Crystal Structures of Interest

Transcription

1 rystal Structures of Interest Elemental solids: Face-centered cubic (fcc) Hexagonal close-packed (hcp) ody-centered cubic (bcc) Diamond cubic (dc) inary compounds Fcc-based (u 3 u,nal, ß-ZnS) Hcp-based (α-zns) cc-based (sl, Nb 3 Sn) MSE 200 Everything else

2 fcc and hcp from Stacking lose-packed Planes MSE 200 There are two ways to stack spheres The sequence creates hcp The sequence creates fcc = hcp The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may = fcc

3 Hexagonal lose-packed HP does not have a primitive cell 2 atoms in primitive cell of hexagonal lattice 6 atoms in cell drawn to show hexagonal symmetry ommon in Divalent elements: e, Mg, Zn, d Transition metals and rare earths: Ti, Zr, o, Gd, Hf, Rh, Os nisotropy limits engineering use of these elements MSE 200

4 Face-entered ubic Structure stacking Fcc cell View along diagonal (<111>) F is cubic stacking of close-packed planes ({111}) 1 atom in primitive cell; 4 in cell with cubic symmetry <110> is close-packed direction ommon in Natural and noble metals: u, g, u, Pt, l, Pb Transition metals: Ni, o, Pd, Ir MSE 200

5 Interstitial Sites: Octahedral Voids in fcc Octahedral interstitial site is equidistant from six atoms Octahedral void Located at {1/2,1/2,1/2} and {1/2,0,0} There are 4 octahedral voids per fcc cell One per atom MSE 200

6 Interstitial Sites: Tetrahedral Voids in F Tetrahedral site is equidistant from four atoms tetrahedral void Located at {1/4,1/4,1/4} - center of cell octet There are 8 tetrahedral voids per fcc cell Two per atom MSE 200

7 Interstitial Sites: Voids between lose-packed Planes In both F and HP packing: Tetrahedral void above and below each atom (2 per atom) Octahedral void in third site between planes Stacking including voids: Fcc:...(aa)c(bb)a(cc)b(aa) Hcp:...(aa)c(bb)c(aa) (octahedral voids all on c-sites) Size and shape of voids are the same in fcc and hcp MSE 200

8 The Diamond ubic Structure Fcc plus atoms in 1/2 of tetrahedral voids lose-packed plane stacking is...abc or... abc... Each atom has four neighbors in tetrahedral coordination Natural configuration for covalent bonding D is the structure of the Group IV elements, Si, Ge, Sn (grey) re all semiconductors or insulators MSE 200

9 inary ompounds: Examples Substitutional: cc: sl Fcc: u 3 u Interstitial: Fcc octahedral: Nal Fcc tetrahedral: ß-ZnS Hcp tetrahedral: α-zns cc tetrahedral: Nb 3 Sn (15) MSE 200

10 F Substitutional: u 3 u F parent Stoichiometric formula 3 -atoms on edges -atoms on faces Found in: Intermetallic compounds (u 3 u) s sublattice in complex ionics E.g., perovskites atio 3 (ferroelectric) Ya 2 u 3 O 7 (superconductor) Lattices of + and - ions must interpenetrate since like ions cannot be neighbors MSE 200

11 F Octahedral Interstitial: Nal F parent Stoichiometric formula -atoms on fcc sites -atoms in octahedral voids Either can be Found in: Ionic compounds: Nal, MgO (R /R ~ 0.5) Perovskites (substitutional ordering on both sites) Metallic compounds arbonitrides (Ti, TiN, Hf) MSE 200

12 F Tetrahedral Interstitial: ß-ZnS inary analogue of D Stoichiometric formula -atoms on fcc sites -atoms in 1/2 of tetrahedral voids abc Either element can be Found in: ovalent compounds: Gas, InSb, ß-ZnS, N Ionic compounds: gl Large size difference (R /R <.414) MSE 200

13 Hcp Tetrahedral Interstitial: α-zns Hexagonal analogue of ß-ZnS Stoichiometric formula -atoms on hcp sites -atoms in 1/2 of tetrahedral voids abab Either element can be Found in: ovalent compounds: ZnO, ds, α-zns, Lonsdalite Ionic compounds: Silver halides Large size difference (R /R <.414) MSE 200

14 Description of omplex rystal Structures Most crystals can be referred to a close-packed frame Fcc or hcp network Possibly plus small distortions along symmetry axes ubic tetragonal (edge unique), ubic rhombohedral (diagonal unique) toms in ordered configurations in Substitutional sites Interstital sites: octahedral or tetrahedral Vacancies are useful as atoms to complete the configuration MSE 200

15 Hierarchical Description of omplex rystal Structures onstruct planar layers Network (fcc or hcp) Interstitial planes that contain atoms Identify ordered pattern Primary and interstitial planes Pattern is the same on all planes Including vacancies, if necessary, as species Order layers Physical pattern (fcc or hcp) hemical pattern composition may change from layer to layer (differentiation) Stacking pattern is the same for network and interstitial layers MSE 200

16 Representation of rystal Structures The basic pattern is L t o t L at 0, 1/4, 1/2, 3/4, 1) F: b c a c a b a b c HP: b c a a c b b c a Levels of representation 1 - planar order: X, XY. X 2 Y, X 3 Y 2 - interstitial character: octahedral, tetrahedral(1,2) 3 - stacking pattern: fcc, hcp, polytypic, hexagonal 4 - differentiation: undifferentiated, differentiated MSE 200

17 Substitutional X-ompounds Undifferentiated ll atoms are the same: fcc, hcp, polytypes (e.g., ) Differentiated Planes of atoms alternate: upt, W Note that cubic symmetry is broken in upt: rhombohedral ^ ^ ^ ^ ^ ^ = u = Pt = W = MSE 200

18 Octahedral Interstital X-ompounds = Na = l = s = Ni Undifferentiated Fcc or hcp planes alternate with filled octahedral planes: Nal, Nis Note that o-sites in Nis are ccc, can tell which atom is in octahedral hole Differentiated lternate lattice or interstitial planes differ di 2 : like Nis but octahedral d planes alternate with vacant planes MSE 200

19 Tetrahedral(I) X-compounds = Zn = S = Zn = S Lattice planes plus one plane of tetrahedral voids Examples: Unary: diamond cubic, hexagonal diamond (Lonsdaleite) inary: α-zns, β-zns MSE 200

20 Tetrahedral(II) X-ompounds = a = F Lattice planes plus planes on both tetrahedral sites Fcc-based: af 2 (flourite) and Li 2 O Hcp-based: none known MSE 200

21 Distributions of XY in a plane XY: 3 basic patterns Label I, II, III X 2 Y: 1 basic pattern X 3 Y: 2 basic patterns Label I, II MSE 200

22 inary (XY) Patterns in a Plane XY(I) (common) Note: all planes in the stacking have the same type of order. MSE 200 XY(II) XY(III)

23 Substitutional XY undifferentiated = u = u Only known example is fcc-based uu(i) Has the XY(I) pattern in every plane reates structure in which u, u fill alternate (100) planes ubic symmetry lost: tetragonal MSE 200

24 Differentiated Substitutional XY = u = Pt Fcc example: upt 3 upt planes in XY(I) order alternate with Pt planes Note Pt plane has XY(I) pattern with X=Y Stacking: (upt)(pt)(upt)(pt)(upt)(pt) ubic symmetry broken: rhombohedral No hcp-based examples MSE 200

25 F-based Octahedral XY = Fe = N (Fe,Ni) 2 N Fcc solution of Fe and Ni XY(I) pattern of N and on octahedral layers ubic symmetry broken: tetragonal MSE 200

26 HP-based Octahedral XY Many MO 2 oxides are hcp O on hcp sites M on octahedral planes M alternates to fill all sites Pattern c 1 c 2 TiO 2 å - PbO 2 = O at -sites 0,1 = O at -sites (1/2) = M at c1 sites (1/4) = M at c2 sites (3/4) FeO(OH) Examples: TiO 2 (rutile) = Ti in XY(I), O on HP sites α-pbo 2 = Pb in XY(II) FeO(OH) (geothite) = Fe in XY(III), O and (OH) planes alternate MSE 200

27 X 2 Y Pattern Note that 2 d unit cell contains three atoms ell outlined in red Requires three planes for symmetric coverage of sites MSE 200

28 Octahedral X 2 Y: orundum nalogue of Nis X 2 Y order in the plane Examples: l 2 O 3 FeTiO 3 MSE 200 c 1 c 2 c 3 c 1 Note 6-layer repeat pattern

29 Most ommon X 3 Y Pattern Note that 2 d unit cell contains four atoms MSE 200

30 Octahedral X 3 Y Perovskite Perovskite: atio 3 lso Fe 4 N, Fe 8 N, Ni 4 N lso YO and other oxide superconductors MSE 200

31 Defects in rystals Imperfections are present in all real crystals Often, they are added to control properties Materials engineering is largely defect engineering lassify defects by dimension Point defects: solute atoms (strength, conductivity) Line defects: dislocations (plastic deformation) Surface defects: external surface (crystal shape) Volume defects: voids, inclusions (fracture) MSE 200