chapter 4: the structure of crystalline solids
TRANSCRIPT
Chapter 4 - 1
ISSUES TO ADDRESS...
• What are common crystal structures for
metals and ceramics?
• What features of a metal’s/ceramic’s atomic
structure determine its density?
• How do the crystal structures of ceramic
materials differ from those for metals?
Chapter 4: The Structure of Crystalline Solids고체결정질의구조
공통결정구조
비중
Chapter 4 - 2
Metallic Crystal Structures
• How can we stack metal atoms to minimize
empty space?
2-dimensions
vs.
Now stack these 2-D layers to make 3-D structures
빈공간을최소화하기위해원자가쌓이는방법은?
2차원 공간만 생각하면 좌측이 유리하나 3차원 공간이므로다른결과가나올수있다
Chapter 4 - 3
• Tend to be densely packed.
• Reasons for dense packing:
- Typically, only one element is present, so all atomic radii are
the same.
- Metallic bonding is not directional.
- Nearest neighbor distances tend to be small in order to lower
bond energy.
- Electron cloud shields cores from each other.
• Metals have the simplest crystal structures.
We will examine three such structures...
Metallic Crystal Structures
방향성없음
만일 전자가 없으면 양이온인코어(핵)이 서로 밀어내려고하는 힘이 작용하지만 전자구름이 이를 막아줘서(shield) 조밀하게쌓일수있다는의미
조밀하게쌓이는경향
Chapter 4 - 4
• Rare due to low packing density (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
Simple Cubic Structure (SC)
Fig. 4.2, Callister & Rethwisch 9e.
단순입방결정구조
충진율이작으므로어떠한 금속도이러한 결정구조를갖지않는다. (반금속인폴로늄(Po; polonium)만존재)
• APF for a simple cubic structure = 0.52
최근접원자수는 6개
Atomic Packing Factor(원자충진률)
Chapter 4 - 5
• APF for a simple cubic structure = 0.52
APF =
a3
4
3π (0.5a) 31
atoms
unit cellatom
volume
unit cell
volume
Atomic Packing Factor (APF)
APF = Volume of atoms in unit cell*
Volume of unit cell
*assume hard spheres
Adapted from Fig. 4.2 (a),
Callister & Rethwisch 9e.
close-packed directions
a
R = 0.5a
contains 8 x 1/8 = 1 atom/unit cell
= There are eights of 1/8 atoms.
총단위정부피
단위정내원자부피
Chapter 4 - 6
• Coordination # = 8
Adapted from Fig. 4.1,
Callister & Rethwisch 9e.
• 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 (), Tantalum, Molybdenum
2 atoms/unit cell: 1 center + 8 corners x 1/8
체심입방격자
(# nearest neighbors)
Chapter 4 - 7
Atomic Packing Factor: BCC
APF =
4
3π ( 3a/4 )32
atoms
unit cell atom
volume
a3
unit cell
volume
length = 4R =
Close-packed directions:
3 a
• APF for a body-centered cubic structure = 0.68
aRAdapted from
Fig. 4.1(a), Callister &
Rethwisch 9e.
a
a2
a3청색삼각형
(밑면대각선길이)
Chapter 4 - 8
• Coordination # = 12
Adapted from Fig. 3.1, Callister & Rethwisch 9e.
• 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
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
면심입방격자
(최근접원자수)
Chapter 4 - 9
• APF for a face-centered cubic structure = 0.74
Atomic Packing Factor: FCC
maximum achievable APF
APF =
4
3π ( 2a/4 )34
atoms
unit cell atom
volume
a3
unit cell
volume
Close-packed directions:
length = 4R = 2 a
Unit cell contains:6 x 1/2 + 8 x 1/8
= 4 atoms/unit cella
2 a
Adapted from
Fig. 3.1(a),
Callister &
Rethwisch 9e.
∴R= 2𝑎/4
Chapter 4 - 10
A sites
B B
B
BB
B B
C sites
C C
CA
B
B sites
• ABCABC... Stacking Sequence
• 2D Projection
• FCC Unit Cell
FCC Stacking Sequence
B B
B
BB
B B
B sitesC C
CA
C C
CA
AB
C
A(맨아래 원자)와 C(맨위 원자)가어긋나게쌓여있음
Chapter 4 - 11
• Coordination # = 12
• ABAB... Stacking Sequence
• APF = 0.74
• 3D Projection • 2D Projection
Adapted from Fig. 4.3(a),
Callister & Rethwisch 9e.
Hexagonal Close-Packed Structure
(HCP)
6 atoms/unit cell
ex: Cd, Mg, Ti, Zn
• c/a = 1.633
c
a
A sites
B sites
A sites Bottom layer
Middle layer
Top layer
육방조밀결정
맨위 원자와 맨아래원자가동일위치임
예제 4.3에 HCP단위정부피구하는과정설명되어있음
Chapter 4 - 12
Theoretical Density, r
where n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= 6.022 x 1023 atoms/mol
Density = r =
VCNA
n Ar =
CellUnitofVolumeTotal
CellUnitinAtomsofMass
이론밀도
Chapter 4 - 13
• Ex: Cr (BCC)
A = 52.00 g/mol
R = 0.125 nm
n = 2 atoms/unit cell
ρtheoretical
ρactual
aR
r =
a3
52.002
atoms
unit cellmol
g
unit cell
volume atoms
mol
6.022 x 1023
Theoretical Density, ρ
= 7.18 g/cm3
= 7.19 g/cm3
Adapted from
Fig. 4.1(a), Callister &
Rethwisch 9e.
원자량
Chapter 4 - 15
Ceramic Crystal Structures
– 세라믹은보통금속과비금속원소간의화합물
– 세라믹은최소 2개이상의원소로구성되어있기때문에일반적으로금속의결정구조보다복잡
– 결합은이온결합또는공유결합
암염(NaCl)의결정구조 섬아연광(ZnS)의결정구조
Chapter 4 - 16
세라믹이온배열의기하학적형상(1)
– 금속원자는전자를공여해서양이온(cation)이됨
– 비금속원자는전자를받아음이온(anion)이됨
– 결정질세라믹재료의결정구조는 (1)각구성이온의전하량과(2)양이온대비음이온의크기에의해결정
(1) 전기적중성을이루기위해양이온전하량의합과음이온전하량
합이같은조건(예: CaF2, 여기서 Ca는 +2가이온, F는 -1가이온)
(2) 양이온과음이온반지름의비(rc/ra)에의해배위수(양이온주위음이온의수)가결정
안정한 또는 불안정한 양이온-음이온 배치(청색이 양이온,
적색이음이온)
Chapter 4 - 17
세라믹이온배열의기하학적형상(2)
세라믹 이온배열에서 양이온-
음이온 반지름비에 대한 배위수와배위형상
‒ 그러나 실제 이온은 딱딱한구가 아니므로 보여지는 배위수가절대관계는아님
‒ 이온반경은 배위수가 증가하면증가함
‒ 또한, 이온의 전하도 반경에영향을 준다. 일반적으로 전자를 잃은 양전하는 남아있는 원자가 전자를 더욱 견고하게 결속되어 이온반경이감소됨
Chapter 4 - 18
• 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: small
CaF2: large
(생략)
Chapter 4 - 19
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
산화물
음이온 양이온
침입형
(생략)
Chapter 4 - 20
Factors that Determine Crystal Structure1. Relative sizes of ions – Formation of stable structures:
--maximize the # of oppositely charged ion neighbors.
Adapted from Fig. 4.4,
Callister & Rethwisch 9e.
- -
- -+
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
(생략)
반대 극성의 최 근접이온수최대화
전기적중성도만족
Chapter 4 - 21
• Coordination Number increases with
Coordination Number and Ionic Radii
Adapted from Table 4.3,
Callister & Rethwisch 9e.
2
rcationranion
Coord.
Number
< 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
ZnS
(zinc blende)
NaCl(sodium
chloride)
CsCl(cesium chloride)
rcationranion
To form a stable structure, how many anions can
surround around a cation?
(생략)
배위수(양이온주위의음이온수)
음이온 반지름에 대한양이온의반지름비
Chapter 4 - 22
Computation of Minimum Cation-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
414.012anion
cation =-=r
r
(생략)
Chapter 4 - 23
Bond Hybridization
Bond Hybridization is possible when there is significant
covalent bonding
– hybrid electron orbitals form
– For example for SiC
• XSi = 1.8 and XC = 2.5
• ~ 89% covalent bonding
• Both Si and C prefer sp3 hybridization
• Therefore, for SiC, Si atoms occupy tetrahedral sites
(생략)
혼성화결합(전자 궤도가 중첩되어 최외각전자수가변화되는현상)
Chapter 4 - 24
• 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 4.4,
Callister & Rethwisch 9e.
Example Problem: Predicting the Crystal
Structure of FeO
Ionic radius (nm)
0.053
0.077
0.069
0.100
0.140
0.181
0.133
Cation
Anion
Al3+
Fe2+
Fe3+
Ca2+
O2-
Cl-
F-
(생략)
(NaCl 다음페이지참조)
Chapter 4 - 25
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 octahedral sites
Adapted from Fig. 4.5,
Callister & Rethwisch 9e.
rCl = 0.181 nm
(생략)
6개의배위수
Chapter 4 - 26
MgO and FeO
O2- rO = 0.140 nm
Mg2+ rMg = 0.072 nm
rMg/rO = 0.514
cations prefer octahedral sites
So each Mg2+ (or Fe2+) has 6 neighbor oxygen atoms
Adapted from Fig. 4.5,
Callister & Rethwisch 9e.
MgO and FeO also have the NaCl structure
(생략)
(배위수는 6이나 주위 이온을 연결하는구조는 8면체자리임)
Chapter 4 - 27
AX Crystal Structures
Fig. 4.6, Callister & Rethwisch 9e.
CsCl(Cesium Chloride) structure:
Since 0.732 < 0.939 < 1.0,
cubic sites preferred
So each Cs+ has 8 neighbor Cl-
AX–Type Crystal Structures include NaCl, CsCl, and zinc blende
(생략)
Chapter 4 - 28
AX2 Crystal Structures
• Calcium Fluorite (CaF2)
• Cations in cubic sites
• UO2, ThO2, ZrO2, CeO2
• Antifluorite structure –
positions of cations and
anions reversed
Fig. 4.8, Callister & Rethwisch 9e.
Fluorite structure
(생략)
양이온과음이온의자리가뒤바뀐구조
Chapter 4 - 29
ABX3 Crystal Structures
Fig. 4.9, Callister &
Rethwisch 9e.
• Perovskite structure
Ex: complex oxide
BaTiO3
(생략)
Chapter 4 - 30
Density Computations for Ceramics
Number of formula units/unit cell
Volume of unit cell
Avogadro’s number
= sum of atomic weights of all anions in formula unit
= sum of atomic weights of all cations in formula unit
세라믹의밀도계산
온전한이온(일부가아닌..)
Chapter 4 - 31
Densities of Material Classes
ρmetals > ρceramics > ρpolymers
Why?
Data from Table B.1, Callister & Rethwisch, 9e.
ρ(g
/cm
)
3
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibers
Polymers
1
2
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
3
4
5
0.3
0.4
0.5
Magnesium
Aluminum
Steels
Titanium
Cu,Ni
Tin, Zinc
Silver, Mo
TantalumGold, WPlatinum
Graphite
Silicon
Glass -sodaConcrete
Si nitrideDiamondAl oxide
Zirconia
HDPE, PSPP, LDPE
PC
PTFE
PETPVCSilicone
Wood
AFRE*
CFRE*
GFRE*
Glass fibers
Carbon fibers
Aramid fibers
Metals have...• close-packing
(metallic bonding)
• often large atomic masses
Ceramics have...• less dense packing
• often lighter elements
Polymers have...• low packing density
(often amorphous)
• lighter elements (C,H,O)
Composites have...• intermediate values
In general
Chapter 4 - 32
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-
Figs. 4.10 & 4.11, Callister & Rethwisch
9e crystobalite
규산염
(생략)
Chapter 4 - 33
Bonding of adjacent SiO44- accomplished by the
sharing of common corners, edges, or faces
Silicates
Mg2SiO4 Ca2MgSi2O7
Adapted from Fig.
4.13, Callister &
Rethwisch 9e.
Presence of cations such as Ca2+, Mg2+, & Al3+
1. maintain charge neutrality, and
2. ionically bond SiO44- to one another
(생략)
Chapter 4 - 34
• Quartz is crystalline
SiO2:
• 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+
(soda glass)
Adapted from Fig. 4.12,
Callister & Rethwisch 9e.
Glass Structure
SiO4 tetrahedron4-
Si4+
O2-
Si4+
Na+
O2-
(생략)
Chapter 4 - 35
Layered Silicates
• Layered silicates (e.g., clays, mica, talc)
– SiO4 tetrahedra connected together to form 2-D plane
• A net negative charge is associated with each (Si2O5)
2-
unit
• Negative charge balanced by adjacent plane rich in positively charged cations
Fig. 4.14, Callister &
Rethwisch 9e.
(생략)
Chapter 4 - 36
• Kaolinite clay alternates (Si2O5)2- layer with Al2(OH)4
2+
layer
Layered Silicates (cont)
Note: Adjacent sheets of this type are loosely bound to one another by van der Waal’s forces.
Fig. 4.15, Callister &
Rethwisch 9e.
(생략)
Chapter 4 - 37
Polymorphic Forms of Carbon
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.
Fig. 4.17, Callister &
Rethwisch 9e.
보석
여러 형태의, 다양한.
정사면체
탄소원자하나가주위 4개의 탄소원자와결합된형태의공유결합
탄소는 다이아몬드와 흑연의 2가지 동소체로 존재하며, 일반적으로 금속, 세라믹, 폴리머재료의분류방법에속하지않으나흑연은세라믹으로분류됨
Chapter 4 - 38
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
Fig. 4.18, Callister &
Rethwisch 9e.
흑연
Chapter 4 - 39
Crystallinity in Polymers
• Ordered atomic
arrangements involving
molecular chains
• Crystal structures in terms
of unit cells
• Example shown
– polyethylene unit cell
Fig. 4.19, Callister &
Rethwisch 9e.
결정성
폴리머 재료도 결정질이 존재할 수 있으나 금속이나 세라믹 재료와 달리 분자가 포함되어있기때문에원자배열이더복잡
폴리머 결정성(polymer crystallinity)은 분자사슬이 규칙적으로 적층되어 원자배열이 규칙성을갖도록된상태를의미
결정화도(degree of crystallinity)는 순수 비정질에서 95%의결정질까지가능
금속은거의전체가결정질세라믹은전체가결정질혹은비정질가능
Chapter 4 - 40
• Some engineering applications require single crystals:
• Properties of crystalline materials
often related to crystal structure.
(Courtesy P.M. Anderson)
-- Ex: Quartz fractures more easily
along some crystal planes than
others.
-- diamond single
crystals for abrasives
-- turbine blades
(Courtesy Martin Deakins,
GE Superabrasives, Worthington,
OH. Used with permission.)
Crystals as Building Blocks단결정
기본구조(예: 분자)
Chapter 4 - 41
• Most engineering materials are polycrystals.
• 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 typically range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).
Fig. K, color inset pages
of Callister 5e. (Courtesy of Paul E.
Danielson, Teledyne Wah
Chang Albany)
1 mm
Polycrystals
Isotropic
Anisotropic다결정
하프늄(Hf), 니오븀(Nb), 텅스텐(W)
이방성(비등방성)
grain: 결정립 등방성
Chapter 4 - 42
• Single Crystals
- Properties vary with
direction: anisotropic.
- Example: the modulus
of elasticity (E) in BCC iron:
Data from Table 3.3,
Callister & Rethwisch 9e.
• Polycrystals
- Properties may/may not
vary with direction.
- If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
- If grains are textured,
anisotropic.
200 μm Adapted from Fig.
6.19(b), Callister &
Rethwisch 9e.
Single vs PolycrystalsE (diagonal) = 273 GPa
E (edge) = 125 GPa
질감이 있게배치됨
Chapter 4 - 43
Polymorphism
• Two or more distinct crystal structures for the same
material (allotropy/polymorphism)
titanium
α, β -Ti
carbon
diamond, graphite
BCC
FCC
BCC
1538° C
1394° C
912° C
δ-Fe
γ-Fe
α-Fe
liquid
iron system
동질이상
동소체/동질이상
동소체에서 결정구조는 외부의 온도와압력에의해결정된다
Chapter 4 - 44
선밀도와면밀도
선밀도와 면밀도는 슬립현상을 이해하는 데 중요하며, 슬립은 면밀도가 가장 높은결정면에서선밀도가가장높은방향으로일어난다.
• 선밀도(linear density, LD): 특정한결정방향의단위벡터상에중심이놓여있는원자들의단위길이에대한개수(예; [110]방향에서의선밀도)
• 면밀도(planar density, PD): 특정한결정면에중심을둔원자들의단위면적당개수(예; FCC와 BCC에서 (110)면의면밀도)
FCC BCC
Chapter 4 - 45
ex: linear density of Al in [110]
direction
a = 0.405 nm
Linear Density
• Linear Density of Atoms LD =
a
[110]
Unit length of direction vector
Number of atoms
# atoms
length
13.5 nm
a2
2LD -==
방향벡터의단위길이
방향벡터상에중심을둔원자수
선밀도
Chapter 4 - 46
Planar Density of (100) Iron
Solution: At T < 912° C iron has the BCC structure.
(100)
Radius of iron R = 0.1241 nm
R3
34a =
2D repeat unit
= Planar Density =a 2
1
atoms
2D repeat unit
= nm2
atoms12.1
m2
atoms= 1.2 x 1019
1
2
R3
34area
2D repeat unit
Fig. 4.2(c), Callister & Rethwisch 9e [from W. G. Moffatt, G. W.
Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I,
Structure, p. 51. Copyright © 1964 by John Wiley & Sons, New York.
Reprinted by permission of John Wiley & Sons, Inc.]
면밀도 면(100)의뜻
Chapter 4 - 47
Planar Density of (111) IronSolution (cont): (111) plane 1 atom in plane/ unit surface cell
atoms in plane
atoms above plane
atoms below plane
ah2
3=
a2
1
= = nm2
atoms7.0
m2
atoms0.70 x 1019
3 2R3
16Planar Density =
atoms
2D repeat unit
area
2D repeat unit
333
2
2
R3
16R
3
42a3ah2area ====
앞장의 (100)면에비해면밀도가작음
Chapter 4 - 49
결정구조에따른원자적층방법
• 세라믹원자적층방법
사면체자리(tetrahedral
position): 4개원자틈
팔면체자리(octahedral
position): 6개원자틈
암염(NaCl)의 적층 예:
6개의 음이온 사이에하나의양이온배치
양이온과음이온의비율은 1:1임
Chapter 4 - 50
X선회절: 결정구조의파악• 고체내원자나분자의배열파악은 X-선회절분석으로가능하다
파장이 같은 두 파동이 같은 위상차(phase)를 갖고산란되었다가 경로차가 파장의 정수배를 갖고 간섭을 일으키면 진폭이 합해져 보강간섭이 일어난다.
회절(diffraction)현상의원인이된다.
산란된 두 파동이 같은 위상차(phase)를 갖고 산란되었다가 경로차가파장의절반의정수배가될경우소멸간섭이일어난다.
X-선은고체의원자간격정도의극히짧은파장과높은 에너지를 갖는 전자파의 일종으로 고체 재료에 투사될 때, 빔의 진행 경로에 놓여있는 원자나이온에의해모든방향으로산란된다.
회절보강간섭의결과
Chapter 4 - 51
X-Ray Diffraction
• Diffraction gratings must have spacings comparable to the wavelength of diffracted radiation.
• Can’t resolve spacings λ
• Spacing is the distance between parallel planes of atoms.
회절격자
회절방사선
파장보다작게될수없다
Chapter 4 - 52
X선회절과 Bragg의법칙
n 은반사지수로정수이다.
Bragg의법칙
면간거리 dhkl 을측정하여원자간거리를알아낸다.
결정면사이의거리정보는원자의종류를추정하는데도움이됨
Chapter 4 - 53
X선회절과 Bragg의법칙
X-선 Diffractometer(디프렉토미터): 분말 시편의 회절각도를측정하는기기, 결과로부터결정구조를파악
납분말의회절패턴
시편 S를회전시켜가면서회절이생기는각도를측정
X선광원
검출부
Chapter 4 - 54
X-Rays to Determine Crystal Structure
X-ray intensity (from detector)
θ
θc
d =nλ
2 sinθc
• Incoming X-rays diffract from crystal planes.
Adapted from Fig. 4.29,
Callister & Rethwisch 9e.
reflections must be in phase for a detectable signal
spacing between planes
d
θλ
θ
extra distance travelled
by wave “2”
Measurement of
critical angle, , allows
computation of planar
spacing, d.
θ
Chapter 4 - 55
X-Ray Diffraction Pattern
Adapted from Fig. 3.22, Callister 8e.
(110)
(200)
(211)
z
x
ya b
c
Diffraction angle 2θ
Diffraction pattern for polycrystalline α-iron (BCC)
Inte
nsity (
rela
tive)
z
x
ya b
c
z
x
ya b
c
Chapter 4 - 56
Summary
• X-ray diffraction is used for crystal structure and interplanar
spacing determinations.
• We can predict the density of a material, provided we know the
atomic weight, atomic radius, and crystal geometry (e.g., FCC,
BCC, HCP).
• 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.
• Some materials can have more than one crystal structure.
This is referred to as polymorphism (or allotropy).
• Ceramic crystal structures are based on:
-- maintaining charge neutrality
-- cation-anion radii ratios.
• Interatomic bonding in ceramics is ionic and/or covalent.
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