5 Some Important Crvstal Three Ways to Describe Crystal Structures Structi Why we need to know some ructure 。的小 Structural sketches of P,O, molecules Dion-stacking model: showing O= forms close packing and P (coordination polyhedron model: showing that the connection Gemstone How Can I Tell If My Diamond Is the Real Thing, Not Cubic ZrO2? Three simple way Synthetic ZrO, 2. Density test. Sapphire 3. Fog test Put the rock in front of your mouth and fog it like ou would try to fog a mirror. If it stays fogged for Diamond the heat instantaneously, so by the time you look Garnet Physical Properties of Crystals Form habit a Crystal form habit aForm: directly reflects the underlying atomic g Cleavage fracture structure(bonding, symmetry, etc ).Constant s Hardness interfacial angles a Specific gravity a Luster OHabit: the characteristic way the mineral C grows. Does not always conform to the form e.g e Streak nice perfect crystals, and depends of where grows and how made a Reaction to Acid 8 Other
1 5 Some Important Crystal Structures Why we need to know some important crystal structures? Three Ways to Describe Crystal Structures Three Structural sketches of P4O10 molecules: (a)Stick-ball model：showing that the P-O chemical bond is the tetrahedral coordination and sp3 covalent bonds. (b)ion-stacking model：showing O2- forms close packing and P5+ exists in tetrahedral interstitials. (c)coordination polyhedron model: showing that the connection of the tetrahedral coordination and tetrahedron, and the octahedral interstitials is unoccupied. I Gemstone Sapphire Garnet Topaz Synthetic ZrO2 Diamond Three simple ways: 1.X-ray diffraction. 2.Density test. 3.Fog test: Put the rock in front of your mouth and fog it like you would try to fog a mirror. If it stays fogged for 2-4 seconds, it’s a fake. A real diamond disperses the heat instantaneously ，so by the time you look at it, it has already cleared up. How Can I Tell If My Diamond Is the Real Thing, Not Cubic ZrO2 ? Physical Properties of Crystals Crystal form & habit Cleavage & fracture Hardness Specific gravity Luster Color Streak Taste Reaction to Acid Other… Form & Habit Form: directly reflects the underlying atomic structure (bonding, symmetry, etc.). Constant interfacial angles. Habit: the characteristic way the mineral grows. Does not always conform to the form e.g. nice perfect crystals, and depends of where grows and how made
2D Similarity of NaCl(111) and Urea(111) Epitaxy Growth of Crystal twhen epitaxy growth, both gas and liquid, the match of lattice parameter should be considered 2图包是出盐 For example, in preparation of conducting thin og 099 crystallized from the supersatura =3.82A),the substrate can be the single crystal slice: SrTiO(100).a=3.91A aortio of unres aue te growth slowe than that of NaCl (100) dn hydrothermal deposition of TiO, thin film aThe 2D similarity of crystal Si(100), the lattice parameter of TiO structure cause such phenomena. b=10917A,d12=2a(a=543A,2a=1 0, so grow TiOg thin film with high 112 orientation. Carbon Allotropes Graphite Carbon shows both Layer and Cage Networks Graphite&s 2各 Diamond Sphalerite (ZnS)vs Diamond Structure Diamond hybrid C Ta group strongest/hardest material 深x known shows us the 4-fold coordination in bot High thermal conductivity (unlike ceramics) structures Transparent in the visible and infrared with high index of refraction Semiconduct doped to make devices Metastable (transforms to see the“ diamond carbon when heated)
2 2D Similarity of NaCl(111) and Urea(111) (3 Cl- constitute equilateral triangle; 3 urea molecules constitute triangle. Compare the two triangles,the lateral length of the latter is twice that of the former. (octahedral NaCl crystal can be crystallized from the supersaturated solution of NaCl with urea. Absorption of Urea (111) on the NaCl (111) planes cause the growth rate of NaCl (111) rather slower than that of NaCl (100). (The 2D similarity of crystal structure cause such phenomena. Epitaxy Growth of Crystal When epitaxy growth, both gas and liquid, the match of lattice parameter should be considered. For example, in preparation of YBa2Cu3O7-d superconducting thin film, (a=3.88 Å, b=3.82 Å)，the substrate can be the single crystal slice: SrTiO3 (100), a=3.91 Å 。 In hydrothermal deposition of TiO2 thin film on Si(100), the lattice parameter of TiO2 : (a=5.354 Å, b=10.917 Å), d112=2asi,(a=5.43 Å, 2a=10.86 Å), so grow TiO2 thin film with high 112 orientation. Carbon shows both Layer and Cage Networks Carbon Allotropes Diamond Graphite Diamond sp3 hybrid C Td group One of the strongest/hardest material known High thermal conductivity (unlike ceramics) Transparent in the visible and infrared, with high index of refraction. Semiconductor (can be doped to make electronic devices) Metastable (transforms to carbon when heated) Sphalerite (ZnS) vs Diamond Structure Ball and stick shows us the 4-fold coordination in both structures Looking at tetrahedra in the structure helps us see the “diamond shape
Structures with the diamond framework reaction energy graphite(s)2 diamond (s) less dense more dense Diamond The diamond network with a single atom type The phase diagram The diamond network with alternate Zn &S 2atoms Reaction Energy vs Structure Pressure vs Structure reaction energy H2O(s 2 H2O( less dense more dense less dense more dense im chloride trueta reaction energy a-tin (s) z B-tin(s The transformation of (gray tin, diamond tetrahedral he rock salt to the structure stable below 13 c) accomplished at 298 K high P(10°atm Structures of Ionic Solids based on CCP Structures of ionic solid: Some Rules for Counting Atoms in a Unit Cell Ionic structures are prototypes for a wide range of solids entirely to that cell and counts as one atom Many of structures effectively described as close packed anions (occasionally cations)with 2. Face: An ion on a face is shared by two cells and nterstitial holes filled by cations(occasionally contributes y atom to the cell in question 3. Edge: An ion on an edge is shared by four cells and contributes 1 atom to the count 4. Corner. lon on a cornel cells and contributes 1/8 atom to the count
3 Structures with the Diamond Framework Diamond The diamond network with a single atom type Zinc Blende (ZnS) The diamond network with alternate Zn & S atoms The phase diagram for diamond and graphite (from J. Geophys. Res. 1980, 85, B12, 6930.) Reaction Energy vs Structure (gray tin, diamond structure, stable below 13oC) tetrahedral white tin Pressure vs Structure pressure + P - P The transformation of sodium chloride from the rock salt to the cesium chloride structure can be accomplished at 298 K at high P (~105 atm). pressure Structures of Ionic Solids Ionic structures are prototypes for a wide range of solids: Many of structures effectively described as close packed anions (occasionally cations) with interstitial holes filled by cations (occasionally anions). Some Rules for Counting Atoms in a Unit Cell 1.Body: An ion in the body of a cell belongs entirely to that cell and counts as one atom 2.Face: An ion on a face is shared by two cells and contributes ½ atom to the cell in question 3.Edge: An ion on an edge is shared by four cells and contributes ¼ atom to the count 4.Corner: An ion on a corner is shared by eight cells and contributes 1/8 atom to the count Structures of Ionic Solids based on CCP
Structures of lonic solids Structures of ionic solids Polyhedral Representations Some variations achieved by different filling of interstitial holes Defining the coordination environment of an ion as a 风回◆ 鄒灬 OCTAHEDRON l。T Structures of Ionic solids based on CCP Type and The rock salt structure Interstitial Hole Filling Hnlfoctahedral (Alternate 跚 Octahedral hole Rock salt structure in FCc structure Sodium chloride structure Structures of lonic solids based on ccp Cou Na+=6x+8x1/8 4 ions in cell C上=1+12x% 4 ions in cell NaF, NaBr, Nal Lix Kx, Rbx AgF, AgCl, AgBr, Mgo CaO, SrO, BaO, MnO, Coo, NiO, Cdo, NaH Mgs, Cas, SrS. BaS (=halides)
4 Polyhedral Representations Defining the coordination environment of an ion as a polyhedron Structures of Ionic Solids Polyhedral representations of structures by linking coordination polyhedra together Some variations achieved by different filling of interstitial holes Structures of Ionic Solids Formula Type and fraction of sites occupied CCP HCP All octahedral NaCl Rock Salt NiAs Nickel Arsenide AB Half tetrahedral (T+ or T-) ZnS Sphalerite ZnS Wurtzite AB2 All tetrahedral Na2O Anti-Fluorite CaF2 Fluorite not known AB3 All octahedral & tetrahedral Li3Bi not known Half octahedral (Alternate layers full/empty) A2B CdCl2 CdI2 Half octahedral (Ordered framework arrangement) TiO2 (Anatase) CaCl2 TiO2 (Rutile) A3B Third octahedral Alternate layers 2/3 full/empty YCl3 BiI3 Locations of Octahedral Holes in FCC Structure The Rock Salt Structure Rock Salt Structure Interstitial Hole Filling Structures of Ionic Solids based on CCP FCC Sodium Chloride Structure NaF, NaBr, NaI, LiX, KX, RbX, AgF, AgCl, AgBr, MgO, CaO, SrO, BaO, MnO, CoO, NiO, CdO, NaH, MgS, CaS, SrS, BaS (X=halides) Na+ = 6 x ½+ 8 x 1/8 = 4 ions in cell Cl- = 1 + 12 x ¼ = 4 ions in cell 1 ½ ½ ½ ½ ½ ½ 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ Structures of Ionic Solids based on CCP Counting Atoms
Structures of Ionic solids based on ccp Rock Salt(NaCD Structure Nearest(N and Next. Nearest (NN Neighbors 樂怒 NaCl CCP. O sites: 100% Motif: Cl at(0,0,0); Cs at (/z"z, 1p cScL CsCl Structures of ionic solids based on ccp Coordination:8-8(cubic) Adoption by chlorides, bromides and iodides of larger cations The Rock Salt Structure e.g. Cs*, TI. NH+ Coordination numl CN of each type of ion is 6 Cation cn Anion cn Structures of Ionic Solids based on CCP Structures of Ionic Solids based on CCP Fluorite structure CaF. /(Na,O Anti Fluorite) Rock Salt Structure-Summary oCCP CI with Nat in all Octahedral holes LAttice: FCC oMotif Clat(0.0.0): Na at(1.0.0 04Nacl in ur CCP Cas with F- in all Tetrahedral holes o Coordination: 6: 6(octahedraL) Motif. Ca=at(0,0,0); 2F-at(,. y,)&eg ye v2 OCation and anion sites are topologically HCaF, in unit cel identical In the netted Anti F ite s rudtutrt rc Anion positions are reversed
5 Nearest (N) and Next-Nearest (NN) Neighbors C N N N N N N NN NN NN NN NN NN NN NN NN NN NN NN Structures of Ionic Solids based on CCP Rock Salt (NaCl) Structure NaCl; CCP, O sites: 100% •Motif: Cl at (0,0,0); Cs at (1 / 2 , 1 / 2 , 1 / 2 ) •1CsCl in unit cell •Coordination: 8:8 (cubic) •Adoption by chlorides, bromides and iodides of larger cations, •e.g. Cs+ , Tl+ , NH4 + CsCl The Rock Salt Structure Coordination Numbers CN of each type of ion is 6 (6,6) coordination Cation CN Anion CN Structures of Ionic Solids based on CCP Rock Salt Structure ¾ Summary CCP Cl- with Na+ in all Octahedral holes Lattice: FCC Motif: Cl at (0,0,0); Na at (1/2 ,0,0) 4NaCl in unit cell Coordination: 6:6 (octahedral) Cation and anion sites are topologically identical Structures of Ionic Solids based on CCP CCP Ca 2+ with Fin all Tetrahedral holes Lattice: FCC Motif: Ca2+ at (0,0,0); 2F- at (1 / 4 , 1 / 4 , 1 / 4 ) & (3 / 4 , 3 / 4 , 3 / 4 ) 4CaF2 in unit cell Coordination: Ca 2+ 8 (cubic) : F- 4 (tetrahedral) In the related Anti-Fluorite structure Cation and Anion positions are reversed Structures of Ionic Solids based on CCP Fluorite structure CaF2 / {Na2O Anti-Fluorite}