Crystal Structures of Interest

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Kelley Dickerson
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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

2 The ommon rystal Structures: ody-entered ubic () toms at the corners of a cube plus one atom in the center Is a ravais lattice, but drawn with 2 atoms/cell to show symmetry cc is not ideally close-packed losest-packed direction: <111> losest-packed plane: {110} ommon in lkali metals (K, Na, s) Transition metals (Fe, r, V, Mo, Nb, Ta) MSE 200

The Face-entered ubic (fcc) and Hexagonal lose-packed (hcp) Structures Fcc: atoms at the corners of the cube and in the center of each face Is a ravais lattice, but drawn with 4 atoms/cell to show

3 The Face-entered ubic (fcc) and Hexagonal lose-packed (hcp) Structures Fcc: atoms at the corners of the cube and in the center of each face Is a ravais lattice, but drawn with 4 atoms/cell to show symmetry Found in natural and noble metals: l, u, g, u, Pt, Pb Transition metals: Ni, o, Pd, Ir Hcp: close-packed hexagonal planes stacked to fit one another Does not have a primitive cell (two atoms in primitive lattice of hexagon) Divalent solids: e, Mg, Zn, d Transition metals and rare earths: Ti, Zr, o, Gd, Hf, Rh, Os MSE 200

4 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

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

5 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

6 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

7 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

8 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

9 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

10 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

11 Solid Solutions and ompounds Solid solution Solute distributed through solid Substitutional: solutes on atom sites Interstitial: solutes in interstitial sites Ordinarily small solutes (, N, O, ) Ordered solution (compound) Two or more atoms in regular pattern ( x y ) toms may be substitutional or interstitial on parent lattice ompound does not imply distinguishable molecules MSE 200

12 tomic Resolution Image of Gum Metal Gum metal : Ti-23Nb-0.7Ta-2Zr-1.2O MSE 200

13 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

14 Substitutional: sl parent Stoichiometric formula -atoms on edges -atoms in centers Either specie may be Found in: Ionic solids (sl) Small size difference R /R > to avoid like-ion impingement Intermetallic compounds uzn (ß-brass) MSE 200

15 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

16 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

17 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

18 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

19 Interstitial Sites: Octahedral Voids in cc rystals Octahedral voids in face center and edge center Located at {1/2,1/2,0} and {1/2,0,0} Octahedral voids in bcc are asymmetric Each has a short axis parallel to cube edge (O x, O y, O z ) Total of six octahedral voids, three of each orientation MSE 200

20 Interstitial Sites: Tetrahedral Voids in cc rystals Tetrahedral voids in each quadrant of each face Located at {1/2,1/4,0} 12/cell => 6/atom Tetrahedral voids in bcc are asymmetric MSE 200

21 cc Tetrahedral Interstitial: Α15 omplex derivative Stoichiometric formula 3 -atoms on bcc sites -atoms in 1/2 of tetrahedral voids Form chains in x, y, and z Found in: 15 compounds: Nb 3 Sn, Nb 3 l, Nb 3 Ge, V 3 Ga These are the type-ii superconductors used for wire in high-field magnets, etc. MSE 200

22 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

23 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

24 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

25 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

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

27 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

Solids. The difference between crystalline and non-crystalline materials is in the extent of ordering

Solids. The difference between crystalline and non-crystalline materials is in the extent of ordering Chapter 3 The Structure t of Crystalline Solids The difference between crystalline and non-crystalline materials is in the extent of ordering Both materials have the same composition but one is ordered