Lattice Parameters Of Solid Solutions Research Articles

Experimental investigation of the solid phase equilibria at 300 K in the SnBi2Te4-PbBi2Te4-Bi2Te3 system

The phase equilibria of the SnBi2Te4-PbBi2Te4-Bi2Te3 system were experimentally studied using differential thermal analysis (DTA), X-ray diffraction (XRD), and scanning electron microscopy (SEM) techniques. According to the experimental results, the isothermal section of the system at 300 K were constructed and 4 single-phase and 3 two-phase regions were identified. It was shown that along with previously confirmed SnBi2Te4–PbBi2Te4 and SnBi4Te7–PbBi4Te7 sections, SnBi6Te10–PbBi6Te10 section forms continuous series of solid solutions with a tetradymite-type layered structure. Lattice parameters of solid solutions were determined by full-profile Rietveld refinements and results show that both a and c parameters increase linearly with the Pb concentration according to Vegard's law. This study can help elucidate the phase equilibria of the SnTe-PbTe-Bi2Te3 pseudo-ternary system which provides important information for the design of new tetradymite-type layered phases with topological insulator and thermoelectric properties.

Crystal Structure, Magnetic and Photocatalytic Properties of Solid SolutionsBi2‐xLaxFe4O9 (x=0.05, 0.1)

AbstractSolid solutions Bi2–xLaxFe4O9 at small x‐values (x=0.05, 0.1) were synthesized by the solid‐state reaction method. Here larger Bi3+ ions were partially substituted by smaller La3+ ions. It is shown that the above solid solutions had an orthorhombic mullite‐type crystal structures. Crystal lattice parameters of solid solutions were very close to the respective parameters for pure Bi2Fe4O9 ferrite. It was determined that the substitution of Bi3+ ions by La3+ ions in Bi2Fe4O9 leads to the increase of specific magnetizations of the samples. All studied samples were antiferromagnets with Neel temperatures TN of 258 K, 246 K, ∼243 K for x=0, 0.05, 0.1 respectively. Hence at the substitution of Bi3+ ions by La3+ ions, TN decreases. It is shown that solid solution Bi1.9La0.1Fe4O9 had good photocatalytic activity for the oxidation of Acid Telon Blue dye in the aqueous solution under visible light irradiation.

PHASE RELATIONS IN THE Sb2Te2S-Bi2Te2S SYSTEM AND CHARACTERIZATION OF Sb2-xBixTe2S SOLID SOLUTIONS

The phase equilibria of the Sb2Te2S-Bi2Te2S system was studied by powder X-ray diffraction (PXRD), differential thermal analysis (DTA), scanning electron microscope (SEM) and energy dispersive Xray (EDX) microanalysis. It was shown that due to incongruent melting of the Sb2Te2S compound the system is non-quasibinary, but it is stable below the solidus and characterized by the formation of a continuous series of solid solutions with a tetradymite-like hexagonal structure. The lattice parameters were determined from powder diffraction patterns. It was established that the crystal lattice parameters of solid solutions vary linearly with composition

PHASE RELATIONS AND CHARACTERIZATION OF SOLID SOLUTIONS IN THE SnBi2Te4–PbBi2Te4 AND SnBi4Te7–PbBi4Te7 SYSTEMS

Phase equilibria in SnBi2Te4¬–PbBi2Te4 and SnBi4Te7–PbBi4Te7 systems were studied using differential thermal analysis (DTA) and X-ray diffraction (XRD) techniques. It has been shown that both systems are characterized by the formation of a continuous series of solid solutions with a tetradymite-like layered structure. The lattice parameters of solid solutions are linear functions of composition

THE SbBiTe2Se-SbBiTe2S PHASE DIAGRAM OF THE Sb-Bi-S-Se-Te SYSTEM

Using powder X-ray diffraction (PXRD) and differential thermal analysis (DTA), the phase equilibria of the SbBiTe2Se – SbBiTe2S section were studied, and its T-x diagram was constructed. The system is non-quasibinary, due to both initial phases melting in the temperature range. The system is stable below the solidus, which is characterized by the formation of continuous solid solutions (α-phase) with a tetradymite-like hexagonal structure. An analysis of the structural features of tetradymite and other tetradymite-like compounds shows that the substitution of atoms by related atoms is possible in all layers of the packet. In this work sulfur atoms in the central layer can be easily replaced by selenium atoms. This tendency allows us to expect the formation of the range of compositions in the BiSb-Te-Se-S system in which substitutions are realized in cationic and anionic positions. Lattice parameters were determined from the results of powder diffraction patterns. It has been established that the crystal lattice parameters of solid solutions change linearly with composition, which complies with the Vegards rule. Keywords: SbBiTe2Se – SbBiTe2S system, phase diagram, tetradymite-like structure, solid solutions, high entropy alloys.

THE SbBiTe2Se-SbBiTe2S PHASE DIAGRAM OF THE Sb-Bi-S-Se-Te SYSTEM

Using powder X-ray diffraction (PXRD) and differential thermal analysis (DTA), the phase equilibria of the SbBiTe2Se – SbBiTe2S section were studied, and its T-x diagram was constructed. The system is non-quasibinary, due to both initial phases melting in the temperature range. The system is stable below the solidus, which is characterized by the formation of continuous solid solutions (α-phase) with a tetradymite-like hexagonal structure. An analysis of the structural features of tetradymite and other tetradymite-like compounds shows that the substitution of atoms by related atoms is possible in all layers of the packet. In this work sulfur atoms in the central layer can be easily replaced by selenium atoms. This tendency allows us to expect the formation of the range of compositions in the BiSb-Te-Se-S system in which substitutions are realized in cationic and anionic positions. Lattice parameters were determined from the results of powder diffraction patterns. It has been established that the crystal lattice parameters of solid solutions change linearly with composition, which complies with the Vegards rule. Keywords: SbBiTe2Se – SbBiTe2S system, phase diagram, tetradymite-like structure, solid solutions, high entropy alloys.

Структура і властивості сталі 25ГСЛ, модифікованої наночастинками заліза

The results of the study of the effect of nanoparticles in the shell of iron oxide Fe2O3, which when injected into the melt and heated up to melt temperature is converted into oxide Fe3O4, on the microstructure of hardened and tempered steel 25GSL and its properties. It is shown that in modified steel martensite crystals thickness is reduced compared to the original steel in average 1.9 times after the quenching, tempered martensite crystal length after tempering hardened steel at 200oC - 3 times, the plate cementite length in troostite after tempering hardened steel at 450 оС – 1,4 times, the carbide length of after tempering of steel at 550 оС – 1,6 times. It has been found that modification of iron nanoparticles in a shell of Fe3O4 oxide leads to dispersion of the subgrain structure (regions of coherent scattering) and to the decrease of the crystal lattice parameters of solid solutions. The mechanism of nanoparticle influence on the reduction of the crystal lattice parameters of solid solutions, which is to accelerate the diffusion of interstitial atoms of the elements into the zones of high stress on the nanoparticles surface, is proposed. It is determined that the optimal improvement mode of the modified steel is quenching at 900 °C and tempering at 550 °C. The yield, tensile strengths and toughness of the modified steel are 894 MPa, 993 MPa and 92 J/mm2, respectively, on 62, 41 and 14% higher than the original steel. The injection of iron nanoparticles in a refractory shell into the steel melt before crystallization predetermines the effective modification and enhancement of mechanical properties. Keywords: iron nanoparticles, structure, martensite, troostite, sorbite, carbides, stresses, phase transformations.

Band gap bowings of ternary REN (RE = Sc, Y, La, and Lu) alloys

Structural and electronic properties of ternary alloys of ScN, YN, LaN, and LuN semiconductors have been investigated within the density functional theory. Fully relativistic band structures were obtained with the modified Becke-Johnson approach. Although the lattice parameters of solid solutions of rare-earth elements nitrides exhibit a linear Vegard’s law behavior, the dependences of band gaps on alloys compositions are strongly nonlinear, i.e., substantial band gap bowings are predicted for systems studied. Such strong band gap bowings were not found in any group III nitrides. The Sc/Y/Lu-based materials are indirect band gap (Γ–X) semiconductors. The ternary REN alloys containing La exhibit mainly direct type of band gaps (X–X), which may be completely closed in some Sc1−xLaxN systems. The findings presented in this work suggest that strong band gap bowings in ternary solid solutions of REN semiconductors may enable obtaining band gaps lower than 0.6 eV being characteristic for LaN, which are unavailable in group III nitride materials.

Binary niobium alloying with low-melting metals by precipitation of nanoparticles

Binary niobium alloys with tin, lead and cadmium were obtained by precipitation of nanosized metal particles dispersed in lowpressure plasma using the thermal fluctuation melting effect. The thermal fluctuation melting effect implies that a small particle is in the quasi-liquid state up to a certain critical size which, if exceeded due to steam condensation or fusion (coalescence) of other quasiliquid particles, results in the drop crystallization. The critical sizes of particles being in the quasi-liquid state and capable of coalescing and forming an alloy – solid solution – were found: Nb – 2.1÷2.2 nm, Sn – 0.4 nm, Pb – 0.6 nm, Cd – 3.2 nm. The following concentrations were determined as the boundary of a range where solid metal solutions exist in niobium, at%: Sn – 25.5, Pb – 23.0, Cd – 64.5. The solid solution is a crystal lattice of the niobium as a matrix metal comprising lead, cadmium and tin atoms. The Nb matrix lattice parameters change with additional stresses arising in it up to its destruction due to the fact that the atom sizes of embedded metals differ from those of matrix niobium. The body-centered cubic lattice parameters of solid solutions increase with the rising Pb, Cd и Sn concentrations since they have larger atomic sizes as compared to niobium. A change in the crystal lattice growth rate was observed for lead and cadmium alloys due to a change in the impurity atom arrangement in the niobium matrix lattice. The critical sizes of metal particles obtained were used to estimate surface tension parameters at the crystal/melt interface as follows: 1.17–1.22 J/m2 for Nb, 1.15·10–2 – for Sn; 1.48·10–2 – for Pb; 0.142 – for Cd. Refractory niobium alloying with tin, lead and cadmium is an example of using the size effect to produce new materials.

Roentgenographic investigation of solid-phase equilibria in the PbSe-AgSbSe2system

The solid-phase equilibria in the 2PbSe-AgSbSe2system were studied by using the powder X-ray diffraction method. It is established that the system is characterized by the formation of ~60 mol% solid solutions basedon AgSbSe2.Solubility based on PbSe is about 3mol%. The cubic lattice parameters of solid solutions are defined.

High-entropy alloys: Interrelations between electron concentration, phase composition, lattice parameter, and properties

An analysis of more than 200 high-entropy alloys (HEA) allowed us to find interrelations between the electron concentration, phase composition, lattice parameter, and properties of solid solutions with bcc and fcc crystal lattices. Main conditions for the appearance of high-entropy chemical compounds, such as Laves, σ, and μ phases were determined. The necessary condition for the formation of 100% high-entropy σ phase is the formation of σ phase in two-component alloys for different combinations of elements, which are components of the HEA, and the electron concentration should be 6.7–7.3 electrons per atom. To form a 100% high-entropy Laves phase, the following conditions should be fulfilled: the total negative enthalpy of mixing of alloy is about –7 kJ/mol and less; the difference between the atom sizes in a pair is more than 12%; the enthalpy of the mixing of two present elements is less than –30 kJ/mol; and the average electron concentration is 6–7 electrons per atom. It was shown that the ratios of lattice parameters of solid-solution HEA, which were experimentally determined, to the lattice parameter of the most refractory metal in the HEA determine the value of the modulus of elasticity.

Synthesis, phase transition and negative thermal expansion of cubic Zr(W1−yMoy)2−xVxO8−x/2 (y = 0.10, 0.20, 0.30, 0.40; 0 ⩽ x ⩽ 0.40) solid solutions

We first prepared tetragonal Zr(W1−yMoy)2−xVxO7−x/2(OH)2⋅2H2O (y=0.10, 0.20, 0.30, 0.40; 0⩽x⩽0.40) hydrate precursors through acidic steam hydrothermal (ASH) treatment. Dehydration of these precursors produces the corresponding low temperature orthorhombic polymorph Zr(W1−yMoy)2−xVxO8−x/2. Upon annealing at 813–873K for 2h this intermediate further transforms to the end product of kinetically favored cubic Zr(W1−yMoy)2−xVxO8−x/2 solid solutions. The dehydration and orthorhombic to cubic phase transition temperatures decrease linearly with increasing Mo and constant V content; the orthorhombic to cubic phase transition temperature also decreases linearly with increasing V content at constant W/Mo ratio. Measurements of thermal stability and expansion indicate that cubic Zr(W1−yMoy)2−xVxO8−x/2 solid solutions have strong negative thermal expansion property. We characterized the average structure of c-Zr(W0.90Mo0.10)1.76V0.24O7.88 using Rietveld refinement method, calculated lattice parameters of solid solutions and solid solubility at different y value, and discuss structural factors that affect cell parameter values.

Mechanical alloying of Ni3Al with molybdenum and arrangement of Mo atoms in sublattices of the intermetallic

Mechanochemical synthesis (MS) of Ni70Al25Mo5 (composition 1) and Ni75Al20Mo5 (composition 2) mixtures, in which 5 at % Mo substitutes for the equal amount of Ni or Al, leads to the formation of Ni-based nanocrystalline (coherent domains are ∼7–12 nm in size) solid solutions; in this case, some amount of molybdenum remains free. A comparison of the lattice parameters of solid solutions, which were determined experimentally, with the magnitudes determined theoretically using Vegard law and Bozollo-Ferrante simulation, which takes into account volume modules of elasticity of elements, showed an increase in interactions between atoms composed the solid solution and the formation of regions characterized by short-range order. The heating of mechanically synthesized three-component Ni(Al, Mo) solid solutions to 720°C in a calorimeter chamber forms the ordered γ′ phase (L12) at T ∼ 450°C. An analysis of the ratio of relative intensities of superlattice and fundamental reflections showed that, whatever the composition of initial mixture, Mo atoms always occupy positions in the Al sublattice. This arrangement of Mo atoms was confirmed by calculations of coefficients of concentrational variations of the lattice parameters. When molybdenum is added to Ni3 Al, Mo atoms, rather than Ni atoms, complete the Al sublattice. In this case, vacancies compensate for the lack of atoms in the Ni sublattice.

Phase equilibria in the refractory oxide systems of zirconia, hafnia and yttria with rare-earth oxides

The systematic study of phase equilibria in the ternary systems HfO 2(ZrO 2)–Y 2O 3–Ln 2O 3 has been first carried out. Phase reactions and crystallization of ceramic alloys in the binary systems ZrO 2–Ln 2O 3, HfO 2–Ln 2O 3, Y 2O 3–Ln 2O 3 and phase equilibria in the series of ternary systems HfO 2–Y 2O 3–Ln 2O 3 and ZrO 2–Y 2O 3–Ln 2O 3 have been developed at high temperature. The most general regularities of the phase reactions in liquid and solid states inherent in these systems have been considered dependent on lanthanide ion radii. Taking into account literature data and newly developed results in binary and ternary systems, the analysis of the main regularities revealed in the constitution of phase diagrams, particularly its dependence on lanthanide ionic radius, was carried out. It was shown that temperature and composition of eutectic reaction, temperature of the pyrochlore phase decomposition, lattice parameters of solid solutions and other parameters of the binary phases linearly depend on ionic radius of lanthanide. For the first time it has been found that the affiliation of lanthanide oxides to cerium or yttrium subgroups predetermines phase relations in the systems and topology of the ternary phase diagrams. The data obtained are the basis for the novel prospective ceramic materials for both structural and functional applications in energetic, medicine, nuclear industry, thermal barrier coatings, solid oxide fuel cells, etc.

Phase equilibria in the systems AgGaS2–SnS2, AgGaSe2–SnSe2

The AgGaS2–SnS2, AgGaSe2–SnSe2 sections of the ternary reciprocal system AgGaS2 + SnSe2 ⇔ AgGaSe2 + SnS2 were studied by the physico-chemical analysis methods. It was established that these sections are quasi-binary, type V of Roozeboom classification. Wide solid solution ranges of AgGaS2 and AgGaSe2 were discovered as well as practically the absence of solid solubility based on SnS2 and SnSe2. The change of the lattice parameters of solid solutions was determined. The existence of the AgGaSnSe4 compound is not confirmed.

Theory of the Microstructure of Disordered AAʹBO[sub 3] and ABBʹO[sub 3] Perovskite-Structure Solid Solutions

A model is considered in which atoms A and A′ or B and B′ of disordered solid solutions A x A 1−x ′ BO3 and AB x B 1−x ′ O3 are distributed over a regular system of points 1(a) and 1(b) of the symmetry group O h 1 characterizing the ideal perovskite structure. The probabilities P(G i |x) of unit cells having crystal-field symmetry at their center lowered to G i =T d , D3d, C3v, C4v, D2h, C2v, C s , or C2 are calculated as a function of the concentration x. The limits for x in which the Jahn-Teller and/or dipole ordering mechanism is probable are determined. In the approximation taking into account only effective pair interactions, the scattering amplitude F hkl is found to depend on a single parameter r0. The theory predicts that the dependence of the intensities of even and odd reflections on sin θ/λ is nonmonotonic and that the distributions of nonuniform strains and of values of the lattice parameters in solid solutions are discrete.

Microwave frequency dielectric properties of hexagonal perovskites in the Ba 5Ta 4O 15–BaTiO 3 system

The dielectric properties of the hexagonal perovskites Ba 8Ta 4+0.8 x Ti 3− x O 24 ( x = 0, 0.4, and 0.8), Ba 10Ta 8−0.8 x Ti x O 30 ( x = 0.6, 0.9, and 1.2) and Ba 5Sr 2Ta 4ZrO 21 were studied at microwave frequencies. XRD analysis did not reveal the presence of impurity phases in the obtained samples and the lattice parameters of solid solutions were linearly dependent on composition. These systems show a relatively high permittivity (27 < ɛ < 44) with a low dielectric loss (10,000 < Q × f < 31,000 GHz). Solid solutions Ba 10Ta 8−0.8 x Ti x O 30 with disordered face-sharing octahedra show higher Q × f values compared to ordered Ba 8Ta 4+0.8 x Ti 3− x O 24 compounds. Filling of empty vacancy layers by multicharged cations in the Ba 5(Ta, Ti) 4+ δ O 15 system (0 < δ < 1) along with Ba 5Sr 2Ta 4ZrO 21 intergrowth leads to decrease a quality factor. The effect of increasing Ti content in the pseudobinary Ba 5Ta 4O 15–BaTiO 3 system on microwave dielectric properties is discussed.

Effects of La substitution for Nd in (Nd 2− xLa x)BaZnO 5 solid solutions on microwave dielectric properties and crystal structure

The synthesis and microwave dielectric characterization of (Nd 2− x La x )BaZnO 5 solid solutions were studied. The samples obtained were single phase over the whole composition range and the lattice parameters of solid solutions were linearly increased with increasing the composition. Moreover, the expansion of the volume in the RO 8 ( R=Nd and La) and BaO 10 polyhedra and ZnO 4 tetrahedron were recognized when Nd ions were substituted by La. These variations in the lattice parameters and volumes of the polyhedra are basically attributed to the differences in ionic radii between Nd 3+ and La 3+ ions. From the evaluation of microwave dielectric properties, it was shown that the appropriate τ f values ranging from 4.6 to −5.0 ppm/°C are obtained by La substitution for Nd ion, and the highest Q · f value was 17,832 GHz at x=2.

Solid solubility metastable extension of rare earth metals in gold

Metastable extended solid solubility of rare earth (RE) metals in gold was studied by measuring the lattice parameters of solid solutions of rapidly solidified Au-RE alloys using X-ray diffraction. The cooling rate used for the preparation of the alloys was about 106 K/s. It was found that the metastable solid solubilities of Ce, Sm, Gd, Dy, Er, Yb and Y in gold were 0.3, 0.4, 1.5, 9.0, 13, 13.4 and 10 atrespectively. The solid solubilities of RE metals in gold increased with decreasing relative difference of atomic radius between the RE metal and gold. The extended solid solubilities of RE metals in Au, Ag, and Cu were compared. The relatively large solid solubility in gold is explained in terms of electron transfer from the RE atoms to gold atoms. Under the conditions of rapid solidification, the Au-RE alloys tended to form amorphous alloys more readily than do Ag-RE alloys.

Effective Ionic Radius of Y3+ Determined from Lattice Parameters of Fluorite‐Type HfO2 and ZrO2 Solid Solutions

Fluorite type HfO2 and ZrO2 solid solutions were prepared by doping with 8 to 14 mol% of Ho2O3 and Y2O3, and their lattice parameters were determined. In both HfO2 and ZrO2 systems, the lattice parameters of the solid solutions containing Ho203 were consistently greater than those containing the same amounts of Y2O3. This indicated that the ionic radius of Ho3+ was larger than that of Y3+ in the fluorite structure solid solutions. The effective ionic radius of Y3+ in eightfold coordination was estimated to be 0.1011 nm by using the measured lattice parameters and the empirical equations to predict the lattice parameters of the fluorite‐type solid solutions.