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Summary. Thermal expansion data up to 920 ~ C by powder X-ray diffraction methods are presented for four noseans, five haiiynes, and one sodalite. The rate of thermal expansion is at first high and increases with temperature ; this is interpreted as due to the untwisting of the partially collapsed framework. Above a certain temperature (which depends on the mineral and its composition) the rate of thermal expansion is much lower and is linear with temperature; this corresponds to the rate of thermal expansion of the more fully expanded framework. Sodalite does not show this second stage below 920 ~ C. The thermal expansion behaviour of other framework silicates is interpreted in analogy to that of the sodalite group. THE thermal expansion behaviour of the framework silicates poses interesting problems. Consisting essentially of a partially covalently bonded three-dimensional framework, they might be expected to have low thermal expansion rates. Unfortunately, there has been little detailed work on the thermal expansion of framework silicates, apart from the silica minerals and the feldspars. The simple picture of a three-dimensional framework is complicated by the fact that their frameworks show varying degrees of collapse at room temperature, which depend on the interframework ions (except for silica), A detailed study of the thermal expansion of the sodalite group of minerals might be expected to give a general understanding of the thermal expansion of framework silicates.The members of the sodalite group of minerals have essentially the same aluminosilicate framework (A16Si6024). Dependent on whether chlorine or sulphate is the predominant interframework anion, the common rock-forming sodalite minerals can be divided into sodalite proper (NasA16Si60~4Cl~) and the nosean-hafiyne solid solution series (Nas_sK0_lCa0_2[~o_l)s(AlsSi~024)(S04)l_ 2 . nH~O. According to Taylor (1967) haiiyne possesses the space group P43n and is richer in calcium and sulphate than nosean, which possesses the space group P43m. The specimens used in this study are taken from the series of sodalite i Present address: Doulton Research Limited, Hanworth Lane, Chertsey, Surrey.

The structural relations of solid solutions in the series (Sr1−xBax)Al2O4 were studied using room- and high-temperature X-ray methods, infra-red spectroscopy, and DTA. At room temperature, SrAl2O4 and solid solutions with x up to 0.31 are monoclinic, between x = 0.31 and 0.43 monoclinic and hexagonal forms coexist, and between x = 0.43 and 1.0 only hexagonal forms occur. On heating, a member of the monoclinic series of solid solutions transforms to hexagonal symmetry over a range of temperature within which both monoclinic and hexagonal forms coexist. The proportion of the hexagonal form increases instantaneously as the temperature is raised. The transformation temperature decreases with increasing BaAl2O4 in solid solution and, in addition, the temperature width of the region of coexistence is markedly enlarged. SrAl2O4 transforms over the range 665–705 °C and (Sr0.7Ba0.3)Al2O4 over 170–405 °C. The DTA trace for SrAl2O4 shows a peak at 677 °C. On cooling, the transformations show hysteresis of 15 to 25 °C.The coexisting monoclinic and hexagonal forms are believed to be isochemical, and discontinuities in cell parameters occur within the region of coexistence both in the compositional series at room temperature and in the elevated temperature transformation experiments. The low-to-high transformation is accompanied by a volume change of −0.2 to −0.3 %, and is believed to be first-order displacive with additional characteristics similar to those of martensitic transformations.The thermal expansion behaviour of structures in the (Sr,Ba)Al2O4, series indicates that two tilt systems are operative: co-operative rotation of tetrahedra about the c-axis, and tilting of tetrahedra relative to the 0001 plane.The results for the (Sr,Ba)Al2O4 series are shown to be invaluable in reinterpreting the structural behaviour of members of the nepheline and leucite groups of minerals.

We combine chemical lattice imaging with digital pattern recognition to map, at near-atomic resolution, the compositional change across GaAs/AlGaAs interfaces of the highest optical quality. These maps quantify the information content of each unit cell of the lattice image. Our results show that state-of-the-art GaAs/AlGaAs interfaces contain substantial atomic roughness on scales finer than suggested by optical measurements.

SUMMARY. This paper gives a revision and expansion of an earlier interpretation of the thermal expansion behaviour of the framework silicates. The partially-collapsed and ideal fully-expanded structures of quartz, cristobalite, and sodalite are chm-acterized by the geometric relationship between the angle of rotation of their tetrahedra from the ideal fully-expanded state, their cell parameters, and the length of the tetrahedron edge. Their thermal expansion behaviour is interpreted as due mainly to the effect of the rotation of the tetrahedra towards the fully-expanded state modified by anisotropic thermal motion of the framework oxygens and distortion of the tetrahedra from a regular form. With the leucite and sodalite groups the significance of the interframework cations is discussed.TAYLOR (1968) and Taylor and Henderson (1968) developed a simple interpretation of the thermal expansion behaviour of the sodalite and leucite groups of minerals, but subsequent detailed examination of the structural changes in quartz and cristobalite on heating has indicated a need for revision and clarification.When a crystalline substance is heated there is an increase in the amplitude of the bending and stretching modes of the different combinations of the atoms. At the same time there is a contribution to the total crystal or bond energy, which affects the interatomic distances (Drechsler and Nicholas, I967). In addition, there is often a change in the detailed geometry, as evidenced by structural transitions, which are possibly a result of the increase in the amplitude of the bending and stretching modes. The possibility of anharmonic thermal vibrations in molecules complicates any simple model for thermal expansion behaviour because they lead to apparent shortening of the bonds (Cruickshank, 1956). The effect of heat on the total crystal or bond energyis expected to show a relationship between the degree of change in interatomic distance and the bond type; for example, one may contrast the high thermal expansions of the largely-ionic alkali halides with the low expansion of the covalent diamond crystal.The framework silicates, as their name implies, consist of linked SiO~, or SiO4 and AlOe, tetrahedra with all their oxygens shared. By this means a three-dimensional framework is built with spaces that can be occupied by other ions or molecules. The framework, while strong, is not rigid, for there are no forces holding it fully expanded. The general observation is, therefore, that the structures of framework silicates at room temperature are partially collapsed and distorted versions of the ideal fullyexpanded structures. The structural collapse is brought about by rotation and bending of the framework tetrahedra about their shared oxygens. By rotation it is not implied that the tetrahedra rotate continuously but merely that they turn through a 9

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ABSTRACT. X-ray powder methods have been used to study the room-temperature structures of the synthetic sodalites: Li8(AI6Si6024)CI2, KT.6Nao.4(A16Si6Oz4)CI2, and Nas(A16Si6024)I ~. Natural sodalite was also studied and the atomic coordinates show satisfactory agreement with those determined from the single-crystal data of L6ns and Schulz (1967). The LiC1-and KCI-as well as the NaCl-sodalites refined in the expected sodalite space group PTl3n, but the NaI-sodalite fitted 1713m better. The resulting structural data reveal shortcomings in the previous computer models for sodalite structures and an improved computer modelling procedure is devised which successfully predicts atomic coordinates, starting from the experimental a value and an estimate of the cation anion distance. The method incorporates the experimental result that the average T O distance (T = A1, Si) throughout the samples is ~ 1.678 A, and Si-O and AI-O are set at 1.618 and 1.738A, respectively. Although T-O remains little changed throughout the samples, the data confirm the inverse relationship between /_ T-O T and the tetrahedron tilt angle ~b, in which I_T-O-T approaches ~ 160 ~ as ~b ~ 0 ~ and the sodalite cage becomes fully expanded.