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  1. Ionic Conductors: Characterisation of Defect Structure Lectures 1-4Introduction to Crystal ChemistryDr. I. AbrahamsQueen Mary University of London Lectures co-financed by the European Union in scope of the European Social Fund

  2. Crystal Chemistry What is crystal chemistry? The study of the structures of crystals including: Description and classification of crystal structures Factors that govern structure types adopted Structure prediction Structure-property relationships What is a crystal? A solid that shows a regularly repeating structure that can be characterised by a basic repeating unit known as a unit cell. Lectures co-financed by the European Union in scope of the European Social Fund

  3. Unit Cells Parallelepiped The unit cell is generally chosen as the smallest repeating unit with the highest symmetry. The unit cell, when repeated in 3D, must cover all the space in the crystal lattice. Different crystal structures have different unit cells. Unit cells are defined by six parameters in 3D. a, b, c are the unit cell edges and ,  and  are the inter-axial angles. (0 is the origin and its position is arbitrary). Lectures co-financed by the European Union in scope of the European Social Fund

  4. Crystal Systems There are seven crystal systems. These can be distinguished by the different unit cell shapes and their minimum intrinsic symmetry. Crystal system Unit cell shape Minimum symmetry Triclinic abc; 90 None Monoclinic 1 two fold axis or (standard setting) abc; ==90, 90 mirror plane Orthorhombic abc; ===90 3 two fold axes or mirror planes Tetragonal a=bc; ===90 1 four fold axis Trigonal 1 three fold axis (rhombohedral setting) a=b=c; ==90 (hexagonal setting) a=bc; ==90=120 Hexagonal a=bc; ==90=120 1 six fold axis Cubic a=b=c; ===90 4 three fold axes The symbol  used here refers to not necessarily equal to. In some cases there is accidental equivalence, but the minimum symmetry is not present. Lectures co-financed by the European Union in scope of the European Social Fund

  5. Fractional Coordinates The location of the origin is arbitrary, but is usually chosen to correspond to a point of symmetry. It need not be an atom position. Atoms positions can be defined with respect to the unit cell using fractional coordinates x, y, z x = X/a where X is the distance parallel to the a-axis y = Y/b where Y is the distance parallel to the b-axis z = Z/c where Z is the distance parallel to the c-axis Lectures co-financed by the European Union in scope of the European Social Fund

  6. Introduction to Crystal Chemistry There are many crystalline solids, but only a few basic structures. Many simple structures can be visualised in terms of close packing of identical spheres, in some case with smaller spheres in the spaces between the close packed spheres. Atoms or ions can be regarded as “squashy” spheres. The squashy character is a result of polarisation of the electronic cloud surrounding these atoms or ions. Different compounds with the same structure have the same geometry, but different size, i.e. different ionic radii and bond lengths. Lectures co-financed by the European Union in scope of the European Social Fund

  7. e.g. NaCl, MgO, LiI, TiC all exhibit the rocksalt structure For compounds that adopt the rocksalt structure there is no direct correlation between structure and bonding, i.e. the rocksalt structure is adopted by ionic and covalent compounds. Lectures co-financed by the European Union in scope of the European Social Fund

  8. Close Packing (cp) Identical spheres can pack in a number of ways. The closest way is known as close packing. Consider some arrays of identical spheres. cp, CN = 2 cp, CN = 6 1-D 2-D Lectures co-financed by the European Union in scope of the European Social Fund

  9. 3-D cp, CN = 12 Lectures co-financed by the European Union in scope of the European Social Fund

  10. Hexagonal and Cubic Close Packing There are two types of 3-D close packed arrays. Hexagonal close packing hcp ABA….. Cubic close packing ccp ABC… A A B B A C Lectures co-financed by the European Union in scope of the European Social Fund

  11. hcp and ccp Unit Cells Like all crystalline solids hcp and ccp based solids can be described by unit cells. hcp ccp Lectures co-financed by the European Union in scope of the European Social Fund

  12. Non-Close Packed Arrays Compare two similar 2-D arrays. 2-D 2-D cp, CN = 6 Non-cp, CN = 4 Lectures co-financed by the European Union in scope of the European Social Fund

  13. 3D Non-Close Packed Arrays Body centred cubic (bcc) packing is a non-close packed array. bcc CN = 8 Packing density Even in close packed arrays there are spaces between the spheres. A measure of how closely packed spheres are is the packing density e.g in ccp Lectures co-financed by the European Union in scope of the European Social Fund

  14. Packing Density Look at a single unit cell face in ccp. Diameter of sphere = 2r  face diagonal = 4r Packing Density hcp 74% ccp 74% bcc 68% Therefore the maximum packing density for identical spheres is 74% for a cp array Lectures co-financed by the European Union in scope of the European Social Fund

  15. Metals Metal atoms can be considered to be spherical and adopt structures that exhibit high coordination numbers in order to achieve maximum overlap of atomic orbitals. Metallic elements In metallic elements since all atoms are of the same type and size ccp, hcp and bcc packing are typically adopted. However, it should be noted that in some cases although a cp geometry is adopted the packing density may be lower than 74% i.e. not truly close packed. eg ccp Ag, Au, Fe, Pb hcp Be, Co,Mg bcc Ba, Cr, K Lectures co-financed by the European Union in scope of the European Social Fund

  16. Alloys Metallic compounds with more than one atom type . If the atom sizes are similar then as with metallic elements ccp, hcp or bcc structures are adopted. e.g Cu:Au Alloy disordered ccp Note at certain compositions Cu and Au can order over the lattice. Lectures co-financed by the European Union in scope of the European Social Fund

  17. Interstitial Sites In order to describe inorganic compounds using close packing it is first necessary to describe the interstitial sites present in a cp array. There are two important types of interstitial site 1. Tetrahedral sites Consider atoms from just two cp layers. Spheres in the top layer fit into dips between 3 spheres in the bottom layer and vice versa. This gives a tetrahedral interstitial site. There are two types of tetrahedral interstitial site T+ T (pointing up) (pointing down) A tetrahedron has 4 faces and 6 edges Lectures co-financed by the European Union in scope of the European Social Fund

  18. Interstitial Sites - Tetrahedra Number of T+ sites = Number of T sites The tetrahedral sites do not lie strictly between the cp layers. T+ in layer below T in layer above The maximum radius rT of a sphere in a tetrahedral site is given by rT = rcp  0.225 Where rcp is the radius of the close packed sphere. Lectures co-financed by the European Union in scope of the European Social Fund

  19. Interstitial Sites - Octahedra 2. Octahedral sites Where dips in the top and bottom layers coincide we get an octahedral site. An octahedron has 8 faces and 12 edges. The maximum radius rO for an atom to fit into an octahedral site is rO = rcp 0.414 i.e. much bigger than a tetrahedral site. Lectures co-financed by the European Union in scope of the European Social Fund

  20. Location of interstitial sites in cp unit cells 1. hcp Octahedral Tetrahedral Lectures co-financed by the European Union in scope of the European Social Fund

  21. 2. ccp Tetrahedral Octahedral Lectures co-financed by the European Union in scope of the European Social Fund

  22. Close packing described by polyhedra One can view cp structures as built up from polyhedra (representing the interstitial sites) that share faces, edges or corners. Using this type of representation (a) The centre of the polyhedron represents the interstitial site (b) The corner of the polyhedron represents the cp atom Polyhedral representations are very important as they emphasize the CN of the interstitial ions, their relative positions and linkage. Lectures co-financed by the European Union in scope of the European Social Fund

  23. Interstitial sites in cp structures 1. hcp Interstitial sites between cp layers 1 and 2, and 2 and 3 are identical and stacked one above the other resulting in mirror symmetry about B. (a) Octahedra Octahedra share faces perpendicular () to cp planes Octahedra share edges parallel (  ) to cp planes Results in columns of octahedra perpendicular to cp planes. Lectures co-financed by the European Union in scope of the European Social Fund

  24. (b) Tetrahedra Tetrahedra share faces and corners  to cp layers Tetrahedra share edges  to cp layers T+ shares a face with T in layer below Tshares a face with T+ in layer above T+ shares edges with T within cp layer Tshares edges with T+ within cp layer (c) Inter-polyhedral linkages Octahedra and tetrahedra share faces within cp layer. T+ and T sharing faces gives a trigonal bipyramidal site CN = 5 Unique to hcp. Lectures co-financed by the European Union in scope of the European Social Fund

  25. 2. ccp Orientation of layers 1 and 2 and 2 and 3 now different. Octahedra are not above octahedra Tetrahedra are not above tetrahedra. Octahedra share only edges  to cp planes Octahedra share only edges  to cp planes Tetrahedra share only edges  to cp planes Tetrahedra share only edges  to cp planes T+ shares edges with T only Tshares edges with T+ only Comparison of oct and & tet linkages in hcp and ccp Oct shares face with oct in hcp only Tet shares faces with tet in hcp only Lectures co-financed by the European Union in scope of the European Social Fund

  26. Interstitial Sites Summary Lectures co-financed by the European Union in scope of the European Social Fund

  27. Important Inorganic Structures Based on cp Many inorganic structures are based on close packing of spheres and can be described by close packing of one ion sublattice with counter ions in all or part of the interstitial sites. While these structures are not truly close packed (i.e. the ions do not touch each other), their geometry can be described as close packed. In the case of ionic conducting inorganic solids, many adopt ordered or disordered forms of the classic inorganic structural types. Lectures co-financed by the European Union in scope of the European Social Fund

  28. ccp Based Structures 1. Cubic close packed structures (a) Li3Bi Li3Bi is an intermetallic compound and can be described as ccp Bi with Li in all the octahedral and tetrahedral sites. The Li3Bi structure therefore shows the complete filling of all interstitial sites. Lectures co-financed by the European Union in scope of the European Social Fund

  29. (b) NaCl ccp Cl with Na+ in all the octahedral sites. ccp Cl at corners and face centres of unit cell Na+ in oct sites at centre of cube and mid point of each edge. NB Tet sites empty Clcp planes are  to body diagonal. NaCl6 oct share all 12 edges with other NaCl6 oct. NaCl6 oct share faces with empty tet sites. Unit cell NaCl6 oct Shared edge Lectures co-financed by the European Union in scope of the European Social Fund

  30. Radius ratio Remember maximum ratio for octahedral coordination in cp system is 0.414 Therefore Cl ions in NaCl are not close packed, but do have cp geometry with an fcc unit cell. Note each Cl is surrounded by 6 Na+ ions (and each Na+ is surrounded by 6 Cl ions). Many binary compounds exhibit the rocksalt structure. All are isostructural, but have different properties and bonding. Lectures co-financed by the European Union in scope of the European Social Fund

  31. Lectures co-financed by the European Union in scope of the European Social Fund

  32. (c) Zinc blende or sphalerite (ZnS) ccp S2 with Zn2+ in half the tet sites. Tet sites all T+(or T) avoiding edge sharing. Each S2 is surrounded by 4 Zn2+ and each Zn2+ surrounded by 4 S2. ZnS C (diamond) Si Many other structures can be derived from zinc blende GaAs GaP Lectures co-financed by the European Union in scope of the European Social Fund

  33. (d) Fluorite (CaF2) ccp Ca2+ with F in all the tet sites. (Oct empty). Both T+ and T occupied. Therefore tet share edges and corners, but Ca2+ large and not cp.  tet centres are far apart. Total 4 Ca2+ per cell and 8 F per cell  Ca:F = 1:2 i.e. CaF2 CaF8 = cubic coordination Antifluorite ccp anions with cations in all tet sites. e.g. Na2O Lectures co-financed by the European Union in scope of the European Social Fund

  34. hcp based structures 2. Structures based on hcp (a) Nickel Arsenide (NiAs) hcp As with Ni in all the oct sites. (tet empty). Ni at 2/3, 1/3, 1/4 and 2/3, 1/3, 3/4 Lectures co-financed by the European Union in scope of the European Social Fund

  35. NiAs6 octahedra AsNi6 also 6 coordinate but not oct (trigonal prismatic) Each NiAs6 oct shares 2 faces with other NiAs6 oct resulting in columns of face sharing oct. NiAs is the hcp analogue of NaCl(ccp), but with face sharing. NaCl: Na+ Na+ repulsions favour ccp. NiAs: Ni2+Ni2+ repulsion reduced due to covalence and Ni-Ni bonding  hcp favoured. Structure adopted by FeS, NiS and CoS Lectures co-financed by the European Union in scope of the European Social Fund

  36. (b) Wurtzite (ZnS) hcp S2 with Zn2+ in half the tet sites. (Oct empty). Zn2+ on edges 0,0,5/8 Zn2+ in cell at 1/3, 2/3, 1/8 Lectures co-financed by the European Union in scope of the European Social Fund

  37. Only T+ or T occupied. Avoids tet sharing faces which is energetically unfavourable. Also avoids tet sharing edges. ZnS4 tet corner sharing only SZn4 also tet ZnS either wurtzite or zinc blende Both tet ZnS4 Both corner share Wurtzite more ionic Lectures co-financed by the European Union in scope of the European Social Fund

  38. Layered structures (a) CdCl2 and CdI2 The structures of CdCl2 and CdI2 can be described as being based on ccp and hcp halide lattices respectively with Cd2+ filling octahedral sites in alternate layers. This results in layered compounds with alternate layers held together by van der Waals forces. In both structures CdX6 octahedra share edges with other octahedra in same layer Cdl2 CdCl2 Lectures co-financed by the European Union in scope of the European Social Fund

  39. (b) CrCl3 and BiI3 The structures of CrCl3 and BiI3 can be described as being based on ccp and hcp halide lattices respectively. In both structures 1/3 of the available oct sites are occupied. 2/3 of the oct sites in alternate layers are filled by cations resulting in layered structures. Each octahedron shares edges with 3 other octahedra within a layer. Lectures co-financed by the European Union in scope of the European Social Fund

  40. Other Important Structures (a) Rutile (TiO2) Essentially distorted hcp O2 with Ti4+ in half the oct sites. Every alternate octahedron is filled resulting in chains of edge sharing TiO6 octahedra. Columns of octahedra with alternate columns empty. Columns corner share with neighbouring columns. The columns run parallel to the cp layers OTi3 trigonal planar O2 coordination. Other examples MnO2, SnO2, CrO2, MnF2. Lectures co-financed by the European Union in scope of the European Social Fund

  41. (b) Corundum (-Al2O3) hcp O2 with Al3+ in 2/3 of the oct sites. Al3+ displaced resulting in distorted tet coordination for O2. Corundum is noted for its hardness. Doping with Cr or Ti results in the gemstones ruby and sapphire. Other examples Ti2O3 V2O3 Cr2O3 Ga2O3. Lectures co-financed by the European Union in scope of the European Social Fund

  42. (c) ReO3 ccp O2 with ¼ of the O2 ions missing. Re6+ locate in ¼ of the the octahedral sites. The resulting structure is a 3-dimensional array of corner sharing ReO6 octahedra. Each ReO6 octahedron shares all six corners with other ReO6 octahedra and linear Re-O-Re linkages. Other examples ScF3 NbF3 TaF3 MoF3 Lectures co-financed by the European Union in scope of the European Social Fund

  43. (d) Perovskite (CaTiO3) Closely related to ReO3..A ccp array of O2 with ¼ of the O2 ions missing. Ti4+ located in ¼ of the the octahedral sites. Ca2+ is located in the oxide ion vacancy. TiO6 octahedra share corners to give the 3-D framework, with Ca2+ in essentially a 12 CN site. However distortion lowers the coordination number to 8. Lectures co-financed by the European Union in scope of the European Social Fund

  44. (e) Spinel (MgAl2O4) ccp array of O2 with Al3+ located in 1/2 of the the octahedral sites and Mg2+ in 1/8 of the tetrahedral sites. The structure consists of columns of edge sharing octahedra which share edges with parallel columns. The tetrahedra share corners with the octahedra. Inverse spinel Fe2MgO4 adopts an inverse spinel structure. With half the Fe ions (Fe3+) in tetrahedral sites and the other half in octahedral sites with Mg2+. Lectures co-financed by the European Union in scope of the European Social Fund

  45. Lectures co-financed by the European Union in scope of the European Social Fund

  46. Lectures co-financed by the European Union in scope of the European Social Fund