On the stochastic phase stability of Ti2AlC-Cr2AlC

Abstract

The quest towards expansion of the Mn+1AXn design space has been accelerated with the recent discovery of several solid solution and ordered phases involving at least two Mn+1AXn end members. Going beyond the nominal Mn+1AXn compounds enables not only fine tuning of existing properties but also entirely new functionality. This search, however, has been mostly done through painstaking experiments as knowledge of the phase stability of the relevant systems is rather scarce. In this work, we report the first attempt to evaluate the finite-temperature pseudo-binary phase diagram of the Ti2AlC-Cr2AlC via first-principles-guided Bayesian CALPHAD framework that accounts for uncertainties not only in ab initio calculations and thermodynamic models but also in synthesis conditions in reported experiments. The phase stability analyses are shown to have good agreement with previous experiments. The work points towards a promising way of investigating phase stability in other MAX Phase systems providing the knowledge necessary to elucidate possible synthesis routes for Mn+1AXn systems with unprecedented properties.

High-throughput reaction engineering to assess the oxidation stability of MAX phases

“…] at elevated temperatures; here x is the stoichiometric weight of each element in the compound, ΔH form is the formation enthalpy; and ΔG SISSO is SISSO predicted entropic contribution to the ΔG form 21 . We note that the calculation of the finite-temperature phase stability of just one system may take millions of supercomputing CPU-hours, and months of actual calculation time, as demonstrated in work by a subset of these authors in the investigation of the phase stability in the Ti 2 AlC-Cr 2 AlC quaternary system 19 .…”

“…Fortunately, it has been demonstrated that DFT calculations augmented with machine learning and experimentally acquired information provides the means for predicting material properties quickly and accurately 21 . The SISSO framework, for example, is an emerging machine-learning algorithm capable of arriving at accurate predictions of material properties through models that employ physically meaningful features [17][18][19] . Here, we utilize the descriptor-based model from Bartel for the finite-temperature Gibbs energy of an arbitrary inorganic stoichiometric phase 21 :…”

“…On the computational front, assessment of the phase stability of a materials system under oxidation requires full knowledge of the finite-temperature thermodynamics of all phases likely to take part in equilibrium at particular conditions (temperature and composition of the system). This information may not be readily available in conventional thermodynamic databases and is exceedingly expensive to acquire from firstprinciples methods 19 .…”

Quantified uncertainty in thermodynamic modeling for materials design

“…In recent years, the CALPHAD community has begun to address some of these issues. In 2017, Duong et al constructed Bayesian CALPHAD models for multicomponent M AX nanolaminate materials [14]. In that work, they assessed the relative probability of stability of a number of phases by drawing samples from the CALPHAD parameter distributions and a range of composition at a specified temperature.…”

Effect of cooling rate and chromium doping on the microstructure of Al-25 at.% Ni Raney type alloy

“…As a consequence, in a number of previous studies the Al Cr phase has been omitted from the refinement due to the lack of crystal structure data (see e.g. [23]). To obtain a fit, a model of the Al Cr unit cell had to be constructed based on published atom coordinates [22].…”