Concentration Of Interstitial Atoms Research Articles

STUDY ON SELF-DIFFUSION IN ALLOY AuCuSi WITH FCC STRUCTURE: DEPENDENCE ON TEMPERATURE, PRESSURE, CONCENTRATION OF SUBSTITUTIONAL ATOMS, CONCENTRATION OF INTERSTITIAL ATOMS AND STRAIN

This article presents a self-diffusion theory, including analytical expressions for activation energy, pre-exponential factor, and self-diffusion coefficient, dependent on temperature, pressure, the concentration of substitutional atoms, the concentration of interstitial atoms, and strain for substitutional and interstitial ternary alloys with the FCC structure, based on the statistical moment method (SMM). The theoretical results are applied to numerical calculations for the AuCuSi alloy. The SMM numerical results for AuCuSi are compared with those for AuSi, AuCu, and Au. The variation of self-diffusion quantities with temperature and strain in AuCuSi follows the same patterns as in AuCu, AuSi, and Au. The variation with the interstitial atom concentration in AuCuSi follows the same pattern as in AuSi, while the variation with the substitutional atom concentration follows the same pattern as in AuCu. The SMM numerical results for Au's self-diffusion quantities agree well with experimental data and other calculation results. Other SMM numerical results for self-diffusion quantities are novel and predict future experimental outcomes.

Precipitation of Cr-rich clusters in Fe-Cr alloys: Effects of irradiation from first principles modeling and experimental observations

Using exchange Monte Carlo (MC) simulations based on an ab initio-parameterized Cluster Expansion (CE) model, we explore the phase stability of low-Cr Fe-Cr alloys as a function of vacancy (Vac), carbon, and nitrogen content. To parameterize the CE model, we perform Density Functional Theory calculations for more than 1600 supercells containing Cr-Vac-C-N clusters of various sizes in pure bcc Fe, Cr, and Fe-Cr alloys. MC simulations performed for T=650 K show that Cr clustering in Fe-3.28 at.%Cr alloys does not occur if there are no defects or if only vacancies are present. But the addition of a small amount of C or N, at the level as low as 0.02 at.% in an alloy with no vacancies, routinely results in the formation of ordered compounds containing a high amount of Cr, C and N. Cr segregates to interstitial atoms and Cr content in such Cr-rich clusters increases as a function of C and/or N concentration. In the presence of vacancies, C/N aggregate to the core regions of vacancy clusters, making segregation of Cr-rich clusters less pronounced. The structure of Cr-rich clusters varies significantly, depending on the concentration of interstitial atoms and on the ratio of N to C. Predictions derived from MC simulations agree with experimental observations of Fe-Cr alloys exposed to ion irradiation. The concentration of Cr found in clusters containing C and N interstitial atoms is in qualitative agreement, and the absolute Cr content found in the clusters simulated at 650 K is in quantitative agreement with experimental Atom Probe Tomography (APT) observations of Fe-3.28 at.%Cr alloys irradiated at 623 K. The measured C and N content of 42±5 and 151±3 atomic ppm likely results from the contamination that occurred during ion beam irradiation.

Study on the Thermodynamic Properties of Thin Film of FCC Interstitial Alloy AuSi at Zero Pressure Using the Statistical Moment Method

We built a model and proposed a theory about the thermodynamic properties of face-centered cubic (FCC) binary interstitial alloy’s thin films based on the statistical moment method and performed numerical calculations for AuSi (gold silicide). First, the statistical moment method (SMM) calculations for the thermodynamic properties of Au are compared with reported experiments and calculations that show a good agreement between the calculations in this paper and earlier studies. Additionally, the SMM calculations for thermodynamic properties of AuSi alloy films are performed, which show that the thermal expansion coefficient, the specific heat at constant volume, and the specific heat at constant pressure increases, while the isothermal elastic modulus decreases with increasing temperature and increasing interstitial atom concentration. Furthermore, when the number of layers reaches 100, the thermodynamic properties of the film are similar to those of the bulk material. The achieved theoretical results for AuSi films are novel and can be useful in designing future experiments.

TEMPERATURE DEPENDENCE OF THE DEFORMATION BEHAVIOR OF HIGH-ENTROPY ALLOYS CO20CR20FE20MN20NI20, CO19CR20FE20MN20NI20С1 AND CO17CR20FE20MN20NI20С3. MECHANICAL PROPERTIES AND TEMPERATURE DEPENDENCE OF YIELD STRENGTH

This paper discusses the temperature dependence of the mechanical properties of multicomponent alloys Co20Cr20Fe20Mn20Ni20 (Cantor alloy), Co19Cr20Fe20Mn20Ni20С1 and Co17Cr20Fe20Mn20Ni20С3 under uniaxial static tension in the temperature range from 77 to 473 K. It is shown that after thermomechanical treatment all the alloys have an fcc crystal structure, but unlike single-phase Co20Cr20Fe20Mn20Ni20 and Co19Cr20Fe20Mn20Ni20С1 alloys, the alloy with 3 at % carbon exhibits large incoherent chromium carbides. Alloying with carbon causes solid solution strengthening of the austenitic phase and dispersion hardening, and promotes grain refinement in the Cantor alloy. Solid solution strengthening contributes to an increase in the athermal and thermal stress components of σ0.2, leading to higher yield stress values and stronger temperature dependences σ0.2( T ) in Co19Cr20Fe20Mn20Ni20С1 and Co17Cr20Fe20Mn20Ni20С3 alloys than in the Cantor alloy. The results of X-ray diffraction and microscopic analysis indicate that despite the differences in the total concentration of interstitial atoms in Co19Cr20Fe20Mn20Ni20С1 and Co17Cr20Fe20Mn20Ni20С3 alloys, the concentrations of carbon dissolved in the crystal lattice of the austenite phase are close. However, the higher strength properties of Co17Cr20Fe20Mn20Ni20С3 compared to Co19Cr20Fe20Mn20Ni20С1 are determined primarily by grain boundary strengthening and, to a lesser extent, by dispersion hardening. Both factors such as lowering the deformation temperature and alloying with carbon contribute to an increase in the deforming stresses of the Cantor alloy. It is shown that alloying with carbon affects the staged plastic flow of the Cantor alloy: the tensile curves of Co19Cr20Fe20Mn20Ni20С1 carbon alloy exhibit a well-defined stage of microplastic deformation, and the flow curves of Co17Cr20Fe20Mn20Ni20С3 alloy at the initial stages of plastic flow have a parabolic shape, typical of the deformation of alloys with large incoherent particles. The elongation to failure of Co20Cr20Fe20Mn20Ni20 and Co19Cr20Fe20Mn20Ni20С1 alloys increases linearly with decreasing deformation temperature, i.e., the mechanical properties of single-phase alloys are improved in the region of low test temperatures. For Co17Cr20Fe20Mn20Ni20С3 alloy, an increase in strength properties during low-temperature deformation is accompanied by a decrease in ductile characteristics, and the alloy becomes brittle from the viewpoint of macromechanical behavior.

Equilibrium vacancy concentration and thermodynamic quantities of BCC defective alloys FeCrSi and VWSi under pressure

In this paper, we present the analytic expressions of the cohesive energy, the alloy parameters, the equation of state, the mean nearest neighbor distance, the Helmholtz free energy, equilibrium vacancy concentration and thermodynamic quantities such as the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and at constant pressure for BCC defective ternary substitutional and interstitial alloy ABC derived by the statistical moment method. The obtained thermodynamic quantities depend on temperature, pressure, concentration of substitutional atoms, concentration of interstitial atoms and equilibrium vacancy concentration. Thermodynamic quantities of BCC defective metal A, BCC defective substitutional alloy AB, BCC defective interstitial alloy AC and BCC defective metal A are specific cases for thermodynamic quantities of BCC defective ternary substitutional and interstitial alloy ABC. The theoretical results are calculated numerically to alloys FeCrSi and VWSi. Our calculated results of thermal expansion coefficient and heat capacities at constant pressure for main metals Fe, V are in good agreement with experimental data. Our other calculated results for thermodynamic quantities of alloys FeCrSi and VWSi at different temperature, pressure, concentration of substitutional atoms and concentration of interstitial atoms orient and predict new experimental data in the future

Electroplasticity mechanism study based on dislocation behavior of Al6061 in tensile process

The thermal and athermal influence of electric current on dislocation motion is the fundamental mechanism for the electroplastic effect in different metals. Due to the significant scale difference between dislocation evolution and macroscopic deformation, it is difficult to figure out how the electric current affects the dislocation motion and further leads to the macroscopic electroplastic behavior since several interweaving mobile and immobile dislocations are involved. As a macroscopic manifestation of the interaction between dislocations and interstitial atoms, the Portevin–Le Chatelier (PLC) effect provides a satisfying entry point for solving the above problems by connecting the microscopic dislocation mechanism to the macro-scale electroplastic effect in a straightforward manner. Experiments of Al6061 in the tensile process show that the introduction of current causes two opposite effects, i.e., an increase of the pinning strength and a reduction of the time for dislocations to escape from pinning. Further microscopic characterization reveals that the reasons for the above phenomena include two aspects: (1) Promotion of the dissolution of the precipitated phase and increases in the concentration of interstitial atoms in the system. (2) Promotion of the motion of dislocations and the activation of additional slip systems. Those changes are closely related to the thermal and athermal effects of the current. Based on the observation results in this paper, the contradictions in the existing literature can be well explained. • Study on the influence of electric current on dislocation behavior based on the Portevin-le Chatelier effect. • The influence of currents on dislocation motion has two competing mechanisms related to thermal and athermal effects. • The research results successfully explained the contradictions in the existing research.

Elastic deformation and elastic wave velocity of iron and its binary interstitial alloys: Temperature, pressure and interstitial atom concentration dependences

Based on the BCC binary interstitial alloy model with the condition that the interstitial atom concentration is very small compared to the main metal atom concentration and the elastic deformation theory of this alloy obtained on the basis of statistical moment method, we perform numerical calculations for elastic deformation quantities such as the elastic moduli E, K, G, the elastic constants C11, C12, C44, the longitudinal wave velocity Vd and the transverse wave velocity Vn of metal Fe and alloys FeSi, FeC, FeH. Numerical results for Fe are in good agreement with experiments and other calculations. The temperature and pressure dependence of the elastic deformation quantities for FeSi, FeC, FeH are similar to those for Fe. The elastic deformation quantities of FeSi, FeC, FeH in the range from 0 to 1000 K, from 0 to 10 GPa and from 0 to 5% of silicon (carbon, hydrogen) atom concentrations predict experimental results.

Interstitial concentration effects on incipient plasticity and dislocation behaviors of face-centered cubic FeNiCr multicomponent alloys based on nanoindentation

• The interstitial concentration effects on dislocation behavior and incipient plasticity of a typical equiatomic FeNiCr multicomponent alloy are newly investigated via systematic nano-mechanical experimental study. • The dislocation nucleation of FeNiCr alloy processes in a manner of heterogenous nucleation mode with an activation volume exceeding one single principal atom, by the exchange between primary atoms and vacancies. • Interstitial-atom effects severely suppress the mobility of dislocations in the FeNiCr multicomponent alloys, which hinder the occurrence of pop-ins. • With increasing the concentration of interstitial atoms, both the critical shear stress and activation volume corresponding to the onset of incipient plasticity are enhanced. Interstitial atoms that commonly occupy the octahedral or tetrahedral interstices of face-centered cubic (FCC) lattice, can significantly affect the dislocation behaviors on deformation. Recently, interstitial doping has been applied to tune the mechanical properties of the emerging multicomponent, often termed high-entropy alloys (HEAs) or medium-entropy alloys (MEAs). However, the fundamental mechanisms of the dislocation nucleation and the onset of plasticity of interstitial multicomponent alloys governed by the concentration of interstitial atoms are still unclear. Therefore, in the present work, an instrumented nanoindentation was employed to investigate the interstitial concentration effects of carbon atoms on single FCC-phase equiatomic FeNiCr MEAs during loading. The results show that the pop-in events that denote the onset of incipient plasticity are triggered by the sudden heterogeneous dislocation nucleation via the primary atoms-vacancy exchange with the instant stress field, regardless of the interstitial concentration. Moreover, the measured activation volumes for dislocation nucleation of the FeNiCr MEAs are determined to be increased with the interstitial concentration, which definitely suggests the participation of interstitial atoms in the nucleation process. Besides, it is also found that the average value measured in statistics of the maximum shear stress corresponding to the first pop-in is enhanced with the interstitial concentration. Such scenario can be attributed to the improved local change transfer and lattice cohesion caused by the interstitial atoms with higher concentrations. Furthermore, the significant drag effect of interstitial carbon atoms hinders the mobile dislocations before exhaustion, which severely suppresses the subsequent occurrence of pop-in events in the carbon-doped specimens. The work gives a microscale view of interstitial effects on the mechanical properties of multicomponent alloys, which can further help to develop new interstitial strengthening strategies for structural materials with remarkable performance.

SỰ KHUẾCH TÁN TRONG CÁC KIM LOẠI Au, Cu VÀ CÁC HỢP KIM XEN KẼ AuSi, CuSi

The paper performs numerically the vacancy activation volume, the activation energy, the pre-exponential factor, and the diffusion coefficient for metals Au, Cu, and alloys AuSi, CuSi in the interval of the concentration of interstitial atoms from zero to 4%, in the interval of temperature from 700 to 1873 K, in the interval of pressure from zero to 180 GPa and the interval of strain from zero to 5%. The paper determines the dependence of the diffusion coefficient on pressure and stress for above mentioned metals and alloys. SMM numerical results show that the Arrhenius law is satisfied for metals and interstitial alloys at different pressures and concentrations of interstitial atoms. SMM numerical results for Au at T = 1000 K and T = 1250 K and at zero pressure are in good agreement with experiments for the activation energy (errors are below 10%) and agree in terms of magnitude for the pre-exponential factor and the diffusion coefficient. SMM numerical results of the diffusion coefficient for Au in the interval of temperature from 977 to 1321 K and for Cu in the interval of temperature from 933.95 to 1336.15 K are compared with experiments and other calculations and there are rather good agreement in terms of magnitude. SMM numerical results of the activation volume of Au and Cu agree well with other calculations. SMM numerical results for diffusion quantities of interstitial alloys AuSi, CuSi in different temperatures, pressures, stresses, and concentrations of interstitial atoms anticipate and orient experiments in the future.

BIẾN DẠNG ĐÀN HỒI VÀ VẬN TỐC SÓNG ĐÀN HỒI CỦA CÁC HỢP KIM TAM NGUYÊN FeCrSi VÀ AuCuSi

The paper uses the model of cubic ternary substitutional and interstitial alloy and conditions in which the interstitial atom concentration is very small compared to the substitutional atom concentration, the substitutional atom concentration is very small compared to the main metal atom concentration. On that basis together with the elastic wave and the elastic deformation theory of this alloy obtained by the statistical moment method, we perform numerical calculations for temperature, pressure, the concentration of substitutional atoms, and concentration of interstitial atoms dependences of the elastic moduli E, K, G, the elastic constants C11, C12, C44, the longitudinal wave velocity Vd and the transverse wave velocity Vn of alloys FeCrSi and AuCuSi. Numerical results for FeCrSi and AuCuSi are compared with that of Fe, FeCr, FeSi, Au, AuCu, AuSi, and other calculations, and experiments. Numerical results for ternary alloys predict experimental results in the future.

Effects of annealing on the micro-internal stress induced by interstitial defects in aluminum crystal by molecular dynamics simulations

Micro-internal stress caused by self-interstitial defects in aluminum crystals was studied by using the molecular dynamics method. The effects of annealing on the lattice structure near the interstitial defects and the evolution of atoms near defects are analyzed. For octahedral, tetrahedral, and crowdion self-interstitial atoms, the atomic stress in the affected area after annealing decreases significantly compared with that before annealing. For dumbbell self-interstitial atoms, there are no obvious changes in atomic stresses in all regions before and after annealing. For four configurations of interstitial defects, the internal stress obviously decreased after annealing. Different concentrations of interstitial atoms have different effects on the internal stress and the size of the space region with internal stress. The size of the space region increases with the increase in concentration, and it can be reduced by annealing. When the concentration of interstitial atoms is within a certain range, annealing can effectively reduce the internal stress. When the concentration is low or high, annealing can only eliminate the internal stress in the local spatial regions and may increase the internal stress in other spatial regions.

Structure Formation in Vanadium-Alloyed Chromium-Manganese Steel with a High Concentration of Interstitial Atoms C + N = 1.9 wt % during Electron-Beam Additive Manufacturing

Structure Formation in Vanadium-Alloyed Chromium-Manganese Steel with a High Concentration of Interstitial Atoms C + N = 1.9 wt % during Electron-Beam Additive Manufacturing

EQUILIBRIUM VACANCY CONCENTRATION AND THERMODYNAMIC QUANTITIES OF FCC DEFECTIVE ALLOYS AuCuSi AND PtCuSi UNDER PRESSURE AND TEMPERATURE

We present the analytic expressions of the cohesive energy, the alloy parameters, the equation of state, the mean nearest neighbor distance, the Helmholtz free energy, equilibrium vacancy concentration, and thermodynamic quantities such as the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and constant pressure for facecentered cubic (FCC) defective ternary substitutional and interstitial alloy ABC derived by the statistical moment method (SMM). The obtained thermodynamic quantities depend on temperature, pressure, the concentration of substitutional atoms, the concentration of interstitial atoms, and equilibrium vacancy concentration. Thermodynamic quantities of FCC defective metal A, FCC defective substitutional alloy AB, and FCC defective interstitial alloy AC are specific cases for thermodynamic quantities of FCC defective ternary substitutional and interstitial alloy ABC. The theoretical results are calculated numerically to alloys AuCuSi and PtCuSi. Our calculated results of thermal expansion coefficient and heat capacities at constant pressure for main metals Au, Pt are in good agreement with experimental data. Our other calculated results for thermodynamic quantities of alloys AuCuSi and PtCuSi at different temperatures, pressure, the concentration of substitutional atoms, and concentrations of interstitial atoms orient and predict new experimental data in the future.

Ab initio calculation of total energy of a bcc iron cell containing three dissolved carbon atoms, and internal friction in Fe–C solid solutions

Carbon interstitial atoms, when dissolved in bcc Fe, induce elastic dipoles with tetragonal symmetry. Mechanical loss spectra indicate the presence of interstitial atoms by Snoek peaks. The magnitude of the peaks is proportional to the concentration of interstitial atoms in solution and the dipole strength. The ab initio computer simulation of lattice parameters and local structure distortions caused by the Fe–C system with three carbon atoms in different octahedral positions of one sublattice has been carried out using WIEN2k software. The simulation results allowed us to propose a way to estimate the dipole strength. The value found are λ1- λ2 = 0.58.

STUDY ON ELASTIC PROPERTY OF STAINLESS STEEL UNDER PRESSURE

The paper presents analytic expressions of the Helmholtz free energy and characteristic elastic deformation quantities such as the elastic moduli E, K, G and the elastic constants C11, C12, C44 for BCC interstitial and substitutional alloy with four components are determined by the statistical moment method. The obtained elastic quantities depend on temperature, pressure, the concentration of interstitial atoms, and the concentration of substitutional atoms. This is the elastic deformation theory of BCC interstitial and substitutional alloy with four components published for the first time. The elastic deformation theories of BCC metal, BCC binary interstitial alloy, BCC binary substitutional alloy, and BCC ternary interstitial and substitutional alloy are limit cases of the elastic deformation theory of BCC substitutional and interstitial alloy with four components. Our numerical calculations of the obtained theoretical results for metal Fe and alloy FeSi are in good agreement with other calculations and experiments. Other numerical calculations for alloys FeCr, FeNi, FeCrSi, FeNiSi, FeCrNiSi (some atoms Fe are substituted by atoms Cr and some other atoms Fe are substituted by atoms Ni) called stainless steels predict and orient experimental results in the future. Our numerical calculations for alloy FeCrNiSi are published for the first time.

Evolution of ion-irradiated point defect concentration by cluster dynamics simulation* *Project supported by the Special Funds for the Key Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2017YFB0702201).

The relationship between ions irradiation and the induced microstructures (point defects, dislocations, clusters, etc.) could be better analyzed and explained by simulation. The mean field rate theory and cluster dynamics are used to simulate the effect of implanted Fe on the point defects concentration quantitatively. It is found that the depth distribution of point defect concentration is relatively gentle than that of damage calculated by SRIM software. Specifically, the damage rate and point defect concentration increase by 1.5 times and 0.6 times from depth of 120 nm to 825 nm, respectively. With the consideration of implanted Fe ions, which effectively act as interstitial atoms at the depth of high ion implantation rate, the vacancy concentration C v decreases significantly after reaching the peak value, while the interstitial atom concentration C i increases significantly after decline of the previous stage. At the peak depth of ion implantation, C v dropped by 86%, and C i increased by 6.2 times. Therefore, the implanted ions should be considered into the point defects concentration under high dose of heavy ion irradiation, which may help predict the concentration distribution of defect clusters, further analyzing the evolution behavior of solute precipitation.

Влияние фазовых превращений в процессе электронно-лучевой 3D-печати и последующей термической обработки на закономерности пластической деформации и разрушение образцов высокоазотистой Cr-Mn-стали

We investigated the phase composition, plastic deformation and fracture micromechanisms of Fe-(25-26)Cr-(5-12)Mn-0.15C-0.55N (wt. %) high-nitrogen chromium-manganese steel. Obtained by the method of electron-beam 3D-printing (additive manufacturing) and subjected to a heat treatment (at a temperature of 1150°C following by quenching). To establish the effect of the electron-beam 3D-printing process on the phase composition, microstructure and mechanical properties of high-nitrogen steel, a comparison was made with the data for Fe-21Cr-22Mn-0.15C-0.53N austenitic steel (wt. %) obtained by traditional methods (casting and heat treatment) and used as a raw material for additive manufacturing. It was experimentally established that in the specimens obtained by additive manufacturing method, depletion of the steel composition by manganese in the electron-beam 3D-printing and post-built heat treatment contributes to the formation of a macroscopically and microscopically inhomogeneous two-phase structure. In the steel specimens, macroscopic regions of irregular shape with large ferrite grains or a two-phase austenite-ferrite structure (microscopic inhomogeneity) were observed. Despite the change in the concentration of the basic elements (chromium and manganese) in additive manufacturing, a high concentration of interstitial atoms (nitrogen and carbon) remains in steel. This contributes to the macroscopically heterogeneous distribution of interstitial atoms in the specimens - the formation of a supersaturated interstitial solid solution in the austenitic regions due to the low solubility of nitrogen and carbon in the ferrite regions. This inhomogeneous heterophase (ferrite-austenite) structure has high strength properties, good ductility and work hardening, which are close to those of the specimens of the initial high-nitrogen austenitic steel used as the raw material for additive manufacturing.

Phase Composition and Thin Structure of Steel Surface after Plasma Electrolytic Carbonitriding

Using the transmission electron microscopy of thin foils the paper studies the phase composition and fine structure of 0.18С–1Cr–3Ni–1Mo–Fe steel after plasma electrolytic carbonitriding carried out through the surface saturation with nitrogen and carbon. The steel specimens are studied before and after carbonitriding on the surface and at a ~40 μm distance from the surface. It is found that carbonitriding causes significant qualitative and quantitative changes in the steel structure. Thus, the layers of residual austenite appear along the boundaries of martensitic lamellas, and the particles of alloyed cementite and carbonitrides are observed inside the lamellas. The layers of residual austenite locate at a ~40 μm depth along the boundaries of all martensitic crystals, while inside the crystals there are only particles of alloyed cementite and carbonitride M23(C, N)6. The control parameter of changes in the structure and phase composition is the concentration of interstitial atoms of carbon and nitrogen. Changes in this concentration lead to the system deviation from thermodynamic equilibrium. The transition of system to equilibrium or quasi-equilibrium states is considered to be performed through the transition of crystal lattices, which form a gradient structural-unstable state of the matrix, intermetallics and carbonitride compounds, to a low-stability state.

Концентрационные и диффузионные характеристики атомов внедрения (C, O, N) и модули упругости в ванадии и сплавах V – 4 Cr – 4 Ti, V – W – Cr, V – Ta – Cr – Zr

The elastic (Young’s) modulus and relaxation properties (amplitude-independent internal friction) of bcc metals and alloys (vanadium, V–4Cr–4Ti, V–W–Cr, and V–Ta–Cr—Zr alloys) have been studied in the temperature range of 25–400°С by means of dynamic mechanical spectroscopy within a low-frequency range (0.5–30.0 Hz). No carbon in vanadium and V–W–Cr alloy in solid-solution state is revealed. In the case of vanadium and V–W–Cr alloy, the solid-solution concentrations of oxygen and nitrogen and the diffusion characteristics thereof (diffusion activation energy, characteristic relaxation time, and the preexponential factor in the diffusion equation) have been determined. In the case of V–4Cr–4Ti alloy, carbon, oxygen, and nitrogen solid solutions have not been observed. In V–Ta–Cr–Zr alloy, the solid-solution concentrations of interstitial atoms (C, O, N) are substantially lower than those in vanadium and V–W–Cr alloy. The values of elastic modulus in vanadium alloys can be either higher or lower than the elastic modulus inherent in vanadium depending on type of alloy (alloying) and on temperature. The V–4Ti–4Cr alloy exhibits the smallest value of the elastic modulus among all the materials under study. The temperature curves of the elastic (Young’s) modulus for the studied materials exhibit no features, except for a slight local relaxation of the Young’s modulus in the case of vanadium and V–W–Cr alloy in the temperature range of the relaxation peaks.

Thermodynamic properties of interstitial alloy FeC with BCC structure under pressure

The analytic expressions for the thermodynamic quantities such as the mean nearest neighbor distance, the free energy, the isothermal compressibility, the thermal expansion coefficient, the heat capacities at constant volume and at constant pressure of binary interstitial alloy with body-centered cubic (BCC) structure and the small concentration are derived by the statistical moment method. The theoretical results are applied to the interstitial FeC alloy in the interval of temperature from 50 to 1000K and in the interval of interstitial atom concentration from 0 to 5%. In special cases, we obtain the thermodynamic quantities of the main Fe metal. Our calculated results for the thermal expansion coefficient and the heat capacity under constant pressure of main metal Fe are in good agreement with experiments.