This is the kick-off meeting for the new Marie Curie Research Training Network on Multi-scale modelling and characterisation for phase transformations in advanced materials (MULTIMAT). Many applications of so-called smart materials are based on changes in their atomic, nano- and microstructure brought about by phase transformations. In order to further develop and apply these materials we need a better and fundamental understanding of the underlying principles of these processes. MULTIMAT aims to continue existing and fruitful collaborations between strong theoretical and experimental research groups active in this exciting and promising field of advanced materials. The meeting combines introductory courses for PhD students and Postdocs delivered by leading experts in the field with the presentation of the current research of the teams (see programme).
This lecture will focus on introducing the basic concepts used in the study of phase transitions. Topics covered will include:- Types of phase transitions: order-disorder, displacive, first order, second order, tricritical.- Critical exponents.- Models of phase transitions: the Ising Model, Landau-Ginzberg theory.- Phase transitions and microstructures, twin walls and surfaces.- Experimental measurements and simulations of phase transitions.
Phase transition kinetics is a classical area of thermodynamics and statistical mechanics dealing with the transient dynamical evolution of a system that relaxes towards equilibrium from an initial metastable or unstable state. These non-equilibrium processes involve competition between different thermodynamic phases and give rise to late-times emerging mesostructures which determine the macroscopic properties (mechanical, electric, magnetic, ...) of these systems to a large extent. In this lecture some of the most fundamental topics in the theory of phase transition kinetics will be introduced. Taking a binary alloy a prototypical example, phenomena such as nucleation, spinodal decomposition and domain growth will be discussed. For systems undergoing magnetic and structural transitions the relevance of disorder and long-range interactions arising from compatibility effects will also be considered. These effects are responsible for the existence of a complex energy landscape, which is at the origin of avalanche behaviour and athermal kinetics found experimentally. These concepts will be discussed and simple statistical models aimed at accounting for the observed phenomenology will be introduced.
The main points will be:1. Stress-strain-temperature experiments on single crystals2. Construction of stress-temperature maps, their meaning and calculation.3. Crystallographic model - modeling of polycrystals based on single crystal data.4. Comparison of model predictions with experiments (neutron diffraction, acoustics).
The lecture will summarise the use of conventional as well as novel microscopic techniques for the study of phase transformations. The focus will be on transmission electron microscopy and related spectrocopic techniques used to investigate the behaviour of the internal volume of a material but some surface techniques will also be introduced. Examples of work on alloys and oxides, bulk as well as nanostructures and diffusional as well as displacive transformations will be included.
Experimental methods currently used at IoP ASCR in Prague for investigation of martensitic transformations in shape memory alloys (single crystals or polycrystalline samples) in-situ during thermomechanical loads will be briefly reviewed. The methods include: in situ ultrasonic studies of the propagation of acoustic waves in solids, in-situ electric resistivity measurements, in-situ neutron diffraction, in situ TEM using a dedicated thin foil holder for observation under applied stress, in-situ optical microscopy. Selected results achieved recently on CuAlNi and NiTi single and polycrystalline samples will be presented and discussed.
I describe some results and methods that have been developed in the last years for the study of the overall behavior of variational problems for large lattice systems (e.g. atomistic system with pair potentials, variational models of vision, resistor networks, etc.) Upon scaling, some of the questions may be equivalently stated in terms of the limit of variational problems for lattice systems as the lattice spacing tends to zero, that are described by a continuous energy. This limit must be understood in a variational sense (Gamma-limit) and is in general (quite) different from the pointwise limit.
Some issues that have been addressed are: determination of the scaling properties of the discrete energies that correspond to continuous energies of specific type ('elastic', 'brittle fracture', 'softening' type, etc.) multi-scale analysis describing 'phase-transition' and 'boundary-layer' type effects homogenization formulas for the effective energies, and interpretation of such formulas in terms of the Cauchy-Born hypothesis optimal bounds for discrete composites and comparison with continuous bounds percolation analysis of random discrete problems.
While the classification of cristals made up by just one atom per cell is well-known and understood (Bravais lattices), that for more complex structures is not. We present a geometric way classifying these crystals and an arithmetic one, the latter introduced in solid mechanics only recently. The two approaches are then compared. Our main result states that they are actually equivalent; this way a geometric interpretation of the arithmetic criterion in given.
