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Jun 05, 2023

Scientific Reports volume 13, Article number: 13631 (2023) Cite this article

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B1-type MX ceramics are composed of transition metals (M) and C, N, and/or O (X) occupying the M and X sites, respectively, and having M–X nearest neighbor (NN) bonds and M–M and X–X next nearest neighbor (NNN) bonds. Substitution of the elements and the formation of structural vacancies in B1-type ceramics change the numbers and strengths of the bonds, leading to novel properties. The change in elastic modulus of off-stoichiometric TiC in equilibrium with a Ti–Mo solid solution phase was experimentally investigated based on the rule of mixtures from the Voigt model. The experimentally obtained values agreed well with the results of density functional theory calculations. The bulk modulus (K) of TiC increased from 205.6 to 239.2 GPa as the fraction of Ti sites occupied by Mo increased from 0.11 to 0.33, whereas the Young’s modulus (E) and the shear modulus (G) remained nearly constant. On the other hand, all three elastic moduli decreased with increasing vacancy fraction at the C sites. These results suggest that the M–X bond strength should be the dominant factor in these moduli and the effect of M–M bond on K is greater than that of G and E.

B1-type MX compounds composed of transition metals (M) and C, N, and/or O (X), occupying the M and X sites, respectively, mainly with covalent M–X bonds, exhibit attractive material properties, such as low density, high melting point, high hardness, good wear resistance, and moderate electric conductivity1,2,3. Consequently, these ceramic phases are widely used in thin films, as coatings for cutting tools, as hard phases in cermets, etc., and they are also found as nanosized precipitates in some steels2,4,5,6,7,8. One drawback of B1-type compounds is their brittleness; for example, the fracture toughness of stoichiometric TiC is only about 3 MPa(m)1/29,10. If this poor toughness could be improved without a commensurate decrease in strength, the applications of the resulting ceramics would further expand as ultra-high temperature materials that can be used to improve the energy efficiency of gas turbines and jet engines and for thermal-protection systems in spacecraft bodies11,12,13,14,15.

B1-type MX compounds can have relatively high degrees of off-stoichiometry compared with other ceramics, such as SiC and MAX phases13,14,15,16,17. For example, the compositional region for Ti2AlC is very narrow in the Ti–Al–C ternary system, even at 1300 °C18. On the other hand, the TiC phase region in the Mo–Ti–C ternary system expands toward both the Ti-rich and the Mo-rich regions, and these off-stoichiometries change the properties of the material by changing the types and numbers of bonds due to elemental substitution and the formation of structural vacancies19.

In the field of intermetallic compounds, there is a long history of studies on how material properties change due to off-stoichiometry. For example, B2-type intermetallic compounds have been extensively studied for the effects of off-stoichiometry on their defect structures and properties20,21,22,23,24,25,26,27. Here, it is well known that the defect structure of B1-type MX compounds is of the vacancy type in the transition-metal-rich region28,29,30,31. In the early studies, shifts in the binding energy and band structure of off-stoichiometric TiC were already discussed32,33. Over the last two decades, the phase stabilities and elastic moduli of B1-type MX compounds relating to the defect structure have been investigated by means of density functional theory (DFT) calculations34,35,36,37. Elastic properties of multicomponent B1-type MX compounds with vacancies38,39 or without vacancies40,41,42,43 have also been investigated by means of DFT calculations. It is more meaningful to investigate further the off-stoichiometric effect with structural vacancies on the material properties of multicomponent B1-type MX compounds experimentally and computationally.

The off-stoichiometry may slightly improve the toughness and/or plastic deformability of B1-type MX compounds. Fe–Ti–C alloys containing near-stoichiometric TiC in equilibrium with an Fe phase exhibited low ductility, and their elongation simply decreased with increasing the volume fraction of TiC44. On the other hand, Ti–Mo–Al alloys containing off-stoichiometric TiC exhibited better deformability than the alloys lacking TiC45. TiC-added Mo–Si–B (MoSiBTiC) alloys exhibit greater strength at high temperatures and better fracture toughness at room temperature than Mo–Si–B alloys46,47,48,49. TiC in MoSiBTiC alloys is in equilibrium with Mo solid-solution and Mo5SiB2 phases, and it contains more than 20 at% of Mo and less than 50 at% of C50. Off-stoichiometric TiC in the fractography of the MoSiBTiC alloys showed river patterns, suggesting a small amount of plastic deformation. Moreover, the fracture toughness of MoSiBTiC alloys increased with increasing total volume fractions of Mo and TiC phases48. These results suggest that the off-stoichiometric TiC deformed plastically and acts as a fracture resistant phase. On the other hand, Sangiovanni et al. reported that high-entropy refractory ceramics with B1-type structures exhibit plasticity using both ab initio molecular dynamics simulations and nanoindentation51. These results suggest that TiC might acquire slight plastic deformability through off-stoichiometry, and the plastic behavior should be related to the elastic properties of the alloys again.

Therefore, the elastic modulus change by off-stoichiometry in (Ti, Mo)Cx in equilibrium with a Mo–Ti solid solution is experimentally investigated in this study. DFT calculations are also used to estimate the elastic properties of the off-stoichiometric (Ti, Mo)Cx in the Mo–Ti–C ternary system. By comparing the elastic moduli obtained from the experiments with those from the DFT calculations, factors controlling the elastic properties of the off-stoichiometric B1-type (Ti, Mo)Cx are clarified, and the material property change by off-stoichiometry in the multicomponent (Ti, Mo)Cx is discussed.

The microstructures of the alloys studied are shown in Fig. 1. Alloys in the ternary system consisted of a Mo phase (A2-type structure) with a bright contrast and a TiC phase with a dark contrast in the SEM-backscattered electron images (BEI) (Fig. 1a–c). Part of the Mo phase precipitated in TiC. Alloys in the Ti–C binary system were composed of an α-Ti phase (A3-type structure) with a bright contrast and TiC with a dark contrast in the BEI (Fig. 1d). The bright phase also precipitated in TiC. Furthermore, a finer phase with a sharper interface than the α-Ti phase shown in Fig. 1d was also observed in the TEM-bright field image (TEM-BFI; Fig. 1e). The finer phase was identified as an α-Ti phase, and the finer α-Ti phase had a habit plane of (111)TiC (Fig. 1f,g). The coarse α-Ti phase shown in Fig. 1d with a bright contrast is likely to be formed by the transformation of the β-Ti phase (A2-type structure) formed during heat treatment at 1500 °C, whereas the finer α-Ti phase shown in Fig. 1e would precipitate during cooling after heat treatment. Superlattice spots of the vacancy-ordered Ti2C phase, as mentioned in some reports in the literature52,53,54,55, were also observed in the TiC matrix (Fig. 1f,h). Two types of structure of the Ti2C phase have been reported: an R\(\stackrel{\mathrm{-}}{3}\)m type and an Fd3m type. However, it was found that a higher spatial resolution would have been required to identify the structure of the Ti2C phase.

Backscattered electron images (BEIs) and TEM images of the microstructures of alloys in the ternary system after heat treatment at 1800 °C for 72 h (a–c) and in the binary system after heat treatment at 1500 °C for 72 h (d–h): (a) BEI of Mo–20.0Ti–20.0C, (b) BEI of Mo–37.9Ti–25.0C, (c) BEI of Mo–53.2Ti–25.0C and (d) BEI of Ti–10.0C, (e) Bright-field image (B = 110TiC) of Ti–5C, (f) Selected-area diffraction pattern (SADP) taken from whole area of (e), (g,h) SADP taken from the areas shown by the corresponding dotted circles in (e).

An isothermal section of the Mo–Ti–C ternary system at 1800 °C is shown in Fig. 219,56,57. All compositions of the Mo–Ti–C ternary alloys examined in this study are plotted on the colored tie lines drawn in the Mo/TiC two-phase region. Hereafter, these tie lines are referred to as Tie Lines 1–4 from the Mo–rich composition, respectively, and the tie line in the Ti/TiC two-phase region in the Ti–C binary system is referred to as Tie Line 5. The terminal compositions of TiC for Tie Lines 1–3 had almost the same C content, whereas the C content markedly decreased in Tie Lines 4 and 5. The constituent phases, the composition and lattice parameter of the constituent phases, and the volume fraction of TiC are summarized in Table 1. All TiC phases measured in equilibrium with the solid-solution phase had a C-poor composition. The lattice parameters of TiC measured in this study were smaller than that of stoichiometric TiC (4.327 Å)3. This can be attributed to a vacancy defect structure at the C site, as previously reported28,29,30,31. Therefore, the structural defect in off-stoichiometric TiC in the Mo–Ti–C ternary system can be assumed to be a substitution of Mo at Ti sites and the formation of vacancies at the C sites. The Mo-fraction dependence at the Ti sites and the vacancy-fraction dependence of TiC are divided by the Mo fraction at Ti sites (\(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\)) and the vacancy fraction at C sites (\(f{}_{\text{Va}}^{ \, {\text{C}}}\)). These are given by the following equations:

where \(x{}_{\text{Mo}}^{\text{TiC}}\), \(x{}_{\text{Ti}}^{\text{TiC}}\), and \(x{}_{\text{C}}^{\text{TiC}}\) are the Mo, Ti, and C compositions of TiC, respectively. Therefore, increases in \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) and \(f{}_{\text{Va}}^{ \, {\text{C}}}\) imply a substitution of Mo at Ti sites and the formation of vacancies at C sites, respectively. The lattice parameters of TiC are summarized by using \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) and \(f{}_{\text{Va}}^{ \, {\text{C}}}\) in Fig. 3. In the case of TiC with \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\)= 0, the lattice parameter of stoichiometric TiC was the highest, and the lattice parameter of TiC decreased with the formation of vacancies. The lattice parameters of TiC with almost the same values of \(f{}_{\text{Va}}^{ \, {\text{C}}}\) decreased with increasing \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\)3. This change corresponds to a difference in atomic size, as the Mo atom is smaller than the Ti atom58. Therefore, it can be concluded that the structural defects in off-stoichiometric TiC in the Mo–Ti–C ternary system result from the substitution of Mo at Ti sites and the formation of vacancies at C sites.

Isothermal section at 1800 °C of the Mo–Ti–C ternary system19,56,57. The tie lines of each alloy in the Mo/TiC two-phase region of Mo–Ti–C ternary system are shown by the colored lines.

Changes in the lattice parameter of TiC with the terminal compositions of Tie Lines 1–3 (\(f{}_{\text{Va}}^{\text{C}}\) = 0.2) as a function of the Mo fraction, together with binary TiC data (\(f{}_{\text{Va}}^{\text{C}}\) = 0)3.

Figure 4 shows the change in enthalpy (H) and the elastic constants obtained from DFT calculations for TiC as a function of \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) and \(f{}_{\text{Va}}^{ \, {\text{C}}}\). H for TiC at \(f{}_{\text{Va}}^{ \, {\text{C}}}\) = 0 and 0.25 decreased with increasing \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\), whereas H for TiC with \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) = 0 increased with increasing \(f{}_{\text{Va}}^{ \, {\text{C}}}\). The elastic constants of TiC basically increase and decrease as H decreases and increases, respectively. This is because H roughly corresponds to the cohesive energy as shown in the case of C11. On the other hand, C44 of TiC with \(f{}_{\text{Va}}^{ \, {\text{C}}}\) = 0 and 0.25 did not always increase and, in some cases, decreased with decreasing H. As a result, especially for TiC with \(f{}_{\text{Va}}^{ \, {\text{C}}}\) = 0.25, the difference between C44 and C12 became smaller as \(f{}_{\text{Mo}}^{\text{ Ti}}\) increased. Similarly, the difference between C44 and C12 of TiC with \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) = 0 became smaller as \(f{}_{\text{Va}}^{ \, {\text{C}}}\) increased. This is because the rate of decrease of C12 with increasing \(f{}_{\text{Va}}^{ \, {\text{C}}}\) was more gradual than that of C44. C44 of TiC with \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) = 0 decreased with increasing \(f{}_{\text{Va}}^{ \, {\text{C}}}\).

Changes in enthalpy and elastic constants calculated by DFT for (a,c,e) TiC with \(f{}_{\text{Va}}^{ \, {\text{C}}}\) = 0, 0.25 as a function of \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) and (b,d,f) TiC with \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) = 0 as a function of \(f{}_{\text{Va}}^{ \, {\text{C}}}\): (a,b) enthalpy, H, (c,d) C11, (e,f) C12 and C44.

The changes in E, G, and K experimentally obtained for bulk alloys on Tie Lines 1–5 are plotted as functions of the volume fraction of TiC (VTiC) in Fig. 5. The results are summarized in Table 2. All elastic moduli of the solid-solution phase (VTiC = 0%) increased with increasing Mo content. The elastic moduli changed linearly with increasing VTiC. This means that the rule of mixtures of the Voigt model is applicable:

where Xbulk is the elastic modulus of the bulk alloy, X1 and X2 are the elastic moduli of the constituent phases, and V1, V2 are the volume fractions of the constituent phases59. By using the rule of mixture, the elastic moduli of TiC with the terminal composition of each tie line can be estimated. The estimated elastic moduli and K/G of TiC on Tie Lines 1–5 are summarized in Table 3, along with \(f{}_{{\text{M}}{\text{o}}}^{ \, {\text{Ti}}}\), \(f{}_{\text{Va}}^{ \, {\text{C}}}\). The values of \(f{}_{\text{Mo}}^{ \, {\text{Ti}}}\) and \(f{}_{\text{Va}}^{ \, {\text{C}}}\) were calculated by using the average value for each terminal composition of TiC.

Changes in elastic moduli of alloys on Tie Lines 1–5 with the volume fraction of TiC: (a) Young’s modulus, E, (b) shear modulus, G and (c) bulk modulus, K. The elastic moduli change with the volume fraction of TiC; the elastic moduli of TiC with the terminal compositions described by the triangle symbols were calculated by using the rule of mixtures of the Voigt’s model.

Details of the changes in elastic modulus with substitution by Mo at Ti sites and vacancy formation at C sites will now be discussed. Figure 6 shows the changes in E, G and K obtained from the experimental results and DFT calculations as functions of \(f{}_{\text{Mo}}^{\text{Ti}}\) and \(f{}_{\text{Va}}^{ \, {\text{C}}}\)60,61. Since the values of \(f{}_{\text{Va}}^{ \, {\text{C}}}\) for Tie Lines 1–3 are almost the same (\(f{}_{\text{Va}}^{ \, {\text{C}}}\) = 0.2), the elastic moduli of TiC on Tie Line 1–3 were dependent on the Mo fraction (Fig. 6a,c,e). The vacancy fraction dependence was determined from the elastic modulus of binary TiC (Tie Line 5), as well as that of ternary TiC, calculated as \(f{}_{\text{Mo}}^{\text{Ti}}\) = 0 by using the Mo fraction dependence (Fig. 6b,d,f). The value of K in the experimental results at \(f{}_{\text{Va}}^{ \, {\text{C}}}\) = 0.2 increased with increasing \(f{}_{\text{Mo}}^{\text{Ti}}\), whereas G and K were almost constant, regardless of \(f{}_{\text{Mo}}^{\text{Ti}}\) (Fig. 6a,c,e). E, G, and K of the experimental results at \(f{}_{\text{Mo}}^{\text{Ti}}\) = 0 decreased with increasing \(f{}_{\text{Va}}^{ \, {\text{C}}}\) and the degree of change in E and G was larger than that in K (Fig. 6b,d,f). Note that the experimental results and DFT calculations were in good agreement. Moreover, the reported DFT data for binary TiC31,35,39 and (Ti,Mo)C41 also show similar tendencies. Therefore, E and G are highly dependent on the fraction of vacancies, whereas K is highly dependent on the fraction of Mo.

Changes in the elastic moduli of TiC obtained from experimental data and DFT calculations, together with reference data for stoichiometric TiC59,60: (a,b) Young’s modulus, E (c,d) shear modulus, G, (e,f) bulk modulus, K. (a,c,e) Changes in elastic moduli with \(f{}_{\text{Mo}}^{\text{Ti}}\) in TiC with specific value of \(f{}_{\text{Va}}^{ \, {\text{C}}}\). (b,d,f) Changes in elastic moduli with \(f{}_{\text{Va}}^{ \, {\text{C}}}\) in TiC with specific vacancy value of \(f{}_{\text{Mo}}^{\text{Ti}}\).

Here, the factors controlling the elastic moduli of TiC are discussed in relation to the bond strength. Figure 7 shows the structures of TiC with and without off-stoichiometry. In stoichiometric TiC, Ti atoms at the Ti sites and C atoms at the C sites form six nearest neighbor (NN) Ti–C (M–X) bonds, and twelve next nearest neighbor (NNN) Ti–Ti (M–M) and C–C (X–X) bonds (Fig. 7a).

Structure of TiC phase: (a) stoichiometric TiC, (b) off-stoichiometric TiC that forms a vacancy at a C site, (c) off-stoichiometric TiC in which Mo is substituted at a Ti site, (d) off-stoichiometric TiC that forms a vacancy at a C site and substitutes a Mo at a Ti site.

When a vacancy is formed on a C site by off-stoichiometry, the six NN Ti–C bonds disappear (Fig. 7b), and the total NN bond strength decreases. Therefore, it is ready to understand that the elastic moduli decrease as \(f{}_{\text{Va}}^{ \, {\text{C}}}\) increases. This tendency is also observed in MCx carbides and MNx nitrides34,62,63.

When a Mo atom substitutes into a Ti site in stoichiometric TiC, the six NN Ti–C bonds change to the NN Mo–C bonds and the NN bond strength should be changed (Fig. 7c). Here, it was observed that G and E are almost constant, but K increases with the substitution of Mo (Fig. 6a,c,e). These results suggest that not only NN bonds but also NNN bonds affect the elastic moduli and the degree of influence of NNN bonds on each elastic modulus is different. When a Mo atom substitutes at the Ti site in stoichiometric TiC, the twelve NNN Ti–Ti bonds change to twelve NNN Ti–Mo bonds. Furthermore, when a vacancy is formed at a C site neighboring the Mo atom, six NN M–C bonds and twelve NNN C–C bonds disappear (Fig. 7d) and the effect of the M–M bonds may become more significant. Here, it is inferred that the strength of the NNN Mo–Ti and Mo–Mo bonds are stronger than that of the Ti–Ti bond because the elastic modulus of the Mo phase decreases with increasing Ti content (Fig. 5). On the other hand, the Mo–C bond strength appears to be weaker than that of the Ti–C bond because G and E remain constant as the Mo fraction increases. On the other hand, K increases with increasing Mo fraction even if vacancies are formed (Fig. 6a,c,e). This is because the effect of M–M bond strength on K is greater than that of G and E. Therefore, K can be increased by increasing the NNN M–M bond strength. A similar phenomenon was observed in (Ti, W)C. The values of E and G for TiC and (Ti0.5, W0.5)C are almost identical, whereas K for (Ti0.5, W0.5)C is significantly higher (312 GPa)41 than that for TiC or (Ti0.5, Mo0.5)C, as calculated in this study. This can be reasonably explained by the fact that the elastic modulus of W is higher than that of Ti and Mo, which increases the NNN M–M bond strength64. Furthermore, this idea rationalizes the facts that VC and TaC have almost the same values of E and G, whereas the value of K for TaC is higher than that for VC: this is because the elastic modulus of Ta is higher than that of V35,64. Further investigations of the strength of M–M and M–X bonds are needed to clarify the factors controlling the elastic properties of B1-type MX compounds.

The change in the elastic moduli of the B1-type MX, TiC, with off-stoichiometry was investigated experimentally and by DFT calculations for Mo–Ti–C ternary alloys. Our conclusions can be summarized as follows.

The elastic moduli of off-stoichiometric TiC in equilibrium with a solid-solution phase can be measured experimentally from the rule of mixtures of the Voigt model.

The elastic moduli of off-stoichiometric TiC at room temperature can be predicted by DFT calculations.

The bulk modulus (K) of TiC increases with increasing Mo fraction at Ti sites, whereas the Young’s modulus (E) and shear modulus (G) remain almost constant. On the other hand, all the elastic moduli decrease with increasing the fraction of vacancies at C sites. These results suggest that the M–X bond strength should be the dominant factor in these moduli and the effect of M–M bond on K is greater than that of G and E.

The compositions of the alloys studied, expressed as atomic percentages, were Mo–(4.8–53.2)%Ti–(0.6–25.0)%C in the (Mo,Ti)/TiC two-phase region or the Mo–Ti single-phase region in the Mo–Ti–C ternary system, and Ti–(5, 10, 15)% C of the Ti/TiC two-phase region in the Ti–C binary system19,56,57. (Hereafter, all compositions are expressed as atomic percentages). These alloys were prepared as 9–10 cm3 ingots from pure Mo (99.99 wt%), Ti (99.9 wt%), and TiC (99 wt%) by conventional arc melting under an Ar atmosphere. Each ingot was melted five times and turned over each time to prevent segregation. To ensure that phase equilibria were attained, heat treatment in an Ar atmosphere was performed at 1800 °C for 72 h for the Mo–Ti–C ternary alloys and at 1500 °C for 72 h for the Ti–C binary alloys; this was followed by furnace cooling. The microstructure of the alloys was examined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). TEM disks with a thickness of 0.1 mm and a diameter of 3 mm were machined and mechanically polished. These were then subjected to dimple grinding followed by ion milling. Phase identification and lattice-parameter measurements of the constituent phases were conducted by X-ray diffractometry. Compositional analyses of the phases were performed by using a field-emission electron-probe microanalyzer (EPMA) equipped with a wavelength-dispersive X-ray spectroscope (WDX) at 10 kV and 5.0 × 10−8 Å. Details of the compositional analyses are described elsewhere19. The elastic parameters of the alloys after heat treatment were measured by the electromagnetic acoustic resonance (EMAR) method, assuming an isotropic elastic medium. The elastic moduli measurements were performed at room temperature in a magnetic field of 0.5 T in a frequency range of 200–1400 kHz with a step frequency of 1 kHz. Details of the EMAR measurements and analysis are also presented elsewhere65.

The Vienna ab initio simulation package (VASP)66 was used to perform the DFT calculations within the generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE)67. Electron–ion interactions were modeled by using the projector-augmented wave potentials68, and the total energies were minimized and converged to within 10–5 eV/atom. The k-point grids for the Monkhorst–Pack method69 and the cut-off energy were set to 6 × 6 × 6 and 600 eV, respectively.

The formation energies of B1-type MoxTi1–xC, TiC1–y, and MoxTi1−xC0.75 were calculated across the full composition range (0 < x, y < 1) by using the following equation:

where x is the fraction of Mo at Ti sites, y is the fraction of vacancies of the C sites, and EX is the total energy of X per atom. The special quasi-random structure was obtained by using the Alloy Theoretic Automated Toolkit (ATAT)70: The number of atoms n in the supercells was 64 with Mo concentrations x = 0.00, 0.125, 0.250, 0.375, 0.500, and 1.000, and vacancy concentrations y = 0.00, 0.125, 0.250, 0.375, 0.500, and 1.000.

The elastic constants C11, C12, and C44 were obtained by fitting the calculated strain energy–strain curves with strain (δ) δ = ± 0.001 and ± 0.002. The various elastic constants were calculated by using the following equations:

The isotropic Young’s modulus (E), bulk moduli (K) and shear moduli (G) were determined based on the Voigt–Reuss–Hill approach71 and calculated from the elastic constants given above and the following equations:

Storms, E. K. The Refractory Carbides (Academic Press, 1967).

Google Scholar

Rajabi, A., Ghazali, M. J. & Daud, A. R. Chemical composition, microstructure and sintering temperature modifications on mechanical properties of TiC-based cermet: A review. Mater. Des. 67, 95–106 (2015).

Article CAS Google Scholar

Dubrovinskaia, N. A., Dubrovinsky, L. S., Saxena, S. K., Ahuja, R. & Johansson, B. High-pressure study of titanium carbide. J. Alloys Compd. 289, 24–27 (1999).

Article CAS Google Scholar

Garcia, J. & Pitonak, R. The role of cemented carbide functionally graded outer-layers on the wear performance of coated cutting tools. Int. J. Refract. Met. Hard Mater. 36, 52–59 (2013).

Article CAS Google Scholar

Veprek, S., Veprek-Heijman, M. G. J., Karvankova, P. & Prochazka, J. Different approaches to superhard coatings and nanocomposites. Thin Solid Films 476, 1–29 (2005).

Article ADS CAS Google Scholar

Durlu, N. Titanium carbide based composites for high temperature applications. J. Eur. Ceram. Soc. 19, 2415–2419 (1999).

Article CAS Google Scholar

Le Flem, M., Allemand, A., Urvoy, S., Cédat, D. & Rey, C. Microstructure and thermal conductivity of Mo–TiC cermets processed by hot isostatic pressing. J. Nucl. Mater. 380, 85–92 (2008).

Article ADS Google Scholar

Compton, B. G. & Zok, F. W. Impact resistance of TiC-based cermets. Int. J. Impact Eng. 62, 75–87 (2013).

Article Google Scholar

Endo, H., Ueki, M. & Kubo, H. Microstructure and mechanical properties of hot-pressed SiC–TiC composites. J. Mater. Sci. 26, 3769–3774 (1991).

Article ADS CAS Google Scholar

Maerky, C., Guillou, M.-O., Henshall, J. L. & Hooper, R. M. Indentation hardness and fracture toughness in single crystal TiC0.96. J. Mater. Sci. Eng. A 209, 320–336 (1996).

Article Google Scholar

Perepezko, J. H. The hotter the engine, the better. Science 326, 1068–1069 (2009).

Article ADS CAS PubMed Google Scholar

Pollock, T. M. Alloy design for aircraft engines. Nat. Mater. 15, 809–815 (2016).

Article ADS CAS PubMed Google Scholar

Pedture, N. P. Advanced structural ceramics in aerospace propulsion. Nat. Mater. 15, 804–809 (2016).

Article ADS Google Scholar

Tang, S. & Hu, C. Design, preparation and properties of carbon fiber reinforced ultra-high temperature ceramic composites for aerospace applications: A review. J. Mater. Sci Technol. (Shenyang, China). 33, 117–130 (2017).

Article CAS Google Scholar

Fahrenholtz, W. G. & Hilmas, G. E. Ultra-high temperature ceramics: Materials for extreme environments. Scr. Mater. 129, 94–99 (2017).

Article CAS Google Scholar

Marshall, D. B. & Cox, B. N. Integral textile ceramic structures. Annu. Rev. Mater. Res. 38, 425–438 (2008).

Article ADS CAS Google Scholar

Jin, X., Fan, X., Lu, C. & Wang, T. Advanced in oxidation and ablation resistance of high and ultra-high temperature ceramics modified or coated carbon/carbon composite. J. Eur. Ceram. Soc. 38, 1–28 (2018).

Article CAS Google Scholar

Pietzka, M. A. & Schuster, J. C. Summary of constitutional data on the aluminum–carbon–titanium system. J. Phase Equilib. 15, 392–400 (1994).

Article CAS Google Scholar

Ida, S., Sekido, N. & Yoshimi, K. Solidification pathways and phase equilibria in the Mo–Ti–C ternary system. High Temp. Mater. Processes (Berlin Ger.). 39, 164–170 (2020).

Article ADS CAS Google Scholar

Bradley, A. J. & Taylor, A. An X-ray analysis of the nickel–aluminum system. Proc. R. Soc. Lond. Ser. A 159, 56–72 (1937).

Article ADS CAS Google Scholar

Westbrook, J. H. Temperature dependence of hardness of the equi-atomic iron group aluminides. J. Electrochem. Soc. 103, 54–63 (1956).

Article CAS Google Scholar

Westbook, J. H. Defect structure and the temperature dependence of hardness of an intermetallic compound. J. Electrochem. Soc. 104, 369–373 (1957).

Article Google Scholar

Ball, A. & Smallman, R. E. The deformation properties and electron microscopy studies of the intermetallic compound NiAl. Acta Metall. 14, 1349–1355 (1966).

Article CAS Google Scholar

Yang, W. J., Lin, F. & Dodd, R. A. Structure of vacancy-defective NiAl. Scr. Metall. 12, 237–241 (1978).

Article CAS Google Scholar

Tan, Y., Shinoda, T., Mishima, Y. & Suzuki, T. Defect hardening by the deviation from stoichiometry in NiAl. Nippon Kinzoku Gakkaishi 57, 220–227 (1993).

CAS Google Scholar

Pike, L. M., Chang, Y. A. & Liu, C. T. Solid-solution hardening and softening by Fe additions to NiAl. Intermetallics 5, 601–608 (1997).

Article CAS Google Scholar

Hahn, K. H. & Vedula, K. Room temperature tensile ductility in polycrystalline B2 NiAl. Scr. Metall. 23, 7–12 (1989).

Article CAS Google Scholar

Sundgren, J.-E. Structure and properties of TiN coatings. Thin Solid Films 128, 21–44 (1985).

Article ADS CAS Google Scholar

Williams, W. S. Scattering of electron by vacancy in nonstoichiometric crystals of titanium carbide. Phys. Rev. A 135, A505–A510 (1964).

Article ADS Google Scholar

Williams, W. S. Transition-metal carbides. Prog. Solid State Chem. 6, 57–118 (1971).

Article ADS CAS Google Scholar

Williams, W. S. Transition metal carbides, nitrides, and borides for electronic applications. JOM 49, 38–42 (1997).

Article CAS Google Scholar

Lye, R. G. & Logothetis, E. M. Optical properties and band structure of titanium carbide. Phys. Rev. 147, 622–635 (1966).

Article ADS CAS Google Scholar

Ramqvist, L., Hamrin, K., Johansson, G., Gelius, U. & Nordling, C. VC, NbC and TaC with varying carbon content studied by ESCA. J. Phys. Chem. Solids 31, 2669–2672 (1970).

Article ADS CAS Google Scholar

Hugosson, H. W., Korzhavyi, P., Jansson, U., Johansson, B. & Eriksson, O. Phase stabilities and structural relaxations in stoichiometric TiC1–x. Phys. Rev. B 63, 1651116 (2001).

Article Google Scholar

Korzhavyi, P. A., Pourovskii, L. V., Hugosson, H. W., Ruban, A. V. & Johansson, B. Ab initio study of phase equilibria in TiCx. Phys. Rev. Lett. 88, 015505 (2002).

Article ADS CAS PubMed Google Scholar

Dridi, Z., Bouhaf, B., Ruterana, P. & Aourag, H. First-principles calculations of vacancy effects on structural and electronic properties of TiCx and TiNx. J. Phys. Condens. Matter 14, 10237–10249 (2002).

Article ADS CAS Google Scholar

Yu, X.-X., Thompson, G. B. & Weinberger, C. R. Influence of carbon vacancy formation on the elastic constants and hardening mechanisms in transition metal carbides. J. Eur. Ceram. Soc. 35, 95–103 (2015).

Article CAS Google Scholar

Kindlund, H. et al. Vacancy-induced toughening in hard single-crystal V0.5Mo0.5Nx/MgO(001) thin films. Acta Mater. 77, 394–400 (2014).

Article ADS CAS Google Scholar

Razumovskiy, V. I., Ruban, A. V., Odqvist, J., Dilner, D. & Korzhavyi, P. A. Effect of carbon vacancies on thermodynamic properties of TiC–ZrC mixed carbides. CALPHAD Comput. Coupling Phase Diagr. Thermochem. 46, 87–91 (2014).

Article CAS Google Scholar

Jhi, S.-H., Ihm, J., Louie, S. G. & Cohen, M. L. Electronic mechanism of hardness enhancement in transition-metal carbonitrides. Nature 399, 132–134 (1999).

Article ADS CAS Google Scholar

Edstöm, D. et al. Elastic properties and plastic deformation of TiC- and VC-based pseudobinary alloys. Acta Mater. 144, 376–385 (2018).

Article ADS Google Scholar

Li, Y., Katsui, H. & Goto, T. Phase decomposition of (Ti, Zr)(C, N) solid solutions prepared by spark plasma sintering. J. Eur. Ceram. Soc. 39, 4588–4594 (2019).

Article CAS Google Scholar

Cap, Z., Jin, N., Ye, J., Du, X. & Liu, Y. First-principles study on the effects of N and Al doping on the mechanical properties and electronic structures of TiC. RSC Adv. 10, 36295 (2020).

Article ADS Google Scholar

Ida, S., Watanabe, K. & Yoshimi, K. Solidification microstructure and mechanical properties of B1-type TiC in Fe–Ti–C ternary alloys. Tetsu to Hagane 109, 224–233 (2023) (in Japanese).

Article Google Scholar

Lu, Y. et al. Microstructures and mechanical properties of TiC-particulate-reinforced Ti–Mo–Al intermetallic matrix composites. Mater. Sci. Eng. A 790, 139523 (2020).

Article CAS Google Scholar

Miyamoto, S. et al. Phase equilibria, microstructure, and high-temperature strength of TiC-added Mo–Si–B Alloys. Metall. Mater. Trans. A 45, 1112–1123 (2014).

Article CAS Google Scholar

Kamata, S. Y. et al. Ultrahigh-temperature tensile creep of TiC-reinforced Mo–Si–B-based alloy. Sci. Rep. 8, 10487 (2018).

Article ADS PubMed PubMed Central Google Scholar

Moriyama, T. et al. Room-temperature fracture toughness of MoSiBTiC alloys. Intermetallics 84, 92–102 (2017).

Article CAS Google Scholar

Yamamoto, S., Yoshimi, K., Kim, J. & Yokoyama, K. Effects of microstructure on high-temperature strength of TiC-added Mo–Si–B alloys. Nippon Kinzoku Gakkaishi 80, 51–59 (2016).

CAS Google Scholar

Uemura, S. et al. Quantitative evaluation of microstructure in Mo–Si–B–TiC alloy produced by melting and tilt casting method. Mater. Trans. 59, 136–145 (2018).

Article CAS Google Scholar

Sangiovanni, D. G., Mellor, W., Harrington, T., Kaufmann, K. & Vecchio, K. Enhancing plasticity in high-entropy refractory ceramics via tailoring valence electron concentration. Mater. Des. 209, 109932 (2021).

Article CAS Google Scholar

Eibler, R. New aspects of the energetics of ordered Ti2C and Ti2N. J. Phys. Condens. Matter 19, 196226 (2007).

Article ADS Google Scholar

Tsurekawa, S. & Yoshinaga, H. Identification of long range ordered Structure in TiC0.59 by transmission electron microscopy. Nippon Kinzoku Gakkaishi 56, 133–141 (1992).

CAS Google Scholar

Tsuda, H., Ozaki, T. & Mori, S. Precipitation of titanium carbide particles dispersed in titanium matrix composites synthesized from Ti–C–N system powder mixtures using arc-melting method. Mater. Trans. 61, 1090–1095 (2020).

Article CAS Google Scholar

Tsuda, H., Ozaki, T. & Mori, S. Effects of chromium and nitrogen contents on microstructural changes in TiC particles in (α+β)- and β-titanium matrix composites. Mater. Trans. 53, 1405–1411 (2012).

Article Google Scholar

Bandyopadhyay, D., Haldar, B., Sharma, R. C. & Chakraborti, N. The Ti–Mo–C (titanium–molybdenum–carbon) system. J. Phase Equilib. 20, 332–336 (1999).

Article CAS Google Scholar

Pierson, H. O. Handbook of Refractory Carbides and Nitrides: Properties, Processing and Applications (Noyes Publications, 1996).

Google Scholar

Teatum, E. T., Gschneidner, K. A., Waber, J. T. Compilation of calculated data useful in predicting metallurgical behavior of the elements in binary alloy systems, Los Alamos Science Laboratory, Los Alamos, NM (1968). https://www.osti.gov/servlets/purl/4789465 (accessed 1 Feb 2023).

Voigt, W. Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik) (Springer, 1928).

MATH Google Scholar

Chang, R. & Graham, L. J. Low-temperature elastic properties of ZrC and TiC. J. Appl. Phys. 37, 3778–3783 (1966).

Article ADS CAS Google Scholar

Yang, Q., Lengauer, W., Koch, T., Scheerer, M. & Smid, I. Hardness and elastic properties of Ti(CxN1–x), Zr(CxN1–x) and Hf(CxN1–x). J. Alloys Compd. 309, L5–L9 (2000).

Article CAS Google Scholar

Valeeva, A. A. & Gusev, A. I. Effect of nonstoichiometry on elastic properties of niobium carbide NbCy. J. Refract. Met. Hard Mater. 95, 105435 (2021).

Article CAS Google Scholar

Kral, C., Lengauer, W., Rafaja, D. & Ettmayer, P. Critical review on the elastic properties of transition metal carbides, nitrides and carbonitrides. J. Alloys Compd. 265, 215–233 (1998).

Article CAS Google Scholar

Allard, S. (ed.) International Tables of Selected Constants. Metals, Thermal and Mechanical Data Vol. 16 (Pergamon, 1969).

Google Scholar

Zhao, M., Yoshimi, K., Maruyama, K. & Yubuta, K. Thermal vacancy behavior analysis through thermal expansion, lattice parameter and elastic modulus measurements of B2-type FeAl. Acta Mater. 64, 382–390 (2014).

Article ADS CAS Google Scholar

Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).

Article ADS CAS Google Scholar

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

Article ADS CAS PubMed Google Scholar

Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

Article ADS Google Scholar

Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

Article ADS MathSciNet Google Scholar

van de Walle, A. et al. Efficient stochastic generation of special quasirandom structures. CALPHAD Comput. Coupling Phase Diagr. Thermochem. 42, 13–18 (2013).

Article Google Scholar

Hill, R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. Lond. Sect. A 65, 349–354 (1952).

Article ADS Google Scholar

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This work was partly supported by MIRAI Program (JPMJMI17E7) from the Japan Science and Technology (JST), a Grant-in-Aid for scientific research (A) (Grant No. 21H04606) from the Japan Society for the Promotion of Science (JSPS) and MEXT Program: Data Creation and Utilization Type Material Research and Development Project Grant Number JPMXP1122684766.

Department of Materials Science, Graduate School of Engineering, Tohoku University, 6-6-02 Aramaki Aza Aoba, Aoba-ku, Sendai, 980-8579, Japan

Shuntaro Ida, Kotaro Hoshizaki, Takahiro Kaneko, Xi Nan, Nobuaki Sekido & Kyosuke Yoshimi

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S.I. and K.Y. designed this research. S.I. and K.H. were carried out the experiments and calculated the data. S.I., and K.Y. wrote the main manuscript text. All authors contributed to discussion of the results.

Correspondence to Shuntaro Ida.

The authors declare no competing interests.

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Ida, S., Hoshizaki, K., Kaneko, T. et al. Off-stoichiometry and molybdenum substitution effects on elastic moduli of B1-type titanium carbide. Sci Rep 13, 13631 (2023). https://doi.org/10.1038/s41598-023-40969-x

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Received: 28 May 2023

Accepted: 19 August 2023

Published: 21 August 2023

DOI: https://doi.org/10.1038/s41598-023-40969-x

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