Accurate and Efficient Calculation of the Solution Enthalpy and Diffusivity of Solutes in Liquid Metals Using Machine Learning Potential.

Liquid metals (LMs) have various applications in energy systems, such as coolants in advanced nuclear reactors. In addition, room-temperature LMs are attracting attention as flexible components in robotics and electronics and as novel chemical reaction media to form low-dimensional materials. In many of these applications, the capabilities of LMs can be further enhanced if one can better understand and control the chemical reactivity of LMs, which is largely affected by the stability and mobility of solutes in LMs. Here, we propose an automated method using a machine learning moment tensor potential to efficiently calculate the solution enthalpy and diffusivity of solutes in LMs. From several test cases in liquid Na, we demonstrate that the method can achieve an accuracy comparable to that of a direct calculation using first-principles molecular dynamics, while significantly reducing the calculation cost to the order of 1/10 to 1/100. The method is expected to contribute to the advancement of LM chemistry and the development of new LMs.

Correction methods for first-principles calculations of the solution enthalpy of gases and compounds in liquid metals.

Liquid metals (LMs) have a wide range of engineering applications, such as in coolants, batteries, and flexible electronics. While accurate calculation methods for thermodynamic properties based on density functional theory (DFT) have been extensively developed for solid materials, including methods to correct identified systematic errors, almost no attempt has been made for LMs. In the present study, four correction methods for the first-principles calculation of the solution enthalpy of gases and compounds in LMs are proposed, namely, Correction-1, using the experimental binding energy of an impurity gas molecule; Correction-2, additionally using the experimental enthalpy of formation of a solid compound composed of LM and gas-impurity elements; Correction-3, using the concept of the fitted elemental-phase reference energies (FERE) method; and Correction-4, using the concept of the coordination corrected enthalpies (CCE) method. The performance of each method is examined with hydrogen, nitrogen, oxygen, and iodine gases and their sodium compounds in liquid sodium, and the operating principle of each method is clarified. In general, the four correction methods effectively reduce the calculation error, and Correction-2 reduces the error to less than 10 kJ mol-1, while the uncorrected errors are up to several tens of kJ mol-1. This study demonstrates that, with appropriate correction, the DFT calculation of the solution enthalpy of impurities in LMs can achieve the same level of accuracy as in precise experiments.

Solution enthalpy calculation for impurity in liquid metal by first-principles calculations: A benchmark test for oxygen impurity in liquid sodium.

The solution enthalpy of oxygen in liquid Na was calculated as a test case for the computational method to evaluate the solution enthalpy in liquid metal using first-principles calculations. To obtain the necessary thermodynamic quantities at high temperatures, (i) first-principles molecular dynamics for pure and O-including liquid Na systems, (ii) vibration analysis for an O2 molecule, and (iii) phonon-based quasi-harmonic approximation for solid Na and Na2O were conducted. The calculation results were compared with available experimental data to validate the method. Consequently, the O2 solution enthalpy was calculated to be -387.1 kJ/mol at 600 K and -374.0 kJ/mol at 1000 K, comparable to the experimental data of -375.7 kJ/mol at 600 K and -369.3 kJ/mol at 1000 K. The Na2O solution enthalpy was calculated to be 28.6 kJ/mol at 600 K and 38.2 kJ/mol at 1000 K, while the experimental data gave a temperature-independent value of 46.9 kJ/mol. The possible causes of errors in the calculations were discussed. This work shows that computational calculations can contribute to establishing a fundamental database on the solubility of impurities in liquid metals.

Structural and chemical analysis of second-row impurities in liquid lead-bismuth eutectic by first-principles molecular dynamics.

The structural and chemical states of the second-row impurities in liquid lead-bismuth eutectic (LBE) are studied by first-principles molecular dynamics. First, several structural quantities such as the number of first-neighboring atoms and the LBE-impurity-LBE characteristic angle are obtained to determine the impurity-LBE local structure. Next, the impurity charge states and the electronic density of states are analyzed to reveal the chemical states of the impurities in the liquid LBE. It is observed that for the majority of impurities the 2p-6p interaction specifies the local structure around the impurity as well as the chemical state of the impurity. The anisotropy in the 2p-6p covalent interaction causes the tetrahedron-wise structures for B, C, N, and O, and the ionic interaction is relatively strong for Li and F. The change in the interaction scheme over the second-row impurities can be explained from the downward shift of the 2s and 2p orbital energy levels as the atomic number increases. Further, some impurities indicate interaction preferences for either Pb or Bi. These findings can assist the understanding and prediction of the behavior of impurity atoms in liquid LBE.