Effects of solutes on thermodynamic properties of (TMZrU)C (TM = Ta, Y) medium-entropy carbides: a first-principles study
0Abstract
High entropy carbide ceramics have garnered significant interest as a novel class of ultra-high temperature and superhard metallic materials. In the present work, a comparative investigation was conducted for the first time on the stability, mechanical, and thermodynamic properties of two medium entropy carbides (MECs), (TaZrU)C and (YZrU)C, using high-throughput first-principles calculations. Additionally, data from groups IV and V transition metal monocarbides were employed for comparison. The temperature-dependent thermodynamic properties, including bulk modulus (B), constant volume/constant pressure heat capacity (Cv/Cp), Gibbs free energy, volume, entropy, and thermal conductivity, were evaluated using the Debye-Gruneisen model. The results demonstrate that (TaZrU)C and (YZrU)C exhibit similar trends in their thermodynamic properties, with (YZrU)C displaying slightly superior performance as the temperature rises. This work provides valuable insights into the design of innovative high entropy fuels, holding significant implications for the advancement of MEC ceramic fuels in advanced nuclear power systems and nuclear thermal propulsion systems.
Keywords
INTRODUCTION
Being one kind of ultra-high temperature ceramics[1-10], transition metal carbide ceramics of the IVB, VB, and VIB groups have found wide applications in various fields, such as hard cutting tools, high-temperature abrasives, aerospace industry, submarine equipment, and nuclear energy[1,2,10-13]. They also present several attractive properties, including excellent thermal and electrical conductivity, chemical corrosion resistance, high melting point and hardness, abrasion resistance, oxidation and radiation resistance, and high temperature stability[14-16]. In recent years, a new approach to alloy design has emerged with the development of polymetallic solid solution compounds. These alloys, known as high entropy materials (HEMs)[17-21], are formed by combining five or more principal elements, each with a concentration between 35 and 5 at.% and exhibiting a mixing entropy S > 1.5R. Owing to the contributions of high entropy, HEMs exhibit unique characteristics different from those of metal simple substances, which can be summarized as four major effects, including high entropy effects, sluggish diffusion effects, severe lattice distortion effects, and cocktail effects.
High entropy carbide ceramics (HECs) are single-phase solid solutions composed of four or more transition metal (TM) atoms. Theoretical studies have helped scientists to prepare and study HECs more efficiently and economically through different simulation methods[22,23]. For instance, high-throughput computing and machine learning (ML) have been used to study HEMs[22,24-29]. Castle et al. experimentally fabricated the high entropy carbides (HECs) and inherited the four effects of HEMs[30,31]. Medium entropy carbides (MECs) were then derived from the concept of HECs, with a mixing entropy between 1R and 1.5R. MECs, such as HECs, have excellent mechanical and functional properties. The study of the properties of MECs in multicomponent solid solutions has been widely reported[32-36]. Compared to traditional binary carbides, HECs and MECs exhibit superior physical and chemical performances, such as high thermal stability, good corrosion resistance, high fracture toughness, high Young’s modulus, and high hardness[24,30,37-42].
In the field of nuclear energy, the Nuclear Thermal Propulsion (NTP) engine systems are attractive options for planetary exploration applications due to their high performance, such as Mars exploration[43-46]. In order to achieve better performance of NTP systems, the NTP reactors will be utilized at temperatures above
In recent decades, there has been a progression in the development of carbide fuels, transitioning from single-component compositions[52-57] to multicomponent compositions, such as (ZrU)C and (ZrNbU)C[35]. Notably, Pelaccio et al. have designed solid-solution (ZrU)C ceramic fuels, which currently serve as the primary source of nuclear fuel for NTP reactors, offering improved reliability[58]. Composite ceramic fuels, including UC or (ZrU)C, exhibit advantageous properties such as high melting point temperatures and high thermal conductivity. Unfortunately, the compatibility of composite ceramics, such as UC or (ZrU)C, with fuse-resistant alloys is limited at higher temperatures. Further exploration of incorporating a third metal atom into the (ZrU)C system holds the potential to unveil the future prospects of carbide fuels, specifically MEC ceramic fuels, for advanced nuclear power systems. Multicomponent (ZrNbU)C fuels are regarded as the preferred choice for realizing high thrust nuclear-powered spacecraft in the future, and in the study, a powder metallurgical process combining carbothermal reduction and liquid phase sintering is used to prepare poly (ZrNbU)C fuels. The mechanisms and laws of the process parameters on the reaction kinetics, phase structure, thermal conductivity, and microstructure of multi-element (ZrNbU)C fuel are investigated[59]. Additionally, (UxZr1-x)Cy systems exhibit promise as design concepts/strategies for advanced nuclear power systems due to their unique nuclear properties and thermal stability[60].
In the present work, tantalum (Ta) or yttrium (Y) is added as the third metal atom to the (ZrU)C system to explore their effects on the properties of MECs. Proper doping of trace elements has been shown to promote the densification and grain growth of ceramic materials and extend their service life[61]. It has been reported that the utilized temperature of (TaZrU)C fuel could be improved by the addition of Ta and Zr into the classical UC one[62], which is selected as the investigated candidacy fuel in the present work. This work investigates the physical property changes and thermodynamic properties of (TMZrU)C (TM = Ta, Y) MECs in detail using high-throughput first-principles calculations, providing valuable data and technical support for the design of new high entropy fuel from both an electronic and atomic perspective. Specifically, we focus on examining the equilibrium volume (V0), Gibbs free energy, constant volume heat capacity (Cv), constant pressure heat capacity (Cp), bulk modulus (B0), and thermal conductivity of the (TMZrU)C structures. This research holds promise for the advancement of carbide materials, specifically MEC ceramic fuels, with implications for NTP systems.
MATERIALS AND METHODS
Multicomponent supercell construction via similar atomic environment
Consideration of the possible quasirandom structure with lattice distortion is important in the modeling of disordered structures. In the present work, the similar atomic environment (SAE) toolkit combined in the Professional Materials at Extreme (ProME) platform is utilized to construct the supercells of the multicomponent system[63,64], which has the capability to systematically screen the optimal structure of the fuel doping system. It is noted that the SAE approach is a novel structural modeling method that employs a similarity function to quantitatively describe the deviation between the current configuration and the desired disordered solid solution structure. This approach enables the construction of quasirandom structures to be transformed into a minimization problem of configuration space. The superlattices of (TaZrU)C and (YZrU)C with 64 atoms were constructed using the SAE method, as shown in Figure 1, based on the cell structures of ZrC (the space group number No. 225 and the lattice parameter
Figure 1. The 64 atoms supercells of investigated medium-entropy carbides (MECs) generated by the SAE method. (A) (TaZrU)C;
where
Computational methods
The first-principles calculations were carried out using the Vienna ab initio simulation package (VASP), which is based on the density functional theory (DFT) framework[65]. To treat the interactions between valence electrons and ionic cores, the projector augmented wave (PAW) method was utilized[66], and the exchange-correlation energy was calculated using the generalized gradient approximation (GGA) parametrized by Perdew-Burke-Ernzerh (PBE)[67]. Throughout the present work, the plane-wave basis energy cut-off was set to 1.4 times the maximum energy of each component. During the optimization, the total energies calculated by VASP finally converged within 1 × 10-6 eV/atom, and the Monkhorst-Pack scheme[68] was used to sample special k-points by automatically generating k-points grid in the Brillouin zone. Full relaxation of the supercell is carried out using the Methfessel-Paxton technique[69]. The total energy and electronic density of states (DOS) calculations were performed by using the tetrahedron method with Blöchl correction[70]. The bulk modulus, equilibrium volume, and the pressure derivative of the bulk modulus were determined from the total energy calculated, and these results were fitted to the four-parameter Birch-Murnaghan (BM4) equation of state (EOS)[71]. The bounding charge density (∆ρ) was defined as[72]:
Where ρtotal is the total electron density, and ρIAM is the density related to the superposition of free and unbonded atoms, also known as the Independent Atomic Model (IAM). The Visualization for Electronic and Structural Analysis (VESTA) code was used to generate the isosurface structures of (TMZrU)C with different values of ∆ρ[73].
To investigate the thermodynamic properties, the temperature- and volume-dependent Helmholtz free energy is needed, which is calculated in the following form[74]:
where E0 represents the static energy at 0 K, corresponding to the energy of the ground state when the ion is fixed in its lattice position. Additionally, Fel accounts for the thermal free energy arising from electronic excitation, while Fion represents the vibrational contribution to the free energy, Sconf is the configuration entropy of the system. The equilibrium structure of a crystal at any given temperature (T) and volume (V) can be determined by minimizing the Helmholtz free energy F(V, T). Once the minimum Helmholtz free energy F(V, T) is determined for a particular T and V, other thermodynamic functions and properties of the crystal can be deduced as implemented. For instance, entropy (S), isothermal bulk modulus (BT), heat capacity at constant volume (CV), and heat capacity at constant pressure (Cp) can be calculated accordingly and expressed as[75]:
All these thermodynamic properties are estimated using the mean-field potential (MFP) method proposed by Wang et al.[76] and later improved by Song et al.[75] to extend its applicability to more general cases and complex structural crystals[77-79]. This method is suitable for various complex systems and has significant potential for predicting the thermodynamic properties of multicomponent alloys.
RESULTS AND DISCUSSION
Structural stability
The structures are optimized through full relaxation to obtain the energies E of MECs and their binary carbides as a function of volumes V. A series of energy-volume data points around the equilibrium volume were calculated by minimizing the total energy to optimize the crystal structure. Then, the energy-volume data points of the calculated MECs and their corresponding individual metal binary carbides were fitted using the fourth-order Birch-Murnaghan EOS[80], as shown in Figure 2.
Figure 2. The calculated Energy-Volume (E-V) curves of (TaZrU)C and (YZrU)C.
The present results show the effect of TMs on the total energy and volume of MECs. Specifically, the equilibrium volume for binary carbides is found to increase in the order of TaC < ZrC < UC < YC, which is roughly consistent with the trend of pure metal atomic size change, i.e., Ta < U < Zr < Y. In addition, the equilibrium volume of MECs also increases with the increasing volume of TM atoms, in the order of (TaZrU)C < (YZrU)C. Meanwhile, the total energy of middle entropy carbides, (TaZrU)C < (YZrU)C, also increases with the improved volumes of TM atoms.
The fitted E-V curves provide valuable information about the equilibrium atomic energy E0, equilibrium volume V0, bulk modulus B0, first derivative of bulk modulus with respect to pressure B0’, and lattice constants a at zero temperature and pressure for MECs and their corresponding pure carbides. These predicted properties listed in Table 1 are in good agreement with the experimental and theoretical properties reported in the literature[81-87]. Specifically, the predicted E0 and V0 for (TaZrU)C and (YZrU)C are -9.7095 eV, -8.8862 eV and 13.3873 Å3, 15.1241 Å3, respectively. The lattice constants are a = 9.5097 Å for (TaZrU)C and a = 9.9043 Å for (YZrU)C. These values are very close to the average values of the equilibrium atomic energies E0, equilibrium volumes V0, and lattice constants a of the three component binary carbides. Furthermore, the bulk modulus B0 of (TaZrU)C and (YZrU)C are also comparable to the average value of the three binary carbides. Similar to most HECs, the equilibrium properties of MECs, (TaZrU)C and (YZrU)C, follow the mixture rule[88], as seen in their equilibrium atomic energy, volume, lattice constant, and bulk modulus.
The calculated properties of HECs in the present work at ground state (0 K), including equilibrium atomic energy (E0), equilibrium atomic volume (V0), equilibrium bulk modulus (B0), the derivative of B0 (B’), and lattice parameter (a)
| Composition | E0 (eV/atom) | V0 (Å3/atom) | B0 (GPa) | B’ | a (Å) |
| (TaZrU)C | -9.7059 | 13.3873 | 235.14 | 4.11 | 9.5097 |
| (YZrU)C | -8.8862 | 15.1241 | 173.71 | 4.45 | 9.9043 |
| TaC | -11.1001 -11.1a, -11.1b | 11.2312 | 324.88 322.15b, 365.3j | 4.23 4.22b | 4.48 4.479b, 4.42j |
| ZrC | -9.7315 -9.74a, -9.73b | 13.0724 | 222.11 219.3b, 220.1e | 3.97 4.06b | 4.71 4.711b, 4.71e |
| UC | -10.3533 | 14.9923 | 186.77 158f, 191g | 3.66 | 4.93 4.96f, 4.97g |
| YC | -7.8109 | 16.4216 | 123.98 128j, 124.3e | 4.06 4.451d | 5.08 5.08j, 5.09e |
Mechanical properties are critical to the industrial applications of materials. Interestingly, (TaZrU)C has a greater bulk modulus B0 than (YZrU)C, indicating that (TaZrU)C has a higher strength than (YZrU)C and will be validated by the following bonding charge density analysis. However, the first derivative of bulk modulus with respect to pressure B0’ of (TaZrU)C is smaller than that of (YZrU)C. Despite the absence of experimental data for comparison, the current findings can serve as valuable references for future experimental and theoretical research.
Temperature-dependent thermo-physical properties
The investigation of the thermodynamic properties of materials is crucial in the field of high-temperature engineering applications. In order to gain a deeper understanding of the thermodynamic properties of (TaZrU)C and (YZrU)C in the temperature range of 0-2,000 K, the Debye-Gruneisen model implemented in MFP[76] was utilized in this study. The calculated thermodynamic properties are presented in Table 2, including the equilibrium volume V0, Gibbs free energy, constant volume heat capacity Cv, constant pressure heat capacity Cp, bulk modulus B0, and thermal conductivities. The thermodynamic properties of materials can be determined through various experimental techniques, including differential thermal analysis[60], chemical analysis[89], and X-ray diffraction[61,90,91]. Additionally, the hardness of a material is commonly measured using Vickers hardness, which can be determined using a nanometer indentation method[82]. However, with the advancement of science and technology towards extreme conditions, it becomes increasingly challenging to experimentally obtain accurate thermodynamic data. As a result, there are currently no available experimental or theoretical data on the thermodynamic properties of (TaZrU)C and (YZrU)C. Therefore, the present findings are of significant value in guiding future research efforts to develop advanced NTP fuels.
Based on quasiharmonic approximation, thermodynamic properties of (TaZrU)C and (YZrU)C predicted by first-principles calculations, including equilibrium volume (V0), Internal energy, Gibbs free energy, Constant volume heat capacity (Cv), Constant pressure heat capacity (Cp), and Isothermal bulk modulus (B0)
| Composition | V0 (Å3/atom) | Internal (eV) | Gibbs (eV) | Cv (J/mol/K) | Cp (J/mol/K) | B0 (GPa) |
| (TaZrU)C | 13.446 | -9.6614 | -9.7428 | 23.098 | 23.412 | 228.34 |
| (YZrU)C | 15.211 | -8.8405 | -8.9249 | 23.174 | 23.610 | 167.46 |
The heat capacity is a fundamental parameter that links the thermodynamic and dynamic properties of materials. The constant volume heat capacity CV was estimated using an expression
Figure 3. Temperature dependence of heat capacity of benchmark binary carbides together with available reported data. (A) Constant volume heat capacity Cv; (B) Constant pressure heat capacity Cp. The values for comparison are derived from the theoretical results reported by Aliakbari[93], Zhang[94], Yang[57], Mankad[95], and Iikubo[96].
Figure 4. The predicted temperature-dependent thermodynamic properties of (TaZrU)C and (YZrU)C. (A) Constant volume heat capacity - CV; (B) Constant pressure heat capacity - Cp; (C) Isothermal bulk modulus - B; (D) Entropy - S; (E) Gibbs free energy;
Estimating the strength of materials is crucial for their practical applications, and the bulk modulus B is a measure of resistance to compression of a material. An increase in bulk modulus leads to a stronger material. The bulk modulus is calculated using
Entropy is a fundamental thermodynamic parameter that describes the degree of disorder in a crystal structure. A higher entropy value indicates a higher degree of disorder in the crystal structure. The entropy value is a crucial factor for defining HEMs, and its variation is related to the formation, stability, and phase transformation of such materials. The equilibrium entropy is calculated using
The theoretical thermal conductivity can be calculated according to the following equation[92]:
where A = 3.04 × 10-8, Mα is the atomic mass of the atom, θα is the Debye temperature, δ3 is the volume per atom, and γ is the Gruneisen parameter. Figure 5 shows the corresponding graphs of the thermal conductivities of (TaZrU)C and (YZrU)C. It can be seen from the obtained results that the thermal conductivity trends of (TaZrU)C and (YZrU)C are similar to each other. For the heavier element Ta, the thermal conductivity of the compound (TaZrU)C is larger than that of (YZrU)C. Moreover, the difference in thermal conductivity decreases at high temperatures, and the thermal conductivity of (TaZrU)C is larger than that of (YZrU)C. The reason for this is that the strength of Ta-C bonds is higher than that of Y-C bonds in similar crystal structures, and the covalent interactions in (YZrU)C are weaker than those in (TaZrU)C.
Figure 5. The temperature-dependent lattice thermal conductivity of (TaZrU)C and (YZrU)C.
Basic physical properties and mechanical properties
Lattice distortion is a crucial microstructural feature that affects the mechanical properties of materials, especially in high-entropy materials. From the perspective of bond charge density, the mechanical and chemical effects of lattice distortion/misfit caused by constituent atoms can be comprehensively characterized. Figure 6 shows the isosurface of bonding charge densities of MECs with Δρ = 0.016 e -Å-3, demonstrating the electronic rearrangement caused by solute atoms and lattice distortion. The red color indicates the loss of electrons, while the green color represents the gain of electrons. Additionally,
Figure 6. The chemical bonding of investigated medium entropy carbides (MECs) characterized by the 3D and 2D views of bonding charge density isosurfaces (Δρ = 0.016 e -Å-3), (A) (TaZrU)C; (B) (YZrU)C. The green and the pink colors are utilized to highlight those atoms presenting the negative and the positive charge, respectively.
Figure 7. The chemical bonding of investigated medium entropy carbides (MECs) in the views of individual positive and negative modules of bonding charge density isosurfaces, (A) and (C) the negative and positive charge of (TaZrU)C, respectively; (B) and (D) the negative and positive charge of (YZrU)C, respectively.
In order to gain a deeper understanding of the bonding behavior of the two MECs, we conducted an analysis of the charge density distribution on the (001) plane, and contour plots are shown in Figure 8. It can be seen from the figure that the charge distribution is strongly perturbed by the chemical disorder. In particular, we observed significant hybridization between the carbon and TM atoms, which suggests the formation of covalent bonds between them. Interestingly, the charge overlap region between TM atoms and non-metal atoms in (TaZrU)C is noticeably wider and more delocalized than that in (YZrU)C. Additionally, the color between TM and carbon atoms in (TaZrU)C is orange, whereas it is yellow and green in (YZrU)C. This observation suggests that the enhanced bonding charge densities among those atoms in (TaZrU)C result in increased bonding strength between TM and carbon atoms. As a consequence, the hardness of (TaZrU)C will be further enhanced, which is consistent with the findings from the analysis of Δρ from both 3D and 2D perspectives.
Figure 8. The contour plots of bonding charge density distributions of (001) plane of medium entropy carbides (MECs), (A) (TaZrU)C and (B) (YZrU)C. In order to get a clearer view of the electron distribution in the diagram, only the position of metal atoms has been marked, while the position of C atoms has not been marked, which is between two metal atoms. Plots are generated by the Visualization for Electronic and Structural Analysis (VESTA) package.
The DOS is a crucial quantity in theoretical chemistry as it helps to understand the internal chemical bond interactions and the stability mechanisms of a compound structure. To gain a deeper understanding of the electronic structure, bonding, and properties of (TaZrU)C and (YZrU)C, their total (TDOS) and partial DOS (PDOS) are shown in Figure 9. The vertical blue line in the figure marks the Fermi energy (EF) which has been set to zero. Figure 9A shows that both MECs have TDOS values above zero at the Fermi energy level N(EF), indicating clear metallic behavior. However, (YZrU)C exhibits a smaller deviation between its Fermi level and pseudo-gap, and the DOS at the Fermi level is also smaller than (TaZrU)C. This indicates that (YZrU)C is more stable, as a lower DOS at the Fermi level N(EF) means higher stability. Due to the similarities in the PDOS details between (TaZrU)C and (YZrU)C, (TaZrU)C is chosen as the prototype for further analysis. As shown in Figure 9B, the two main peaks are located between -3 and 1 eV, with the Fermi energy approximately in the middle of this range. The primary bonding peaks located between -5 and -3 eV are predominantly derived from the valence electrons of the C(p), U(f), Ta(d), and Zr(d) orbitals. Meanwhile, the bonding peaks between -3 eV and 1 eV are generated through the hybridization of the C(p), U(f), Ta(d), and Zr(d) orbitals, with a minor contribution from the U(d), Ta(p), and Zr(p) orbitals. These PDOS features indicate the presence of covalent-like bonds in (TaZrU)C. Similarly, (YZrU)C exhibits the same PDOS features.
Figure 9. (A) Total electron density of states (TDOS) and (B) Partial electron density of states (PDOS) of (TaZrU)C and (YZrU)C. The blue vertical dotted lines at 0 eV dictate the Fermi level.
CONCLUSION
In the present work, the electronic and thermodynamic properties of (TaZrU)C and (YZrU)C have been investigated by first-principles calculations, referring to the traditional binary carbides, such as TaC, ZrC, UC, and YC, and presenting a good agreement with available experimental or theoretical results in the literature. It is found that the equilibrium volume and energy of (TaZrU)C and (YZrU)C are positively correlated with the size of each solute atom. Due to the random occupation of TM elements, local lattice distortion occurs, leading to changes in the charge distribution and chemical bonds. The electron DOS (eDOS) displays the bonding ability of the two MECs, showing significant hybridization between the carbon and the TM atoms near the Fermi level, indicating the formation of covalent bonds. The predicted bonding structures in view of bonding charge density indicate that (TaZrU)C and (YZrU)C exhibit covalent characteristics accompanied by ionicity, with (TaZrU)C showing stronger covalent interactions. Based on the Debye-Grüneisen model, several fundamental properties of (TaZrU)C and (YZrU)C were further studied, including constant volume and constant pressure heat capacities, bulk modulus, thermodynamic entropy, Gibbs free energy, volume, and thermal conductivity. While the high-temperature softening behavior is similar in those investigated carbides, (TaZrU)C has stronger chemical bonds and greater hardness due to its larger volume modulus and thermal conductivity, making it more suitable for engineering applications. Since the entropy was found to increase significantly with temperature for both carbides, (YZrU)C becomes more stable at high temperatures due to its greater contribution from entropy. Therefore, the present work provides some reference value for the optimization and application of future medium entropy ceramic NTP fuels.
DECLARATIONS
Authors’ contributionsInvestigation, Methodology, Calculation, Data curation, Analysis, Writing - original draft, Writing - review and editing: Liu Y
Conceptualization, Methodology, Investigation, Resources, Writing - original draft, Writing - review and editing, Supervision, Funding acquisition: Wang WY
Investigation, Data curation, Analysis, Writing - review and editing: Li J
Conceptualization, Methodology, Software: Zhang Y
Conceptualization, Methodology, Software, Data curation, Analysis: Yin J
Conceptualization, Methodology, Supervision, Writing - review and editing: Pan X, Gao X, Chen Y, Song H, Lu Y
Resources, Writing - review and editing, Project administration, Funding acquisition: Li J
Availability of data and materialsNot applicable.
Financial support and sponsorshipThis work was financially supported by the National Defense Basic Scientific Research
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participateNot applicable.
Consent for publicationNot applicable.
Copyright© The Author(s) 2023.
REFERENCES
1. Nisar A, Zhang C, Boesl B, Agarwal A. A perspective on challenges and opportunities in developing high entropy-ultra high temperature ceramics. Ceram Int 2020;46:25845-53.
2. Akrami S, Edalati P, Fuji M, Edalati K. High-entropy ceramics: review of principles, production and applications. Mater Sci Eng R Rep 2021;146:100644.
3. Demirskyi D, Borodianska H, Suzuki TS, Sakka Y, Yoshimi K, Vasylkiv O. High-temperature flexural strength performance of ternary high-entropy carbide consolidated via spark plasma sintering of TaC, ZrC and NbC. Scr Mater 2019;164:12-6.
4. Golla BR, Mukhopadhyay A, Basu B, Thimmappa SK. Review on ultra-high temperature boride ceramics. Prog Mater Sci 2020;111:100651.
5. Peters AB, Zhang D, Nagle DC, Spicer JB. Reactive two-step additive manufacturing of ultra-high temperature carbide ceramics. Addit Manuf 2023;61:103318.
6. Ni D, Cheng Y, Zhang J, et al. Advances in ultra-high temperature ceramics, composites, and coatings. J Adv Ceram 2022;11:1-56.
7. Dai F, Wen B, Sun Y, Ren Y, Xiang H, Zhou Y. Grain boundary segregation induced strong UHTCs at elevated temperatures: a universal mechanism from conventional UHTCs to high entropy UHTCs. J Mater Sci Technol 2022;123:26-33.
8. Guo R, Mao H, Shen P. Ultra-fast high-temperature synthesis and densification of high-entropy diborides and diboride-carbide ceramics. J Eur Ceram Soc 2023;43:5763-73.
9. Morris BA, Povolny SJ, Seidel GD, Tallon C. Effects of oxidation on the effective thermomechanical properties of porous ultra-high temperature ceramics in compression via computational micromechanics and MPM. Open Ceram 2023;15:100382.
11. Wei X, Liu J, Li F, Qin Y, Liang Y, Zhang G. High entropy carbide ceramics from different starting materials. J Eur Ceram Soc 2019;39:2989-94.
12. Zhou J, Zhang J, Zhang F, Niu B, Lei L, Wang W. High-entropy carbide: a novel class of multicomponent ceramics. Ceram Int 2018;44:22014-8.
13. Yan X, Constantin L, Lu Y, Silvain J, Nastasi M, Cui B. (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics with low thermal conductivity. J Am Ceram Soc 2018;101:4486-91.
14. Zeng Y, Wang D, Xiong X, et al. Ablation-resistant carbide Zr0.8Ti0.2C0.74B0.26 for oxidizing environments up to 3,000 °C. Nat Commun 2017;8:15836.
15. Csanádi T, Castle E, Reece MJ, Dusza J. Strength enhancement and slip behaviour of high-entropy carbide grains during micro-compression. Sci Rep 2019;9:10200.
16. Wang F, Yan X, Wang T, et al. Irradiation damage in (Zr0.25Ta0.25Nb0.25Ti0.25)C high-entropy carbide ceramics. Acta Mater 2020;195:739-49.
17. Yeh J, Chen S, Lin S, et al. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes†. Adv Eng Mater 2004;6:299-303.
18. Ma J, Huang C. High entropy energy storage materials: synthesis and application. J Energy Storage 2023;66:107419.
19. Ying T, Yu T, Qi Y, Chen X, Hosono H. High entropy van der Waals materials. Adv Sci 2022;9:e2203219.
20. Moghaddam A, Fereidonnejad R, Cabot A. Semi-ordered high entropy materials: the case of high entropy intermetallic compounds. J Alloys Compd 2023;960:170802.
21. Yao G, Wang W, Li P, et al. Electronic structures and strengthening mechanisms of superhard high-entropy diborides. Rare Met 2023;42:614-28.
22. Sarker P, Harrington T, Toher C, et al. High-entropy high-hardness metal carbides discovered by entropy descriptors. Nat Commun 2018;9:4980.
23. Yao G, Wang WY, Zou C, et al. Local orders, lattice distortions, and electronic structure dominated mechanical properties of (ZrHfTaM1M2)C (M = Nb, Ti, V). J Am Ceram Soc 2022;105:4260-76.
24. Dai F, Wen B, Sun Y, Xiang H, Zhou Y. Theoretical prediction on thermal and mechanical properties of high entropy (Zr0.2Hf0.2Ti0.2Nb0.2Ta0.2)C by deep learning potential. J Mater Sci Technol 2020;43:168-74.
25. Kaufmann K, Maryanovsky D, Mellor WM, et al. Discovery of high-entropy ceramics via machine learning. npj Comput Mater 2020;6:42.
26. Chen L, Chen Z, Yao X, et al. High-entropy alloy catalysts: high-throughput and machine learning-driven design. J Mater Inf 2022;2:19.
27. Zhou Y, Zhang Z, Wang D, et al. New trends in additive manufacturing of high-entropy alloys and alloy design by machine learning: from single-phase to multiphase systems. J Mater Inf 2022;2:18.
29. Pak AY, Sotskov V, Gumovskaya AA, et al. Machine learning-driven synthesis of TiZrNbHfTaC5 high-entropy carbide. npj Comput Mater 2023;9:7.
30. Castle E, Csanádi T, Grasso S, Dusza J, Reece M. Processing and properties of high-entropy ultra-high temperature carbides. Sci Rep 2018;8:8609.
31. Dusza J, Švec P, Girman V, et al. Microstructure of (Hf-Ta-Zr-Nb)C high-entropy carbide at micro and nano/atomic level. J Eur Ceram Soc 2018;38:4303-7.
32. Xiong K, You L, Zhang S, et al. Pressure and temperature effects on (TiZrTa)C medium-entropy carbide from first-principles. J Mater Res Technol 2023;23:2288-300.
33. Jin C, Xiong K, Guo L, et al. A DFT insight into the mechanical, electronic and thermodynamic properties of (TiZrHf)C medium-entropy carbide ceramic. Results Phys 2022;35:105341.
34. Demirskyi D, Suzuki TS, Yoshimi K, Vasylkiv O. Synthesis and high-temperature properties of medium-entropy (Ti,Ta,Zr,Nb)C using the spark plasma consolidation of carbide powders. Open Ceram 2020;2:100015.
35. Demirskyi D, Nishimura T, Suzuki TS, Sakka Y, Vasylkiv O, Yoshimi K. High-temperature toughening in ternary medium-entropy (Ta1/3Ti1/3Zr1/3)C carbide consolidated using spark-plasma sintering. J Asian Ceram Soc 2020;8:1262-70.
36. Peng C, Tang H, He Y, et al. A novel non-stoichiometric medium-entropy carbide stabilized by anion vacancies. J Mater Sci Technol 2020;51:161-6.
37. Deng H, Xie Z, Wang M, et al. A nanocrystalline AlCoCuNi medium-entropy alloy with high thermal stability via entropy and boundary engineering. Mater Sci Eng A 2020;774:138925.
38. Chen H, Xiang H, Dai F, et al. High porosity and low thermal conductivity high entropy (Zr0.2Hf0.2Ti0.2Nb0.2Ta0.2)C. J Mater Sci Technol 2019;35:1700-5.
39. Peng C, Gao X, Wang M, et al. Diffusion-controlled alloying of single-phase multi-principal transition metal carbides with high toughness and low thermal diffusivity. Appl Phys Lett 2019;114:011905.
40. Wang Y, Csanádi T, Zhang H, Dusza J, Reece MJ, Zhang R. Enhanced Hardness in high-entropy carbides through atomic randomness. Adv Theory Simul 2020;3:2000111.
41. Ye B, Wen T, Chu Y. High-temperature oxidation behavior of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics in air. J Am Ceram Soc 2020;103:500-7.
42. Wang Y, Zhang R, Zhang B, et al. The role of multi-elements and interlayer on the oxidation behaviour of (Hf-Ta-Zr-Nb)C high entropy ceramics. Corros Sci 2020;176:109019.
43. Levack D J, Horton J F, Jennings T, et al. Evolution of low enriched uranium nuclear thermal propulsion vehicle and engine design. In: AIAA Propulsion and Energy 2019 Forum; 2019 Aug 19-22; Indianapolis, IN, USA. American Institute of Aeronautics and Astronautics, Inc.; 2019. p. 3943.
44. Reynolds CB, Horton JF, Joyner CR, Kokan T, Levack DJ. Applications of nuclear thermal propulsion to lunar architectures. In: AIAA Propulsion and Energy 2019 Forum; 2019 Aug 19-22; Indianapolis, IN, USA. American Institute of Aeronautics and Astronautics, Inc.; 2019. p. 4032.
45. Ji Y, Zhang H, Sun J, Shi L. Thermal performance optimization of a fuel element in particle bed reactors for nuclear thermal propulsion. Nucl Eng Des 2019;355:110316.
46. Reynolds CB, Joyner CR, Kokan TS, Levack DJ, Muzek BJ. Mars opposition missions using nuclear thermal propulsion. In: AIAA Propulsion and Energy 2020 Forum; 2020 Aug 24-28; virtual event. American Institute of Aeronautics and Astronautics, Inc.; 2020. p. 3850.
47. Burns D, Johnson S. Nuclear thermal propulsion reactor materials. In: Nuclear Materials. IntechOpen; 2021. Available from: https://www.intechopen.com/chapters/71396. [Last accessed on 16 Aug 2023].
48. Lin CS, Youinou GJ. Design and analysis of a 250 MW plate-fuel reactor for nuclear thermal propulsion. Available from: https://www.osti.gov/biblio/1638498. [Last accessed on 15 Aug 2023].
49. Thody A. Irradiation capsule development for composite fuels for nuclear thermal propulsion. Available from: https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/6395wd417. [Last accessed on 15 Aug 2023]
50. Searight WT, Palomares KB, Werner JE, Todosow M, Lenox KE. Subscale maturation of advanced reactor technologies (SMART): a path forward for nuclear thermal propulsion fuel and reactor development. Prog Nucl Energy 2022;153:104432.
51. Wang SB, Ma Y, Guo SM, Xie QL. Comparation and analysis of nuclear thermal propulsion reactor fuel. Manned Spaceflight 2018;24:784-95. (in Chinese). Available from: https://www.cnki.net/kcms/doi/10.16329/j.cnki.zrht.2018.06.012.html. [Last accessed on 15 Aug 2023].
52. Farhadizadeh AR, Ghomi H. Mechanical, structural, and thermodynamic properties of TaC-ZrC ultra-high temperature ceramics using first principle methods. Mater Res Express 2020;7:036502.
53. Tsuppayakorn-aek P, Ektarawong A, Sukmas W, Alling B, Bovornratanaraks T. Thermodynamic stability and superconductivity of tantalum carbides from first-principles cluster expansion and isotropic Eliashberg theory. Comput Mater Sci 2022;202:111004.
54. Di Y, He Z, Wang J. New insights into the mechanical and thermal properties of UN1-xCx from first-principles calculations. J Nucl Mater 2022;571:153991.
55. Gökbulut M, Koç H, Bölükdemir MH, Eser E. Analytical study of the heat capacity and entropy of ZrM (M=N and C) compounds. Int J Mod Phys B 2023:2450276.
56. He R, Fang L, Han T, et al. Elasticity, mechanical and thermal properties of polycrystalline hafnium carbide and tantalum carbide at high pressure. J Eur Ceram Soc 2022;42:5220-8.
57. Yang XY, Lu Y, Zheng FW, Zhang P. Mechanical, electronic, and thermodynamic properties of zirconium carbide from first-principles calculations. Chin Phys B 2015;24:116301.
58. Pelaccio DG, El-Genk MS, Butt DP. A review of carbide fuel corrosion for nuclear thermal propulsion applications. Am Inst Phys 1994;301:905-18.
59. Wu XZ, Wei GL, Guo X. Study on preparation technology and performance mechanism of multi-component (U,Zr,Nb)C fuel. Sci Technol At Energy 2023;9:1-9. (in Chinese) Available from: http://kns.cnki.net/kcms/detail/11.2044.tl.20230626.1905.008.html. [Last accessed on 15 Aug 2023]
60. Butt DP, Wallace TC. The U-Zr-C ternary phase diagram above 2473 K. J Am Ceram Soc 1993;76:1409-19.
61. Bourgeois L, Dehaudt P, Lemaignan C, Hammou A. Factors governing microstructure development of Cr2O3-doped UO2 during sintering. J Nucl Mater 2001;297:313-26.
62. Koroteev AS. Nuclear propulsion system application in the space exploration. In: The 10th International Burn and Combustion Summit (2003).
63. Tian F, Lin DY, Gao X, Zhao YF, Song HF. Erratum: “a structural modeling approach to solid solutions based on the similar atomic environment” [J. Chem. Phys. 153, 034101 (2020)]. J Chem Phys 2020;153:034101.
64. Song H, Tian F, Hu Q, et al. Local lattice distortion in high-entropy alloys. Phys Rev Mater 2017;1:023404.
65. Kresse G, Furthmüller J. Efficient iterative schemes for
67. Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett 1996;77:3865-8.
68. Monkhorst HJ, Pack JD. Special points for Brillouin-zone integrations. Phys Rev B 1976;13:5188-92.
69. Methfessel M, Paxton AT. High-precision sampling for Brillouin-zone integration in metals. Phys Rev B 1989;40:3616-21.
70. Blöchl PE, Jepsen O, Andersen OK. Improved tetrahedron method for Brillouin-zone integrations. Phys Rev B 1994;49:16223-33.
71. Murnaghan FD. The Compressibility of media under extreme pressures. Proc Natl Acad Sci U S A 1944;30:244-7.
72. Nakashima PN, Smith AE, Etheridge J, Muddle BC. The bonding electron density in aluminum. Science 2011;331:1583-6.
73. Momma K, Izumi F.
74. Ma D, Grabowski B, Körmann F, Neugebauer J, Raabe D.
75. Song H, Liu H. Modified mean-field potential approach to thermodynamic properties of a low-symmetry crystal: beryllium as a prototype. Phys Rev B 2007;75:245126.
76. Wang Y, Li L. Mean-field potential approach to thermodynamic properties of metal: Al as a prototype. Phys Rev B 2000;62:196-202.
77. Wang Y, Xu Y, Liu Y, et al. First-principles study of the role of surface in the heavy-fermion compound CeRh2Si2. Phys Rev B 2021;103:165140.
78. Wu J, Yang Z, Xian J, Gao X, Lin D, Song H. Structural and thermodynamic properties of the high-entropy alloy AlCoCrFeNi based on first-principles calculations. Front Mater 2020;7:590143.
79. Wu J, Wang YC, Liu Y, et al. First-principles study on the electronic structure transition of
80. Birch F. Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300°K. J Geophys Res 1978;83:1257-68.
81. Ye B, Wen T, Nguyen MC, Hao L, Wang C, Chu Y. First-principles study, fabrication and characterization of (Zr0.25Nb0.25Ti0.25V0.25)C high-entropy ceramics. Acta Mater 2019;170:15-23.
82. Jiang S, Shao L, Fan T, Duan J, Chen X, Tang B. Elastic and thermodynamic properties of high entropy carbide (HfTaZrTi)C and (HfTaZrNb)C from ab initio investigation. Ceram Int 2020;46:15104-12.
83. Maibam J, Indrajit Sharma B, Bhattacharjee R, Thapa R, Brojen Singh R. Electronic structure and elastic properties of scandium carbide and yttrium carbide: a first principles study. Phys B Condens Matter 2011;406:4041-5.
84. Korir K, Amolo G, Makau N, Joubert D. First-principle calculations of the bulk properties of 4
85. Shi H, Zhang P, Li S, Sun B, Wang B. Electronic structures and mechanical properties of uranium monocarbide from first-principles LDA + U and GGA + U calculations. Phys Lett A 2009;373:3577-81.
86. Mei Z, Ye B, Yacout AM, Beeler B, Gao Y. First-principles study of the surface properties of uranium carbides. J Nucl Mater 2020;542:152257.
87. Isaev EI, Simak SI, Abrikosov IA, et al. Phonon related properties of transition metals, their carbides, and nitrides: a first-principles study. J Appl Phys 2007;101:123519.
88. Zhao Y, Qiao J, Ma S, et al. A hexagonal close-packed high-entropy alloy: the effect of entropy. Mater Des 2016;96:10-5.
89. Wang Z, Qiu W, Yang Y, Liu C. Atomic-size and lattice-distortion effects in newly developed high-entropy alloys with multiple principal elements. Intermetallics 2015;64:63-9.
90. Viennois R, Bérardan D, Popescu C. Crystal structure, lattice dynamics, and thermodynamic properties of a thermoelectric orthorhombic BaCu2Se2 compound. J Phys Chem C 2020;124:13627-38.
91. Wen T, Ye B, Nguyen MC, Ma M, Chu Y. Thermophysical and mechanical properties of novel high-entropy metal nitride-carbides. J Am Ceram Soc 2020;103:6475-89.
93. Aliakbari A, Amiri P. Structural, elastic, electronic, thermal, and phononic properties of yttrium carbide: first-principles calculations. Mater Chem Phys 2021;270:124744.
94. Zhang P, Ye L, Chen F, Han W, Wu Y, Zhao T. Stability, mechanical, and thermodynamic behaviors of (TiZrHfTaM)C (M = Nb, Mo, W, V, Cr) high-entropy carbide ceramics. J Alloy Compd 2022;903:163868.
95. Mankad VH, Jha PK. Thermodynamic properties of nuclear material uranium carbide using density functional theory. J Therm Anal Calorim 2016;124:11-20.
Cite This Article
Export citation file: BibTeX | RIS
OAE Style
Liu Y, Lu Y, Wang WY, Li J, Zhang Y, Yin J, Pan X, Gao X, Chen Y, Song H, Li J. Effects of solutes on thermodynamic properties of (TMZrU)C (TM = Ta, Y) medium-entropy carbides: a first-principles study. J Mater Inf 2023;3:17. http://dx.doi.org/10.20517/jmi.2023.19
AMA Style
Liu Y, Lu Y, Wang WY, Li J, Zhang Y, Yin J, Pan X, Gao X, Chen Y, Song H, Li J. Effects of solutes on thermodynamic properties of (TMZrU)C (TM = Ta, Y) medium-entropy carbides: a first-principles study. Journal of Materials Informatics. 2023; 3(3): 17. http://dx.doi.org/10.20517/jmi.2023.19
Chicago/Turabian Style
Liu, Ya, Yonghong Lu, William Yi Wang, Jia Li, Ying Zhang, Junlei Yin, Xiaoqiang Pan, Xingyu Gao, Yong Chen, Haifeng Song, Jinshan Li. 2023. "Effects of solutes on thermodynamic properties of (TMZrU)C (TM = Ta, Y) medium-entropy carbides: a first-principles study" Journal of Materials Informatics. 3, no.3: 17. http://dx.doi.org/10.20517/jmi.2023.19
ACS Style
Liu, Y.; Lu Y.; Wang WY.; Li J.; Zhang Y.; Yin J.; Pan X.; Gao X.; Chen Y.; Song H.; Li J. Effects of solutes on thermodynamic properties of (TMZrU)C (TM = Ta, Y) medium-entropy carbides: a first-principles study. J. Mater. Inf. 2023, 3, 17. http://dx.doi.org/10.20517/jmi.2023.19
About This Article
Special Issue
Copyright
Data & Comments
Data
0
Cite This Article 9 clicks
Like This Article 4
likes
Comments
Comments must be written in English. Spam, offensive content, impersonation, and private information will not be permitted. If any comment is reported and identified as inappropriate content by OAE staff, the comment will be removed without notice. If you have any queries or need any help, please contact us at support@oaepublish.com.