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

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 -  0.732 ~ 1 X Z Y a [112] [111]

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

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

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

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

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

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)

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

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

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…

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:

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

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)

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

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

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

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

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

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++

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

11. Graphite Structure

11. CNT (Carbon Nano Tube) Structure:

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

11. Graphene Structure:

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

12. Perovskite (BaTiO3): cubic  tetragonal

12. Perovskite (BaTiO3):

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

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