Objectives By the end of this section you should: recognise a range of basic crystal structures appreciate that a variety of important crystal structures can be described by close-packing be able to compare and contrast similar structures

Why? All crystal structures can be described by: unit cell + symmetry + atomic positions symmetry Unit cell (cubic)

Why? All crystal structures can be described by: unit cell + symmetry + atomic positions It is also helpful to be descriptive! Can use concepts of close packing, polyhedra, interstitials to compare structures Complex structures can be related back to basic ones Correlate with properties?

Example 1 – Diamond Structure Carbon atoms in all fcc positions Carbon atoms in half of tetrahedral positions (e.g. T+) Carbon coordinated to 4 other carbon atoms – all are tetrahedral Looking at tetrahedra in the structure helps us see the “diamond shape”

Diamond Structure Silicon, germanium and -tin also adopt this structure (all group 4 elements) Melting Point (ºC) Conductor? Carbon 3550 Insulator Silicon 1410 Semiconductor Germanium 940 -Tin 230 Conductor radius

Example 2 - Zinc Blende (ZnS: Sphalerite) Sulphur atoms in all fcc positions Zinc atoms in half of tetrahedral positions (e.g. T+) Comparison with Diamond Very important in semiconductor industry (e.g. GaAs) Ball and stick model shows us the 4-fold coordination in both structures

Example 3 – Fluorite/Antifluorite structure Antifluorite, Na2O Oxygen atoms in all fcc positions Sodium atoms in ALL tetrahedral sites Fluorite, ZrO2 Zr atoms in all fcc positions O atoms in ALL tetrahedral sites Note formulae: blue atoms (fcc) – 4 per unit cell red atoms (tetrahedral) – 8 per unit cell

Example 4 - Nickel Arsenide (NiAs) h.c.p. analogue of rocksalt structure h.c.p. arsenic with octahedral Ni c pointing towards us c pointing upwards

Coordination of As is also 6 but as a trigonal prism: In the c-direction, the Ni-Ni distance is rather short. Overlap of 3d orbitals gives rise to metallic bonding. The NiAs structure is a common structure in metallic compounds made from (a) transition metals with (b) heavy p-block elements such as As, Sb, Bi, S, Se.

Descriptions of Structures With ccp anion array: Rock salt, NaCl O occupied Zinc Blende, ZnS T+ (or T-) occupied Antifluorite, Na2O T+ and T- occupied With hcp anion array: Wurtzite, ZnS T+ (or T-) occupied With ccp cation array: Fluorite, ZrO2 T+ and T- occupied

Summary (see web pages)

Summary of AX structures  wurtzite ZnS  CN = 4  sphalerite NaCl, NiAs CN = 6 CsCl CN = 8 General trend is to get higher coordination numbers with larger (heavier) cations. This is seen also with AX2 structures

Summary of AX2 structures SiO2, BeF2 silica structure CN = 4 : 2 TiO2, MgF2 rutile structure CN = 6 : 3 CdCl2, CdI2 layer structure CN = 6 : 3 PbO2, CaF2 fluorite structure CN = 8 : 4 Compare: 1) Be, Mg, Ca fluorides 2) Si, Ti, Pb dioxides

Ionic radii and bond distances Ionic radii cannot be accurately “measured” - estimated from trends in known structures or from “electron density maps” (crystallography) (reference - Shannon, Acta Cryst. (1976) A32 751) Oxygen ion: r0 taken as 1.26 Å

Compromise PX3012 will return to this concept later in the course

Refs: Krug et al. Zeit. Phys Chem. Frankfurt 4 36 (1955) Krebs, Fundamentals of Inorganic Crystal Chemistry, (1968)

Summary Many important structures can be described by close packing with different interstitial sites filled Similar structures sometimes have similar properties (but see section 7) Comparison of structures can give important information on ionic radii (and trends).