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Acta Crystallographica Section A

Acta Crystallographica Section A: Foundations and Advances covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination

Published: 2017-06-21


A first-prototype multi-determinant X-ray constrained wavefunction approach: the X-ray constrained extremely localized molecular orbital–valence bond method


All the current variants of Jayatilaka's X-ray constrained wavefunction (XCW) approach work within the framework of the single-determinant wavefunction ansatz. In this paper, a first-prototype multi-determinant XCW technique is proposed. The strategy assumes that the desired XCW is written as a valence-bond-like expansion in terms of pre-determined single Slater determinants constructed with extremely localized molecular orbitals. The method, which can be particularly suitable to investigate systems with a multi-reference character, has been applied to determine the weights of the resonance structures of naphthalene at different temperatures by exploiting experimental high-resolution X-ray diffraction data. The results obtained have shown that the explicit consideration of experimental structure factors in the determination of the resonance structure weights may lead to results significantly different compared with those resulting only from the simple energy minimization.

Reduction of small-angle scattering profiles to finite sets of structural invariants


This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters called Kn which are related to the shape of the object of study. These Kn, together with a radius R, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and the Dmax parameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.

Thermoelectric transport properties in magnetically ordered crystals


The forms of the tensors describing thermoelectric transport properties in magnetically ordered crystals are given for frequently used orientations of the 122 space-time point groups up to second order in an applied magnetic field. It is shown which forms are interchanged for the point groups of the hexagonal crystal family by two different conventions for the connection between the Hermann–Mauguin symbol and the orientation of the Cartesian coordinate system. The forms are given in Nye notation, which conspicuously shows how the forms for different point groups are related. It is shown that the measurable effects in magnetically ordered crystals can be decomposed into an effect occurring in all crystals and one coming from the magnetic ordering. Errors in the literature are pointed out.

Hard-sphere displacive model of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56°, a) contraction twins in magnesium


Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation (56°, a). The classical shear theory of deformation twinning does not specify the atomic displacements and does not explain why contraction twinning is less frequent than extension twinning. The paper proposes a new displacive model in line with our previous work on martensitic transformations and extension twinning. A continuous angular distortion matrix that transforms the initial hexagonal close-packed (h.c.p.) crystal into a final h.c.p. crystal is determined such that the atoms move as hard spheres and reach the final positions expected by the orientation relationship. The calculations prove that the distortion is not a simple shear when it is considered in its continuity. The ({0{\overline 1}1}) plane is untilted and restored, but it is not fully invariant because some interatomic distances in this plane evolve during the distortion process; the unit volume also increases up to 5% before coming back to its initial value when the twinning distortion is complete. Then, the distortion takes the form of a simple shear on the ({0{\overline 1}1}) plane with a shear along the direction [{18,{\overline 5},{\overline 5}}] of amplitude 0.358. Experiments are proposed to validate or disprove the model.