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Chapter 5

Common Crystal Structures

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Experimental Determinationof Crystal Structures

Bragg’s Law2 d sinθ = n λ

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Crystal Structures of Metals

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Unit Cells InCubic Crystal Structures

simple cubic(primitive cubic)

bcc fcc

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abab

Hexagonal close-packed structure

abcabc

Cubic close-packed structure

= Face-centered cubic

polytypes

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Table 5.1 Packing in Metals

Type of Packing Packing Efficiency Coordination Number

Simple cubic (sc) 52% 6

Body-centered cubic (bcc) 68% 8

Hexagonal closed-packed (hcp)

74% 12

Cubic close-packed (ccp) 74% 12

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rh/r = 0.156

rh/r = 0.225

rh/r = 0.414

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Unit Cell of Rock-Salt(Sodium Chloride)

Cl- at fcc

Na+ at Oh holesCoord. #: Na+: 6; Cl-: 6atom/ unit cellNa: Cl= 4: 4 = 1: 1 NaCl

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Unit Cell of NiAs

As3- at hcp

Ni3+ at Oh holesPolariable cation & anion

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Unit Cell of Cesium Chloride

Cl- at primitive cubicCs+ at Cubic holes

Coord. #: Cs+: 8; Cl-: 8atom/ unit cellCs: Cl= 1: 1 CsCl

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Unit Cell of Cubic Zinc Sulfide(Sphalerite or Zinc blende)

S2- at fccZn2+ at ½ Td holes

Coord. #: Zn2+: 4; S2-: 4atom/ unit cellZn: S = 4: 4 = 1: 1 ZnS

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Unit Cell of Hexagonal Zinc Sulfide (Wurtzite)

S2- at hcp

Zn2+ at ½ Td holesPolymorph of ZnS

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Unit Cell of Fluorite Structure(Calcium Fluoride)

Ca2+ at fccF- at Td holesCoord. #: Ca2+: 8; F-: 4

atom/ unit cellCa: F= 4: 8 = 1: 2 CaF2

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• Fluorite Structure- MX2 Large M

•Antifluorite structure- M2XLarge X, e.g. Li2O, Na2O

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Unit Cell of Rutile TiO2

O2- at hcpTi4+ at ½ Oh holes

Coord. #: Ti: 6; O: 3atom/ unit cellTi: O= 2: 4 = 1: 2

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Quartz SiO2

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Increasing covalency

A Structural Map for compounds of MX2

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Salts of highly polarizing cations and easily polarizable anions have layered structures.

CdCl2Cl- at ccpCd 2+ at ½ Oh sites

(alternate O layers)

van der Waals force

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CdI2I- at hcpCd 2+ at ½ Oh sites

(alternate O layer)

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298pm

366pm

MoS2Mo4+ at hcpS2- at Td sites

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TiO2

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Unit Cell of ReO3

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Unit Cell of PerovskiteCaTiO3

AIIBIVO3

AIIIBIIIO3

A and O together at ccpB at 1/4 Oh holes

Coord. #: A: 12; B: 6atom/ unit cellA: B: O= 1: 1: 3

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YBa2Cu3O7

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Unit Cell of SpinelMgAl2O4

Normal SpinelAII[BIII]2O4, AIV[BII]2O4 , AVI[BI]2O4

e.g. NiCr2O4, Co3O4 , Mn3O4

Inverse SpinelB[AB]O4e.g. Fe3O4

O 2- at fccA at 1/8 Td holesB at 1/2 Oh holes

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Mineral Ideal formulab CECc (meq/100 g)

Dioctahedral minerals Pyrophyllite Al2(Si4O10)(OH)2 0 Montmorillonite Nax(Al2-xMgx)(Si4O10)

(OH)2.zH2O 60 - 120

Beidellite Mx(Al2)(AlxSi4-xO10) (OH)2.zH2O

60 - 120

Nontronite Mx(Fe3+,Al)2(AlxSi4-xO10) (OH)2.zH2O

60 - 120

Trioctahedral minerals

Talc Mg3(Si4O10)(OH)2 0 Hectorite (Na2Ca)x/2(LixMg3-x)

(Si4O10)(OH)2.zH2O 60 - 120

Saponite Cax/2Mg3(AlxSi4-xO10) .zH2O

60 - 120

Sauconite Mx(Zn,Mg)3(AlxSi4-xO10) .zH2O

a: Only major cations are shown. b: x depends on the origin of the mineral; montmorillonites can show a degree of substitution x in the octahedral sheet in the range 0.05- 0.52. Natural samples generally show substitutions in both octahedral and tetrahedral sheets, which renders the real situations more complex. c: Cation-exchange capacity.

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