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The thermal equation of state (TEOS) for solids is a mathematic model among pressure, temperature and density, and is essential for geophysical, geochemical, and other high pressure–temperature (high P–T) researches. However, in the last few decades, there has been a growing concern about the accuracy of the pressure scales of the calibrants, and efforts have been made to improve it by either introducing a reference standard or building new thermal pressure models. The existing thermal equation of state,P(V,T) = P(V,T₀) + P_th(V,T), consists of an isothermal compression and an isochoric heating, while the thermal pressure is the pressure change in the isochoric heating. In this paper, we demonstrate that, for solids in a soft pressure medium in a diamond anvil cell, the thermal pressure can neither be determined from a single heating process, nor from the thermal pressure of its calibrant. To avoid the thermal pressure, we propose to replace the thermal pressure with a well-known thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghan-expansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghan-expansion VPT TEOS model matches the experimental pressure of zero (0) GPa very well, while the pressure prediction from the approximated Anderson PVT TEOS exhibit a big deviation and a wrong trend.

 

In this work, a dataset including structural and mechanical properties of refractory multicomponent alloys was developed by fusing computations of phase diagram (CALPHAD) and density functional theory (DFT). The refractory multicomponent alloys, also named refractory complex concentrated alloys (CCAs) which contain 2–5 types of refractory elements were constructed based on Special Quasi-random Structure (SQS). The phase of alloys was predicted using CALPHAD and the mechanical property of alloys with stable and single body-centered cubic (BCC) at high temperature (over 1,500°C) was investigated using DFT-based simulation. As a result, a dataset with 393 refractory alloys and 12 features, including volume, melting temperature, density, energy, elastic constants, mechanical moduli, and hardness, were produced. To test the capability of the dataset on supporting machine learning (ML) study to investigate the property of CCAs, CALPHAD, and DFT calculations were compared with principal components analysis (PCA) technique and rule of mixture (ROM), respectively. It is demonstrated that the CALPHAD and DFT results are more in line with experimental observations for the alloy phase, structural and mechanical properties. Furthermore, the data were utilized to train a verity of ML models to predict the performance of certain CCAs with advanced mechanical properties, highlighting the usefulness of the dataset for ML technique on CCA property prediction. 

Refractory complex concentrated alloys (RCCAs) have drawn increasing attention recently owing to their balanced mechanical properties, including excellent creep resistance, ductility, and oxidation resistance. The mechanical and thermal properties of RCCAs are directly linked with the elastic constants. However, it is time consuming and expensive to obtain the elastic constants of RCCAs with conventional trial-and-error experiments. The elastic constants of RCCAs are predicted using a combination of density functional theory simulation data and machine learning (ML) algorithms in this study. The elastic constants of several RCCAs are predicted using the random forest regressor, gradient boosting regressor (GBR), and XGBoost regression models. Based on performance metrics R-squared, mean average error and root mean square error, the GBR model was found to be most promising in predicting the elastic constant of RCCAs among the three ML models. Additionally, GBR model accuracy was verified using the other four RHEAs dataset which was never seen by the GBR model, and reasonable agreements between ML prediction and available results were found. The present findings show that the GBR model can be used to predict the elastic constant of new RHEAs more accurately without performing any expensive computational and experimental work. 

In this work, the performance of the carbon doped compositionally complex alloy (CCA) MoNbTaW was studied under ambient and high pressure and high temperature conditions. TaC and NbC carbides were formed when a large concentration of carbon was introduced while synthesizing the MoNbTaW alloy. Both FCC carbides and BCC CCA phases were detected in the sample compound at room temperature, in which the BCC phase was believed to have only refractory elements MoNbTaW while FCC carbide came from TaC and NbC. Carbides in the carbon doped MoNbTaW alloy were very stable since no phase transition was obtained even under 3.1 GPa and 870 °C by employing the resistor-heating diamond anvil cell (DAC) synchrotron X-ray diffraction technique. Via in situ examination, this study confirms the stability of carbides and MoNbTaW in the carbon doped CCA even under high pressure and high temperature. 

Hardness is an essential property in the design of refractory high entropy alloys (RHEAs). This study shows how a neural network (NN) model can be used to predict the hardness of a RHEA, for the first time. We predicted the hardness of several alloys, including the novel C0.1Cr3Mo11.9Nb20Re15Ta30W20 using the NN model. The hardness predicted from the NN model was consistent with the available experimental results. The NN model prediction of C0.1Cr3Mo11.9Nb20Re15Ta30W20 was verified by experimentally synthesizing and investigating its microstructure properties and hardness. This model provides an alternative route to determine the Vickers hardness of RHEAs. 

In this work, the formation of carbide with the concertation of carbon at 0.1 at.% in refractory high-entropy alloy (RHEA) Mo15Nb20Re15Ta30W20 was studied under both ambient and high-pressure high-temperature conditions. The x-ray diffraction of dilute carbon (C)-doped RHEA under ambient pressure showed that the phases and lattice constant of RHEA were not influenced by the addition of 0.1 at.% C. In contrast, C-doped RHEA showed unexpected phase formation and transformation under combined high-pressure and high-temperature conditions by resistively employing the heated diamond anvil cell (DAC) technique. The new FCC_L12 phase appeared at 6 GPa and 809 °C and preserved the ambient temperature and pressure. High-pressure and high-temperature promoted the formation of carbides Ta3C and Nb3C, which are stable and may further improve the mechanical performance of the dilute C-doped alloy Mo15Nb20Re15Ta30W20.