coordinates are related to the direction indices (i.e., u'v'w') as follows.

1]uvtw[]'w'v'u[ ®

z

Chapter 3 - 39

=

=

=

'wwt

v

u

)vu( +-

)'u'v2(31 -

)'v'u2(31 -=

Fig. 3.24(a), Callister & Rethwisch 3e.

-a3

a1

a2


Crystallographic Planes

Chapter 3 - 40



Crystallographic Planes• Miller Indices: Reciprocals of the (three) axial

intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices.

• Algorithm1. Read off intercepts of plane with axes in

terms of a, b, c2. Take reciprocals of intercepts3. Reduce to smallest integer values4. Enclose in parentheses, no

commas i.e., (hkl)

Chapter 3 - 41

• Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices.

• Algorithm1. Read off intercepts of plane with axes in

terms of a, b, c2. Take reciprocals of intercepts3. Reduce to smallest integer values4. Enclose in parentheses, no

commas i.e., (hkl)


Crystallographic Planesz

x

ya b

c

4. Miller Indices (110)

z

1. Intercepts 1 1 ¥2. Reciprocals 1/1 1/1 1/¥

1 1 03. Reduction 1 1 0

example a b c

Chapter 3 - 42

xexample a b c

z

x

ya b

c


1. Intercepts 1/2 ¥ ¥2. Reciprocals 1/½ 1/¥ 1/¥

2 0 03. Reduction 2 0 0


Crystallographic Planesz

ya b

c·

··

example1. Intercepts 1/2 1 3/4

a b c

2. Reciprocals 1/½ 1/1 1/¾2 1 4/3

3. Reduction 6 3 4

Chapter 3 - 43

xa b


3. Reduction 6 3 4

(001)(010),

Family of Planes {hkl}

(100), (010),(001),Ex: {100} = (100),


Crystallographic Planes (HCP)• In hexagonal unit cells the same idea is used

example a1 a2 a3 c1. Intercepts 1 ¥ -1 12. Reciprocals 1 1/¥

1 0 -1-1

11 a2

z

Chapter 3 - 44

4. Miller-Bravais Indices (1011)

1 0 -1 13. Reduction 1 0 -1 1

a2

a3

a1

Adapted from Fig. 3.24(b), Callister & Rethwisch 3e.


Crystallographic Planes• We want to examine the atomic packing of

crystallographic planes• Iron foil can be used as a catalyst. The

atomic packing of the exposed planes is important.

a) Draw (100) and (111) crystallographic planes for Fe.

b) Calculate the planar density for each of these planes.

Chapter 3 - 45

• We want to examine the atomic packing of crystallographic planes

• Iron foil can be used as a catalyst. The atomic packing of the exposed planes is important.

a) Draw (100) and (111) crystallographic planes for Fe.

b) Calculate the planar density for each of these planes.


Planar Density of (100) IronSolution: At T < 912°C iron has the BCC structure.

(100) R3

34a =

2D repeat unit

Chapter 3 - 46

Radius of iron R = 0.1241 nmAdapted from Fig. 3.2(c), Callister & Rethwisch 3e.

= Planar Density =a2

1atoms

2D repeat unit

= nm2

atoms12.1m2

atoms= 1.2 x 10191

2

R3

34area2D repeat unit


Planar Density of (111) IronSolution (cont): (111) plane 1 atom in plane/ unit surface cell

atoms in plane

atoms above plane

atoms below plane

ah23=

a2

Chapter 3 - 47

333 2

2

R3

16R3

42a3ah2area =÷÷ø

öççè

æ===

ah2

=

1= =

nm2atoms7.0

m2atoms0.70 x 1019

3 2R3

16Planar Density =

atoms2D repeat unit

area2D repeat unit


A sites

B B

B

BB

B B

C sites

C C

CA

B

B sites

• ABCABC... Stacking Sequence• 2D Projection

FCC Stacking Sequence

B B

B

BB

B B

B sitesC C

CA

C C

CA

Chapter 3 - 48

BC sites

• FCC Unit Cell

B

AB

C


• Some engineering applications require single crystals:

• Properties of crystalline materials often related to crystal structure.

-- diamond singlecrystals for abrasives

-- turbine bladesFig. 9.40(c), Callister & Rethwisch 3e. (Fig. 9.40(c) courtesy of Pratt and Whitney).

(Courtesy Martin Deakins,GE Superabrasives, Worthington, OH. Used with permission.)

Crystals as Building Blocks

Chapter 3 - 49

• Properties of crystalline materials often related to crystal structure.

(Courtesy P.M. Anderson)

-- Ex: Quartz fractures more easily along some crystal planes than others.


Polycrystalline Materials

Small crystallite nuclei Growth of crystallites

Chapter 3 -Materials Science - Prof. Choi, Hae-Jin 50

Small crystallite nuclei Growth of crystallites

Completion of solidification Grain structure under microscope

Grain boundary

• Most engineering materials are polycrystals.

Adapted from Fig. K, color inset pages of Callister 5e.(Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)

1 mm

Polycrystals Anisotropic

Chapter 3 - 51

• Nb-Hf-W plate with an electron beam weld.• Each "grain" is a single crystal.• If grains are randomly oriented,

overall component properties are not directional.• Grain sizes typ. range from 1 nm to 2 cm

(i.e., from a few to millions of atomic layers).

1 mm

Isotropic


• Single Crystals-Properties vary withdirection: anisotropic.

-Example: the modulusof elasticity (E) in BCC iron:

Data from Table 3.7, Callister & Rethwisch 3e. (Source of data is R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley and Sons, 1989.)

• Polycrystals

Single vs PolycrystalsE (diagonal) = 273 GPa

E (edge) = 125 GPa

Chapter 3 - 52

• Polycrystals-Properties may/may notvary with direction.

-If grains are randomlyoriented: isotropic.(Epoly iron = 210 GPa)

-If grains are textured,anisotropic.

200 mm Adapted from Fig. 5.19(b), Callister & Rethwisch 3e.(Fig. 5.19(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)


Polymorphism • Two or more distinct crystal structures for the same

material (allotropy/polymorphism)

titaniuma, b-Ti

carbondiamond, graphite

1538ºCd-Fe

liquid

iron system

Chapter 3 - 53

• Two or more distinct crystal structures for the same material (allotropy/polymorphism)

titaniuma, b-Ti

carbondiamond, graphite

BCC

FCC

BCC

1538ºC

1394ºC

912ºC

d-Fe

g-Fe

a-Fe


X-Ray Diffraction

Chapter 3 - 54

• Diffraction gratings must have spacings comparable to the wavelength of diffracted radiation.

• Can’t resolve spacings < l• Spacing is the distance between parallel planes of

atoms. Materials Science - Prof. Choi, Hae-Jin

X-Rays to Determine Crystal Structure• Incoming X-rays diffract from crystal planes.


reflections must be in phase for a detectable signal

spacing between d

ql

qextra distance travelled by wave “2”

Chapter 3 - 55

X-ray intensity (from detector)

q

qc

d =nl

2 sin qc

Measurement of critical angle, qc, allows computation of planar spacing, d.

spacing between planes

d


X-Ray Diffraction Pattern

(110)

(211)

z

x

ya b

c

Intensity (relative)

z

x

ya b

cz

x

ya b

c

Chapter 3 - 56

Adapted from Fig. 3.20, Callister 5e.

(200)

Diffraction angle 2q

Diffraction pattern for polycrystalline a-iron (BCC)

Intensity (relative)


• Atoms may assemble into crystalline or amorphous structures.

• We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP).

SUMMARY

• Common metallic crystal structures are FCC, BCC, and HCP. Coordination number and atomic packing factor are the same for both FCC and HCP crystal structures.

Chapter 3 - 57

• We can predict the density of a material, provided we know the atomic weight, atomic radius, and crystal geometry (e.g., FCC, BCC, HCP).

• Crystallographic points, directions and planes are specified in terms of indexing schemes. Crystallographic directions and planes are related to atomic linear densities and planar densities.

• Ceramic crystal structures are based on:-- maintaining charge neutrality-- cation-anion radii ratios.

• Interatomic bonding in ceramics is ionic and/or covalent.


• Some materials can have more than one crystal structure. This is referred to as polymorphism (or allotropy).

SUMMARY

• Materials can be single crystals or polycrystalline. Material properties generally vary with single crystal orientation (i.e., they are anisotropic), but are generally non-directional (i.e., they are isotropic) in polycrystals with randomly oriented grains.

Chapter 3 - 58

• Some materials can have more than one crystal structure. This is referred to as polymorphism (or allotropy).

• X-ray diffraction is used for crystal structure and interplanar spacing determinations.


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