No abstract

No abstract

No abstract

Crystallographic data concerning geometric properties of hexagonal lattices of C,~, Zn, B%, Ti,~, Zr~, Mg and Cd are obtained from two different computation techniques. These properties are related to the relative orientations of identical hexagonal lattices 1 and 2 which superimpose two multiple cells M1 and M2 within a given small deformation. These orientations are listed for ratios 27 = Ivolume of cells M1 (or M2)/volume of the unit cell l varying from 1 to 25. Their number are limited by choosing all the principal strains transforming M1 into M2 less than or equal to 1%. IntroductionThree techniques have been used to determine the relative orientations of identical hexagonal crystals which give rise to a near coincidence of two cells of the two crystal lattices 1 and 2, cells denoted hereinafter M 1 and M2 respectively. [This has been referred to by previous workers as a 'coincidence' or 'near-coincidence site lattice' or 'orientation de macle',* where the number 271 (or 2~2) is defined by the ratio volume of M1 (or M2)/volume of the unit cell.] Two techniques depend either upon searching for vectors of common length arising from rational values of (c/a) 2 (Fortes, 1973;Warrington, 1975) or in searching for coincidences arising from rotation about specific axes, chosen a priori, of (low) crystallographic index (Bruggeman, Bishop & Hartt, 1972). The first method derives from that used by Warrington & Bufalini * We note for the benefit of our readers whose mother tongue is English that the term 'orientation de macle' as defined by Friedel (1964) is more general a concept than the nearest English equivalent of'twin' used in its restrictive sense.0567-7394/81/020184-06501.00 (1971) for cubic crystals; the second from the use of a 'generation function' typified by Ranganathan (1966) and Goux (1961). The third technique (Bonnet & Cousineau, 1977), tested on Zn/Zn and NiaA1 (cubic)/ Ni3Nb(orthorhombic ), depends on a numerical method of calculation capable of treating the case of general lattices and envisaged in part by Santoro & Mighell (1973). It takes into account the experimental [rather than idealised or rational values of (c/a) 2] values of the lattice parameters. The technique determines relative orientations that, with additional imposed constraints (which may be chosen arbitrarily small) on M1, will give full or true coincidence with M2. Determination of relative orientationsIn searching for a 'constrained coincidence' the worker must compromise and set limits on the deviation from exact coincidence that is to be allowed. In the numerical method (Bonnet & Cousineau, 1977) this is represented by a maximum value of S = It, ll + l e21 + lea1 where e 1, e 2, e a are the principal strains of the pure deformation D transforming lattice 1 into lattice 2. D -~ transforms lattice 2 into a fictitious lattice denoted lattice 2', which can be exactly superposed onto lattice 1 (Bonnet & Durand, 1975). The unit cell of this CSL (coincidence site lattice) is defined either by M1 or by the deformed cell M2, d...

Tables are given of all coincidence orientations with multiplicity Z 9 3 6 for rhombahedral lattices with axial ratios in the range of corundum type structures (2.696 < c/a < 2.765). Measurements of the relative orientation of 133 pairs of neighbouring grains in sintered a-alumina showed that near-coincidence boundaries (14 cases) and one-dimensional coincidence boundaries (17 cases) occurred more frequently than would be the case for randomly distributed orientations and that many of these special boundaries contained periodic arrays of grain boundary dislocations. Their Burgers vectors have been determined for a rhombohedral twin boundary in order to decide which one among three possible coincidence descriptions best represents the boundary structure. $1. INTRODUCTIONThe relative orientation of 133 pairs of neighbouring grains in sintered a-alumina has been determined using transmission electron microscopy (TEM). It has been found that relative orientations with symmetry translation vectors of both grains in near coincidence appear more frequently than would be the case for randomly distributed orientations. Near-coincidence grain boundaries often contain periodic arrays of dislocations, suggesting that small deviations from a low-energy boundary are compensated by grain-boundary dislocations. The experimental results are interpreted by means of systematic mathematical results on the exact or approximatecoincidence of symmetry translations of the rhombohedral lattices of neighbouring grains.The symmetry translations of two neighbouring grains of u-alumina form two rhombohedral lattices 1 and 2 respectively. If lattice 2 is obtained from lattice 1 by a 180" rotation around a lattice vector perpendicular to the threefold axis of lattice 1, then the two lattices will have vectors in common which form a three-dimensional lattice. Its traditional name coincidence site lattice is somewhat misleading because common translations do not imply the coincidence of sites. A more appropriate name is coincidence lattice (CL). The volume ratio of unit cells for the CL and the original lattice 014l%alO/90 3300 Q 1990 Taylor 8 Francis Ltd.

A computation method is presented for determining: (i) pairs of non-primitive cells M1 and M2, constructed on three translation vectors of a lattice 1 and three vectors of a lattice 2 respectively, such that the sizes of M1 and M2 are (almost) identical; (ii) Z~ (E2), defined by the number of primitive cells of lattice 1 (lattice 2) contained in M1 (M2); (iii) a characteristic relative orientation of the two lattices for which M1 and M2 coincide exactly or approximately, for which the transformation relating M1 to M2 (denoted A in general) is a pure deformation, whose principal strains are calculated; (iv) base vectors for the DSC-1 and DSC-2 lattices, so that the Burgers vectors of intrinsic phase (or grain) boundary dislocations are determined. The DSC-1 lattice is constructed by summing the vectors of lattice 1 and lattice 2', deduced from lattice 2 by A-1. The DSC-2 lattice is derived from the DSC-1 lattice by A. Tables of results are presented for a lattice 1/lattice 2 of Zn/Zn, up to ZI = Z2 = 25, and for Ni3A1 (cubic)/Ni3Nb (orthorhombic), up to E1 =21 and Z 2 = 10.

High-resolution electron microscopy technique has been applied to a detailed study of the 60°d islocations at the atomic layer molecular-beam-epitaxial GaAs/Si interface. Their deformation fields strongly interact with neighbor dislocations inducing irregular spacing between the cores and possible dissociations. Biatomic silicon steps were observed at the interface, but never inside 60°d islocation cores. Computer image simulation and elasticity calculations of the atomic displacement field have been used in order to determine the structure of the 60°dislocation; however, due to the Eshelby effect and to interaction with some neighbor dislocations, in many cases no theoretical model could explain some observations.

To study the respective deformation modes of the Al and CuAl2 lamellae as well as the interface properties (phase boundaries, lamellar faults) in lamellar eutectic monograins, in situ creep experiments are performed in a high voltage electron microscope between 270 and 350 °C. They are completed by conventional observations of crept samples. At 300 °C a transition occurs: at lower temperatures the CuAl2 phase is brittel by lack of dislocations while above 300 °C dislocation multiplication and movement are possible, involving high friction forces. Outlines for two corresponding deformation models are proposed, involving the observed interface sliding, dislocation sources in volume or at the phase boundaries, shearing of the Al lamellae, and a heterogeneous deformation. These models are discussed in terms of the activation parameters measured in macroscopic creep tests presented in another article.