Sequence of disorder-order and order-order transitions accompanying the formation of M<Subscript>2</Subscript>X superstructures

The symmetry analysis of the trigonal, cubic, and tetragonal M₂X superstructures formed in strongly nonstoichiometric compounds MX _y with the B1 structure has been performed. Disorder-order MX _y → M₂X transition channels have been revealed. It has been shown that three physically allowable sequences of transitions associated with the formation of ordered M₂X phases and order-order transitions between them are possible in nonstoichiometric carbides and nitrides MX _y of the transition metals of group IV with a decrease in the temperature.     

Ordering of MX y nonstoichiometric compounds with the formation of M 2 X superstructures

A symmetry analysis of trigonal, cubic, and tetragonal superstructures of the M ₂ X type that are formed in strongly nonstoichiometric compounds MX _y with the B1 structure has been performed. The channels of disorder-order transitions MX _y → M ₂ X have been determined. It has been demonstrated that, in nonstoichiometric carbides and nitrides MX _y of Group IV transition metals, a decrease in the temperature can lead to three physically allowable sequences of transformations associated with the formation of M ₂ X ordered phases.     

Order-disorder phase transformations and specific heat of nonstoichiometric vanadium carbide

AbstractA study has been made of the order-disorder phase transformations in the homogeneity region of the VC_y nonstoichiometric cubic vanadium carbide (0.66<y<0.88). It has been established that an ordered V₆C₅ phase with monoclinic (space group C2/m) or trigonal (P3₁) symmetry, and a cubic (space group P4₃32) ordered V₈C₇ phase can form in the VC_y carbide below 1450 K, depending on the actual composition. The effect of off-stoichiometry and structural vacancy ordering on the specific heat of the VC_y carbide has been investigated. The temperatures and heats of the reversible order-disorder equilibrium transitions have been determined. The ordering in the VC_y carbide is shown to be a first-order phase transition. An equilibrium diagram of the V-C system taking into account ordering in the nonstoichiometric vanadium carbide has been constructed. Fiz. Tverd. Tela (St. Petersburg) 41, 529–536 (March 1999)     

Sequence of transformations during ordering of nonstoichiometric compounds with the formation of M 3 X 2-type superstructures

A symmetry analysis of monoclinic, orthorhombic, and trigonal M ₃ X ₂-type superstructures, which can be formed in highly nonstoichiometric MX _y compounds with B1 structure, has been performed. Channels of disorder-order transitions MX _y → M ₃ X ₂ have been determined. It has been shown that two physically allowed sequences of transformations associated with the formation of M ₃ X ₂ superstructures are possible in nonstoichiometric MX _y compounds of Group IV transition metals with decreasing temperature, i.e., “cubic (space group \(Fm\bar 3m\) ) disordered MX _y phase → orthorhombic (space group Immm) ordered M ₃ X ₂ phase → orthorhombic (space group C222₁) ordered M ₃ X ₂ phase” and “cubic (space group \(Fm\bar 3m\) ) disordered MX _y phase → orthorhombic (space group Immm) ordered M ₃ X ₂ phase → monoclinic (space group C2) ordered M ₃ X ₂ phase.”     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

Symmetry analysis of the monoclinic Pd<Subscript>6</Subscript>B superstructure: Long- and short-range orders

A symmetry analysis of the monoclinic (space group C2/c) Pd₆B superstructure formed in the cubic (with structure B1) boron solid solution PdB _y in palladium has been performed. The formation of this superstructure occurs as a first-order phase transition via the disorder-order transition channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the monoclinic (space group C2) Pd₆B superstructure, the distribution function of boron atoms has been calculated and the interval of admissible values of long-range order parameters has been determined. It has been shown that the found transition channel is identical to the channel of the formation of the monoclinic (space group C2/c) M ₆ X superstructure; therefore, the Pd₆B superstructure can be described with the same accuracy in space group C2. The higher symmetry of the monoclinic (space group C2/c) model suggests that it more accurately describes the structure of the phase Pd₆B (Pd₆B□₅) and mutually inverse phases M ₆ X□₅ and M ₆ X ₅□ than the model with space group C2. It has been demonstrated that there are two types of the nearest environment of metal atoms with non-metal sublattice sites arranged in the first and second coordination spheres in M ₆ X□₅-type superstructures (space groups C2/c, C2, C2/m, and P3₁) and in inverse M ₆ X ₅□-type superstructures with the same space groups.     

Long- and short-range order in the Pd<Subscript>6</Subscript>B monoclinic superstructure and M<Subscript>6</Subscript>X<Subscript>5</Subscript> and M<Subscript>6</Subscript>X allied superstructures

Symmetry analysis of the Pd₆B monoclinic superstructure (space group C2/c) formed in the cubic (with the B1 structure) solid solution of boron in palladium (PdB _y ) has been carried out. The formation of this superstructure proceeds as a first-order phase transition via the disorder-order channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the Pd₆B monoclinic super-structure (space group C2/c), the distribution function for boron atoms is calculated and the interval of admissible values of the long-range order parameters is defined. It is shown that the transition channel determined in this way coincides with the channel in which the M₆X monoclinic superstructure (space group C2) is formed; therefore, the Pd₆B superstructure can also be described in space group C2 to the same degree of accuracy. The higher symmetry of the monoclinic model (space group C2/c) suggests that it describes the structure of the Pd₆B phase (Pd₆B□₅), as well as of mutually inverse phases M₆X□₅ and M₆X₅□, more adequately than the model with space group C2. It is shown that superstructures of the M₆X□₅ type (space groups C2/c, C2, C2/m, and P3₁) and inverse superstructures of the M₆X₅□ type with the same space groups have the positions of the nearest surrounding of metal atoms by two types of nonmetallic sublattice sites located in the first and second coordination spheres.     

Accounting for nonstoichiometry of niobium carbide NbC y upon milling to a nanocrystalline state

The dependence of the size of particles in the prepared nanocrystalline powders on the composition of nonstoichiometric compounds within their homogeneity intervals has been considered in terms of the high-energy ball milling model. It has been shown that the effect of nonstoichiometry on the milling manifests itself in the concentration dependences of the main characteristics (parameters of the crystal structure, energy of interatomic bonds, elastic properties) of the milled nonstoichiometric compound. The results of model calculations performed for nonstoichiometric cubic niobium carbides NbC _y have been compared with the experimental data on milling of the NbC_0.93 carbide.     

Determination of the probability of existence of pair interactions in the formation of M2tX2t?1Superstructures in MXy nonstoichiometric compounds

An analytical method has been proposed for calculating the probabilities P _i ^(2)(s) of existence of X-X, X−□, and □−□ pair interactions in the nonmetal sublattice of M _2tX_2t−1 superstructures formed in strongly nonstoichiometric compounds MX _y (MX _y □_1−y) and M ₂X _y (MX_y/2□_1−y/2) with a high content of structural vacancies □. The main characteristics necessary for the quantitative determination of the probabilities P_i(2)(s) as functions of the composition, degree of long-range order, symmetry, and structure type have been determined for all the known superstructures M _2tX_2t−1.     

Microinhomogeneity of the Structure of Nanocrystalline Niobium and Vanadium Carbides

The evolution of the microstructure of nonstoichiometric niobium carbides NbC_y (y = 0.77, 0.84, 0.96) and vanadium carbide V₈C₇ subjected to high-energy milling has been studied by the time-of-flight neutron diffraction method. It has been found that milled nanocrystalline powders have microinhomogeneous structure: two fractions with different sizes of particles have been identified in them. The content of the nanofraction is more than 90 wt %; the size of particles of this fraction varies from 90 to 250 Å, depending on the composition of the initial carbide and the duration of milling. The size of particles of the second fraction is more than 2000 Å. Anisotropic deformation distortions have been revealed. The mean size of coherent scattering regions and microstrains in nanocrystallites have been estimated.     

Disorder-order phase transformations and electrical resistivity of nonstoichiometric titanium carbide

Phase transformations of the disorder-order type in the homogeneity region of nonstoichiometric titanium carbide TiC_y (0.5<y<1.0) have been studied. It has been established that, depending on the actual composition of TiC_y, there may form in it for T<980–1000 K a cubic or a trigonal ordered Ti₂C phase (space groups Fd3m and , respectively) and a rhombic ordered Ti₃C₂ phase (space group C222₁). The effect of ordering on the electrical resistivity of the nonstoichiometric carbide TiC_y was studied, and the temperatures of the reversible disorder-order equilibrium transitions determined. The ordering in titanium carbide is shown to be a first-order phase transition. Fiz. Tverd. Tela (St. Petersburg) 40, 1332–1340 (July 1998)     

Identification of structural vacancies in carbides,oxides, and sulfides by Doppler broadening of the gamma-ray line

A method has been developed to identify the sublattices of a crystal structure in which there are atomic vacancies. This method is based on determining the chemical environment of vacancies and is implemented using the method of the positron annihilation by measuring the momentum distribution of core electrons. To determine the characteristic momentum distribution of electrons, a special two-detector spectroscopy is used, which ensures measurements of Doppler broadening of the annihilation gamma-ray line with a high (up to 10⁶) signal-to-noise ratio. To test the method, vacancies in irradiated silicon carbide (6H-SiC), sintered nonstoichiometric titanium carbides (TiC _y ) and titanium monoxides (TiO _y ), and chemically deposited lead and cadmium sulfides (PbS and CdS) have been identified. Vacancies in the carbon and silicon sublattices have been identified in silicon carbide after irradiation by low- and high-energy electrons, respectively. Vacancies in the nonmetal sublattice have been identified in TiC _y . Vacancies in the metal sublattice have been identified in TiC _y , as well as in PbS and CdS.     

Influence of hydrogenation on the electronic structure and the itinerant-electron metamagnetic transition in strong magnetocaloric compound La(Fe0.88Si0.12)13

The influence of interstitial hydrogen on the electronic structure and the itinerant-electron metamagnetic (IEM) transition in strong magnetocaloric compound La(Fe_0.88Si_0.12)₁₃H_1.6 has been investigated by Mössbauer spectroscopy. A slight change in the average hyperfine field at 4.2 K was observed after hydrogen absorption. In contrast, the thermally induced first-order transition related to the IEM transition for y=1.6 appears at the Curie temperature T_C=330 K, much higher than T_C=195 K for y=0.0. The increase of isomer shift δ_IS at 4.2 K indicates that the valence electron transfer from hydrogen to Fe is negligibly small, hence the change in the magnetic state is closely associated with a volume expansion after hydrogen absorption. No change in shape by hydrogenation for the Mössbauer spectra in the paramagnetic state has been observed except for a difference in only δ_IS, indicating the volume expansion by hydrogenation is isotropic. Accordingly, the significant increase of T_C by hydrogen absorption is attributed to the magnetovolume effect associated with characteristic feature in IEM compounds. A discontinuous change of ferromagnetic moment, ΔM, around T_C has been observed by Mössbauer spectra, as expected from the magnetization measurement. The value of ΔM is slightly decreased by increase of T_C after hydrogenation but its magnitude is almost the same due to the stabilization of ferromagnetic moment. As a result, strong magnetocaloric effect is maintained up to room temperature after hydrogenation.     

Ordering in the ζ-Ta<Subscript>4</Subscript>C<Subscript>3−<Emphasis Type="Italic">x</Emphasis></Subscript> carbide phase

The structure of the ζ-Ta₄C_3?x nonstoichiometric trigonal (rhombohedral) carbide, which is formed in the tantalum-carbon system, has been analyzed by neutron diffraction, x-ray diffraction, and metallography. The ordered distributions of carbon atoms and structure vacancies have been experimentally determined and the distribution function of carbon atoms over the nonmetallic-sublattice sites, where ordering occurs, has been calculated. The parameters of the unit cell of the ζ-Ta₄C_3?x (TaC_0.67) trigonal (space group \(R\overline 3 m\)) carbide are found to be a_H = 0.3123 nm and c_H = 3.0053 nm. It has been shown that the metallic close packed sublattice of the ζ-Ta₄C_3?x carbide is formed by alternating blocks, where metal atoms are located both in the fcc and hcp sublattices of the TaC_y cubic and Ta₂C hexagonal carbides, respectively.     

快淬(Er1-xSmx)2Fe17Cy化合物的结构与磁性

用快速急冷方法制备了(Er_1-xSm_x)₂Fe₁₇C_y(x≤0.8,1.5≤y≤2.5)化合物,它们具有菱方Th₂Zn₁₇型结构,并且在高温是稳定的。与相应的不含C的(Er_1-xSm_x)₂Fe₁₇化合物比较,当C含量y=2.5时,引起单胞体积增加～6.3％,居里温度增     

Ordering of nonstoichiometric hexagonal compounds <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript><Emphasis Type="Italic">X</Emphasis>: A sequence of special figures

An ensemble of figures required for the analysis of the atomic-vacancy ordering in nonstoichiometric compounds M ₂ X _y (M ₂ X _y ▭_{1 − y} ) with an L′3 hexagonal structure has been determined by the order-parameter functional method. It has been demonstrated reasoning from the crystal lattice geometry that, in order to describe M ₂ X _y compounds with an L′3 structure, it is necessary to use the basis cluster in the form of a trigonal prism consisting of six sites of the nonmetal lattice with a metal atom at the center. The overlapping figures that, together with the basis cluster, form a sequence of special figures uniquely describing the L′3 structure have been found. The equilibrium conditions for disorder-order transformations in nonstoichiometric compounds M ₂ X _y have been determined in the general form.     

Fine structure of the field-induced magnetic transition in Nd0.1La0.9Fe11.5Al1.5

For the Nd_0.1La_0.9Fe_11.5Al_1.5 compound, the fine structure of the magnetic transition from the ferromagnetic (FM) to the antiferromagnetic (AFM) states has been studied carefully by means of magnetization (M) and heat capacity (C_p) measurements. Although a single phase with the cubic NaZn₁₃-type structure (Fm3c) has been proved by the room temperature X-ray diffraction pattern, the phase transition has been clearly found to be a stepwise process in M(T) and C_p(T) curves under proper fields. Due to the strong competition between the FM order and AFM order, the characteristic is especially evident under low fields, weakens gradually with the increasing applied field and finally vanishes when the field is higher than 2 T. This multi-step magnetic transition results from the inhomogeneity of the sample, probably due to the inhomogeneous distribution of Nd atoms.     

Effect of carbon vacancies on the electric resistivity of nonstoichiometric VC<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> vanadium carbide

The influence of the temperature, concentration, and distribution of structure vacancies of the carbon sublattice on the electric resistivity ρ of nonstoichiometric VC _y vanadium carbide (0.66 ≤ y ≤ 0.875) has been studied in the temperature range of 300–1200 K. The symmetry and structure characteristics of the ordered V₆C₅ and V₈C₇ phases formed owing to low-temperature annealing on various sections of the homogeneity region of the VC _y carbide. The dependence of the residual electric resistivity on the content of the disordered vanadium carbide is explained by the atom-vacancy interaction and the change in the carrier concentration in the homogeneity region of VC _y .     

Composition of cementite in the dependence on the temperature. In situ neutron diffraction study and Ab initio calculations

The structure state of carbon eutectoid steel has been studied by the in situ neutron diffraction method in the temperature range from room temperature to 800°C. It has been shown that an increase in the temperature is accompanied by a decrease in the concentration of carbon in cementite, whereas its weight fraction and the parameters of the orthorhombic lattice change slightly. The ab initio calculations of the nonstoichiometric carbides Fe₃C _x (0 < x < 1) indicate that the structure of cementite remains stable upon the appearance of vacancies in the carbon sublattice with a relatively low formation energy. Thus, cementite should be considered as an interstitial phase Fe₃C _x with a wide homogeneity range.     

Magnetic entropy change and large refrigerant capacity of Ce6i2Si3-type GdCoSiGe compound

Magnetic entropy change (Δ S_M) and refrigerant capacity (RC) of Ce₆Ni₂Si₃-type Gd₆Co_1.67Si_2.5Ge_0.5 compounds have been investigated. The Gd₆Co_1.67Si_2.5Ge_0.5 undergoes a reversible second-order phase transition at the Curie temperature T_C = 296 K. The high saturation magnetization leads to a large Δ S_M and the maximal value of Δ S_M is found to be 5.9 J/kg,cdot,K around T_C for a field change of 0--5 T. A broad distribution of the Δ S_M peak is observed and the full width at half maximum of the Δ S_M peak is about 101 K under a magnetic field of 5 T. The large RC is found around T_C and its value is 424 J/kg.