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This study focuses on developing precise machine learning (ML) regression models for predicting energy bandgap values based on chemical compositions and crystal structures. The primary aim is to match the accuracy of predictions derived from GGA-PBE calculations and validate them through density functional theory (DFT)-based band structure calculations. We assessed eight standalone ML regression models, including AdaBoost, Bagging, CatBoost, LGBM, RF, DT, GB, and XGB. These models were analyzed for their ability to predict GGA-PBE bandgap values across diverse material structures and compositions, using a dataset containing bandgap values for 106,113 compounds. Additionally, we constructed four ensemble models using the stacking method and seven using the bagging method. These ensemble models incorporated RidgeCV and LassoCV to explore if ensemble techniques could enhance prediction accuracy. The dataset was divided into subsets of varying sizes: 10,000, 25,000, 50,000, and 100,000 entries. We determined feature importance through permutation techniques and established a correlation coefficient matrix using the Pearson correlation method. The Random Forest (RF) model emerged as the top performer among standalone models, achieving an R2 value of 0.943 and an RMSE value of 0.504 eV. Bagging regression demonstrated improved performance across different dataset sizes with streamlined feature selection. Ensemble models, particularly bagging, consistently outperformed standalone models, achieving the best R2 value of 0.948 and an RMSE value of 0.479 eV in the test dataset. Using the best-performing model, we predicted bandgap values for new half-Heusler compounds with 18 valence electron counts. These predictions were successfully validated using accurate DFT calculations. DFT calculations indicated that the newly predicted compounds are narrow bandgap semiconductors with dynamic stability., Comment: 17 pages, 17 figures, Research paper

In this study, we attempted to model vacancy ordered half Heusler compounds with 18 valence electron count (VHH) derived from 19 VEC compounds such as TiNiSb such that the compositions will be Ti0.75NiSb, Zr0.75NiSb and Hf0.75NiSb with semiconducting behavior. The main motivation is that such a vacancy-ordered phase not only introduces semi conductivity but also it disrupts the phonon conducting path in HH alloys and thus reduces the thermal conductivity and as a consequence enhances the thermoelectric figure of merit. In order to predict the formation energy ({\Delta}Hf) from composition and crystal structure we have used 4684 compounds for their {\Delta}Hf values are available in the material project database and trained a machine learning model with R2 value of 0.943. Using this trained model, we have predicted the {\Delta}Hf of a list of VHH. From the predicted database of VHH we have selected Zr0.75NiSb and Hf0.75NiSb to validate the machine learning prediction using accurate DFT calculation. The calculated {\Delta}Hf for these two compounds from DFT calculation are found to be comparable with our ML prediction. The calculated electronic and lattice dynamics properties show that these materials are narrow band gap semiconductors and are dynamically stable as their all-phonon dispersion curves are having positive frequencies. The calculated Seebeck coefficient, electrical conductivity as well as thermal conductivity, power factor and thermoelectric figure of merit are analyzed., Comment: 5 pages, 2 figures, conference

The alloys with 8/18/24 valence electron count (VEC) are promising candidates for efficient energy conversion and refrigeration applications at low as well as high temperatures. The full potential linearized augmented plane wave method as implemented in WIEN2k code was used to investigate electronic structure and TE transport properties with the PBE$-$GGA and TB$-$mBJ exchange potentials and Boltzmann transport theory. The calculated single crystal elastic constants, phonon dispersion and phonon density of states confirm that these systems are mechanically and dynamically stable. The TE transport properties is calculated by including the lattice part of thermal conductivity ($\kappa_{L}$) obtained from two methods one from the calculated elastic properties calculation ($\kappa^{elastic}_{L}$) and the other from phonon dispersion curve ($\kappa^{phonon}_{L}$). The strong phonon$-$phonon scattering by large mass difference/strain fluctuation of isovalent/aliovalent substitution at Ti/Sn sites of Fe$_{2}$TiSn reduces the lattice thermal conductivity which results in high \textit{ZT} value of 0.81 at 900\,K for Fe$_{2}$Sc$_{0.25}$Ti$_{0.5}$Ta$_{0.25}$Al$_{0.5}$Bi$_{0.5}$. The comparative analysis of TE transport properties using the band structures calculated with the PBE$-$GGA and TB$-$mBJ functional shows that the \textit{ZT} value obtained from TB$-$mBJ scheme is found to be significantly higher than that based on PBE$-$GGA. The calculated relatively low lattice thermal conductivity and high \textit{ZT} values suggest that isovalent/aliovalent substituted Fe$_{2}$TiSn are promising candidates for medium to high temperature waste heat recovery.

In this study, we have reported electronic structure, lattice dynamics, and thermoelectric (TE) transport properties of a new family of pentanary substituted TiNiSn systems using the 18 valence electron count (VEC) rule. From our calculated band structures and density of states, we show that by preserving the 18 VEC through aliovalent substitutions at the Ti site of TiNiSn semiconducting behavior can be achieved, and hence one can tune the band structure and band gap to maximize the thermoelectric figure of merit (ZT) value. Two approaches have been used for calculating the lattice thermal conductivity ($\kappa_{L}$), one by fully solving the linearized phonon Boltzmann transport (LBTE) equation from first$-$principles anharmonic lattice dynamics calculations implemented in Phono3py code and other using Slack's equation with calculated Debye temperature and Gr\"{u}neisen parameter using the calculated elastic constant values. The calculated $\kappa_{L}$ values decrease from parent TiNiSn to pentanary substituted TiNiSn systems as expected due to fluctuation in atomic mass. The calculated $\kappa_{L}$ for Hf containing systems La$_{0.25}$Hf$_{0.5}$V$_{0.25}$NiSn and non Hf containing system La$_{0.25}$Zr$_{0.5}$V$_{0.25}$NiSn calculated from Phono3py (Slack's equation) are found to be 0.37 (1.04) and 0.16 (0.95) W/mK, at 550\,K, respectively and the corresponding ZT value are found to be 0.54 (0.4) and 0.77 (0.53). Among the considered systems, the calculated phonon spectra and heat capacity show that La$_{0.25}$Hf$_{0.5}$V$_{0.25}$NiSn has more optical$-$acoustic band mixing which creates more phonon$-$phonon scattering and hence lower the $\kappa_{L}$ value and maximizing the ZT. Based on the calculated results we conclude that one can design high-efficiency thermoelectric materials by considering the 18 VEC rule with aliovalent substitution., Comment: 16 pages, 10 figures, full article

To understand the effect of isoelectronic substitution on thermoelectric properties of TiCoSb based half - Heusler (HH) alloys, we have systematically studied the transport properties with substitution of Zr at Ti and Bi at Sb sites. The electronic structure of TixZr1-xCoSbxBi1-x (x = 0.25, 0.5, 0.75) and parent TiCoSb are investigated using the full potential linearized augmented plane wave method and the thermoelectric transport properties are calculated on the basis of semiclassical Boltzmann transport theory. The band analysis of the calculated band structures reveal that TixZr1-xCoSbxBi1-x has semiconducting behavior with indirect band gap at x = 0.25, 0.5 concentration and direct band gap behavior at x = 0.75 concentration. The TixZr1-xCoSbxBi1-x (x = 0.25, 0.5, 0.75) compounds show smaller band gap values as compared to the pure TiCoSb. The d electrons of Ti/Zr and Co dominate the electronic transport properties of TixZr1-xCoSbxBi1-x system. All these systems follow the empirical rule of 18 valence-electron content to bring semiconductivity in HH alloys. The isoelectronic substitution in TiCoSb can tune the band structure by shifting the Fermi level. This provides us lot of possibilities to get the desired band gap values for designing thermoelectrics with high efficiency. In this study we have showed that the isoelectronic substitution at both Ti and Sb site of TiCoSb has very small effect for increasing the ZT values and one should go for isoelectronic substitution at any one sites of TiCoSb HH alloys alone to improve ZT.

The electronic structures of TixZrx/2CoPbxTex, TixZrx/2Hfx/2CoPbxTex (x = 0.5), and the parent compound TiCoSb were investigated using the full potential linearized augmented plane wave method. The thermoelectric transport properties of these alloys are calculated on the basis of semi-classical Boltzmann transport theory. From the band structure calculations we show that the substitution of Zr,Hf in the Ti site and Pb and Te in the Sb site lower the band gap value and also change the indirect band (IB) gap of TiCoSb to the direct band (DB) gap. The calculated band gap of TiCoSb, TixZrx/2CoPbxTex, and TixZrx/2Hfx/2CoPbxTex are 1.04 eV (IB), 0.92 eV (DB), and 0.93 eV (DB), respectively. All these alloys follow the empirical rule of 18 valence-electron content which is essential for bringing semiconductivity in half Heusler alloys. It is shown that the substitution of Hf at the Ti site improve the ZT value (~1.05) at room temperature, whereas there is no significant difference in ZT is found at higher temperature. Based on the calculated thermoelectric transport properties, we conclude that the appropriate concentration of Hf substitution can further improve the thermoelectric performance of TixZrx/2Hfx/2CoPbxTex.

In order to improve the thermoelectric performance of TiCoSb we have substituted 50% of Ti equally with Zr and Hf at Ti site and Sb with Sn and Se equally at Sb site. The electronic structure of Ti0.5Zr0.25Hf0.25CoSn0.5Se0.5 is investigated using the full potential linearized augmented plane wave method and the thermoelectric transport properties are calculated on the basis of semi-classical Boltzmann transport theory. Our band structure calculations show that Ti0.5Zr0.25Hf0.25CoSn0.5Se0.5 has semiconducting behavior with indirect band gap value of 0.98 eV which follow the empirical rule of 18 valence-electron content to bring semiconductivity in half Heusler compounds, indicating that one can have semiconducting behavior in multinary phase of half Heusler compounds if they full fill the 18 VEC rule and this open-up the possibility of designing thermoelectrics with high figure of merit in half Heusler compounds. We show that at high temperature of around 700K Ti0.5Zr0.25Hf0.25CoSn0.5Se0.5 has high thermoelectric figure of merit of ZT = 1.05 which is higher than that of TiCoSb (~ 0.95) suggesting that by going from ternary to multinary phase system one can enhance the thermoelectric figure of merit at higher temperatures.