Structures of Solids. Prof Andrew Goodwin Michaelmas 2014

Structures of Solids Prof Andrew Goodwin Michaelmas 2014

Li + Be 2+ N 3 O 2 F r/n ~ Polarisability Li + B C 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34

3D (non-polarised) ionic structures Stoichiometry M 2 X MX MX 2 4 CCP anti-fluorite e.g. Li 2 O HCP CCP ZnS zinc blende HCP ZnS wurtzite CCP SiO 2 cristobalite HCP SiO 2 tridymite Metal coordination number 6 All T d holes Would require 12-coordinate anions CCP NaCl rocksalt T d holes HCP NiAs nickel arsenide All O h holes CCP 1/4 T d holes O h holes HCP TiO 2 rutile CaCl 2 dist. rutile 8 Would require 16-coordinate anions CsI CaF 2 fluorite Anions not close packed

Close packing: holes 1/4, 3/4 1/4, 3/4 3/8, 5/8 3/8, 5/8 3/8, 5/8 1/8, 7/8 3/8, 5/8

Anti-fluorite: Li 2 O Cubic close packed O 2 with Li + in all tetrahedral holes 1/4, 3/4 [LiO 4 ] tetrahedra [OLi 8 ] cubes

Anti-fluorite: Li 2 O Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 Most group 1 oxides/sulfides/ (chalcogenides) e.g. Li 2 S, Na 2 S, Na 2 O, but not Cs 2 O, Ag 2 O, Au 2 O

Why is there no HCP equivalent? Distance between tetrahedral holes is too small

What about Cs 2 O, Ag 2 O, Au 2 O? Cs + polarisable will discuss next week! Cu 2 O, Ag 2 O, Au 2 O anti-cristobalite structures driven by preference of this group for linear coordination in +1 oxidation state! (latter not usually examined at Prelims)

Tetrahedral MX: zinc blende (ZnS) Cubic close packed S 2 with Zn 2+ in half tetrahedral holes 1/4 3/4 3/4 1/4 [ZnS 4 ] tetrahedra [SZn 4 ] tetrahedra

Tetrahedral MX: wurtzite (ZnS) Hexagonal close packed S 2 with Zn 2+ in half tetrahedral holes 5/8 5/8 1/8 5/8 5/8 [ZnS 4 ] tetrahedra [SZn 4 ] tetrahedra

Zinc blende / wurtzite Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 Small M 2+ chalcogenides BeO, ZnO, ZnS (also CdS, ) Cu + halides CuCl, CuBr, CuI

Zinc blende / wurtzite Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 III-V semiconductors GaN, GaP

Zinc blende / wurtzite Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 Diamond, SiC, SiGe

Why not choose other T d holes? 1/4 1/4 1/4 1/4 (For HCP: only one choice to avoid close M M contacts)

Tetrahedral MX 2 : cristobalite Open structure with significant Si O covalency! Related to CCP oxide lattice with one quarter T d holes occupied 1/4 3/4 [SiO 4 ] tetrahedra [OSi 2 ] linear rods

Octahedral MX: rocksalt (NaCl) Cubic close packed Cl with Na+ in all octahedral holes [NaCl6] octahedra [ClNa6] octahedra

Octahedral MX: rocksalt (NaCl) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 Group 1 halides Silver(I) halides

Octahedral MX: rocksalt (NaCl) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 Group 2 chalcogenides (but not BeO) Some Group 12 chalcogenides (more in 3rd year)

Octahedral MX: rocksalt (NaCl) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 All divalent 3d TM oxides, except ZnO (some have structural subtleties, especially CuO)

Octahedral MX: nickel arsenide (NiAs) Hexagonal close packed As3 with Ni3+ in all octahedral holes 1/4, 3/4 [NiAs6] octahedra [AsNi6] trigonal prisms

Octahedral MX: nickel arsenide (NiAs) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 Many 3d TM chalcogenides, pnictides (Usually requires unpaired electrons / M M bonding)

Octahedral MX 2 : rutile (TiO 2 ) Distorted hexagonal close packed O 2 with Ti 4+ in half octahedral holes [TiO 6 ] octahedra [OTi 3 ] triangles

Octahedral MX 2 : rutile (TiO 2 ) Calcium chloride is a distorted variant of rutile, with same coordination [TiO 6 ] octahedra [OTi 3 ] triangles

Octahedral MX 2 : rutile (TiO 2 ) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 All TM dioxides, except ZrO 2 and HfO 2 SnO 2 and PbO 2

Octahedral MX 2 : rutile (TiO 2 ) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 All TM difluorides except CdF 2, HgF 2 CaCl 2

Cubic MX: cesium iodide (CsI) Primitive cubic packing of I with Cs + in all cubic holes CsCl, CsBr, CsI NH 4 Cl, (NH 4 Br) [CsI 8 ] cubes [ICs 8 ] cubes

Cubic MX 2 : fluorite (CaF 2 ) Primitive cubic packing of F with Ca 2+ in half cubic holes 1/4, 3/4 [CaF 8 ] cubes [FCa 4 ] tetrahedra

Cubic MX 2 : fluorite (CaF 2 ) Cubic close packing of Ca 2+ with F in all tetrahedral holes 1/4, 3/4 [CaF 8 ] cubes [FCa 4 ] tetrahedra

Cubic MX 2 : fluorite (CaF 2 ) Li + Be 2+ N 3 O 2 F Li + B C r/n ~ Polarisability 76 22 48 70 133 Na + Mg 2+ Al 3+ Si 4+ P 3 S 2 Cl 102 36 18 10 70 92 181 K + Ca 2+ Sc 3+ Ti 3+ V 2+ Cr 2+ Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Ga 3+ Ge 4+ As 3+ Se 2 Br 138 50 25 22 39 40 41 36 37 35 36 37 21 13 19 99 196 Rb + Sr 2+ Y 3+ Zr 4+ Nb 3+ Mo 4+ Tc 4+ Ru 3+ Rh 3+ Pd 2+ Ag + Cd 2+ In 3+ Sn 4+ Sb 3+ Te 2 I 152 59 30 18 24 16 16 32 32 43 115 47 27 17 25 110 220 Cs + Ba 2+ Hf 4+ Ta 3+ W 4+ Re 4+ Os 4+ Ir 3+ Pt 2+ Au + Hg 2+ Tl 3+ Pb 4+ Bi 3+ Ln 3+ Po At 167 67 18 24 16 16 16 32 40 137 51 30 17 34 All Ln/Ac dioxides Later group 2 fluorides, CdF 2, HgF 2, SrCl 2