RO I

focuses on the application of highly advanced characterisation techniques to the chosen problems in the phase transformations of interest. The groups involved develop novel experimental techniques in house and are thus best placed to apply them to concrete cases, preferably with the emphasis on getting quantitative data. In team 1 domain and defect structures at different length scales and resulting from or playing an important role in solid state phase transformations are characterised by highly advanced transmission electron microscopy (TEM) methods. The different length scales range from the atomic scale through the nanoscale up to the micron scale. The characterisation results in structural as well as electronic and chemical information. In team 6 X-ray diffractometry, electron microscopy, dielectric spectroscopy and NMR spectroscopy will be applied for the investigation of fast ionic transport in twin domain walls. They also focus on magnetic TEM and magnetic force microscopy to characterise magnetic structures, while team 7 will perform neutron diffraction, elastic constants, calorimetric and magnetisation and acoustic emission measurements of the related phase transformations. The experimentation in team 10 focuses on in-situ characterisation of phases and phase transformations under applied stress. For this purpose, in-situ TEM, acoustic emission, ultrasonic and in-situ neutron diffraction techniques are being developed and applied to study deformation processes occurring during thermomechanical loads on single and polycrystals of phase transforming materials. The choice of materials, as elaborated in the list of tasks in B1.5, will ensure direct collaboration with other teams not involved in materials characterisation as such. Indeed, the design of the experiments and the interpretation of the experimental data will be performed with a strong input from the mathematical and theoretical models developed and provided by the other teams.

RO II

centres on the detailed investigation of the symmetry properties of crystalline materials and their consequences, both in simplified models based on the concept of a simple Bravais lattice and within the more detailed framework of ‘multi-lattices’ (or ‘lattices with a basis’). The main method for symmetry investigation in this context is given by ‘Arithmetic Crystallography’, which produces explicit criteria for the systematic enumeration of all possible periodic crystal structures, i.e., it gives a complete structure database. For instance, it can generate all the distinct crystal structures (with a given number of atoms in their unit cell) that share the same space group; this information is not available in the International Tables of Crystallography or in other sources at present. Production of such databases is topic of considerable interest, as such they are expected to become a cornerstone of materials science in the near future. When coupled with efficient ab initio methods, they can indeed be mined to produce a host of new stable structures for crystalline materials, suggested from theory. Also, the improved understanding of deformable-crystal kinematics coming from the clarification of symmetry relations helps in constructing explicit classes of constitutive functions that model the behaviour of multiphase crystals: (a) in the range of finite, but not too-large deformations, as is the case in symmetry-breaking martensitic transformations; and (b) in the range of large deformations, such as those involved in reconstructive phase changes, or the large lattice shears involved in the formation of dislocations in crystalline lattices. A further by-product of investigating symmetry is the possibility of a more detailed characterisation of the microstructure produced by solid-state transformations in crystalline materials. In suitable alloys, the morphology of such microstructure can be shown to depend on the parameters of the crystal lattice in the parent and product phases, which in turn depend on composition. Therefore one expects that microstructure formation can at least to some extent be controlled through the careful monitoring of alloy composition, in order for instance to enhance the self-accommodation properties of the material.

RO III

The goal of RO III is to develop and apply new and general mathematical methods for multiscale problems arising in phase transitions. There is a track-record of a strong two-way interaction with the experimental groups. On the one hand experimental observations provide the motivation for the mathematical analysis. On the other hand new mathematical predictions and possible design criteria for new materials can be tested by the experimental groups.
The current mathematical theory is most advanced for minimisation problems without internal length scales (such as the Ball-James theory for the formation of microstructure in martensitic transformations). In this case the effective behaviour can in principle be obtained (through quasiconvexification) without having to resolve the details on the microscopic scale. The implementation of these ideas in concrete examples, however, still poses a formidable challenge, partly due the subtleties of quasiconvexity. Theories which also involve a small internal length scale are needed to study details of the geometry of the microstructure, e.g. twin branching or the development and interaction of topological singularities in thin magnetic films. The mathematical analysis of dynamic multi-scale problems and important macroscopic effects such as hysteresis and dissipation (e.g. through pinning) is still in its infancy. We plan to make progress on this by simultaneously working on the development of general tools and on certain case studies carried out in close interaction with the experimental teams. Finally the development of mathematical tools to capture the transition from atomistic to continuum models (which is crucial e.g. for the understanding of ultrathin films, the Cauchy-Born rule and fracture) is also in its beginning, although important progress was made recently, partly by the members of this network.
Moreover, in the context of phase transformation, one of the most popular continuous approaches is the phase-field modelling. One of the main characteristics of this approach is that it is fairly easy to incorporate into the formalism the strain-induced long-range elastic interactions generated by the lattice misfits between precipitates and the matrix into which they evolve, as well as the elastic interactions between the different variants of the same phase. Moreover, the applicability of the phase-field method has recently been extended to dislocations and their dynamics. This opens the route for the development of a realistic theory that incorporates on the same footing the dynamics of microstructures inherited from a phase transformation and the dynamics of dislocations, i.e. plasticity, as well as their interplay.

RO IV

In RO IV the aim is to compute effective parameters like lattice parameters, bulk moduli and elastic constants, but also to perform mathematical and numerical analysis of such coupled simulations in order to validate the existing methods, to clarify their range of validity, or to propose new numerical approaches. In particular, the coupling of ab initio simulations and continuous mechanics computations is often sequential. Instead of this "linear" coupling a more parallel and non-linear coupling may be better suited. Today’s modern first principle calculations of electronic structures are a mature theory which can provide important values such as total energy, bulk moduli and others and are well-suited for compact structures like metallic alloys. Methods like Full-Potential Augmented Plane Wave (FP-APW) can be performed with mid-size crystal structures with an accuracy of a few percentage, thanks to the rapid increase in computer power. A detailed experimental-theoretical comparison will be achieved at the level of the density of states with the help of high-resolution spectroscopy, nowadays available in EELS in connection with RO I.
The macroscopical behaviour of shape memory alloys and other smart materials is governed by effects on the atomistic level and even finer length scales. Therefore it is essential to target the problem on the full hierarchy of scales. For this it is necessary to develop both analytical and numerical techniques to bridge the different levels. In addition to analytical techniques to derive models on larger scales rigorously from finer scales discussed in RO III an important goal is to develop methods to couple models on different length scales numerically, i.e. to deal with different scales and models within a single simulation. Then it will be necessary to compare the achieved results with experimental data to verify the newly developed analytical and numerical techniques.

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