Recently, a model was proposed to predict cv as a function of temperature from the absolute zero to the melting temperature applied. This solution was based on critical grain nucleation to determine the volume, which contains the total number of modes for a particular equilibrium and non-equilibrium state to calculate the density of state (DoS), which is strongly dependent on the nucleus radius for both pure element and compound. Electronic and rotational energies were regarded for both elements and compounds in this formulation. The anomalies associated with cv can be easily considered in terms of their entropies, independent of their nature, as a local change in the DoS. Comparisons of cv for elements and compounds are performed against Thermodynamics software simulations and experimental data.

Abstract The solidification of metals and alloys and the resulting microstructures, which as a function of thermal and solutal parameters can evolve as planar, cellular and dendritic, are important from a practical point of view, since they strongly influence the properties and quality of the final product. In many practical situations it is impracticable to develop analytical solutions permitting reliable predictions of microstructural growth during unsteady-state solidification conditions. The Phase Field method has become very popular and effective in modeling complex solid/liquid interfaces due to its ability to simulate the interface kinetics and the formation and evolution of different morphologies along the solidification process. In this work, a numerical analysis of the microstructural evolution during the transient solidification of dilute alloys of the Al-Cu-Si system is developed, which uses a phase-field approach for the simulation of ternary alloys. The phase-field, energy and solute concentration equations were numerically solved for the correspondent ternary system, varying the mesh parameters, temperature and alloy composition. The analysis performed were confronted with existing theoretical models and the results obtained are in agreement with the solidification theory.

Abstract This work presents an analytical method for the study of the solid state diffusion process in binary systems of two phases with cylindrical radial atomic flux. The method is developed from the differential equation that describes Fick's second law that is modified by geometric function and suitable changes of variables. The modified differential equation is solved by using a well-known closed form solution based on the error function, and then analytical equations are obtained to analyze the diffusion interface position as a function of time, and the concentration profiles as a function of time and position. The predictions provided by the analytical method are compared with numerical results.

The phase-field methods were developed mainly for studying solidification of pure materials, being then extended to the solidification of alloys. In spite of phase-field models being suitable for simulating solidification processes, they suffer from low computational efficiency. In this study, we present a numerical technique for the improvement of computational efficiency for computation of microstructural evolution for both pure metal and binary alloy during solidification process. The goal of this technique is for the computational domain to grow around the microstructure and fixed the grid spacing, while solidification advances into the liquid region. In the numerical simulations of pure metal, the phase-field model is based on the energy and phase equations, while, for binary alloy, the said model is based on the concentration and phase equations. Since the thermal diffusivity in the energy equation is much larger than the diffusivity term in phase equation in pure metal system, about twenty eight times the difference between them. The computational domain growth around the microstructure is controlled according with the thermal diffusivity for pure material in the liquid region. In the numerical simulation of dendritic evolution of Fe-C alloy, the idea is similar, i.e., the solute diffusivity in concentration equation is larger than the diffusivity term in phase equation in the liquid region, in this case eleven times the difference in Fe-C alloy system. The computational domain growth is controlled via solute diffusivity in the liquid region. Hence, phase-field model is proposed with an adaptive computational domain for efficient computational simulation of the dendritic growth in a system for both pure metal and binary alloy. The technique enables us to reduce by about an order of magnitude the run time for simulation of the solidification process. The results showed that the microstructure with well-developed secondary arms can be obtained with low computation time.

Nesse trabalho, a transição colunar/equiaxial (TCE) foi investigada experimentalmente na solidificação unidirecional de três ligas multicomponentes à base de alumínio (Al-nSi-3Cu), com “n” igual a 5,5, 7,5 e 9% em massa. Os principais parâmetros analisados foram o gradiente de temperatura (GL), a velocidade de deslocamento da isoterma liquidus (VL), a taxa de resfriamento (TR) e a composição de Si. Um dispositivo de solidificação direcional refrigerado à agua para fluxo de calor transitório foi utilizado. Para todas as ligas examinadas, os resultados mostram que a concentração de soluto inflencia na posição da TCE, a qual ocorre para uma taxa de resfriamento igual a 1.17 0C/s. A análise comparativa entre os resultados desse trabalho com os da literatura, propostos para analizar a TCE em ligas Al-Si, é conduzida e os resultados mostram que o final da região colunar acontece para uma taxa de resfriamento sete vezes maior que a encontrada para ligas Al-Si.

In this work the columnar to equiaxed transition (CET) was experimentally investigated in the unidirectional solidification of three aluminum based multicomponent alloys (Al-nSi-3Cu), with "n" equal to 5.5, 7.5 and 9 wt.%. The main parameters analyzed include the tip temperature gradient (GL), tip growth rate (VL), tip cooling rate (TR) and Si content. A water-cooled solidification experimental setup was developed, and specimens were solidified under unsteady state heat flow conditions. It is shown that for the alloys examined, the solute concentration influences the position of the CET, which occurs for an average cooling rate of about 1.17 0C/s. A comparative analysis between the results of this work and those from literature proposed to analyze the CET during upward vertical solidification of Al-Si alloys is reported and the results show that the end of the columnar region is abbreviated as a result of seven times higher critical cooling rate than that verified for Al-Si alloys.