Solid State Phenomena Vols. 172-174

Abstract: Product phases from various phase transformations often exhibit fascinating morphologies. Facets of unique crystallographic orientations are characteristic of the morphologies. Based on a comparison of facets in the surfaces and interfaces of crystals, this paper proposes to use singularity as the common features of facets on a crystal. While association of facets with energy singularity has been established from the Wulff construction, we defined singularity in structure with an absence of one or more types of defects common to a vicinal surface or interface. Singularity in an interfacial structure is described in terms of both ledges and dislocations. When dislocations are involved, the candidates of the singular interfaces derive mainly from the principal O-lattice planes. The orientations of these planes are defined by Δg’s, which are measurable in diffraction patterns. Singularity with respect to the orientation relationship results from further eliminating defects, which is permitted by a special arrangement of Δg’s. The candidates of singular interface confined by the arrangement of discrete Δg’s are helpful for understanding the crystallographic morphology. One example from an Mg alloy is provided to show the association of the singular interfaces with Δg’s. The effect of the potential presence of a long-range strain and kinetic effects are briefly discussed.

Abstract: Dry granular matter, with infinite tangential friction, is modeled as a connected graph ofgrains linked by purely repulsive contacts. The degrees of freedom of a grain are non-slip rotationon, and disconnection from another. The material stability under shear (jamming) is ensured by oddcircuits of grains in contact that prevent the grains from rolling on each other. A dense granularmaterial with high stiffness-to-load ratio has two possible states: fragile solid, blocked by odd circuits,and dry fluid or bearing, in the absence of odd circuits, that flows under shear by creation and glide ofa pair of dislocations as in plasticity of continuous media. In this paper, we introduce the notions of blob, a region of the material containing only even circuits, and of critical contact that closes an oddcircuit. The granular material is then represented, at low energies and critical applied shear, as a chainof blobs connected by critical contacts. The transition between dry fluid and fragile solid occurs byintermittency.

Abstract: Continuous Displacement Cluster Variation Method is employed to study binary phase equilibria on the two dimensional square lattice with Lennard-Jones type pair potentials. It is confirmed that the transition temperature decreases significantly as compared with the one obtained by conventional Cluster Variation Method. This is ascribed to the distribution of atomic pairs in a wide range of atomic distance, which enables the system to attain the lower free energy. The spatial distribution of atomic species around a Bravais lattice point is visualized. Although the average position of an atom is centred at the Bravais lattice point, the maximum pair probability is not necessarily attained for the pairs located at the neighboring Bravais lattice points. In addition to the real space information, k-space information are calculated in the present study. Among them, the diffuse intensity spectra due to short range ordering and atomic displacement are discussed.

Abstract: The kinetics of phase transformations for which nucleation occurs on parent-micro-structure grain boundaries, and the resulting microstructures, were investigated by means ofgeometric simulations. The influences of parent microstructure grain-boundary area density,parent grain-size distribution and parent→product kinetics were analysed. Additionally, thesimulated kinetics were compared with predictions from two kinetic models, namely a modelproposed for spatially random nucleation and a model proposed for grain-boundary nucleation.It was found that the simulated transformed fraction as function of time lies in between the twomodel predictions for all investigated parent microstructures and parent→product kinetics.

Abstract: A mixed control mode is developed to model the ledge growth of pro-eutectoid ferrite, considering coupled effects of migration of austenite/ferrite interface and carbon diffusion in austenite. Carbon concentration of austenite at the austenite/ferrite interface increases from the bulk carbon concentration to a steady level, which is lower than that in local equilibrium, during the ferrite growth process. Correspondingly, ferrite grows rapidly at the beginning since all the driving force of ferrite transformation is dissipated on the interface migration. In the later stage of isothermal transformation, the growth rate of ferrite decreases towards a steady level since a part of driving force is dissipated on carbon diffusion in austenite. The effect of interface migration on ferrite growth rate by changing the interface mobility is emphatically discussed. In the case of the low interface mobility, the growth rate of ferrite is very small while the growth is dominated by the carbon diffusion ability in the case of large interface mobility. When a medium interface mobility is obtained, the growth rate of ferrite may reach a maximum value, which exceed the limitation of diffusion control and interface control modes. After comparing the modeled growth rate of ferrite with the experimental data of 0.11-0.49 wt% C alloy at 973-1113 K, the pre-expontential factor (M₀) of interface mobility is estimated within the range of 0.1-1 mol m J^-1 s^-1, around the value 0.5 mol m J^-1 s^-1 theoretically estimated.

Abstract: A three-dimensional cellular automata (CA) model is developed for the kinetic and microstructural modelling of the relevant metallurgical mechanisms occurring in the annealing stage of low–alloy steels: recrystallisation, pearlite–to–austenite transformation and ferrite–to–austenite transformation on heating and austenite–to–ferrite transformation on cooling. In this model the austenite–to–ferrite transformation is described by a mixed–mode approach, which implies that the transformation kinetics is controlled by both the interface mobility and the diffusivity of the partitioning elements. This approach also allows incorporation of the ferrite nucleation occurring on structural defects. The developed CA algorithm, in which the transformation rules for the grain boundary and interface cells are controlled by the growth kinetics of the forming phase, allows three-dimensional systems to be treated within relatively short simulation times. The simulated microstructure reproduces quite well the microstructure observed in experimental samples. A good agreement is obtained between the experimental and simulated ferrite recrystallisation and ferrite and austenite transformation kinetics. The present approach also models the development of the carbon concentration profile in the austenite, which is, for instance, essential for subsequent martensite formation.

Abstract: The consistent and computationally efficient stochastic statistical approach is suggestedto study kinetics of decomposition of metastable alloys. An important parameter of the theory is thesize of locally equilibrated regions at the nucleation stage which is estimated using the ``maximumthermodynamic gain'' principle suggested. For several realistic models of Fe-Cu alloys studied, the re-sults obtained agree well with kinetic Monte Carlo simulations. Application of methods developed tostudies of decomposition of Fe-Cu-Mn alloys revealed a great sensitivity of evolution to both the con-figurational and kinetic interatomic interactions in an alloy. Using for these interactions the availablefirst-principle and CALPHAD estimates, we can well reproduce the peculiar features of decomposi-tion of Fe-Cu-Mn alloys observed in experiments.

Abstract: Elastic fields, generating by precipitates, cracks, dislocations and other defects of the structure, influence the diffusion processes. It leads to the alteration of the phase transformation kinetic, segregation formation and changes of the alloy properties. However, understanding the effects of strain on diffusion in solids is now limited. One of the chief aims of our approach is to obtain the general equations for the diffusion fluxes under strain that give the possibility of using these equations at low temperatures, as in this case, the strain influence on the diffusion fluxes is manifested in maximal degree. Recently some important generalization of our approach was done and equations for the vacancy fluxes in cubic metals were obtained. Now we have made the next step in the development of approach: general equations for the fluxes in interstitial alloys are obtained for different kinds of jumps in bcc and fcc structures. We are going to discuss the main features of the theory of diffusion under stress, to compare the equations for the fluxes and to present results of theory applications that are obtained with the help of computer simulations.

Abstract: Being an effective sintering enhancer boron is gaining relevance for obtaining high density PM steels. Thermodynamic calculations are an important tool for studying the roll of alloying elements in the formation of a liquid during sintering. In the present work, the system Fe-Cr-B was obtained by combining up to date thermodynamic descriptions for the subsystems Fe-Cr, Cr-B and B-Cr. The calculations were carried out with Thermo-Calc software to predict isothermal sections for the ternary diagram for 1210 and 1250°C. The analysis of the isothermal sections indicates that the solid phases in equilibrium with the liquid are M₂B and a-BCC solid solution. The generation of the liquid is based on a eutectic reaction (Lða+(FeCr)₂B) involving the mixed borides previously formed. On the other hand, simulations for PM steels with constant boron but higher chromium content allowed realising that the formation of the liquid may be completely inhibited, within the temperature range under consideration, as materials with too high Cr/Fe ratios are used. This study was also supported by selected experiments which were in excellent agreement with the thermodynamic calculations.