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
Unit cell (cubic) symmetry Why? • All crystal structures can be described by: • unit cell + symmetry + atomic positions
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”
radius Diamond Structure Silicon, germanium and -tin also adopt this structure (all group 4 elements)
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, ZnST+ (or T-) occupied With ccp cation array: Fluorite, ZrO2 T+and T- occupied
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
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).