Based on the analysis of phase diagrams of carbide-forming systems M-C (M = Ti, Zr, Hf), an empirical relationship is proposed between the elastic stiffness constants c ij of nonstoichiometric cubic carbides of titanium, zirconium and hafnium and their melting temperature. The dependences of the melting temperatures of nonstoichiometric cubic carbides TiCy, ZrCy and HfCy on their composition in homogeneity regions are calculated using the elastic stiffness constants c 11 ( y ) and c 44 ( y ) of these carbides. The calculated maximum melting temperatures are observed for carbides- TiC 0.80 ,- ZrC 0.82 and- HfC 0.94-0.95 and are equal to 3345, 3708 and 4192 K, respectively. There is a qualitative correlation between the concentration dependences of the melting temperatures T m ( y ) of TiCy, ZrCy and HfCy carbides and the anisotropy of the elastic properties of these carbides.

The elastic stiffness constants c11, c12, and c44 are determined semiempirically for the first time as functions of the relative carbon content y in the homogeneity region HfC0.60 - HfC1.00 of disordered cubic HfCy hafnium carbide. It is established that the elastic stiffness constants cij of disordered HfCy carbide decrease as the composition of hafnium carbide deviates from stoichiometry. An increase in the deviation of the HfCy composition from stoichiometry leads to a growth in the anisotropy of the elastic properties. It is found that the values of elastic moduli depend on the crystallographic direction [hkl], and the maximum and minimum the Young's moduli are observed in the [001], [010], [100] or [+/- 1 +/- 1 +/- 1] directions of cubic HfCy carbide, respectively. Noticeable changes in the elastic characteristics of HfCy depending on the [hkl] direction indicate an elastic anisotropy of disordered cubic hafnium carbide. It is shown that polycrystalline disordered cubic hafnium carbides are brittle substances. The calculated Vickers hardness of polycrystalline disordered cubic HfCy carbide increases with a change in its composition from HfC0.60 to HfC1.00.

For the first time, the elastic constants c(11), c(12) and c(44) of disordered cubic titanium monoxide TiOy were determined depending on the oxygen content y in the homogeneity region from TiO(0.80 )to TiO1.25. It has been established that the values of the elastic moduli depend on the oxygen contenty y and the crystallographic direction [hkl]. Large changes in the elastic characteristics of TiOy depending on the [hkl] direction indicate a strong anisotropy of the elasticity of disordered cubic titanium monoxide.

Sulfide (ZnS)(Ag2S)x heteronanostructures of various composition were obtained by co-deposition from water colloidal solutions of silver and zinc nitrates using sodium sulfide as a sulfidizer and sodium citrate as a stabilizer. The formation of (ZnS)(Ag2S)x heteronanostructures was confirmed using the XRD, HAADF-STEM, SEM, EDX and Raman spectroscopy. The size of ZnS and Ag2S nanoparticles in heteronanostructures (ZnS)(Ag2S)x with x <= 0.01 is 2-4 and no more than 3 nm, respectively. Raman spectroscopy showed that addition of silver sulfide nanoparticles into (ZnS)(Ag2S)x heteronanostructures leads to Ag2S deposition onto the surface of ZnS nanoparticles. Doping ZnS with only 1 mol.% of colloidal Ag2S nanoparticles is sufficient to produce a silver sulfide shell on the surface of ZnS nanoparticles.

Heteronanostructures (ZnS)(Ag2S)x, where x = 0.002–0.50, are synthesized by hydrochemical coprecipitation. The ZnS nanoparticle size in the resulting heteronanostructures is 2–4 nm. Annealing of the synthesized (ZnS)(Ag2S)x heteronanostructures in air at temperatures of 25–530°C and above leads to a change in their phase composition due to the oxidation of cubic zinc sulfide to hexagonal zinc oxide. Oxidation begins at a temperature of 250°C; the zinc oxide content in the heteronanostructures after annealing at 530°C achieves 26–30 wt

Sulfide composites ZnS/Ag2S with various contents of silver sulfide have been synthesized by chemical co‑deposition. The sizes of ZnS and Ag2S nanoparticles in ZnS/Ag2S composites containing less than 1.0 mol

The band structure calculation indicated that cubic Nb3O3 niobium monooxide is a com-pound with metallic conductivity. The anisotropy of the elastic properties of cubic (space group Pm (3) over barm) niobium monoxide Nb3O3 has been studied. The elastic stiffness constants c(ij) for cubic Nb3O3 monoxide are computed using the density functional theory. The dependences of the Young's, bulk and shear moduli, as well as the Poisson's ratio in the (100), (110) and (111) planes of cubic niobium monoxide Nb3O3 on the crystallographic direction [hkl] are calculated. It is found that the maximum the Young's and shear moduli are observed in the [001], [010], and [100] directions, and the minimum values of the Young's and shear moduli are observed in the [+/- 1 +/- 1 +/- 1] directions of cubic niobium monoxide, respectively. Relatively small changes in the elastic characteristics of Nb3O3 depending on the [hkl] direction indicate a slight anisotropy of its elastic properties. Cubic niobium monoxide is mechanically and dynamically stable. The hardness H-V and the Debye temperature theta(D) of poly-crystalline cubic niobium monoxide Nb3O3 are determined to be 17.2 GPa and similar to 640 K, respectively.

The elastic constants c11, c12, c44 are determined for the first time as functions of the carbon content y in the homogeneity region ZrC0.60 -ZrC1.00 of nonstoichiometric disordered cubic ZrCy zirconium carbide. It is established that the elastic stiffness constants cij of disordered ZrCy carbide decrease with an increase in the defectiveness of the carbon sublattice of zirconium carbide. An increase in the deviation of the ZrCy composition from stoichiometry leads to a slight decrease in the anisotropy of the elastic properties. The elastic properties of zirconium carbide are anisotropic, since they change depending on the crystallographic direction [hkl] due to differences in the arrangement of atoms and interatomic bonds in various directions. It is found that the values of elastic moduli depend on the crystallographic direction [hkl], and the maximum and minimum the Young's moduli are observed in the [001], [010], [100] or [+/- 1 +/- 1 +/- 1] directions of cubic ZrCy carbide, respectively. Small changes in the elastic characteristics of ZrCy depending on the [hkl] direction indicate a weak elastic anisotropy of cubic zirconium carbide. It is shown that the calculated Vickers hardness and Debye temperature of polycrystalline disordered cubic ZrCy carbide increase non-linearly with increasing relative carbon content y.

Carbides of IV and V group transitional metals with B1 structure contain large amounts of vacancies in the carbon sublattice. Ordering of the vacancies leads to formation of new phases with various stoichiometry. Ordered structures were discovered and studied for all the IV and V group transitional metal carbides except carbides of hafnium and tantalum. Nevertheless, recent theoretical works have predicted large variety of ordered structures in non-stoichiometric HfCy and TaCy including unusual Hf7C6 and Ta7C6. Such a stoichiometry is not typical for the ordered carbides. In this work, we study in detail the new M7X6 type of vacancy ordered structures using ab initio methods. For both compounds Hf7C6 and Ta7C6, we have found two B1-derived vacancy-ordered phases: trigonal (space group R (3) over bar) and monoclinic (space group C2/m). The comparison of their formation enthalpies with the disordered B1 structure has showed that the only ordered phase Hf7C6 can be trigonal phase while in Ta7C6 both trigonal and monoclinic structures are possible. Using the predicted monoclinic superstructure, we explain some peculiarities of the neutron diffraction pattern of the annealed partially ordered samples of TaC0.83-0.85. The theoretical and experimental data on the short range structural order in superstructures is discussed. We also study the influence of the M7X6 type of ordered structure on mechanical properties. The highest Vickers hardness similar to 27.1 GPa is expected for the trigonal ordered Hf7C6 phase.

Silver sulfide phases, such as body-centered cubic argentite and monoclinic acanthite, are widely known. Traditionally, acanthite is regarded as the only low-temperature phase of silver sulfide. However, the possible existence of other low-temperature phases of silver sulfide cannot be ruled out. Until now, there have been only a few suggestions about low-temperature Ag2S phases that differ from monoclinic acanthite. The lack of a uniform approach has hampered the prediction of such phases. In this work, the use of such an effective tool as an evolutionary algorithm for the first time made it possible to perform a broad search for the model Ag2S phases of silver sulfide, which are low-temperature with respect to cubic argentite. The possibility of forming Ag2S phases with cubic, tetragonal, orthorhombic, trigonal, monoclinic, and triclinic symmetry is considered. The calculation of the cohesion energy and the formation enthalpy show, for the first time, that the formation of low-symmetry Ag2S phases is energetically most favorable. The elastic stiffness constants cij of all predicted Ag2S phases are computed, and their mechanical stability is determined. The densities of the electronic states of the predicted Ag2S phases are calculated. The prediction of low-temperature Ag2S structures indicates the possibility of synthesizing new silver sulfide phases with improved properties.

A critical analysis of the conditions of elastic stability of crystal structures of different symmetry as restrictions imposed on their elastic constants cij has been carried out. It is shown that the conditions of elastic stability of all crystals, except for cubic ones, are described by polynomials from the second to sixth powers of their elastic constants cij. Necessary and sufficient conditions for the elastic stability of crystals of different symmetry are presented explicitly.

Changes in the elastic constants cij of disordered cubic TaCy tantalum carbide with an increasing the defectiveness of the carbon sublattice are estimated for the first time. The deviation of tantalum carbide from the stoichiometric composition TaC1.0 leads to a decrease in the elastic stiffness constants cij of disordered TaCy carbide with a simultaneous increase in elastic anisotropy. The distributions of the Young's modulus E and the Poisson's ratio μ in the (100) plane and the distributions of the shear modulus G in the (100), (110), and (111) planes have been calculated as functions on the crystallographic direction [hkl] and on the relative carbon content y in TaCy carbide. The Vickers hardness HV of disordered tantalum carbide was calculated using the inverse Pugh's ratio G/B and the experimental data on the dependences of the bulk modulus B and the shear modulus G on the composition of disordered TaCy. Influence of nonstoichiometry of nanocrystalline powders of cubic tantalum carbide TaCy on anisotropy of strain distortions is established. The value of microstrains εhkl is estimated with allowance for their anisotropy.

A search for ordered TanCm phases in nonstoichiometric tantalum carbide has been performed with the use of an evolutionary algorithm. Three thermodynamically stable phases Ta2C, Ta6C5, and TaC with trigo-nal, monoclinic and cubic symmetry as well as metastable Ta3C2, Ta4C3, Ta7C5, Ta9C7, Ta10C7, Ta5C4, Ta7C6, Ta8C7, Ta10C9, and Ta9C8 phases have been predicted in the composition range TaC0.5-TaC1.0. The disorder-order phase transition channels Ta2Cy -> Ta2C and TaCy -> Ta6C5 associated with the formation of stable trigonal and monoclinic superstructures have been determined for the first time. The distribution func-tions of carbon atoms over the sites of these trigonal Ta2C and monoclinic Ta6C5 superstructures have been calculated. The elastic stiffness constants c(ij) of all the predicted TanCm phases have been also calcu-lated. All the predicted TanCm tantalum carbides are mechanically stable. The calculated values of inverse Pugh's ratio k = G/B values for all the predicted TanCm carbides (except Ta2C) are greater than 0.57 indi-cating that the considered materials are brittle. The calculated Debye temperatures theta(D) of all TanCm phases grow almost monotonically with decreasing concentration of vacancies in TanCm (TaCy with y = m/n) car-bides. The calculated heat capacity of all TanCm phases (except the trigonal Ta3C2 phase) decrease almost monotonically when the concentration of vacancies in TanCm carbides lowers. (C) 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Phase transformations that take place in nanocrystalline Ag2S silver sulfide have been systematically studied at temperatures from 298 to 893 K. The crystal structures of the polymorphic modifications α-Ag2S, β-Ag2S, and γ-Ag2S of nanocrystalline Ag2S have been found. It is established that the interstitial spacings between ions of silver in the superionic phases β-Ag2S and γ-Ag2S are noticeably smaller than diameter of the Ag+ ion. As a result of which, the probabilities of filling the sites of the metal sublattices of these phases with Ag atoms are very small. It was found that the “α-Ag2S—β-Ag2S” and “β-Ag2S—γ-Ag2S” transitions between polymorphic modifications of silver sulfide occur as phase transformations of the first order at temperatures of ~440–442 K and ~850–860 K. The structure of interface forming by nanostructured Ag2S and ZnS is considered, taking into account the anisotropy of elastic properties of these sulfides. It is established that a large amount of cubic zinc sulfide stabilizes the cubic structure of β-Ag2S argentite at 300 K during the co-deposition of Ag2S/ZnS heteronanostructures from colloid solutions. It is found that placing Ag atoms at four crystallographic positions located in one plane of the unit cell of cubic β-Ag2S argentite is most favorable for the appearance of Ag2S/ZnS heterostructures. The smallest strain distortions at the interface are observed at the minimum difference of shear moduli of the components forming heteronanostructure. The distributions of elastic characteristics, including the shear moduli of monocrystalline particles of cubic β-Ag2S argentite and ZnS sphalerite from the [hkl] direction, are found. The formation of Ag2S/ZnS heteronanostructures, in which the interface is formed by the (hk0) ≡ (110) plane of ZnS sphalerite and the (hk 0.4123) ≡ (1 1 0.4123) plane of β-Ag2S argentite, is the most energetically favorable.

Changes in the elastic constants cij of disordered cubic titanium carbide TiCy with an increasing the defectiveness of the carbon sublattice are estimated for the first time. It was found that the deviation of titanium carbide from the stoichiometric composition TiC1.0 leads to a decrease in the elastic stiffness constants cij of disordered TiCy carbide with a simultaneous increase in elastic anisotropy. The distributions of Young's modulus E and Poisson's ratio μ in the (100) plane and the distributions of the shear modulus G in the (100), (110), and (111) planes have been calculated as functions on the crystallographic direction [hkl] and on the relative carbon content y in TiCy carbide. The lowest values of the shear modulus Ghkl for TiCy are observed in the (111) plane. Keywords: Titanium carbide, Nonstoichiometry, Vacancies, Elastic properties.

Possible models for the arrangement of hydrogen atoms in the sites of the cubic lattice of titanium oxyhydride TiO y H p with vacancies in the metallic and nonmetallic sublattices are considered for the first time. It has been established that interstitial H atoms in oxyhydrides occupy vacant octahedral sites 4( b ) of the oxygen sublattice. No displacement of H atoms in tetrahedral sites 8( c ) is observed.

Possible models of the arrangement of hydrogen atoms at the sites of the cubic lattice of titanium oxyhydride TiOyHp with vacancies in the metallic and nonmetallic sublattices are considered. It was found that titanium oxyhydride retains the B1 type crystal lattice of the initial cubic titanium monoxide TiOy and contains structural vacancies in the metal and oxygen sublattices. Comparison of the found analytical expressions for the intensity of diffraction reflections with experimental X-ray and neutron diffraction data showed that interstitial H atoms in oxyhydrides occupy vacant octahedral positions 4(b) of the oxygen sublattice. No displacement of H atoms in tetrahedral positions 8(c) is observed. A disorder-order phase transition channel associated with the formation of an ordered monoclinic titanium oxyhydride of the Ti5O5 type was found. The distribution functions of Ti, O, and H atoms in the partially ordered monoclinic oxyhydride Ti5.33O5.12H0.74 (Ti0.89O0.85H0.12) with a Ti5O5-type structure are calculated for the first time, and the concentrations of these atoms at the positions of its lattice were found.

Carbides of IV and V group transitional metals with B1 structure have large homogeneity regions due to high amounts of vacancies in the carbon sublattice. Ordering of the vacancies leads to formation of new phases with different compositions and crystal structures. In this work, we performed a theoretical search for the ordered phases in hafnium carbide using evolutionary algorithm USPEX for crystal structure prediction. Four thermodynamically stable compounds with stoichiometries Hf3C2, Hf4C3, Hf7C6 and Hf9C8 as well as near-to-equilibrium variants Hf9C7, Hf5C4, and Hf6C5 have been found in the composition range HfC0.67-HfC1.0. All the stable and meta-stable phases are formed by vacancy ordering in the carbon sublattice of B1 structure. We also described possible ordered structures for hypothetical compositions Hf10C7, Hf7C5, Hf8C7 and Hf10C9. This allowed us to investigate the effect of vacancy concentration on the structural and mechanical properties. The calculations have demonstrated the ordered vacancies with a concentration of less than approximately 11% do not deteriorate the mechanical properties of hafnium carbide. The hardness of ordered phases with vacancy concentrations less than 16.7% is higher as compared to the defect-free HfC. (C) 2021 Elsevier B.V. All rights reserved.

Possible models of the arrangement of hydrogen atoms at the sites of the cubic lattice of titanium oxyhydride TiOyHp with vacancies in the metallic and nonmetallic sublattices are considered. It was found that titanium oxyhydride retains the B1 type crystal lattice of the initial cubic titanium monoxide TiOy and contains structural vacancies in the metal and oxygen sublattices. Comparison of the found analytical expressions for the intensity of diffraction reflections with experimental X-ray and neutron diffraction data showed that interstitial H atoms in oxyhydrides occupy vacant octahedral positions 4( b) of the oxygen sublattice. No displacement of H atoms in tetrahedral positions 8( c) is observed. A disorder-order phase transition channel associated with the formation of an ordered monoclinic titanium oxyhydride of the Ti5O5 type was found. The distribution functions of Ti, O, and H atoms in the partially ordered monoclinic oxyhydride Ti5.33O5.12H0.74 (Ti0.89O0.85H0.12) with a Ti5O5-type structure are calculated for the first time, and the concentrations of these atoms at the positions of its lattice were found. Keywords:Titanium monoxide, Hydrogen, Nonstoichiometry, Vacancies, Octahedral and tetrahedral positions, Distribution function.