Lattice distortion in high‐entropy carbide ceramics from first‐principles calculations

Abstract

The idea of high‐entropy alloys (HEAs) has profoundly stimulated the recent development of novel entropy‐stabilized ceramics. Herein we explore the local lattice distortion, one of the core effects in HEAs responsible for their extraordinary properties, in typical high‐entropy ceramic (HEC) carbides with single‐phase rock salt structures. We first quantify the local distortions based on first‐principles calculations, and then investigate their influences on the structural properties, lattice stability, electronic structures, mechanical deformation, defect energetics, and thermodynamic properties. Our results show that carbon generally exhibits the most substantial distortion. On average, large local distortion is found in (NbTiVZr)C and (MoNbTaVW)C. Such distortion plays a crucial role in stabilizing HECs by lowering their enthalpy of formation. The electronic structure of HECs depends strongly on the local distortion, which can enhance charge transfer between transition metals and carbon atoms. We further show that distortion makes HECs soft and ductile due to the delocalization of electronic charges. The formation energies of C vacancies decrease significantly due to local distortion, resulting in high concentrations of C vacancies. The presence of high‐concentration C vacancies release distortion and helps to retain the high strength of HECs. Finally, we show that lattice distortion has a great impact on the thermodynamic quantities of HECs, such as thermal expansion coefficient and Debye temperature.

Effect of alloying elements on stacking fault energies and twinnabilities in high‐entropy transition‐metal carbides

“…The influence of LLD on a is insignificant. a of ZrNbTa‐based HETMCs with distortion is in good agreement with the available experimental and theoretical data, 12,14–17,19,47,49,50 demonstrating that the present calculation is highly reliable. The phase stabilities of ZrNbTa‐based HETMCs without and with distortion are discussed in terms of formation enthalpies ∆H f calculated as Equation (2): 12 where E tot is the total energy of supercell, N i is the number of atoms in a single cell, and E i is the energy per atom of pure i in the ground state of an elemental solid 12 .…”

“…In high‐entropy materials, lattice distortion occurs because of the coexistence of different elements in the lattice, the size difference of individual atoms, and the variation of electronic structures 44,46–48 . Lattice distortion has a significant influence on the phase stability 47 .…”

“…Figure 1A,B demonstrates the crystal structures of (ZrNbTaHf)C without and with distortion, respectively. Figure 1 presents that C atoms experience the largest distortion compared to other TM elements, leading to the favorable formation of TM‐C bonds 47 …”

“…To quantitative analysis LLD, we investigate the TM‐C bond lengths 47 and standard deviation σ of the first‐ nearest neighbor distortions, as expressed in Equation (1): 48 where corresponds to data values for n data points, and . The TM‐C bond lengths of the first‐ neighbor distortions are shown in Figure 2A–D.…”

Local Lattice Distortion in High-Entropy Carbide Ceramics

“…For HECs, these are used in the theoretical simulation to study the lattice distortion. Ye et al found that the anion C atom severely deviates from its ideal lattice sites based on the ab initio calculations [16,22]. In this work, we propose the general formula to describe the local lattice distortion in HECs based on the Bader atomic radius derived from the local chemical environment.…”