Zeitschrift fur Kristallographie - Crystalline Materials

The CASTEP code for first principles electronic structure calculations will be described. A brief, non-technical overview will be given and some of the features and capabilities highlighted. Some features which are unique to CASTEP will be described and near-future development plans outlined.

CRYSTAL [1] computes the electronic structure and properties of periodic systems (crystals, surfaces, polymers) within Hartree-Fock [2], Density Functional and various hybrid approximations.

CRYSTAL was developed during nearly 30 years (since 1976) [3] by researchers of the Theoretical Chemistry Group in Torino (Italy), and the Computational Materials Science group in CLRC (Daresbury, UK), with important contributions from visiting researchers, as documented by the main authors list and the bibliography.

The basic features of the program CRYSTAL are presented, with two examples of application in the field of crystallography [4, 5].

SHELXE was designed to provide a simple, fast and robust route from substructure sites found by the program SHELXD to an initial electron density map, if possible with an indication as to which heavy-atom enantiomorph is correct. This should be understood as a small contribution to high-throughput structural genomics. The new sphere of influence algorithm combined with a fuzzy solvent boundary enables some chemical knowledge to be incorporated into the density modification in a general and effective manner. In the special cases of high solvent content (greater than 0.6) or very high resolution data (better than 1.5 Å) high quality maps can be produced. This raises the possibility of a new paradigm for atomic resolution structure refinement: instead of alternating atom parameter refinement with weighted electron density maps calculated with the phases of the current model, which inevitably leads to some model bias, all model building should be based on the model free experimental density map!

The crystal structure of Fe₄Al₁₃ was refined using single crystal diffractometer data: Pearson symbol mC102, space group C2/m; a = 15.492(2) Å, b = 8.078(2) Å, c = 12.471(1) Å, β = 107.69(1)°; R_F = 0.053, R_F (w) = 0.044 for 1127 reflections and 137 refined parameters. The coordination numbers of atoms are 9, 10. 11 for iron and 10, 12, 13, 14 for aluminium. The shortest interatomic distances are: Fe–Fe – 2.902 Å, Fe–Al – 2.374 Å, Al–Al – 2.533 Å. A preferred occupation of pentagonal prismatic coordinated positions by aluminium was found. The structural relationship between the Fe₄Al₁₃ structure and chemically homologous and homeotypical structures of aluminium and gallium containing systems with the 3d transition metals is discussed. The greatest similarity was found concerning the coordination polyhedra, especially that of transition metal atoms. The main common feature of these homeotypical structures is the presence of pentagonal “channels”, which is strongly dependent on the chemical composition. With increasing atomic number of the 3d transition metal, the stability range of these structures shifts to the transition metal-rich concentration. It is concluded that there is a connection between the occurrence of aluminium and gallium-containing decagonal and icosahedral phases and the existence of the infinite one-dimensional pentagonal channels in the intermetallic compounds showing a similar chemical composition.

The crystal structure of clinoptilolite has been worked out, based on C2/m, using two crystals from two different localities: one from Kuruma Pass, Japan, a = 17.660(4) Å, b = 17.963(5) Å, c = 7.400(3) Å, β = 116.47(3)°, and the other from Agoura, U. S. A., a = 17.662(4) Å, b = 17.911(5) Å, c = 7.407(3) Å, β = 116.40(3)°. In the tetrahedral framework of the heulandite type there are recognized four kinds of main cation positions, M(l), M(2), M(3), and M(4). At M(l) and M(2), which have so far been known as cation positions in the heulandite structure, Na and C'a are located ; M(l) tends to accommodate more Na than M(2). The new position, M(3), which is specific for K, is located almost at the center of the eight-membered ring of the channel parallel to a. This position is coordinated by six framework oxygen atoms and three water molecules. At M(4), which is octahedrally coordinated by six water molecules, Mg is located. It is very likely that these four positions are characteristic of all members of the heulandite-group zeolites. The difference between clinoptilolite and heulandite is primarily in the difference of site content: for clinoptilolite, M(l) and M(2) are rich in Na, while for heulandite, they are rich in Ca. The occupancy of K at M(3) in clinoptilolite is, in general, higher than that of heulandite. The location and coordination of K explain the evidence that the presence of K in the structure is one of the controlling factors of the thermal behaviour of the heulandite-group zeolites.

Hydrogen plays an extremely important role in the structure and chemistry of the oxide and oxysalt minerals. The characteristics of this role can be profitably analyzed in a simple and intuitive fashion using bond-valence theory. For any crystal structure, the structural unit may be defined as the strongly bonded part of the structure; structural units are linked together by interstitial species, usually alkali or alkaline earth cations and (H₂O)⁰ groups that are involved in much weaker bonding. This scheme gives a binary representation of even the most complex structure. The interaction between the structural unit and the interstitial species can be quantitatively evaluated using the valence-matching principle (Brown, 1981).

As components of the structural unit, (OH)⁻ and (H₂O)⁰ play a major role in dictating the dimensional polymerization of the structural unit because of the very asymmetric nature of the donor-hydrogen and hydrogen…acceptor interactions. As an interstitial component, (H₂O)⁰ can play three different roles. Interstitial (H₂O)⁰ may bond to an interstitial cation, essentially forming a complex cation. In this role, (H₂O)⁰ acts as a bond-valence transformer, moderating the Lewis acidity of the interstitial cations such that it matches the Lewis basicity of the structural unit and the valence-matching principle is satisfied. Interstitial (H₂O)⁰ need not bond to an interstitial cation to occupy well-ordered atomic positions; a stable hydrogen-bonded network can occur in the interstitial regions between structural units. The role of such (H₂O)⁰ is to satisfy the bond-valence requirements of H atoms that are part of the structural unit, propagating the bonding across the interstitial space to other parts of the structural unit. Occluded (H₂O)⁰ may occur in some minerals. Such (H₂O)⁰ is not bonded to interstitial cations and does not participate in a static ordered hydrogen-bond network. However, this type of (H₂O)⁰ will still affect many of the physical properties of a mineral.

The crystal structures of IrAl_2.75 (“Ir₂Al₅”) and RhAl_2.63 (“Rh₂Al₅”) phases have been studied with single crystal methods: space group P23, IrAl_2.75, a = 7.674(1) Å, Z = 8, R_F = 0.053 (457 hkl, 29 parameters) and RhAl_2.63, a = 7.6692(1) Å, R_F = 0.042 (684 hkl, 29 parameters). The unit cell contains three transition metal sites and five aluminum sites. Most aluminum sites reveal strong defects in the occupations, some of them are described as being split. The overall number of atoms in the unit cell is 30(1) for IrAl_2.75 and 29.0(3) for RhAl_2.63. Ordering and full occupation lead either to the AuZn₃ (space group Pm[unk]n) or to the hypothetical “Ir₄Al₁₃” structure (space group Pm[unk]).