Temperature dependence in interatomic potentials and an improved potential for Ti

The process of deriving an interatomic potentials represents an attempt to integrate out the electronic degrees of freedom from the full quantum description of a condensed matter system. In practice it is the derivatives of the interatomic potentials which are used in molecular dynamics, as a model for the forces on a system. These forces should be the derivative of the free energy of the electronic system, which includes contributions from the entropy of the electronic states. This free energy is weakly temperature dependent, and although this can be safely neglected in many cases there are some systems where the electronic entropy plays a significant role. Here a method is proposed to incorporate electronic entropy in the Sommerfeld approximation into empirical potentials. The method is applied as a correction to an existing potential for titanium. Thermal properties of the new model are calculated, and a simple method for fixing the melting point and solid-solid phase transition temperature for existing models fitted to zero temperature data is presented.Comment: CCP 201

Thermodynamic Assessment of the Fe-Te System. Part II Thermodynamic modelling

International audienceA thermodynamic description of the Fe-Te system modeled via the Calphad method is proposed, based on data published in a preceding publication $Part\ I:\ Experimental\ study$, and that available in literature. End-member formation energies for the phases $\beta$; $\beta'$; $\delta$, $\delta'$ and $\epsilon$; as well as lattice stabilities of FCC and BCC tellurium, have been evaluated via DFT and used in the numerical optimization. The final Gibbs energy models fit thermodynamic and phase diagram data well, and inconsistencies are discussed. The thermodynamic description is then used to evaluate Gibbs energy of formation for selected Fe-Te compounds of interest for the modeling of internal corrosion of stainless steel fuel pin cladding during operation of Liquid Metal-cooled Fast Reactors (LMFR)

Experimental study of carbides in the Ti-Cr-C system

The Ti-Cr-C system has been studied by producing samples within the MC-M3C2-M7C3 (M=Ti, Cr) and MC-M3C2-graphite equilibria. The main purpose was to determine the solubility of Cr in MC; however, the solubility of Ti in M3C2 and M7C3 was also of interest, as well as the C content in MC. Heat treatments have been performed at 1673 and 1773 K for 300 h. Thereafter, the phase compositions have been measured with energy-dispersive X-ray spectroscopy (EDS) and wavelength-dispersive X-ray spectroscopy (WDS). X-ray diffraction (XRD), in combination with Rietveld refinement, has been used to determine the lattice parameter for MC. Density functional theory (DFT) calculations were performed to estimate the lattice parameter for MC as a function of composition, and the Rietveld refined lattice parameters for MC have then been recalculated to compositions in order to verify the EDS measurements. The results show that the EDS and XRD measurements give equal results. One conclusion is that, with the current conditions, 300 h is a sufficient heat treatment time in order to reach thermodynamic equilibrium. The other main conclusion is that the solubility of Cr in MC, in general, was overestimated by previous studies due to too short heat treatment times, but also that the solubility is very temperature dependent, especially for the MC-M3C2-graphite equilibrium. This clear temperature dependence was not taken into account in the existing thermodynamic description found in the literature

An improved thermodynamic modeling of the Fe-Cr system down to zero kelvin coupled with key experiments

A thermodynamic modeling of the Fe-Cr system down to 0 K is performed on the basis of our recent comprehensive review of this binary system [W. Xiong, M. Selleby, Q. Chen, J. Odqvist, Y. Du, Evaluation of phase equilibria and thermochemical properties in the Fe-Cr system, Crit. Rev. Solid State Mater. Sci. 35 (2010) 125-152]. The model predicts a sign change for the magnetic ordering energy of mixing rather than the enthalpy of mixing in the bcc phase at 0 K. Designed key experiments are performed not only to check the validity of the present modeling but also to assist in understanding the mechanism for spinodal decomposition of the Fe-Cr alloy. Heat capacities and Curie temperatures of several Fe-rich alloys are determined between 320 and 1093 K by employing differential scanning calorimetry. The measured heat capacities are found to be in remarkable agreement with the prediction based on the present modeling. Microstructural patterns and frequency distribution diagrams of Cr are studied in alloys containing 26.65, 31.95, and 37.76 at.% Cr by using atom probe tomography. The observed phase separation results correspond well with our model-predicted boundary for the spinodal decomposition. Interestingly, a horn on the Cr-rich spinodal boundary is predicted below 200 K for the first time. This work demonstrates a way to bridge the ab initio calculations and CALPHAD approach

Prediction of Martensite Start Temperature for Lightweight Fe–Mn–Al–C Steels

A tailor-made thermodynamic database of the Fe-Mn-Al-C system was developed using the CALPHAD approach. The database enables predicting phase equilibria and thereby assessing the resulting microstructures of Fe-Mn-Al-C alloys. Available information on the martensite start (Ms) temperature was reviewed. By employing the Ms property model in the Thermo-Calc software together with the new thermodynamic database and experimental Ms temperatures, a set of model parameters for the Fe-Mn-Al-C system in the Ms model was optimised. Employing the newly evaluated parameters, the calculated Ms temperatures of the alloys in the Fe-Mn-Al-C system were compared with the available measured Ms temperatures. Predictions of Ms temperatures were performed for the alloys, Fe-10, 15 and 20 wt. Mn-xAl-yC. The predictability of the Ms model can be further validated when new experimental Ms temperatures of the Fe-Mn-Al-C system are available. © 2018, The Author(s)

An insight into using DFT data for Calphad modeling of solid phases in the third generation of Calphad databases, a case study for Al

In developing the next generation of Calphad databases, new models are used in which each term contributing to the Gibbs energy has a physical meaning. To continue the development, finite temperature density-functional-theory (DFT) results are used in the present work to discuss and suggest the most applicable and physically based model for Calphad assessments of solid phases above the melting point (the breakpoint for modeling the solid phase in previous assessments). These results are applied to investigate the properties of a solid in the superheated temperature region and to replace the melting temperature as the breakpoint with a more physically based temperature, i.e., where the superheated solid collapses into the liquid. The advantages and limitations of such an approach are presented in terms of a new assessment for unary aluminum. © 2019 Elsevier Lt

3D analysis of phase separation in ferritic stainless steels

The embrittlement of ferritic stainless steels during low temperature aging is attributed to the phase separation with Fe and Cr demixing. The small scale of the decomposed structure with only minor compositional fluctuations and short distances between the enriched and depleted regions has been a challenge for quite some time. A wide selection of experimental and modeling tools have been used to quantify these types of structures. These analyses often focus on rather late stages of decomposition where the mechanical properties are already seriously affected. The recent advance in 3D tools like phase-field and atom probe tomography have created a need for good quantitative procedures of evaluating the structure and also to link results from the continuum approach to the individual atom measurements. This work aims at addressing this need