Nearest-neighbor Bond Lengths Research Articles

Structural and Electrical Properties of "Cadmium Sulfide- Cobalt" Compound and Using it as a Gas Sensor

Background: Both the cubic (zinc blend) and hexagonal (wurtzite) phases of cadmium sulphide are semiconductors due to the presence of a row of four equally spaced Cd atoms surrounded by one S atom. Both the cubic and hexagonal crystal forms of Cd-S have very similar nearest neighbor bond lengths. Material and Methods: The cadmium sulfide compound was prepared at a concentration of 1 M by dissolving the percentage by weight of each of cadmium(13.326g) and sulfur (3.806g) in 100 ml of distilled water. Cobalt was prepared at a concentration of 0.5M by dissolving a percentage by weight of Cobalt acetate (14.55g) in 100 ml of distilled water. Films CdS and CdS:Co were prepared using the chemical method, which is the thermal chemical spraying technique, which deposited a solution of cadmium sulfide mixture of cobalt solution with cadmium sulfide on a glass floor.
 Results: The thickness of the prepared films was 100 mm. The surfaces of the prepared films were studied by measuring transmission electron microscopy. The results showed that the prepared films are homogeneous and have crystalline granules of spherical shape, and the addition of cobalt to the cadmium sulfide compound led to an increase in the particle size values. The electrical properties represented by measuring the voltaic- current were studied, and the results showed that the relationship between the voltaic- current is linear, and this indicates that the prepared films behave as ohmic.
 Conclusion: The continuous electrical conductivity was also calculated, and the results showed that the addition of cobalt acetate to the cadmium sulfide compound led to an increase in the electrical conductivity values. The gas sensitivity of the prepared films towards hydrogen sulfide gas was studied, and the results showed that the prepared films had good sensitivity, and adding cobalt acetate to the cadmium sulfide compound led to a decrease in the sensitivity values.

Structural and thermodynamic properties of quasi-2D Mo(1–x)W x (S, Se, Te)2 monolayer alloys: a statistical first principle study

In this work, we report an ab initio study of the structural and thermodynamic properties of two-dimensional transition-metal dichalcogenides (2D-TMDC) alloys, Mo(1–x)W x (S, Se, Te)2, using the cluster expansion framework to compute the Helmholtz free energy of alloys as a function of alloy composition and temperature, in the framework of the generalized quasi-chemical approximation. We consider alloying only on the metal sublayer. Our results indicate a weak dependence of the structural properties (lattice constants, nearest-neighbor bond lengths, and layer width) on the alloy composition (i.e. concentrations of W and Mo atoms), in line with the very similar values of the atomic radii of Mo and W atoms. A stronger dependence on the chalcogen is obtained, a trend that reflects the larger variations in atomic radii among the three chalcogen species. As a function of composition, the structural parameters we examined show similar trends, with negligible bowing (i.e. deviations from a Vegard’s law interpolation between end compounds), for the three alloys. Moreover, already at 300 K the behavior of these structural features as a function of composition is very similar to that of the standard-regular-solution (SRS) high-temperature limit. In contrast, the electronic band gaps of the the three alloys as a function of composition show small but significant bowing, as high as −1% to −2% near the x = 0.5 alloy composition. Similarly to the structural features, the band gaps attain the high-temperature SRS limit already at 300 K. Regarding thermodynamic properties, we obtain negative values of the internal energy of mixing for the three alloys over the full range of compositions. Therefore, the theoretical alloying phase diagram for the three alloys is featureless, with stability of a fully-mixed alloy at all temperatures and compositions, with no miscibility gap (hence no bimodal nor spinodal decomposition lines). The thermodynamic potentials (mixing internal energy, mixing entropy, and mixing free energy) reach the high-temperature limit at ∼1000 K, the temperature range of synthesis of 2D-TMDC alloys. These trends of structural and electronic properties of the 2D-TMDC alloys are due to the very similar atomic radii and the nearly identical coordination chemistry of Mo and W. Our results are in agreement with experimental work on the alloying of Mo and W atoms, for samples of Mo(1–x)W x S2 monolayer alloys, that found that the random mixed alloy is the thermodynamically stable state for this alloy, with no segregation or phase separation.

Two-Dimensional Ionic Crystals: The Cases of IA-VII Alkali Halides and IA-IB CsAu

The alkali halides, known as ionic crystals, have the NaCl-type or CsCl-type structure as the ground state. We study the structural, vibrational, and electronic properties of two-dimensional (2D) ionic crystals from first-principles. Two potential structures that are hexagonal and tetragonal are investigated as structural templates. Through phonon dispersion calculations, 4 and 12 out of 20 alkali halides in the hexagonal and tetragonal structures are dynamically stable, respectively. The electronic band gaps range from 6.8 eV for LiF to 3.9 eV for RbI and CsI in the tetragonal structure within the generalized gradient approximation. By considering the Madelung energy and the core–core repulsion, we propose a hard sphere model that accounts for the nearest-neighbor bond length and the cohesive energy of 2D alkali halides. We also predict that the band gap of 2D CsAu is larger than that of the 3D counterpart by a factor of more than two, whereas the 2D structures are unstable for the long wavelength phonons in the acoustic branch.

Magnetic order and spin liquid behavior in [Mo3]11+ molecular magnets

Molecular magnets with one unpaired electron per molecule offer promise in the ongoing search for exotic states of matter, including quantum spin liquids. Here, the authors investigate a series of molecular magnets based on Mo trimer building blocks with one unpaired electron each and find that the magnetic ground states are very sensitive to small changes in the breathing parameter---the ratio between first and second nearest neighbor bond lengths in the breathing kagome lattice that they form. When this parameter is sufficiently close to 1, these materials show an absence of magnetic order and other hallmarks of quantum spin liquid behavior, which may be correlated with plaquette charge ordering.

Evidence of ytterbium doping in YbxZn1-xO nanoparticles synthesized by polymer precursor method

In this work, we report the synthesis of YbxZn1-xO nanoparticles (0.000 ≤x≤ 0.100) by polymer precursor method and the study of their vibrational and structural properties. Thermal analysis of the polymeric precursor showed that the thermal decomposition occurs in few stages, with the crystallization of the wurtzite structure taking place at a temperature below 500 C. Fourier transform infrared spectroscopy indicated the presence of Zn-O and Yb-O bonds. X-ray diffraction data showed the formation of the ZnO wurtzite phase for all samples. The application of the Rietveld method revealed a decrease in the average particle size and an increasing trend in unit cell volume as the Yb3+ content increased. Additionally, the nearest-neighbor bond lengths along and off the c-direction, as well as the bond angles, were calculated. The results obtained provided additional evidence on the efficiency of Yb3+ doping by the polymer precursor method.

Eg[formula omitted]t2g Sub band splitting via crystal field and band anticrossing interaction in NixCd1-xO thin films

In the present work, full composition range of NixCd1-xO thin films, from Cadmium oxide to Nickel oxide are prepared with sol-gel chemical synthesis route on corning glass substrates. The Fourier transform infrared spectra provide a direct indication of compositional dependence for different vibrational modes with increasing Ni doping. The microscopy images reflect the reduced crystallinity and closely packed morphology with increasing Ni doping which endorses the changes reflected in electronic structure. The O K edge, soft X-ray absorption spectra (XAS) for thin films indicate a clear evidence of eg and t2g sub band splitting and has been explained via crystal field splitting and three level band anti-crossing (BAC) interaction phenomena. At higher doping fraction, the inhomogeneous electric field of neighboring ions surrounding the unfilled Ni 3d level results in rupturing of L−S coupling and further crystal field splitting. The BAC interaction brings about partially unoccupied localized Ni 3d and empty d acceptor levels above conduction band minima (CBM). As saturated Fermi level goes below CBM with increasing Ni doping, transitions to antibonding orbital [eg(π*) and t2g(σ*)] with finite energy difference, is reflected as separated eg-t2g peaks in XAS spectra. On the other hand, extended X-ray absorption fine structure for Ni K edge fitting provides a complete information for nearest (Ni-O) and next nearest (Ni-Ni) neighbor bond length.

Structural, Electronic, Magnetic, and Hyperfine Properties of V-doped SnO2 (Sn1–xVxO2, x: 0, 0.042, 0.084, and 0.125). A DFT-Based Study

Ab initio electronic structure calculations were performed to study the effect of V-doping on the structural, electronic, and magnetic properties of tin dioxide (Sn1–xVxO2, x: 0.042–0.125). Calculations have been performed using pseudopotentials and plane-wave and full potential linearized augmented plane-wave methods. State-of-the-art Heyd–Scuseria–Ernzerhof (HSE06) exchange–correlation hybrid functional and the Tran–Blaha-modified Becke–Johnson (TB-mBJ) exchange potential were employed. Our calculations showed that V4+ substitutionally replaces Sn4+ ions inducing a reduction of the volume cell of SnO2 and shortening of the metal–oxygen nearest neighbor bond lengths. Spin polarization at the V sites is predicted. Our results indicate that the magnetic ground state of the resulting system is paramagnetic. TB-mBJ and HSE06 accurately describe the experimentally reported dependence of the band gap with x. Our theoretical results for the hyperfine parameters at the Sn sites are in excellent agreement with Mössbauer experiments. Hyperfine parameters at the V sites are also presented.

Ab-initio simulation studies of chromium solvation in molten fluoride salts

Understanding molten salt chemistry is essential in ongoing research of the molten salt nuclear reactor (MSR). In this context, detailed understanding of the mechanisms underlying selective oxidation of metal species, such as Cr, is required to guide the design of effective corrosion mitigation strategies in molten salts. An important starting point for such mechanistic understanding is knowledge of the solvation structure and its role in controlling metal speciation. In this work, we use ab initio molecular dynamics simulations to study the short-range (on the scale of the nearest-neighbor bond lengths) and medium-range (over length scales of several neighbor spacings) structure in three different fluoride melts with and without Cr addition; namely, 2KF-NaF, 2LiF-BeF2, and 3LiF-AlF3. We find that Cr0,Cr2+,Cr3+ can each be coordinated by different numbers of F-, with the variance in coordination number decreasing as oxidation state increases, and that these coordination geometries are largely independent of solvent. The manner by which Cr changes the medium-range structure, however, is found to be solvent-dependent. While 2KF-NaF melts show short and medium range order that is highly dynamic, 2LiF-BeF2 and 3LiF-AlF3 are characterized by molecular associates that are relatively long-lived that organize into oligomer structures on larger length scales. Rather than being solvated by F- ions alone, we find that Cr can incorporate into and be solvated within this oligomer structure. Fluoroacidity, alone, may therefore prove too simple a metric for assessing the corrosivity of molten fluorides. As our work suggests, the ability of Cr to solvate must be understood in the context of the short- and medium-range structure of the solvent.

The effect of orbital-lattice coupling on the electrical resistivity of YBaCuFeO5 investigated by X-ray absorption

Temperature-dependent X-ray absorption near-edge structures, X-ray linear dichroism (XLD) and extended X-ray absorption fine structure (EXAFS) spectroscopic techniques were used to investigate the valence state, preferred orbital and local atomic structure that significantly affect the electrical and magnetic properties of a single crystal of YBaCuFeO5 (YBCFO). An onset of increase of resistivity at ~180 K, followed by a rapid increase at/below 125 K, is observed. An antiferromagnetic (AFM)-like transition is close to the temperature at which the resistivity starts to increase in the ab-plane and is also observed with strong anisotropy between the ab-plane and the c-axis. The XLD spectra at the Fe L3,2-edge revealed a change in Fe 3d eg holes from the preferential {bf{3}}{{boldsymbol{d}}}_{{{bf{x}}}^{{bf{2}}}{boldsymbol{-}}{{bf{y}}}^{{bf{2}}}} orbital at high temperature (300–150 K) to the {bf{3}}{{boldsymbol{d}}}_{{{bf{3}}{bf{z}}}^{{bf{2}}}{boldsymbol{-}}{{bf{r}}}^{{bf{2}}}} orbital at/below 125 K. The analysis of the Fe K-edge EXAFS data of YBCFO further revealed an unusual increase in the Debye-Waller factor of the nearest-neighbor Fe-O bond length at/below 125 K, suggesting phonon-softening behavior, resulting in the breaking of lattice symmetry, particularly in the ab-plane of Fe-related square pyramids. These findings demonstrate a close correlation between electrical resistivity and coupling of the preferred Fe 3d orbital with lattice distortion of a single crystal of YBCFO.

Evolution of superconductivity in K2−xFe4+ySe5: Spectroscopic studies of X-ray absorption and emission

This study investigates the evolution of superconductivity in K2-xFe4+ySe5 using temperature-dependent X-ray absorption and resonant inelastic X-ray scattering techniques. Magnetization measurements show that polycrystalline superconducting (SC) K1.9Fe4.2Se5 has a critical temperature (T c) of ∼31 K with a varying superconducting volume fraction, which strongly depends on its synthesis temperature. An increase in Fe-structural/vacancy disorder in SC samples with more Fe atoms occupying vacant 4d sites is found to be closely related to the decrease in the spin magnetic moment of Fe. Moreover, the nearest-neighbor Fe-Se bond length in SC samples exceeds that in the non-SC (NS) sample, K2Fe4Se5, which indicates a weaker hybridization between the Fe 3d and Se 4p states in SC samples. These results clearly demonstrate the correlations among the local electronic and atomic structures and the magnetic properties of K2-xFe4+ySe5 superconductors, providing deeper insight into the electron pairing mechanisms of superconductivity.

Anisotropy in the magnetic interaction and lattice-orbital coupling of single crystal Ni3TeO6

This investigation reports on anisotropy in the magnetic interaction, lattice-orbital coupling and degree of phonon softening in single crystal Ni3TeO6 (NTO) using temperature- and polarization-dependent X-ray absorption spectroscopic techniques. The magnetic field-cooled and zero-field-cooled measurements and temperature-dependent Ni L3,2-edge X-ray magnetic circular dichroism spectra of NTO reveal a weak Ni-Ni ferromagnetic interaction close to ~60 K (TSO: temperature of the onset of spin ordering) with a net alignment of Ni spins (the uncompensated components of the Ni moments) along the crystallographic c-axis, which is absent from the ab-plane. Below the Néel temperature, TN~ 52 K, NTO is stable in the antiferromagnetic state with its spin axis parallel to the c-axis. The Ni L3,2-edge X-ray linear dichroism results indicate that above TSO, the Ni 3d eg electrons preferentially occupy the out-of-plane 3d3z2−r2 orbitals and switch to the in-plane 3dx2−y2 orbitals below TSO. The inherent distortion of the NiO6 octahedra and anisotropic nearest-neighbor Ni-O bond lengths between the c-axis and the ab-plane of NTO, followed by anomalous Debye-Waller factors and orbital-lattice in conjunction with spin-phonon couplings, stabilize the occupied out-of-plane (3d3z2−r2) and in-plane (3dx2−y2) Ni eg orbitals above and below TSO, respectively.

Model interatomic potentials and lattice strain in a high-entropy alloy

Abstract

Spectroscopic and Computational Characterization of Diethylenetriaminepentaacetic Acid/Transplutonium Chelates: Evidencing Heterogeneity in the Heavy Actinide(III) Series.

The chemistry of trivalent transplutonium ions (Am3+ , Cm3+ , Bk3+ , Cf3+ , Es3+ …) is usually perceived as monotonic and paralleling that of the trivalent lanthanide series. Herein, we present the first extended X-ray absorption fine structure (EXAFS) study performed on a series of aqueous heavy actinide chelates, extending past Cm. The results obtained on diethylenetriaminepentaacetic acid (DTPA) complexes of trivalent Am, Cm, Bk, and Cf show a break to much shorter metal-oxygen nearest-neighbor bond lengths in the case of Cf3+ . Corroborating those results, density functional theory calculations, extended to Es3+ , suggest that the shorter Cf-O and Es-O bonds could arise from the departure of the coordinated water molecule and contraction of the ligand around the metal relative to the other [MIII DTPA(H2 O)]2- (M=Am, Cm, Bk) complexes. Taken together, these experimental and theoretical results demonstrate inhomogeneity within the trivalent transplutonium series that has been insinuated and debated in recent years, and that may also be leveraged for future nuclear waste reprocessing technologies.

Anisotropy in the thermal hysteresis of resistivity and charge density wave nature of single crystal SrFeO3-\u03b4: X-ray absorption and photoemission studies

The local electronic and atomic structures of the high-quality single crystal of SrFeO3-δ (δ~0.19) were studied using temperature-dependent x-ray absorption and valence-band photoemission spectroscopy (VB-PES) to investigate the origin of anisotropic resistivity in the ab-plane and along the c-axis close to the region of thermal hysteresis (near temperature for susceptibility maximum, Tm~78 K). All experiments herein were conducted during warming and cooling processes. The Fe L3,2-edge X-ray linear dichroism results show that during cooling from room temperature to below the transition temperature, the unoccupied Fe 3d eg states remain in persistently out-of-plane 3d3z2-r2 orbitals. In contrast, in the warming process below the transition temperature, they change from 3d3z2-r2 to in-plane 3dx2-y2 orbitals. The nearest-neighbor (NN) Fe-O bond lengths also exhibit anisotropic behavior in the ab-plane and along the c-axis below Tm. The anisotropic NN Fe-O bond lengths and Debye-Waller factors stabilize the in-plane Fe 3dx2-y2 and out-of-plane 3d3z2-r2 orbitals during warming and cooling, respectively. Additionally, a VB-PES study further confirms that a relative band gap opens at low temperature in both the ab-plane and along the c-axis, providing the clear evidence of the charge-density-wave nature of SrFeO3-δ (δ~0.19) single crystal.

Extended x-ray absorption fine structure and micro-Raman spectra of Bridgman grown Cd1−xZnxTe ternary alloys

We have performed low-temperature micro-Raman scattering and extended x-ray absorption fine-structure (EXAFS) measurements on the Bridgman-grown bulk zinc-blende Cd1−xZnxTe (1.0 ≧̸ x ≧̸ 0.03) ternary alloys to comprehend their structural and lattice dynamical properties. The micro-Raman results are carefully appraised to authenticate the classical two-phonon mode behavior insinuated by far-infrared (FIR) reflectivity study. The composition-dependent EXAFS experiments have revealed a bimodal distribution of the nearest-neighbor bond lengths—its analysis by first-principles bond-orbital model enabled us to estimate the lattice relaxations around Zn/Cd atoms in CdTe/ZnTe to help evaluate the necessary force constant variations for constructing the impurity-perturbation matrices. The simulated results of impurity vibrational modes by average–t–matrix Green’s function (ATM-GF) theory has put our experimental findings of the gap mode ∼153 cm−1 near x ≈ 1 on a much firmer ground.

Microstructural study of high-temperature Cr–Ni–Al–Ti alloys supported by first-principles calculations

Refractory metals present a potential for development of future high-temperature structural materials due to their high melting temperature and good high-temperature strength. However, their poor high-temperature oxidation resistance, creep resistance, and low fracture toughness at low temperatures have to be addressed. The microstructure of two Cr–Ni–Ti–Al alloys is characterized using XRD, LOM, SEM, and TEM. The microstructure of both alloys is comprised of very dilute Cr solid solution grains, intergranular L21 Ni2AlTi phase, and fine NiTi-rich B2 precipitates dispersed in the Cr-rich grains. The small spherical precipitates have a well-defined orientation relationship with the Cr-matrix, and the lattice mismatch between the precipitates and the Cr-alloy matrix is accommodated by the interface dislocations. In order to explain measured composition of L21 and B2, the site preference in these phases is further studied using the first-principles density functional theory (DFT) method at the low temperature limit. The theoretical calculations predict that Al prefers substituting for the Ti site in B2 NiTi. Structure analysis reveals that Al substituting for Ti results in the formation of strong Al–Ni bonds that have much shorter bond lengths than the Al substitution for the Ni site. The predicted Al site or Cr site preference is consistent with established Al–Ni–Ti ternary experiments. As for the L21-Ni2AlTi phase, DFT calculations predict that Cr prefers substitution with the Ni site over Al or Ti sites. This is related to the smallest relaxation effect and formation of stronger Al–Cr and Ti–Cr bonds that have much shorter nearest neighbor bond length compared to other substitution scenarios.

Fitting EXAFS data using molecular dynamics outputs and a histogram approach

The estimation of metal nanoparticle diameter by analysis of extended x-ray absorption fine structure (EXAFS) data from coordination numbers is nontrivial, particularly for particles 5 nm in diameter, for which the undercoordination of surface atoms becomes an increasingly significant contribution to the average coordination number. These undercoordinated atoms have increased degrees of freedom over those within the core of the particle, which results in an increase in the degree of structural disorder with decreasing particle size. This increase in disorder, however, is not accounted for by the standard means of EXAFS analysis, where each coordination shell is fitted with a single bond length and disorder term. In addition, the surface atoms of nanoparticles have been observed to undergo a greater contraction than those in the core, further increasing the range of bond distances. Failure to account for this structural change results in an increased disorder being measured, and therefore, a lower apparent coordination number and corresponding particle size are found. Here, we employ molecular dynamics (MD) simulations for a range of nanoparticle sizes to determine each of the nearest neighbor bond lengths, which were then binned into a histogram to construct a radial distribution function (RDF). Each bin from the histogram was considered to be a single scattering path and subsequently used in fitting the EXAFS data obtained for a series of carbon-supported platinum nanoparticles. These MD-based fits are compared with those obtained using a standard fitting model using Artemis and the standard model with the inclusion of higher cumulants, which has previously been used to account for the non-Gaussian distribution of neighboring atoms around the absorber. The results from all three fitting methods were converted to particle sizes and compared with those obtained from transmission electron microscopy (TEM) and x-ray diffraction (XRD) measurements. We find that the use of molecular dynamics simulations resulted in an improved fit over both the standard and cumulant models, in terms of both quality of fit and correlation with the known average particle size.

Density functional investigation of structures and energetics of pure and Sn-doped small lithium clusters

Ground state geometry, energetics, and bonding of pure Lin(n=2–9) and impure LinSn(n=1–8) small clusters are investigated using the density functional theory. Introducing a single Sn impurity significantly changes the geometry of the host clusters for n>5. Although the Sn atom is not trapped inside the cluster, it has the greatest coordination number among other atoms in the cluster. The analyses showed that the nearest neighbor bond lengths in Sn are approximately 10% shorter than those in Li. The results elucidate that the binding energy per atom in impure clusters is greater than that in pure clusters. Finally, it is shown that for Li8 and Li4Sn clusters that each have with eight valence electrons, the greater gap in the highest occupied molecular orbital and the lowest unoccupied molecular orbital results in a more stable cluster.

Lattice relaxation in the highly-contrasted Zn1−xBexSe alloy: An extended x-ray absorption fine structure study

We have performed extended x-ray absorption fine structure (EXAFS) measurements at the Zn and Se K edges of (Zn,Be)Se alloy. This alloy exhibits an unusually large contrast in the physical properties (bond stiffness and bond lengths) of its constituting bonds, leading to a uniquely well-resolved 1-bond→2-mode behavior in the already reported Raman spectra of this material system. The nearest and next nearest neighbor distances of Zn and Se atoms, the pseudo Debye–Waller factors (σ2) for these distances, as well as various bond angles, are determined as a function of the alloy composition after fitting the EXAFS equations. The lattice relaxation is discussed in terms of the distorted tetrahedral structure of the ternaries. We conclude that the accommodation of the local strain due to the difference in Zn–Se and Be–Se bond lengths is predominantly achieved by a displacement of the Se sublattice toward Be, the (Be,Zn)-mixed cation sublattice remaining quasirigid. Besides, we find that the 1-bond→2-mode behavior in the bond force constants (Raman data) is not paralleled by an obvious 1-bond→2-mode behavior in the bond lengths (EXAFS data). However, the dependence of σ2 for the nearest neighbor bond length as a function of the alloy composition is basically consistent with such a behavior. The difference in Be–Se bond lengths as predicted by earlier ab initio calculations, of 0.04 Å, is probably too small to be resolved by our present EXAFS measurements. Further, by combining the analysis of EXAFS data with available Raman data, we were able to provide a preliminary estimate of the BeSe TO mode Grüneisen parameter.

First-principles study of ternary bcc alloys using special quasi-random structures

Using a combination of exhaustive enumeration and Monte Carlo simulated annealing, we have developed special quasi-random structures (SQSs) for ternary body-centered cubic (bcc) alloys with compositions of A 1B 1C 1, A 2B 1C 1, A 6B 1C 1 and A 2B 3C 3, respectively. The structures possess local pair and multisite correlation functions that closely mimic those of the random bcc alloy. We employed the SQSs to predict the mixing enthalpies, nearest neighbor bond length distributions and electronic density of states of bcc Mo–Nb–Ta and Mo–Nb–V solid solutions. Our convergence tests indicate that even small-sized SQSs can give reliable results. Based on the SQS energetics, the predicting powers of the existing empirical ternary extrapolation models were assessed. The present results suggest that it is important to take into account the ternary interaction parameter in order to accurately describe the thermodynamic behaviors of ternary alloys. The proposed SQSs are quite general and can be applied to other ternary bcc alloys.