To fill the gap between accurate (and expensive) ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials, a new class of descriptions of atomic interactions has emerged and been widely applied; i.e., machine learning potentials (MLPs). One recently developed type of MLP is the Deep Potential (DP) method. In this review, we provide an introduction to DP methods in computational materials science. The theory underlying the DP method is presented along with a step-by-step introduction to their development and use. We also review materials applications of DPs in a wide range of materials systems. The DP Library provides a platform for the development of DPs and a database of extant DPs. We discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

* a~s o Max-PZanck I n s t i t u t fiir Metallforsclnazg, I n s t i t u t J'iir Physik, 7000 S t u t t g a r t 80, F.R.G.Abstract.-The local parameters are introduced to describe the local atomic structure of amorphous metals. They define the structural defects which facilitate the explanation of various properties, including the volume change by annealing.

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This text presents a concise and thorough introduction to the main concepts and practical applications of thermodynamics and kinetics in materials science. It is designed with two types of uses in mind: firstly for one or two semester university course for mid- to - upper level undergraduate or first year graduate students in a materials-science-oriented discipline and secondly for individuals who want to study the materials on their own. The following major topics are discussed: basic laws of classical and irreversible thermodynamics, phase equilibria, theory of solutions, chemical reaction thermodynamics and kinetics, surface phenomena, stressed systems, diffusion and statistical thermodynamics. A large number of example problems with detailed solutions are included as well as accompanying computer-based self-tests, consisting of over 400 questions and 2000 answers with hints for students. Computer-based laboratories are provided, in which a laboratory problem is posed and the experiment described. The student can "perform" the experiments and change the laboratory conditions to obtain the data required for meeting the laboratory objective. Each "laboratory" is augmented with background material to aid analysis of the experimental results.

Abstract.In this paper, we use an extended form of the finite element method to study failure in polycrystalline microstructures. Quasi-static crack propagation is conducted using the extended finite element method (X-FEM) and microstructures are simulated using a kinetic Monte Carlo Potts algorithm. In the X-FEM, the framework of partition of unity is used to enrich the classical finite element approximation with a discontinuous function and the two-dimensional asymptotic crack-tip fields. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack growth simulations can be carried out without the need for remeshing. First, the convergence of the method for crack problems is studied and its rate of convergence is established. Microstructural calculations are carried out on a regular lattice and a constrained Delaunay triangulation algorithm is used to mesh the microstructure. Fracture properties of the grain boundaries are assumed to be distinct from that of the grain interior, and the maximum energy release rate criterion is invoked to study the competition between intergranular and transgranular modes of crack growth.Mathematical subject classification: 74R10.