Basic Structural Chemistry Crystalline state Structure types Degree of Crystallinity ■ľ E -tí m o e a g o L5 ■H E S 3 B řL, L> O Less Structural Order More Structural Order Crystalline - 3D long range order Single-crystalline Polycrystalline - many crystallites of different sizes and orientations (random, oriented) Paracrystalline - short and medium range order, lacking long range order Amorphous - no order, random Degree of Crystallinity Single Crystalline Polycrystalline Semicrystalline Amorphous Grain boundaries Crystal Structure •The building blocks of these two are identical, but different crystal faces are developed Crystals • Crystal consist of a periodic arrangement of structural motifs = building blocks • Building block is called a basis: an atom, a molecule, or a group of atoms or molecules • Such a periodic arrangement must have translational symmetry such that if you move a building block by a distance: T = nxä + n2b +n3č where nx,n2, and n3 are integers, and ä,b,č are vectors. then it falls on another identical building block with the same orientation. • If we remove the building blocks and replace them with points, then we have a point lattice or Bravais lattice. Planar Lattice 2D LATTICE ^—^ / / ■ NP BASIS / MOTIF CRYSTAL STRUCTURE Five Planar Lattices • • • • • • m m • • • 1 • \ • • 1 • • a2 í\ 90° • a2 ^ 90° --* • a2 ^ 90°* -i» • l ■** s* ^ • al al ül (a) (b) • (c) • • • --* í. ^ " • a2 V J20° > ^ -J i" * a2i ^ • ^ a\ (d) Name Number of Bravais lattices Conditions Square 1 a i =a2 , a = 90° Rectangular 2 0^02^ = 90° Hexagonal 1 0 1=02,0!= 120° Oblique 1 a1*a2,o>* 120°, a * 90° o o o o o o o o o o O O o o o o o o o © o O O O o o o o o o o o O o O O © o o o o o o o © O o O O © o o o o o o o o O O O o o = = Motif © O = Motif o o o o o o r 0#«#©#Ö#©#<2 i i O O O O O O -i o#e>#o#0#o#0 O O O O O O e#o#e#o#«#o O O O O O O o#*#©#Q#e>#Q O O O O O O q • = Motif Square lattice * * * * * * * * ♦ o o o o o o o o o Lattice + Basis = Crystal * * * * * * * * • s o»o» - »o^o o»o» •o»o *------>• Primitive lattice vectors Non-primitive lattice vectors Primitive unit cells Non-primitive unit cells Unit Cell: An „imaginary" parallel sided region of a structure from which the entire crystal can be constructed by purely translational displacements Contents of unit cell represents chemical composition Space Lattice: A pattern that is formed by the lattice points that have identical environment. Coordination Number (CN): Number of direct neighbours of a given atom (first coordination sphere) Crystal = Periodic Arrays of Atoms Translation Vectors a, b , C C f Lattice point (Atom, molecule, group of molecules,. 7.) £ ■*a Primitive Cell: • Smallest building block for the crystal lattice. • Repetition of the primitive cell gives a crystal lattice Lattices and Space Groups Bravais Lattice (Lattice point = Basis of Spherical Symmetry) Crystal Structure (Structural motif = Basis of Arbitrary Symmetry) Number of point groups: <7 clTstal ^sterns) 32 (32 crystallographic point groups) Number of space groups: 14 (14 Bravais lattices) 230 (230 space groups) Seven Crystal Systems Z / Cubic a = b = c A a / Z / Tetragonal a = b* c ct = p=Y=90° X C a / / 0/ Orthorhombic atbtc ct = p=Y=9[r A b / Rhombohedral a = b = c a = b* c Hexagonal cx = p=9ü5 Y = 12íF Monoclinic a*b*c c Triclinic a* b* c cx*p*Y*90 ^ Fourteen Bravais Lattices Ä7\ \£¥ Simple cubic S7\ ,<äŕ Simple tetragonal £7\ \£V Face-centered cubic Body-cente red cubic <£7\ V3r Body-centered tetragonal Hexagonal /CA <&7\ Y Y*Y i) Y Simple orthorhombic Body-centered orthorhombic Base-centered orthorhombic Face-centered orthorhombic Rhombohedral Simple Monoclinic Base-cente red monoclinic Triclinic a = b = c aibic Simple Cubic (SC) Conventional Cell = Primitive Cell C * Add one atom at the center of the cube Add one atom at the center of each face Ö Ö Body-Centered Cubic (BCC) Conventional Unit Cell ^ Primitive Cell Face-Centered Cubic (FCC) Primitive Cell A primitive cell of the lattice = volume of space translated through all the vectors in a lattice that just fills all of space without overlapping or leaving voids. A primitive cell contains just one Bravais lattice point. The primitive cell is the smallest cell that can be translated throughout space to completely recreate the entire lattice. There is not one unique shape of a primitive cell, many possible shapes. The primitive cell for the simple cubic lattice is equal to the simple cubic unit cell (they are identical). Body-Centered Cubic (I) Unit Cell (magenta) Primitive Cell Primitive Cell of BCC Rhombohedron primitive cell The primitive cell is smaller or equal in size to the unit cell. The unit cells possesses the highest symmetry present in the lattice (for example Cubic). Nonprimitive Unit Cell vs. Primitive Cell Primitive Cell Face-Centered Cubic (F) Unit Cell Rotated 90° The primitive cell is smaller or equal in size to the unit cell. The unit cells possesses the highest symmetry present in the lattice (for example Cubic). Index System for Crystal Planes (Miller Indices) 1) Find the intercepts on the axes in terms of the lattice constants a, b, c. The axes may be those of a primitive or nonprimitive unit cell. 2) Take the reciprocals of these numbers and then reduce to three integers having the same ratio, usually the smallest three integers. The result enclosed in parenthesis (hkl)9 is called the index of the plane. (200) (100) Miller Indices intercept length reciprocal cleared fraction Miller indice 1 1 1 1 1 1 1 1 1 1 1 1 (111) intercept length reciprocal cleared fraction Miller indice Miller Indices intercept length reciprocal cleared fiaction Miller indice 1 Ů0 \12 1 1 1 l lit 1 0 2 (102) intercept length reciprocal cleared fraction Miller indice plane A b plane B b 1 ŮO 1 1 l l CD 1 1 1 1 111 l 1 0 2 2 0 1 (102) (201) Crystals and Crystal Bonding • metallic (Cu, Fe, Au, Ba, alloys ) metallic bonding • ionic (NaCl, CsCl, CaF2,...) Ionic bonds, cations and anions, electrostatic interactions • covalent (diamond, graphite, Si02, A1N,...) atoms, covalent bonding • molecular (Ar, C60, HF, H20, organics, proteins ) molecules, van der Waals and hydrogen bonding Three Cubic Cells SC or Primitive (P) BCC (I) FCC (F) Table 2 Characteristics of cubic lattices0 Simple Bodv-ceiitered Face-centered Volum e , conventional cell fl3 a3 a3 Lattice points per cell 1 2 4 Volume, primitive cell fl3 U3 ia3 Lattice points per unit volume I/o3 %laz 4/a3 Number of nearest neighbors* 6 8 12 Nearest-neighbor distance a 3UV2 = O.8660 g/21'2 = 0,707a Number of second neighbors 12 6 6 Second neighbor distance 2vla a a Packing fraction1. I* JW5. ÍttV2 = 0.524 = 0.680 = 0.740 Cube a = edge d = face diagonl (d2 = a2 + a2 = 2a2) D = body diagonal (D2 = d2 + a2 = 2a2 + a2 = 3a2) D = V3-a SC = Polonium CN6 Space filling 52% BCC = W Z = 2 (b) Space filling 68% CN8 Fe, Cr, V, Li-Cs, Ba t-# f if1 Sř&V/ •? •• BCC FCC = Copper, Cu = CCP Z = 4 Space filling 74% CN12 Close Packing in Plane 2D (a) An "open" packing (b) Close packing 9UIT} 9UI12S 9ip ye r r r rTTTTTYTr*^» kiiAAÍAi>>Aa. Y Y Y T Y Y Y r t t r k. k A A A A. L £ i J i ř T T T T- T T t TY y : i ^aaaaAaaaa** Y Y Y Y Y Y V Y T r r A A * A A _A A A * * * Y Y r T r Y T r ^ * v * , A * A j í ítt-YÚÉ A A YYTY^Ť^TTTtt Y A A A A A A A ' Y Y T Y Y Y ' yS VASSSSSSSN dn330 9q ;ouu^3 S9joq 3 pue g Close Packing in Space 3D Close-packed layer of spheres (a) (b) (c) Hexagonal HCP Cubic CCP Side view hexagonal Top view of close-packed spheres Tetrahcdral holes (y) Octahedral holes ($) cubic Cover tetrahedral holes in layer B Cover octahedral holes in layer B Hexagonal close-packed Side view Cubic close-packed hexagonal A BA A (Jf ) B (( )( )) a lxj cubic C BA hexagonal cubic * / s m (a) (b) Mg, Be, Zn, Ni, Li, Be, Os, He, Sc, Ti, Co, Y, Ru hexagonal cubic Cu, Ca, Sr, Ag, Au, Ni, Rh, solid Ne-Xe, F2, C60, opal (300 nm) Structures with Larger Motifs BUCKMIN5TERFULLERENE FOOT & MOUTH VIRUS FCC BCC HEXAGONAL CLOSE-PACKING CUBIC Unit CLOSE-PACKING CeM ■ Face-Centred Cubic (FCC) Unit Cell a=b=c a=ß=7 =90° #4 .■■V.".' <■. -í;,---. ■!■■■ Cuboctahedron Coordination Polyhedrons Coordination Polyhedrons Space Filling a = lattice parameter Atom Radius, r Number of Atoms (lattice points), Z Space filling SC a/2 1 52% BCC V3a/4 2 68% FCC V2a/4 4 74% Diamond V3a/8 8 34% Type of Packing Packing Coordination Efficiency Number Simple cubic (sc) Body-centered cubic (bcc) Hexagonal close-packed (hep) Cubic close-packed (ccp or fee) 52% 68% 74% 74% S 12 12 CCP = FCC Close packed layers of CCP are oriented perpendicularly to the body diagonal of the cubic cell of FCC Periodic Table of Meiai Structures Li Na ® Ca1 Rb Cs © Ba Ce SS V Cr ftlrl Fe ©©©© ® SoaS ht> Mo Ta W (TcJ [Su] (Rh) ŕpd) (Ag) (Cd] In Sn Eu (S®®®®@® Q CCP Q HCP Q BCC Q he (4 H] other Two Types of Voids (Holes) 5 Tetrahedral hole 2 Octahedral hole r+ /v r+fv. Tetrahedral Holes T+ Octahedral Holes Tetrahedral Holes T- N cp atoms in lattice cell N Octahedral Holes 2N Tetrahedral Holes Two Types of Voids (Holes) Octahedral Holes Tetrahedral Holes Tetrahedral Holes (2N) Z = 4 number of atoms in the cell (N) N = 8 number of tetrahedral holes (2N) Octahedral Holes (N) Z = 4 number of atoms in the cell (N) N = 4 number of octahedral holes (N) Different Types of Radii Metallic radius 2 Cova lent radius 3 Ionic radius Variation of the electron density along the Li - F axis in LiF P - Pauling radius G - Goldschmidt radius S - Shannon radius. O F GS P CM 00 (DO ■ ■ » ■ oooo O Li Variation of ionic radii with coordination number 2.00 3 Ionic radius The radius of one ion was fixed to a reasonable value (r(02) = 140 pm) (Linus Pauling) That value is then used to compile a set of self consistent values for all other ions. 0.50 Variation of atomic radii through the Periodic table iA General trends for ionic radii 1. Ionic radii increase down a group. (Lanthanide contraction restricts the increase of heavy ions) 2. Radii of equal charge ions decrease across a period 3. Ionic radii increase with increasing coordination number the higher the CN the bigger the ion 4. The ionic radius of a given atom decreases with increasing charge (r(Fe2+) > r(Fe3+)) 5. Cations are usually the smaller ions in a cation/anion combination (exceptions: r(Cs+) > r(F~)) 6. Frequently used for rationalization of structures: „radius ratio" r(cation)/r(anion) (< 1) Cation/anion Radius Ratio rcation/anion ^ 'ueal rcation'ranion ~~ 'ueal nation "ani on ^ 'ueal Stable Stable Unstable CN r/R 12 - hcp/ccp 1.00 (substitution) 8 - cubic 0.732 -1.00 6 - octahedral 0.414 - 0.732 4 - tetrahedral 0.225 - 0.414 optimal radius ratio for given CN ions are in touch Limiting Radius Ratios CsCI 8:8 NaCI 6:6 ZnS 4:4 unit ce// unit caff 1/jh umt ce// cell side a face diagonal a-V2 body diagonal a-# I = 0.732 = 0.414 i 4 -aÍ2 =rY 4 x = 0.225 f A B ] R/ Vr \r1 "<@>" /r Vr\ R \ (c j, u j Structure Map Dependence of the structure type (coordination number) on the electronegativity difference and the average principal quantum number (size and polarizability) AB compounds 0 0.1 0.3 0.5 0.7 0.9 At 1.1 1.3 1.5 1.7 Lattice Enthalpy -o The lattice enthalpy change AH l [s the standard molar enthalpy change for the following process: M+(gas) + X"(gas) -» MX(solid) AH L Because the formation of a solid from a „gas of ions" is always exothermic lattice enthalpies (defined in this way) are usually negative. If entropy considerations are neglected the most stable crystal structure of a given compound is the one with the highest lattice enthalpy. Lattice enthalpies can be determined by a thermodynamic cycle —> Born-Haber cycle _____K+(g)+e-(g)+CI(g) 1122 A Born-Haber cycle for KCl 425 89 438 K+(g)+e-(g) + iCI2(g) -355 K+(g)+C|-(g) , K(g) + iCI^(g) K(s) + iCl^g) KCI(s) 5Z (all enthalpies: kJ mol-1 for normal conditions —» standard enthalpies) standard enthalpies of - formation: 438 - sublimation: +89 (K) - ionization: + 425 (K) - atomization: +244 (Cl2) - electron affinity: -355 (CI) - lattice enthalpy: x Born-Haber cycle o = -AHsluč° + AHsubl° + 1/2 D + IE + EA + L IE = 502 kJ mol Na(g) + CI (g) -i Na(g) + 1/2 Cl2 (g) Ä Na*(m+ Cl (») Vi D= 121 kJ mol -i Na(s) + 1/2 Cl2 (g) AH^u.^lOSkJinol-1 subl AH.i.i^-HlkJmo]-1 1 I EA = - 354 kJ mol Na+(g) + C|- standard enthalpies Lattice Enthalpy ^ ^coul ^ ^rep One ion pair Ecoul = (1/47I8o)ZAZB/d Erep=B/dn n = Born exponent (experimental measurement of compressibilty) Lattice Enthalpy 1 mol of ions Ecoui = NA (e2 / 4 7i s0) (zA zB / d) A Erep = NAB/dn 47T£0d ^ ^coul ^ ^rep Find minimum dL/d(d) = 0 Calculation of lattice enthalpies Coulombic contributions to lattice enthalpies y ab VAB: Coulomb potential (electrostatic potential) A: Madelung constant (depends on structure type) N: Avogadro constant z: charge number e: elementary charge s0: dielectric constant (vacuum permittivity) rAR: shortest distance between cation and anion Coulomb potential of an ion pair Madelung Constant Count all interactions in the crystal lattice Ecoul = (e2 / 4 7t s0)*(zA zB / d)*[+2(l/l) - 2(1/2) + 2(1/3) - 2(1/4) + ....] Ecoui = (e2/4 7is0)*(zAzB/d)*(21n2) / Madelung constant A (for linear chain of ions) = sum of convergent series Calculation of the Madelung constant 3D ionic solids: Coulomb attraction and repulsion Madelung constants: CsCl: 1.763 NaCl: 1.748 ZnS: 1.641 (wurtzite) ZnS: 1.638 (sphalerite) ion pair: 1.0000 (!) „ r 12 8 6 24 A = 6----T + —T----+ —T V2 V3 2 V5 = 1.748... (NaCl) (infinite summation) Madelung constant for NaCl Ecoui = (e2 / 4 ti s0) * (zA zB / d) * [6(1/1) - 12(1/V2) + 8(1/V3) - 6(1/V4) + 24(1/V5)....] convergent series Ecoul = (e2/47is0)*(zAzB/d)*^ Madelung Constants for other Structural Types Structural Type A NaCI 1.74756 CsCI 1.76267 CaF2 2.519 ZnS Sfalerite 1.63805 ZnS Wurtzite 1.64132 Born repulsion VBorn Lattice spacing Repulsion arising from overlap of electron clouds Because the electron density of atoms decreases exponentially towards zero at large distances from the nucleus the Born repulsion shows the same behavior approximation: B and n are constants for a given atom type; n can be derived from compressibility measurements (~8) Total lattice enthalpy from Coulomb interaction and Born repulsion AHi = Min.(VAB + VboJ (set first derivative of the sum to zero) AH0 = L z±z=e 2 1 -N(l—) Measured (calculated) lattice enthalpies (kJ mol-1): NaCl: -772 (-757); CsCl: -652 (-623) (measured from Born Haber cycle) The Kapustinskii equation Kapustinskii found that if the Madelung constant for a given structure is divided by the number of ions in one formula unit (v) the resulting values are almost constant: Structure Madel. const.(A) A/v Coordination CsCI 1.763 0.88 8:8 NaCI 1.748 0.87 6:6 CaF2 2.519 0.84 8:4 a-AI203 4.172 0.83 6:4 —» general lattice energy equation that can be applied to any crystal regardless of the crystal structure AHo 1.079 Wvz+z L r+ -r_ Most important advantage of the Kapustinski equation —» it is possible to apply the equation for lattice calculations of crystals with polyatomic ions (e.g. KN03, (NH4)2S04 ...). —» a set of „thermochemical radii" was derived for further calculations of lattice enthalpies Table 1.13 Thermochemical radii of polyatomic ions* Ion pm Ion pm Ion pm NHÍ 151 CIO4 226 MnOj- 215 Me4N+ 215 CN~ 177 or 144 phi 171 CNS- 199 OH~ 119 A1C1J 281 co§- 164 PtF26- 282 BF4 218 IOi" 108 ptci26- 299 BHJ 179 NJ 181 PtBr2,- 328 Br03- 140 NCCT 189 Ptß- 328 CH3COO- 148 NO^ 178 sor 244 CIOJ 157 N03~ 165 SeOj- 235 *J.E. Huheey (1983) Inorganic Chemistry, 3rd edn, Harper and Row, London, based on data from H.D.B. Jenkins and K.P . Thakur (1979)J Chem. Ed. , 56, 576. Lattice Enthalpy Born - Lande L = NAM ZaZbc2 47TSQd Born - Mayer Z Z e2 ( L = NAM A B AnsQd , \-d v d ) El. config. n He 5 Ne 7 Ar 9 Kr 10 Xe 12 d* = 0.345 Á Lattice Enthalpy Kapustinski M/v je přibližně konstantní pro všechny typy struktur v = počet iontů ve vzorcové jednotce M je nahrazena 0.87 v, není nutno znát strukturu z = l2lo3^ d ŕ 1- v 0,345 d \ J Kapustinski structure M CN stoichm Ml v CsCI 1.763 (8,8) AB 0.882 NaCI 1.748 (6,6) AB 0.874 ZnS sfalerite 1.638 (4,4) AB 0.819 ZnS wurtzite 1.641 (4,4) AB 0.821 CaF2 fluorite 2.519 (8,4) AB2 0.840 Ti02 rutile 2.408 (6,3) AB2 0.803 Cdl2 2.355 (6,3) AB2 0.785 Al203 4.172 (6,4) A2B3 0.834 v = the number of ions in one formula unit Lattice Enthalpy of NaCl Born - Lande calculation L = - 765 kJ mol-1 Only ionic contribution Experimental Born - Haber cycle L = - 788 kJ mol-1 Lattice Enthalpy consists of ionic and covalent contribution Applications of lattice enthalpy calculations: —» thermal stabilities of ionic solids —» stabilities of oxidation states of cations —» Solubility of salts in water —» calculations of electron affinity data —» lattice enthalpies and stabilities of „non existent" compounds Cation/anion Radius Ratio Stable Stable Unstable CN r/R 12 - hcp/ccp 1.00 (substitution) 8 - cubic 0.732 -1.00 6 - octahedral 0.414 - 0.732 4 - tetrahedral 0.225 - 0.414 Pauling Rules • Cation-Anion distance is determined by sums of ionic radii. Cation coordination environment is determined by radius ratio. • The bond valence sum of each ion should equal oxidation state. • Avoid shared polyhedral edges and/or faces, (particularly for cations with high oxidation state & low coordination number) • In a crystal containing different cations those with large valence and small coord, number tend not to share anions. • The number of chemically different coordination environments for a given ion tends to be small. Characteristic Structures of Solids = Structure Types Rock salt NaCl LiCl, KBr, AgCl, MgO, TiO, FeO, SnAs, UC, TiN,... Fluorite CaF, BaCl2, K20, Pb02... Lithium bismutide Li3Bi Sphalerite (zinc blende) ZnS CuCl, HgS, GaAs ... Nickel arsenide NiAs FeS, PtSn, CoS ... Wurtzite ZnS ZnO, MnS, SiC Rhenium diboride ReB2 Structure Types Derived from CCP = FCC all T CaF ZnS alio I/2 T(T+only) all O & T CCP NaCl Li3Bi Structure Types Derived from CCP = FCC Structure Types Derived from CCP = FCC Anions/c ell (= 4) Oct. (Max 4) Tet. (Max 8) Stoichio metry Compound 4 100% = 4 0 M4X4 = MX NaCl (6:6 coord.) 4 0 100% =8 M8X4 = M2X Li20 (4:8 coord.) 4 0 50% = 4 M4X4 = MX ZnS, sfalerite (4:4 coord.) 4 50% = 2 0 M2X4 = MX2 CdCl2 4 100% = 4 100% = 8 M12X4 = M3X Li3Bi 4 spinel 50% = 2 12.5% = 1 M3X4 MgAl204, Comparison between structures with filled octahedral and tetrahedral holes o/t fcc(ccp) hep all oct. NaCI N i As all tetr. CaF2 ReB2 o/t (all) Li3Bi (Na3As) (!) problem y2t sphalerite (ZnS) wurtzite (ZnS) y2o CdCI2 Cdl2 Fluorite CaF2 and antifluorite Li20 Fluorite structure = a face-centered cubic array (FCC) of cations = cubic close packing (CCP) of cations with all tetrahedral holes filled by anions = a simple cubic (SC) array of anions. Antifluorite structure = a face-centred cubic (FCC) array of anions = cubic close packing (CCP) of anions, with cations in all of the tetrahedral holes (the reverse of the fluorite structure). Fluorite (CaF2, antifluorite Li20) F/Li KJPtCU, Cs2[SiF6], [Fe(NH3)6][TaF6] 6J2 Fluorite structures (CaF2, antifluorite Li20) Oxides: Na20, K20, U02, Zr02, Th02 alkali metal sulfides, selenides and tellurides K2[PtCl6], (NH4)2[PtCl6], Cs2[SiF6], [Fe(NH3)6][TaF6]2. CaF2, SrF2 SrCL, BaF2, BaCL, CdF2 HgF2, EuF2, ß-PbF2 PbO, Li20, Li2S, Li2Se, Li2Te, Na20, Na2S, Na2Se, Na2Te, K20, K2S Sphalerite (zincblende, ZnS) Cubic close packing of anions with 1/2 tetrahedral holes filled by cations Sphalerite (zincblende, ZnS) Sphalerite ZnS Sphalerite (zincblende, ZnS) 13-15 compounds: BP, BAs, AIP, AlAs, GaAs, GaP, GaSb, AlSb, InP, InAs, InSb 12-16 compounds: BeS, BeSe, BeTe, ß-MnS (red), ß-MnSe, ß-CdS, CdSe, CdTe, HgS, HgSe, HgTe, ZnSe, ZnTe Halogenides: AgI, CuF, CuCl, CuBr, Cul, NH4F Borides: PB, AsB Carbides: ß-SiC Nitrides: BN Diamond Diamond cubic hexagonal Si02 cristobalite Si02 tridymite ice Cubic Diamond Diamond Structure C, Si, Ge, a-Sn (000)| j^^^^ Add 4 atoms to a FCC Tetrahedral bond arrangement Each atom has 4 nearest neighbors and 12 next nearest neighbors Elements of the 14th Group JÍÄ) d (g.cm ) c 3 566 3.515 si 5.431 2 329 Ge 5.6S7 5.323 a-Sn 6.489 7, £8 S Diamond Lattice (111) Hard Sphere Model Diamond Lattice (111) Hard Sphere Model Face Centered Cubic Lattice (111) Hard Sphere Model Wurzite, ZnS Hexagonal close packing of anions with 1/2 tetrahedral holes filled by cations Wurzite, ZnS ZnO, ZnS, ZnSe, ZnTe, BeO, CdS, CdSe, MnS, Agl, AIN Semiconductors of 13-15 and 12-16 type Structure of lll-V and ll-VI Compound Semiconductors Zinc blende Wurtzite Rock Salt, NaCl G--Q- et Cubic close packing of anions with all octahedral holes filled by cations Rock Salt, NaCl Rock Salt, NaCl Anion and cation sublattices Rock salt structures (NaCl) Hydrides: LiH, NaH, KH Borides: ZrB, HfB Carbides: TiC, ZrC, VC, UC *=*=# Nitrides: ScN, TiN, UN, CrN, VN, ZrN Oxides: MgO, CaO, SrO, BaO, TiO, VO, MnO, FeO, CoO, NiO Chalcogenides: MgS, CaS, SrS, BaS, a-MnS, MgSe, CaSe, SrSe, BaSe, CaTe Halides: LiF, LiCl, LiBr, Lil, NaF, NaBr, Nal, KF, KCl, KBr, KI, RbF, RbCl, RbBr, AgCl, AgF, AgBr Intermetallics: SnAs Other FeS2 (pyrite), CaC2 NiAs - type Hexagonal close packing of anions with all octahedral holes filled by cations NiS, NiAs, NiSb, NiSe, NiSn, NiTe, FeS, FeSe, FeTe, FeSb, PtSn, CoS, CoSe, CoTe, CoSb, CrSe, CrTe, CoSb, PtB (anti-NiAs structure) ReB2 - type Hexagonal close packing of anions with all tetrahedral holes filled by cations Li3Bi - type (anti BiF3) [Cr(NH3)6]Cl3, K3[Fe(CN)6] Li3Bi - type (anti BiF3) ••*=•* •• Fe3Al [Cr(NH3)6]Cl3 K3[Fe(CN)6] Cubic close packing of anions with all tetrahedral and octahedral holes filled by cations Active Y CsCl Primitive cubic packing of anions with all cubic holes filled by cations t í f "T / \ 2-Cs Q-Cl CsCl CsCl is not BCC CsBr, Csl, CsCN, NH4C1, NH4Br, T1C1, TIBr, Tli, CuZn, CuPd, LiHg Re03 SC of Re06 octahedra NaCl structure with 3/4 of cations removed and 1/4 of anions removed UO3, M0F3, NbF3, TaF3, Cu3N Perovskite, CaTi03 Two equvivalent views of the unit cell of perovskite Ti O Ca ° Cubic "close packing" of Ca and O with 1/4 octahedral holes filled by Ti cations Perovskite structure CaTiO TiCt - octahedra Ca012 - cuboctahedra (Ca2+ and 02~ form a cubic close packing) preferred structure of piezoelectric, ferroelectric and superconducting materials Perovskite, CaTi03 Cubic "close packing" of A and X with 1/4 octahedral holes filled by B cations Similarity to CsCl Perovskite, CaTi03 MgSiOs, CaSiOs KNb03, KTa03, KI03, NaNb03, NaW03, LaCo03; LaCr03, LaFe03, LaGa03, LaV03, SrTi03, SrZr03, SrFe03 ThTaN3, BaTa02N CN - stoichiometry Rule AxBy CN(A) / CN(B) = y / x Rutile, Ti02 Ti Distorted hexagonal close packing of anions with 1/2 octahedral holes filled by cations (giving a tetragonal lattice) Rutile, Ti02 Rutile Crystal Structure Ge02, Cr02, Ir02, Mo02, Nb02, ß-Mn02, Os02, V02 (>340K), Ru02, CoF2, FeF2, MgF2, MnF2 The rutile structure: TiO Ti06 - octahedra OTi3 - trigonal planar (alternative to CaF2 for highly charged smaller cations) The spinel structure: MgAl204 fee array of O2- ions, A2+ occupies 1/8 of the tetrahedral and B3+ 1/2 of the octahedral holes —» normal spinel: AB204 —> inverse spinel: B[AB]04(Fe304): Fe3+[Fe2+Fe3+]04 —» basis structure for several magnetic materials Spinel AB2X4 Spinel normal: Cubic close packing of anions with 1/2 octahedral holes filled by B cations and 1/8 tetrahedral holes by A cations MgAl204, CoAl204, MgTi204, Fe2Ge04, NiAl204, MnCr204 AB2X4 Spinel inverse: As for spinel but A cations and 1/2 of B cations interchanged MgFe204, NiFe204, Mgln204, MgIn2S4, Mg2Ti04, Zn2Ti04, Zn2Sn04, FeCo204. Garnets Naturally occuring garnets A3B2Si3012 = A3B2(Si04)3 A3 = divalent cation (Mg, Fe, Mn or Ca) dodecahedral B2 = trivalent (Al, Fe3+, Ti, or Cr) octahedral Si3 = tetravalent, tetrahedral Since Ca is much larger in radius than the other divalent cations, there are two series of garnets: one with calcium and one without: pyralspite contain Al (pyrope, almandine, spessartine) ugrandite contain Ca (uvarovite, grossular, andradite) Synthetic garnets A3B5012 A3 = trivalent cations, large size (Y, La,...) B5 = trivalent (Al, Fe3+, Ti, or Cr) 2B octahedral, 3B tetrahedral Y3A15012 Y3Fe5012 Garnets Pyrope Mg3Al2(Si04)3 Almandine Fe3Al2(Si04)3 Spessartine Mn3Al2(Si04)3 Uvarovite Ca3Cr2(Si04)3 Grossular Ca3Al2(Si04)3 Andradite Ca3Fe2(Si04)3 Garnet Y3A15012 Y3 = red - dodecahedral trivalent cations, large size Al5 = blue 2 octahedral 3 tetrahedral o12 Garnets Al, Al2 Layered Structures Cdl2 Hexagonal close packing of anions with 1/2 octahedral holes filled by cations CoI2, Fel2 Mgl2, Mnl2, Pbl2, Thl2, Til2, Tml2, VI2, Ybl2, Znl2, VBr2 TiBr2, MnBr2, FeBr2, CoBr2, TiCl2, TiS2., TaS2. CdCl2 Cubic close packing of anions with 1/2 octahedral holes filled by cations CdCl2, CdBr2 CoCl2, FeCl2, MgCl2, MnCl2, NiCl2, Nil2, ZnBr2, Znl2, Cs20* (anti-CdCl2 structure) Cdl2 Hexagonal close packing CdCl2 Cubic close packing CdCl2 Cubic close packing High Pressure Transformations zinc blende rock salt __ď i 1 ^-* 'ii \ [>--V i i ^A i ^p \_jr ^^l\ ^^5 c#^??f (lyi%2^0 •high pressure phases •higher density •higher coodination number •higher symmetry •transition to from nonmetal to metal •band mixing •longer bonds Pressure/Coordination Number Rule: increasing pressure - higher CN Pressure/Distance Paradox: increasing pressure - longer bonds X-ray structure analysis with single crystals <^&c^y / / COMPUTER o o o o o o o o o o o o o o p a 4 * / I \ \ I I » 1 PHASES rfJ focused to form an image. ' crystal) —->• O-1 Therefore they are intercepted and measured by a counting device or f f Ť x"raY sensitive film X-RAYS Principle of a four circle X-ray diffractometer for single crystal structure analysis CAD4 (Kappa Axis Diffractometer)