First-principles Phonon Calculations Research Articles

Exploring the effect of alloying elements on the thermoelasticity and strength of bcc Fe-based alloys by first-principles phonon calculations

Designing compositions for novel alloys requires a fundamental grasp of the role of each alloying element in its properties. This study delves into the influence of alloying elements in Ultra-High Strength Steels on essential high-temperature properties, including thermoelasticity, thermal stress, and strength, utilizing first-principles phonon calculations. These properties are pivotal for steels used in high-temperature applications. Our investigation quantitatively forecasts the impact of alloying elements on elastic properties, providing valuable insights for advanced alloy design in high-temperature environments. The introduction of alloying elements markedly amplifies the elastic modulus of Fe-based alloys. The Ni, Mo, Cr, and C elements significantly enhance the anisotropy of the alloy. While refining elastic modulus and mechanical properties, alloying elements induce thermal stress, posing a potential risk of high-temperature cracking. The quantitative analysis underscores the robust strengthening potential for C, Ni, Mo, and W elements, with interstitial C emerging as pivotal in enhancing mechanical properties. The findings of this study illuminate the diverse roles played by different alloying elements and offer theoretical guidance for the design of advanced Ultra-High Strength Steels.

Thermoelectric properties of the bismuth oxychalcogenides Bi2SO2, Bi2SeO2 and Bi2TeO2

We present a detailed theoretical study of the thermoelectric properties of the bismuth oxychalcogenides Bi2ChO2 (Ch = S, Se, Te). The electrical transport is modelled using semi-classical Boltzmann transport theory with electronic structures from hybrid density-functional theory, including an approximate model for the electron lifetimes. The lattice thermal conductivity is calculated using first-principles phonon calculations with an explicit treatment of anharmonicity, yielding microscopic insight into how partial replacement of the chalcogen in the bismuth chalcogenides impacts the phonon transport. We find very good agreement between the predicted transport properties and a favourable cancellation of errors that allows for near-quantitative predictions of the thermoelectric figure of merit ZT. Our calculations suggest recent experiments on n-doped Bi2SeO2 have achieved close to the largest ZT possible in bulk materials, whereas the largest reported ZT for Bi2TeO2 could be improved sixfold by optimising the carrier concentration. We also predict that much larger ZT > 2.5, competitive with the benchmark thermoelectric SnSe, could be obtained for Bi2SO2 and Bi2SeO2 with heavy p-type doping. This study demonstrates the predictive power of this modelling approach for studying thermoelectrics and highlights several avenues for improving the performance of the Bi2ChO2.

Temperature-Dependent Elastic Properties of B4C from First-Principles Calculations and Phonon Modeling

Boron carbide plays a crucial role in various extreme environment applications, including thermal barrier coatings, aerospace applications, and neutron absorbers, because of its high thermal and chemical stability. In this study, the temperature-dependent elastic stiffness constants, thermal expansion coefficient, Helmholtz free energy, entropy, and heat capacity at a constant volume (Cv) of rhombohedral B4C have been predicted using a quasi-harmonic approach. A combination of volume-dependent first-principles calculations (density functional theory) and first-principles phonon calculations in the supercell framework has been performed. Good agreement between the elastic constants and structural parameters from static calculations is observed. The calculated thermodynamic properties from phonon calculations show trends that align with the literature. As the temperature rises, the predicted free energy follows a decreasing trend, while entropy and Cv follow increasing trends with temperature. Comparisons between the predicted room temperature thermal expansion coefficient (TEC) (7.54×10−6 K−1) and bulk modulus (228 GPa) from the quasi-harmonic approach and literature results from experiments and models are performed, revealing that the calculated TEC and bulk modulus fall within the established range from the limited set of data from the literature (TEC = 5.73–9.50 ×10−6 K−1, B = 221–246 GPa). Temperature-dependent Cijs are predicted, enabling stress analysis at elevated temperatures. Overall, the outcomes of this study can be used when performing mechanical and thermal stress analysis (e.g., space shielding applications) and optimizing the design of boron carbide materials for elevated temperature applications.

Entropy-stabilized binary alloys

Alloying W with Re is an effective method for improving its intrinsic ductility. The solubility limit of Re in W is ∼27% at 851 K. However, this alloy possesses a high enthalpy of formation, which can result in phase-instability. Configurational entropy alone cannot stabilize this alloy as a single-phase solid solution. Recent research questions the importance of configurational entropy in determining the single-phase stability of “complex, concentrated solid solutions” and suggests that vibrational entropy may play a critical role. The question arises: Can vibrational entropy contribute significantly enough to ensure single-phase stability in a binary alloy? Our first-principles phonon calculations using density functional theory demonstrate that vibrational entropy is equally essential as the configurational entropy in promoting the formation of a single-phase solid solution in WRe binary alloys. This finding necessitates revisiting the role of vibrational entropy in the single-phase stability of binary alloys.

First-principles phonon calculations of neodymium-magnet compounds

We report first-principles investigations of the light-element effect on phonon states in neodymium-magnet compounds. It is found that B in Nd2Fe14B contributes to acoustic phonon hardening. As for the substitution of other light elements for B, frequencies of phonons that originate from light elements decrease with increasing the atomic number. However, imaginary phonons in Nd2Fe14F are attributed to the electronic states and the atomic configurations, not to the heavier mass of F. In addition, as the effect of the magnetic disordering on the phonon state, we show that the phonons of the paramagnetic Nd2Fe14B are softer than those of the ferromagnetic Nd2Fe14B. This suggests that the phonon effect decreases the Curie temperature through the stabilization of the paramagnetic state.

Anharmonicity Reveals the Tunability of the Charge Density Wave Orders in Monolayer VSe2.

VSe2 is a layered compound that has attracted great attention due to its proximity to a ferromagnetic state that is quenched by its charge density wave (CDW) phase. In the monolayer limit, unrelated experiments have reported different CDW orders with different transition temperatures, making this monolayer very controversial. Here we perform first-principles nonperturbative anharmonic phonon calculations in monolayer VSe2 in order to estimate the CDW order and the corresponding transition temperature. They reveal that monolayer VSe2 develops two independent charge density wave orders that compete as a function of strain. Variations of only 1.5% in the lattice parameter are enough to stabilize one order or the other. Moreover, we analyze the impact of external Lennard-Jones interactions, showing that these can act together with anharmonicity to suppress the CDW orders. Our results solve previous experimental contradictions, highlighting the high tunability and substrate dependency of the CDW orders of monolayer VSe2.

First-principles Phonon Calculations with Phonopy and Phono3py

Harmonic, quasi-harmonic, and anharmonic phonon properties of crystals are getting to be better predicted using first-principles phonon calculations by virtue of the progress of the calculation methods and increasing computer power. In this review, basic formulae of phonon properties are reviewed with the phonon calculation examples performed using the phonon calculation codes, phonopy and phono3py, combined with the first-principles calculations. The computational workflow to utilize the first-principles phonon calculation is straightforward and its automation is of great interest to science. Therefore, a few practical applications of the automated first-principles phonon calculations are also presented.

A new semiconducting full Heusler Li2BeX (X = Si, Ge and Sn): first-principles phonon and Boltzmann calculations

The Full Potential-Linearized Augmented Plane Wave (FP-LAPW) is employed into density functional theory (DFT) within WIEN2k package to explore and investigate the thermoelectric, mechanical, electronic and structural properties of full-Heusler alloys Li2BeX (X = Si, Ge and Sn) were explored. The exchange and correlation potential are treated by different approximations: the generalized gradient approximation with Perdew–Burke–Ernzerhof scheme (GGA-PBE) and Tran–Blaha modified Becke–Johnson (mBJ-GGA). The results achieved for the electronic properties show that these compounds are semiconductor in nature with an indirect band gap, of values: 0.60 eV, 0.55 eV and 0.24 eV for Li2BeSi, Li2BeGe and Li2BeSn, respectively. In addition, these materials are mechanically stable owing to the fact that the conditions required for this mechanical stability satisfy Born’s criteria, and are of a brittle nature due to the calculated values of the ratios (B/G), on the other hand, these compounds are dynamically stable due to the non-presence of negative frequencies following the detailed study of phonons. These compounds are characterized by a high figure of merit (ZT) (close to unity) and high Seebeck coefficient (S), making them promising candidates for thermoelectric applications.

A thermochemical database from high-throughput first-principles calculations and its application to analyzing phase evolution in AM-fabricated IN718

A comprehensive thermochemical database is constructed based on high–throughput first-principles phonon calculations of over 3000 atomic structures in limited concentrations in Ni, Fe, and Co alloys involving a total of 26 elements including Al, B, C, Cr, Cu, Hf, La, Mn, Mo, N, Nb, O, P, Re, Ru, S, Si, Ta, Ti, V, W, Y, and Zr, providing thermochemical data largely unavailable from existing experiments. The database can be employed to predict the equilibrium phase compositions and fractions directly from first-principles by minimizing the chemical potential of a multicomponent system with a fixed overall chemical composition and a fixed temperature. It is applied to the additively manufactured nickel-based IN718 superalloy to analyze the phase evolution with temperature. IN718 is known for its great performance in tensile, fatigue, creep, and rupture strength, combined with easy fabrication and corrosion resistance. In particular, we successfully predicted the formation of L10-FeNi, γ’-Ni3(Fe,Al), α-Cr, δ-Ni3(Nb,Mo), γ”-Ni3Nb, and η-Ni3Ti at low temperatures (below 680 K), γ’-Ni3Al, δ-Ni3Nb, γ”-Ni3Nb, α-Cr, and γ-Ni(Fe,Cr,Mo) at intermediate temperatures (between 680 and 1140 K), and δ-Ni3Nb and γ-Ni(Fe,Cr,Mo) at high temperatures (above 1140 K) in IN718. These predictions are validated by EDS mapping of compositional distributions and corresponding identifications of phase distributions. The database is expected to be a valuable source for future thermodynamic analysis and microstructure prediction of alloys involving the 26 elements.

Effect of twin grain boundary on material thermal expansion

Based on first-principles phonon calculations within the framework of quasiharmonic approximation, we study the effect of twin grain boundary (TGB) on the thermal expansion of insulating materials. We select diamond-structure solids (C, Si, and Ge) and rutile $({\mathrm{SnO}}_{2})$ as representatives of the covalent and ionic bonding materials that are important systems commonly accompanied with TGB. We found distinct effects of TGB on thermal expansion in two types of materials. For diamond-structure solids, the thermal expansion of (111)-oriented twinning structure varies subtly from that of pristine material within the temperature range studied, which is primarily induced by the modification of vibrational phonon mode by the TGB effect. Distinctly, the thermal expansion of $\mathrm{SnO}_{2}$ twinnings increase substantially by comparison with the pristine case and depend strongly on the twin orientation. The (101) twinning shows much larger thermal expansion than the (301) twinning. Further analysis indicates the physical mechanism can be mainly attributed to the effect of rotational degree of freedom of the $\mathrm{SnO}_{6}$ octahedron motif and the stress induced by TGB. Our work reveals the physical mechanism underlying the distinct effect of TGB on thermal expansion caused by different chemical bonding, and meanwhile provides an insightful understanding of the relationship between specific structural features and thermal expansion in solid-phase materials.

Design of Fe2B-based ductile high temperature ceramics: First-principles calculations and experimental validation

Iron Boride (Fe2B) has significant potential to be used as a wear- and corrosion-resistant ceramic because of its high hardness, good corrosion resistance, and low cost. However, the toughness and elastic heat resistance of Fe2B can be further improved under high-temperature wear conditions. First-principles energetics and phonon calculations showed that Ti, Cr, Mn, Co, Ni, Nb, Mo, Ta, and W can dissolve in Fe2B. Among these, Cr, Mn, and Ni can form a continuous solid solution in (Fe, M)2B. Furthermore, Ti, Cr, Mn, Co, Ni, Cu, Y, Nb, Mo, Ta, and W improved the toughness of Fe2B. The results were validated by the experimental results. It was found that the experimental fracture toughness of Fe2B doped with Cr and Ni reached 4.16 and 4.27 MPa m1/2, respectively, which are higher than 3.64 MPa m1/2 of pure Fe2B. Chemical bond analyses showed that the toughness was improved owing to the stiffening of the B–B bond and the invariability of the Fe–B bond in Fe2B by doping Cr and Ni with increasing pressure. The elastic heat resistance of alloyed Fe2B was related to the degree to which the B–B and Fe–B bonds weakened with temperature. The less these bonds strength weakened with increasing temperature, the better the elastic heat resistance. The bond strength of Fe–B and B–B bonds in Fe2B doped with Cr showed a minimum decrease with increasing temperature, whereas the bond strength of Fe–B and B–B bonds in Fe2B doped with Ta showed a maximum decrease with increasing temperature. This indicates that the alloying element Cr can improve the elastic heat resistance of Fe2B, while Ta decreases the elastic heat resistance of Fe2B.

First-principles phonon calculations for lattice dynamics, thermal expansion and lattice thermal conductivity of CoSi in the high temperature region

This study presents the first-principles phonon calculations to understand the experimental thermal expansion () and lattice thermal conductivity of CoSi in the high temperature region. Phonon dispersion is computed using the finite displacement method and supercell approach by taking the equilibrium crystal structures obtained from DFT. The calculation of is done under quasi-harmonic approximation. The is calculated using first-principle anharmonic lattice dynamics calculations under single-mode relaxation time approximation. The calculated in the temperature range 0–1300 K gives a good match with existing experimental data. The calculated value of (∼8.0 W/mK) at 300 K is found to be in good agreement with the experimental value of ∼8.3 W/mK. The temperature dependence of phonon lifetime due to phonon-phonon interaction is calculated to understand the behaviour of . The present study suggests that ground state phonon dispersion obtained from DFT-based methods gives reasonably good explanation of experimental and .

High-Pressure Mg–Sc–H Phase Diagram and Its Superconductivity from First-Principles Calculations

In this work, global search for crystal structures of ternary Mg-Sc-H hydrides (Mg$_x$Sc$_y$H$_z$) under high pressure ($100 \le P \le 200$ GPa) were performed using the evolutionary algorithm and first-principles calculations. Based on them, we computed the thermodynamic convex hull and pressure-dependent phase diagram of Mg$_x$Sc$_y$H$_z$ for $z/(x+y) < 4$. We have identified the stable crystal structures of four thermodynamically stable compounds with the higher hydrogen content, i.e., $R\bar{3}m$-MgScH$_{6}$, $C2/m$-Mg$_{2}$ScH$_{10}$, $Immm$-MgSc$_{2}$H$_{9}$ and $Pm\bar{3}m$-Mg(ScH$_{4}$)$_{3}$. Their superconducting transition temperatures were computationally predicted by the McMillan-Allen-Dynes formula combined with first-principles phonon calculations. They were found to exhibit superconductivity; among them, $R\bar{3}m$-MgScH$_{6}$ was predicted to have the highest $T_{c}$ (i.e. 23.34 K) at 200 GPa.

Thermoelectric performance of novel single-layer ZrTeSe4.

In energy conversion techniques, two-dimensional (2D) thermoelectric materials with high performance are strongly required. This study scrutinizes the electronic and thermoelectric properties of 2D single-layer (1L) ZrTeSe4 based on first-principles calculations combined with Boltzmann transport theory. First-principles molecular dynamics simulations and phonon calculations confirm the thermodynamic stability of 1L-ZrTeSe4. Furthermore, the electron mobility of 1L-ZrTeSe4 is calculated to be ∼5706 cm2 V-1 s-1, which is much higher than that of the typical 2D semiconducting materials. Intriguingly, the calculated lattice thermal conductivity of 1L-ZrTeSe4 is found to be 3.16 W m-1 K-1 at room temperature, which is relatively smaller than that of 2D transition metal dichalcogenides. The maximum figure of merit ZT of 1L-ZrTeSe4 at 900 K is ∼0.8 for both p- and n-type doping at optimal carrier concentrations. As ZT could be improved through the manipulation of its electronic structure, this is an important clue indicating the enormous potential of 1L-ZrTeSe4 in thermoelectric application.

Forming mechanism of equilibrium and non-equilibrium metallurgical phases in dissimilar aluminum/steel (Al\u2013Fe) joints

Forming metallurgical phases has a critical impact on the performance of dissimilar materials joints. Here, we shed light on the forming mechanism of equilibrium and non-equilibrium intermetallic compounds (IMCs) in dissimilar aluminum/steel joints with respect to processing history (e.g., the pressure and temperature profiles) and chemical composition, where the knowledge of free energy and atomic diffusion in the Al–Fe system was taken from first-principles phonon calculations and data available in the literature. We found that the metastable and ductile (judged by the presently predicted elastic constants) Al6Fe is a pressure (P) favored IMC observed in processes involving high pressures. The MoSi2-type Al2Fe is brittle and a strong P-favored IMC observed at high pressures. The stable, brittle η-Al5Fe2 is the most observed IMC (followed by θ-Al13Fe4) in almost all processes, such as fusion/solid-state welding and additive manufacturing (AM), since η-Al5Fe2 is temperature-favored, possessing high thermodynamic driving force of formation and the fastest atomic diffusivity among all Al–Fe IMCs. Notably, the ductile AlFe3, the less ductile AlFe, and most of the other IMCs can be formed during AM, making AM a superior process to achieve desired IMCs in dissimilar materials. In addition, the unknown configurations of Al2Fe and Al5Fe2 were also examined by machine learning based datamining together with first-principles verifications and structure predictions. All the IMCs that are not P-favored can be identified using the conventional equilibrium phase diagram and the Scheil-Gulliver non-equilibrium simulations.

Effect of Halogen Ions on the Low Thermal Conductivity of Cesium Halide Perovskite

The lattice dynamics of CsSnX3 (X = Cl, Br, and I) and CsPbI3, which are low-thermal-conductivity materials, are investigated using first-principles phonon calculations. Because of the strong lattice anharmonicity and the accompanying instability of high-temperature cubic phases, the self-consistent phonon theory, which can incorporate the effect of lattice anharmonicity at a mean-field level, is applied in this study. The calculated lattice thermal conductivity reproduced a low thermal conductivity, as shown experimentally, owing to the short phonon lifetime due to the incoherent scattering contribution of Cs atoms. The halogen ion dependence on thermal conductivity reveals that CsSnCl3 exhibits an anomalous lattice thermal conductivity that is as low as that of CsSnBr3. This indicates that the lattice dynamics cannot be explained merely in terms of the atomic mass of the compounds. The low thermal conductivity of CsSnCl3 is caused by the exceptionally short phonon lifetime; further, a bonding analysis suggests that covalent bonding contributes significantly to the unusual anharmonicity of CsSnCl3.

Controlling the off-center positions of anions through thermodynamics and kinetics in flexible perovskite-like materials

Due to the network flexibility of their BX3 sub-lattice, a manifold of polymorphs with potential multiferroic applications can be found in perovskite-like ABX3 materials under different pressure and temperature conditions. The potential energy surface of these compounds usually presents equivalent off-center positions of anions connected by low energetic barriers. This feature facilitates a competition between the thermodynamic and kinetic control of the transitions from low to high symmetry structures, and explains the relationship between the rich polymorphism and network flexibility. In the rhombohedral phase of iron trifluoride, our first-principles electronic structure and phonon calculations reveal the factors that determine which of the two scenarios dominates the transition. At the experimentally reported rhombohedral-cubic transition temperature, the calculated fluorine displacements are fast enough to overcome forward and backward a barrier of less than 30 kJ mol-1, leading to an average structure with cubic symmetry. In addition, lattice strain effects observed in epitaxial growth and nanocrystallite experiments involving BX3 compounds are successfully mimicked by computing the phase stability of FeF3 under negative pressures. We predict a transition pressure at -1.8 GPa with a relative volume change around 5%, consistent with a first-order transition from the rhombohedral to the cubic structure. Overall, our study illustrates how, by strain tuning, either a thermodynamic or a kinetic pathway can be selected for this transformation.

Temperature-induced phase transition of two-dimensional semiconductor GaTe* *Project supported by the National Natural Science Foundation of China (Grant No. 62004080), Postdoctoral Innovative Talents Supporting Program (Grant No. BX20190143), China Postdoctoral Science Foundation (2020M670834), and Jilin Province Science and Technology Development Program, China (Grant No. 20190201016JC).

GaTe is a two-dimensional III–VI semiconductor with suitable direct bandgap of ∼ 1.65 eV and high photoresponsivity, which makes it a promising candidate for optoelectronic applications. GaTe exists in two crystalline phases: monoclinic (m-GaTe, with space group C2/m) and hexagonal (h-GaTe, with space group P63/mmc). The phase transition between the two phases was reported under temperature-varying conditions, such as annealing, laser irradiation, etc. The explicit phase transition temperature and energy barrier during the temperature-induced phase transition have not been explored. In this work, we present a comprehensive study of the phase transition process by using first-principles energetic and phonon calculations within the quasi-harmonic approximation framework. We predicted that the phase transition from h-GaTe to m-GaTe occurs at the temperature decreasing to 261 K. This is in qualitative agreement with the experimental observations. It is a two-step transition process with energy barriers 199 meV and 288 meV, respectively. The relatively high energy barriers demonstrate the irreversible nature of the phase transition. The electronic and phonon properties of the two phases were further investigated by comparison with available experimental and theoretical results. Our results provide insightful understanding on the process of temperature-induced phase transition of GaTe.

First-Principles Study of Magnetism-Dependent Phonons Governed by Exchange Ligand Field

We present first-principles phonon calculations for ferromagnetic and paramagnetic (disordered local moment) states in B2-type (FeCo, MnNi) and L10-type (CoPt, FePt, FePd) materials. The calculatio...

A Study on Phonon-Mediated Thermal Transport and Lattice Thermal Conductivity Prediction Using First-Principles Calculations

The systematic theoretical approaches and atomistic simulation programs to predict thermal properties of crystalline nanostructured materials within first-principles framework are studied here. Recent progress in computational power has enabled an accurate and reliable way to investigate nanoscale thermal transport in crystalline materials using first-principles based calculations. Extracting a large set of anharmonic force constants with low computational effort remains a big challenge in lattice dynamics and condensed-matter physics. This paper focuses on recent progress in first-principles phonon calculations for semiconductor materials and summarizes advantages and limitations of each approach and simulation programs by comparing accuracy of numerical solutions, computational load and calculating feasibility to a wide range of crystalline materials. This work also reviews and presents the coupling model of first-principles molecular dynamic (FPMD) approach that can extract anharmonic force constants directly and solution of linearized Boltzmann transport equation to predict phonon-mediated lattice thermal conductivity of crystalline materials.