Solid State Phenomena Vols. 172-174

Abstract: The stoichiometric M_pX_q hollow nanospheres are produced by reaction of metallic M nanospheres with the gaseous X phase. In the first stage a sufficiently thick M_pX_q nanoshell on the metallic core of phase M is formed. During this stage high supersaturation of vacancies in the M core or very high hydrostatic stress in the M core, due to the misfit between the core and the nanoshell, are developed and provide favourable conditions for the hollow nucleation. The misfit is caused by the Kirkendall effect. Based on the application of the thermodynamic extremal principle a kinetic model of M_pX_q nanoshell formation is derived. The kinetics is driven by the change of the chemical energy due to reaction of M and X components, of the interface and surface energies, and of the elastic strain energy due to misfit strain of the whole system. The model is used for simulation of the Cu₂O shell growth kinetics due to oxidation of a Cu nanosphere, and the results of simulations are discussed.

Abstract: An exact description of the distribution of 2D bimetallic clusters deposited on a square substrate has been obtained via an exact inventory algorithm. We show that several features of the monometallic distribution can be altered by the presence of a second species within the clusters. The diagram of ground-state morphologies of such clusters is built as a function of the chemical interactions between both components. As a consequence, the maxima in the cluster size distribution that indicate the magic numbers can be smoothened or shifted during co-deposition as a function of the composition of the two-component phase.

Abstract: A model has been developed which is able to predict the kinetics of β → α transformation in industrial multicomponent titanium alloys during complex heat treatments. It isbased on (i) analytical nucleation and growth laws based on simple geometric representationsof the di erent morphologies commonly observed in these alloys; (ii) the assumption of localequilibrium at interfaces, handled within the CalPhaD framework; (iii) averaged solute balancesin each morphology. The potentialities of the model will be demonstrated on the Ti17 industrialalloy upon isothermal holdings and cooling from the β phase field.

Abstract: There is renewed interest in the investigation of austenite formation due to the development and increased use of advanced high strength steels for automotive applications. Intercritical annealing is an essential processing step for cold rolled and coated steel products with multi-phase microstructures. During intercritical annealing the initial ferrite-pearlite microstructure transforms partially to austenite. Models for the austenite formation are critical to predict the austenite fraction as a function of the thermal cycle thereby facilitating the design and control of robust processing paths. Modelling the austenite formation is challenging because of the morphological complexity of this transformation. Phase field models are a powerful tool to describe the evolution of microstructures with complex morphologies, e.g. formation of finger-type features during austenite formation. The present paper gives an overview of model approaches for the austenite formation. Phase field simulations are presented for two scenarios: (i) austenite formation from a fully pearlitic structure with a lamellar arrangement of carbide aggregates and (ii) austenite formation from ferrite-pearlite microstructures. Simulation results are compared with experimental observations for pearlitic steels. The challenges are delineated for the development of austenite formation models with predictive capabilities.

Abstract: This work is dedicated to simulate the spinodal decomposition of Fe-Cr bcc (body centered cubic) alloys using the phase field method coupled with CALPHAD modeling. Thermodynamic descriptions have been revised after a comprehensive review of information on the Fe-Cr system. The present work demonstrates that it is impossible to reconcile the ab initio enthalpy of mixing at the ground state with the experimental one at 1529 K using the state-of-the-art CALPHAD models. While the phase field simulation results show typical microstructure of spinodal decomposition, large differences have been found on kinetics among experimental results and simulations using different thermodynamic inputs. It was found that magnetism plays a key role on the description of Gibbs energy and mobility which are the inputs to phase field simulation. This work calls for an accurate determination of the atomic mobility data at low temperatures.

Abstract: Complex martensitic microstructure evolution in steels generates enormous curiosity among the materials scientists and especially among the Phase Field (PF) modeling enthusiasts. In the present work PF Microelasticity theory proposed by A.G. Khachaturyan coupled with plasticity is applied for modeling the Martensitic Transformation (MT) by using Finite Element Method (FEM). PF simulations in 3D are performed by considering different cases of MT occurring in a clamped system, i.e. simulation domain with fixed boundaries, of (a) pure elastic material with dilatation (b) pure elastic material without dilatation (c) elastic perfectly plastic material with dilatation having (i) isotropic as well as (ii) anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to Fe - 0.3% C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The results indicate that elastic strain energy, dilatation and plasticity affect MT whereas anisotropy affects the microstructure.

Abstract: Despite the tremendous success of phase-field (PF) modelling in predicting many of the experimentally observed microstructures in solids, additional progress is required in order to apply it to predict microstructure evolution in real alloy systems. One way to achieve this is to couple thermodynamic and kinetic databases with PF model. In this work, we present phase-field simulations of spinodal decomposition in Fe-Cr alloy during thermal ageing and anisothermal heating. In the PF method, the local free energy is directly constructed using the CALPHAD method. During isothermal ageing, the morphology of decomposed phases consisted in an interconnected irregular shape for short ageing times, and a further ageing caused the change to a droplet like shape of the decomposed Cr-rich phase. The influence of heating rate on phase transformations is then simulated and compared with experimental results obtained by differential thermal analysis, carried out with heating rates in the range 0.5 °C.min^-1 to 15 °C.min^-1. The simulation results show that heating rate strongly influences the microstructure morphology.

Abstract: We review the description of ferroelastic transitions in terms of spin models. We show how one can systematically obtain a pseudo-spin Hamiltonian from the Landau energy describing the first order transition between Austenite/Martensite phases. It is shown that a Local Mean-field approximation predicts the same microstructure as the continuous Landau model in terms of strain variables. This method can be applied to a wide range of two and three dimensional transitions. We then demonstrate how quenched disorder in such pseudo-spin models yields the existence of a glass phase, characterized by the Edwards-Anderson order parameter. Our approach uses Mean-field approximation and Monte-Carlo simulations (using Zero Field Cooling/Field Cooling experiments) to study the influence of the long-range interactions. Although our model captures the salient features of a ferroelastic material in the presence of disorder, the influence of the disorder on the high symmetry austenite phase is not quite consistent with expected behavior. We examine different means of introducing disorder that can improve upon the results.

Abstract: A phase-field model is described for predicting the diffusional phase transformation process in elastically inhomogeneous polycrystals. The elastic interactions are incorporated by solving the mechanical equilibrium equation using the Fourier-spectral iterative-perturbation scheme taking into account elastic modulus inhomogeneity. A number of examples are presented, including grain boundary segregation, precipitation of second-phase particles in a polycrystal, and interaction between segregation at a grain boundary and coherent precipitates inside grains. It is shown that the local pressure distribution due to coherent precipitates leads to highly inhomogeneous solute distribution along grain boundaries.

Abstract: Superelastic NiTi polycrystalline tubes, when subjected to quasi-static stretching, transform from an initial austenite phase to a high-strain martensite phase by the formation and growth of a macroscopic self-organized helical domain as deformation progresses. This paper performed an experimental study on the effects of the externally applied stretching and tube geometry (length L, wall-thickness h and tube radius R) on the martensitic helical domains in the tubes under very slow (isothermal) stretching. The evolution of the helical domains with the applied strain in different tube geometries are quantified by in-situ optical measurement. We demonstrate that the shape of the self-organized helical domain and its evolution are governed by the competition between bending strain energy and domain front energy in minimizing the total energy of the tube system. The former favors a long slim helical domain, while the latter favors a short fat helical domain. The experimental results provide a strong support to the recently developed theoretical relationship.