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The rhombohedral perovskites are of interest in lattice dynamics (e.g. LaAlO3, PrAlO3) and for their ferroelectric properties (e.g. LiNbO3, PbZr/TiO3). In this paper, data scattered through the literature are correlated, with correction of some misleading mistakes of calculation. Geometrical descriptions are put in a form allowing comparisons. The structures, classified by their space groups, are described in terms of four structural parameters, the octahedron tilt ω, octahedron distortion d, and A- and B-cation displacements s and t, together with an elongation or flattening ζ of the octahedron, deducible with the help of ω from the interaxial angle αrh. Attention is drawn to the variety of physical causes underlying these departures from ideal perovskite. In the R{\bar 3}c structures a correlation not previously noted in the literature is found between the tilt angle ω and a flattening of the octahedron, and some tentative suggestions are made as to its cause. In the R3m and R3c structures, a lack of general correlation between B-cation displacement and the other parameters is noted, in contradiction to earlier reports.

The lattice parameters of NaNbO3 have been measured to a precision between 1 part in 105 and 1 part in 104 at temperatures up to 800°C. Six distinct phases are found: P (room temperature to 373°C), R(373-480°C), S(480-520°C), T1(520-575°C), T2(575-641°C), cubic (> 641°C). Coexistence of phases S and T1 between 520 and 535 °C has been found, together with twinning effects, and a possible explanation for this is given.

The structure of LiNbO3, determined by Abrahams and co-workers, is more easily understood if it is described in terms of displacement parameters from an idealized structure with hexagonally close-packed oxygen atoms. The relationship to perovskite, the significance of the thermal changes, and the atomic movements in the ferroelectric reversal, all become more obvious and predictable in this way.

Comparison of the structures of coesite and felspar shows (1) the usefulness of a model in which all 04 tetrahedra are taken as perfectly regular and identical in size, the position and chemical nature of the central cation being ignored, (2) the possibility of order-of-magnitude correlation of lattice parameters with certain position parameters of O, by relating both geometrically to tilts of regular tetrahedra of the above kind, (3) evidence that the 'crankshaft' feature of the structure is not subject to a tensile stress in coesite, as it is in felspar, (4) an explanation why the felspar framework is not found in any polymorph of Si02.

The structures of NaNb03 in the S phase (480°-520°c) and T1 phase (520°-575°c) have been determined by use of the octahedron tilting schemes of Glazer. Both phases are orthorhombic with unit cell edges approximately twice those of ideal perovskite; their space groups are Pnmm and Ccmm, respectively. An explanation of the T2 to T1 (575°c) transition is given in terms of a soft phonon mode at q = 1/2 1/2 1/2 A comparison is made with the low-temperature transitions in KMnF3.

Bytownite (a plagioclase feldspar with composition aboul An 80 Ab 20 ) closely resembles anorthite in its lattice dimensions and its diffracted intensities, except for the systematic absence of those wiih h + k odd ('c' and 'y' type). The deduction of a body-centred lattice (whence the previous name, 'body-centred anorthite') is here shown to be incorrect. Three-dimensional electron-density maps and difference maps show conspicuously elongated or doubled Ca/Na peaks and 'half-atom splitting' for other atoms. The results are explained in detail if bytownite has a primitive lattice and a structure very close to (but significantly different from) that of anorthite, and if small anti-phase domains are present with origins related by the vector ½(a + b + c). The evidence for this conclusion, and against other possible explanations of the observed facts, is discussed fully. Bond lengths and angles (tabulated in full) resemble those in anorthite, with some significant differences. Inequalities of bond lengths and angles within the same tetrahedron are real; an analysis of their resemblances and differences in corresponding tetrahedra in different feldspars suggeests an empirical approach to the study of the structural stress systems involved, and emphasizes the difference between the groups comprising microcline, reedmergnerite, and low albite on the one hand, and anorthite, bytownite, and high albite on the other. Ordering of Si/Al is nearly complete, on the same set of sites as in anorthite. At a closer approximation, a few Al-rich sites show significant differences in thier Si content, with extreme value of 0% and 30% against the average value of 13 ± 5% for the rest.

L'auteur a etudie aux rayons X la transition du titanate de barium autour de 120° C. Dans un intervalle de quelques degres, il y a coexistence des deux formes cristallines (tetragonale et cubique). Il semble probable qu'il y a une nouvelle transition pres de — 183° C. Il est interessant de noter que ces pointsλ ne peuvent pas etre attribues a une mise en rotation de molecules.

WE have examined the crystal structure of tobermorite, using crystals given to us by Mr. J. D. C. McConnell, who has published a preliminary description of them1. The substance is a hydrated calcium silicate, closely related to, or identical with, the calcium silicate hydrate I found by Taylor2 in set cements. Its composition, as found by McConnell1, is Ca5Si6O22H10, and this is compatible with our present results, so far as they go.

IT has been shown by Bennewitz and Simon1 that the influence of zero-point energy on the properties of a condensed substance is very great for substances of low boiling point. The effect is most marked in helium2, where it actually plays the chief part in determining the properties; but it is large, too, in hydrogen, a substance which is particularly interesting as it possesses two isotopes which have identical binding forces but very different zero-point energies.