1,720,960 research outputs found
Beyond space groups: the arithmetic symmetry of deformable multilattices
Full text linkAbstract: It is well known that the problem of classifying the symmetry of simple lattices leads to consideration of the conjugacy properties of the holohedral crystallographic point groups (`holohedries'). Classical results for the three-dimensional case then state that: (i) the orthogonal classification of the holohedries subdivides the simple lattices into the familiar seven crystal systems (this gives the `geometric symmetry' of simple lattices); (ii) the stricter arithmetic classification of the holohedries subdivides the three-dimensional simple lattices into the well known fourteen Bravais lattice types (this gives the `arithmetic symmetry' of simple lattices, which is more refined than the geometric one). There exists an analogous problem of studying the symmetry of the more complex periodic structures in three dimensions (`multilattices', that is, finite unions of translates of a given simple lattice), which describe in more detail the atomic lattices of the crystalline materials found in nature. In this case, the groups of affine isometries that leave a multilattice invariant, called the `space groups', must be considered. Well known results subdivide the space groups into 219 affine conjugacy (or isomorphism) classes. This corresponds to classifying the `geometric symmetry' of tridimensional multilattices. In crystallography, there does not exist a classical counterpart for multilattices of the above-mentioned arithmetic symmetry of simple lattices. In this paper, a natural framework is proposed in which to study the `arithmetic symmetry of multilattices' and it is shown that the latter gives a finer classification than that based on the 219 classes of space groups, even if site symmetry is taken into account. This approach originates from the investigation of the changes of symmetry in deformable crystalline solids and proves useful for the modelling of phase transitions in crystals and related phenomena
On the definition and classification of Bravais lattices
No full textThe number of Bravais lattices (or lattice types) in three-dimensional space is well known to be 14 if, as is usual, a lattice type is defined as the class of all simple lattices whose lattice groups (that is, arithmetic holohedries) belong to the same conjugacy class in GL(3, Z). However, it is also common in the literature to introduce the lattice types using the original point of view of Bravais (and Cauchy), according to which a type collects all the lattices that can be connected by a continuous deformation along which the lattice symmetry does not decrease. It is shown that these two definitions are in fact nor equivalent. Bravais' own criterion results in only 11 lattice types
Transformation twinning and Mallard's law
No full textThe analysis of microstructure is largely based on the knowledge of the transformation twins in a crystal undergoing a symmetry-breaking phase transition. According to a conjecture referred to as "Mallard's law", the transformation twins generically arise from the lost symmetry planes in the parent phase, and correspond to the conventional Type-1 twins, with their conjugate Type-a twins. The analysis of the generic rank-one connections between potential wells occurring in any of the symmetry-breaking transitions that are possible for simple lattices shows that actually Mallard's law does not hold, because there do exist generic non-conventional twins. The law holds if at least one of the twins in a conjugate pair is required to have a material interface, or if twin genericity is interpreted in a particularly restrictive way
Continuum models for phase transitions and twinning in crystals
No full textContinuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role.
This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys.
Chapman&Hall/CSC, Boca Raton USA, London UK
Non-generic concentrations for shape-memory alloys; the case of CuZnAl
No full textAs is well known, the remarkable properties of many active crystalline materials, such as shape-memory alloys, originate from a symmetry-breaking martensitic phase transformation. A recent analysis (see Pitteri and Zanzotto, Acta mater., 1998, 46, 225) has shown that if a special condition on the strain parameters is satisfied, the twinning ability of a crystal undergoing a cubic-to-monoclinic transformation is considerably increased. As this feature may improve the memory behavior of cubic–monoclinic alloys, it is suggested that these predictions be tested experimentally. A procedure is given to determine explicitly which “non-generic” concentrations allow suitable alloys to produce the extra twins; which concentrations give a volume-preserving transformation are also determined (this condition guarantees self-accommodation of the martensite). As an example, the ternary CuZnAl system is considered, for which, based on the available experimental data, the non-generic concentrations are established. The work indicates that there is a scarcity of the necessary data on the mapping of lattice parameters vs concentrations in alloys with a potential for shape memory. A specific experimental program aiming at the systematic gathering of this information is proposed: building such a database may prove of considerable help in the search and synthesis of new materials with improved performance
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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