1. Crystal Structure and Crystallography of Materials
Chapter 3: Covalent and Ionic Structures

2. 1. CsCl Crystal Structure:
CsCl structure is defined as one type of atoms occupy simple cubic crystal structure and another type of atoms occupy body-centered interstitial site.
Unit cell
Cs+, Cl- cubic interstitial
r + / r -  ~ 1 X Z Y a
[112]
[111]

3. 1. CsCl Crystal Structure:
[112] A B C D E F
Over 400 phases belong to this type such as
Ex. AgCd, AgMg, CuBe, CuZn, CsBr, CsI etc.
Not a BCC structure
Stacking sequence : A B C D E F A B C E D F …
(110) projection

4. 2. NaCl Crystal Structure (Rock-salt structure):
NaCl structure is defined as one type of atoms occupy FCC structure and another type of atoms occupy octahedral interstitial site.
Unit cell
# of host atoms in an unit cell  4
# of octahedral sites in an unit cell  4
stoichiometry 1 : 1

5. 2. NaCl Crystal Structure (Rock-salt structure):
Stacking sequence :
A  B  C  A  B  C  … A  B  C 
(110) projection
[111]

6. 3. NiAs Crystal Structure:
NiAs structure is defined as one type of atoms occupy HCP structure and another type of atoms occupy octahedral interstitial site.
HCP array of Ni and
As occupying 2 octahedral sites
# of host atoms in HCP  2
# of octahedral sites in HCP  2
stoichiometry 1 : 1
(1/3, 2/3, 3/4)
(1/3, 2/3, 1/4) A B

7. a 3. NiAs Crystal Structure: Stacking sequence :
A  B  A  B  A  B …
Distance between 2 cations :
internal compression effect between
2 metallic atoms
 c/a ratio is generally smaller than
that of HCP
C/2 a A B
C   ; Octahedral position

8. 4. ZnS (Zinc Blende) Crystal Structure (Sphalerite):
Sphalerite structure is defined as one type of atoms occupy FCC structure and another type of atoms occupy half tetrahedral interstitial site.
The location of host atoms:
FCC arrangement:
Half Tetrahedral site:
Translation of (1/4,1/4,1/4)

9. 4. ZnS (Zinc Blende) Crystal Structure (Sphalerite):
Stacking sequence :
A  B  C  A  B  C  …
(110) projection A  B  C 
[111] direction
[112] direction

10. 4. ZnS (Zinc Blende): stacking sequence and stacking fault
(110) projection A B   C 
[111]
[110]
 TYPE I
 TYPE II

11. 4. ZnS (Zinc Blende): stacking sequence and stacking fault
Stacking fault of Zinc Blende ; stacking faults & twins involve the insertion or removal of pairs of layers of the same index A…. etc.
Involve no change in the covalent bonds ,  Partial dislocation moves on a TYPE I plane
Stacking seq.
: A  B  C  A  B  C  A … A B   C 
A  C  A  B  C  A Bb…

12. 5. ZnS (Zinc Blende) Crystal Structure (Wurtzite):
Wurtzite structure is defined as one type of atoms occupy HCP structure and another type of atoms occupy half tetrahedral interstitial site.
The location of host atoms:
HCP arrangement:
Half Tetrahedral site:

13. 5. ZnS (Zinc Blende) Crystal Structure (Wurtzite): B 
Stacking sequence :
A  B  A  B  …
A  B
B  C
C  A
Octahedral coordination
A  B
B  C
C  A
Tetrahedral coordination

14. 6. Diamond Crystal Structure:
Diamond structure is defined as one type of atoms occupy FCC structure and the same type of atoms occupy half tetrahedral interstitial site.
The location of host atoms:
FCC arrangement:
Half Tetrahedral site:
Translation of (1/4,1/4,1/4)
Juxtapose two FCC unit cells with different origins of
(000) and (1/4,1/4,1/4)

15. 6. Diamond Crystal Structure:
Stacking sequence :
AABBCCAABBCC…
[110] projection A B C
[110]
Extrinsic stacking fault :
AABBCCAACCBBCC
Intrinsic stacking fault :
AABBCCAACCAA
BB missing
CC inserting

16. 6. Diamond Crystal Structure:
Coordination number : 4
Atomic Packing Factor : 34 %
→ ½ of BCC (why?)
# of atoms in an unit cell : 8
→ In case of BCC x 8 = 16
∴ Packing factor = ½ x BCC

17. 7. CaI2 Structure: A - HCP array of I - Alternating layers of X ; X
octahedral sites ; Ca X A B 
; X
; Ca
Stacking sequence :
A  B A  B A  B …
missing

18. 8. CdCl2 Structure: - FCC array of ClI - Alternating Cd layers in
octahedral position ; Ca
missing
Stacking sequence :
A  B  C  A  B  C  A  B  C  A  B  C
unit cell of the structure :
A  B C  A B  C A  B C  A B  C

19. 9. Al2O3 (Sapphire Structure):
- HCP array of oxygen ions
- Al+++ : 2/3 of available octahedral sites
Stacking sequence :
A 1 B 2 A 3 B 1A 2 B 3 A 1 B 3 2 1 Al A B
1 plane:
Shows the locations where Al+++ are not placed
Unit cell of Al2O3

20. 10. CaF2 (Calcium Difluoride) Structure
- FCC array of Ca
- F : in all tetrahedral sites
Stacking sequence :
A   B   C   A   B   C   Ca F
Every Ca++ ion is surrounded by F- ions
by every ½ cube sites
F- ions form a cubic array with ½
cubic interstitials is occupied by Ca++

21. 11. Graphite Structure Bonding: covalent/van der Waals
4 atoms in an unit cell
Coordination number: 3

22. 11. Graphite Structure

23. 11. CNT (Carbon Nano Tube) Structure:

24. 11. CNT (Carbon Nano Tube) Structure:
SWCNT
DWCNT
Thin-MWCNT
MWNCT

25. 11. Graphene Structure:

26. 11. Other 2-D Layered Structure:
BN Boron nitride P-6m2 (187)
MoS2 Molybdenite P63/mmc (194)

27. 12. Perovskite (BaTiO3):
cubic  tetragonal

28. 12. Perovskite (BaTiO3):

29. 12. Spinel (AB2O4):
MgAl2O4
8 unit cells of FCC

30. 12. Spinel (AB2O4):
Oxygen forms cubic closed packing