Short-range Order Model Research Articles

Analysis of periodic dislocation networks using x-ray diffraction and extended finite element modeling

We combine the extended finite element method with simulations of diffracted x-ray intensities to investigate the diffusely scattered intensity due to dislocations. As a model system a thin PbSe epitaxial layer grown on top of a PbTe buffer on a CdTe substrate was chosen. The PbSe film shows a periodic dislocation network where the dislocations run along the orthogonal ⟨110⟩ directions. The array of dislocations within this layer can be described by a short range order model with a narrow distribution.

Diffraction features due to ordered distribution of twin boundaries in orthorhombic Ni–Mn–Ga crystals

The diffraction intensity distributions for orthorhombic crystals containing the ordered twin boundaries of the system (110), 〈1{\overline 1}0〉 were calculated in the kinematic approach using the Monte Carlo computer simulation technique. A simple model of short-range order in the arrangement of the twin boundaries was assumed to generate the nano-twinned structure. Analysis of the intensity distributions showed that such a twin boundary distribution results in the formation of extra peaks along the reciprocal lattice rods that are perpendicular to the close-packed planes. These extra peak intensities and positions are dependent on the most probable distances between the twin boundaries and on the degree of short-range order.

Thermodynamic evaluation and optimization of the (LiF + NaF + KF + MgF 2 + CaF 2 + SrF 2) system

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the (LiF + NaF + KF + MgF 2 + CaF 2 + SrF 2) system, and optimized model parameters have been found. The (LiF + NaF + KF + MgF 2 + CaF 2) subsystem has been critically evaluated in a previous article. The model parameters obtained for the binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The Modified Quasichemical Model for short-range ordering was used for the molten salt phase, and the low-temperature and high-temperature (CaF 2 + SrF 2) solid solutions were modelled using a cationic substitutional model with an ideal entropy and an excess Gibbs free energy expressed as a polynomial in the component mole fractions. Finally, the (Li, Na, K)(Mg, Ca, Sr)F 3 perovskite phase was modelled using the Compound Energy Formalism.

Modeling the amorphous forming ability of Ti-based alloys with wide supercooled liquid regions and high hardness

Ti-based bulk metallic glasses presented here are designed in a multi-dimensional composition space using a series of modeling tools. A chemical short range order model was used to evaluate the bonding behavior between the constituent species. This technique predicts the local structure present in the amorphous phase. A structural model is then used to further optimize the composition space, ensuring an efficient topology within the amorphous phase. These two models are compared with the predicted liquidus profile. Deep eutectics correlate well with glass forming ability, and their location and depth are located and quantified using a searching technique over a broad compositional range. Ti-based alloys were designed according to these three models, and the alloys with the highest glass forming ability represent a balance between having a densely packed cluster structure and a close proximity to a deep eutectic. Bulk metallic glass compositions have been successfully produced over a wide compositional space with only cost-effective alloying elements, Ni, Cu, Si, and Sn, using these models. The best glass former in this composition space, Ti 48Ni 32Cu 8Si 8Sn 4, demonstrates a supercooled liquid region in excess of 100 K, and was successfully cast into fully amorphous rods, 3 mm in diameter, with a compressive fracture strength of ∼1.8 GPa.

Extended short-range ferromagnetic order with cluster-glass behavior in Dy 2AuSi 3

We present the results of ac and dc susceptibilities, high-field magnetization, magnetic relaxation and electrical resistivity measurements for a ternary intermetallic compound Dy 2AuSi 3 with a hexagonal phase dominant crystal structure derived from the AlB 2-type. Both the ac and dc susceptibilities show a field and frequency dependent peak around T C ∼ 12.5 K, while evident irreversible magnetism and long-time magnetic relaxation behavior can be observed below T C. These metastable magnetic properties suggest that an extended short-range ferromagnetic order occurs near T C, i.e. the formation of ferromagnetic cluster state. This is further confirmed by the magnetization and electrical resistivity measurements and by a dynamic analysis of the ac susceptibility data. According to the extended short-range ferromagnetic order model, ferromagnetic clusters in Dy 2AuSi 3 could exist with larger geometric dimensions, interact magnetically with each other and result in the observed cluster-glass behavior at low temperatures.

A model to calculate the viscosity of silicate melts

AbstractA model has been developed that links the viscosities of silicate melts to their thermodynamic properties. Over the past several years, through critical evaluation of all available thermodynamic and phase equilibrium data, we have developed a quantitative thermodynamic description of multicomponent silicate melts using the Modified Quasichemical Model for short-range ordering. The local structure of the liquid, in terms of the bridging behavior of oxygen, calculated using our thermodynamic model allows us to characterize the structure of the liquid semi-quantitatively using the concepts of Q-species and connectivity of Q-species. The viscosity is modeled by optimizing viscosity parameters that are related to the structure of the liquid. The viscosity of pure liquid silica is modeled using four model parameters and every other unary liquid is modeled using two. The viscosity of all binary liquids is reproduced within experimental accuracy by optimizing one or at most two binary viscosity parameters for each system. In the present article the equations for the viscosity model are derived and analyses for the experimentally well-established systems CaO – SiO2MgO – SiO2, NaO0.5– SiO2, KO0.5– SiO2and AlO1.5– SiO2are presented. This is the first step in the development of a predictive model for the viscosity of multicomponent silicate melts that will be presented in part II.

Evaluation of glass-forming ability in metals using multi-model techniques

Abstract Prediction tools for metallic glass alloy design were created from several modeling techniques, with the goal of accurately describing all the critical physical phenomena that lead to vitrification in metals. This spectrum of phenomena described by the modeling tools includes both kinetic and thermodynamic aspects of amorphization in metals. It was found that using a liquidus-based model to determine the location of deep eutectics in combination with properly describing the local topology of an alloy in question was the most effective design protocol for metallic glasses optimization. Metallic glass compositions tend to be located on or near deep eutectics, but also must have an optimized structural topology. Two distinct topologic models were used, one considers the local structure as composed of solvent–solute clusters, and another is composed of an elastically strained solvent matrix, in which solute–solute clustering is dominant. The tendency for either structure can be determined by using a chemical short-range order (CSRO) model. The protocol outlined in this study has been used to successfully predict compositions in a variety of alloy systems and has been validated with examples from the literature in Mg-, Al-, Ti-, Fe-, Ni-, Cu-, and Zr-based systems.

Long-range antiferromagnetic ordering in theS=12ordered rocksalt oxideLi5OsO6: Comparison with the isoelectronic and isostructural spin glassLi4MgReO6

${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$ and ${\mathrm{Li}}_{5}\mathrm{Re}{\mathrm{O}}_{6}$ polycrystalline samples were synthesized by conventional solid state methods. Employing powder neutron diffraction data, the crystal structure of ${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$ was reinvestigated. ${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$ crystallizes in $C2∕m$ in an ordered NaCl structure type, where $a=5.0472(1)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, $b=8.7827(2)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, $c=5.0079(1)\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, $\ensuremath{\beta}=109.777(2)\ifmmode^\circ\else\textdegree\fi{}$ and $V=208.90(1)\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{3}$. Magnetic susceptibility and heat capacity data indicate an antiferromagnetic long-range order below $40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, although there is evidence for low dimensional short-range order below $80\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. As well, the frustration index, $f=\ensuremath{\mid}\ensuremath{\theta}\ensuremath{\mid}∕{T}_{N}\ensuremath{\sim}1$, in contrast to the isostructural and isoelectronic compound, ${\mathrm{Li}}_{4}\mathrm{Mg}\mathrm{Re}{\mathrm{O}}_{6}$, which is a spin glass below $12\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and has $f\ensuremath{\sim}14$. An attempt was made to rationalize these differences using spin dimer analysis. The key results are that the spin exchange interactions in the Re-based compound are stronger and are consistent with a frustrated triangular lattice model, while a low dimensional short-range order model is better for ${\mathrm{Li}}_{5}\mathrm{Os}{\mathrm{O}}_{6}$. The main reason for this is a strong Jahn-Teller distortion in the $\mathrm{Os}{\mathrm{O}}_{6}$ octahedron material which constrains the unpaired electron to occupy the ${d}_{xy}$ orbital.

Modeling short-range ordering in solutions

Abstract Various aspects of the modeling of short-range order in binary and ternary solutions using the Bragg – Williams (random mixing), associate, and quasichemical models are examined. The models are compared with respect to their ability to predict properties of ternary solutions from optimized binary model parameters in the presence of short-range order. It is shown how introducing short-range order through the quasichemical model can explain the observed flattened shape of most miscibility gaps. The combination of the quasichemical model for nearest-neighbor short-range order with the Bragg – Williams model for the remaining lattice interactions is described.

Temperature dependence of the fine structure of the C and E absorption bands in RbMnF3 below the Néel temperature

The variation in the parameters (width, position, intensity) of the fine structure lines in the C[6 A 1g → 4 A 1g , 4 E g(4 G)] and E[6 A 1g → 4 E g(4 D)] bands in RbMnF3 with temperature is studied in the temperature range 10–70 K. In the C band, two narrow (<6 cm−1) lines are are distinguished at distances of 77 and 80 cm−1 from the exciton line at T = 10 K. The other lines in the C band and all lines in the E band are more than 20 cm−1 wide. It is demonstrated that the narrow lines become allowed because of the spin-exchange interaction within a long-range magnetic order model and originate from the excitation of exciton-magnon bound states and that the other lines are made allowed by the exchange-vibronic mechanism within a short-range magnetic order model and originate from the excitation of bound states composed of an exciton, magnon, and oddparity phonon. The vibrational replicas of the main exciton-magnon-phonon lines are due to the quadratic vibronic interaction with odd-parity vibrations. Variations of the intensities and widths of the absorption lines with temperature indicate that these parameters are affected by relaxation and delocalization of the bound states.

Asymmetric correlation function describing the positional ordering of liquid-phase-epitaxySi–Genanoscale islands

Liquid-phase-epitaxy grown SiGe nanoscale islands on (001)Si form extended chains which are aligned along the ⟨100⟩ directions. The positional ordering within the island chains was studied by x-ray diffuse scattering. The results can be interpreted by a short-range order model. The corresponding correlation function exhibits an asymmetric peak profile. The asymmetry leads to nonequidistantly spaced satellite peaks that disperse outward slightly with increasing lateral momentum transfer. The observed asymmetric island-island correlation is caused by the successive growth of the islands within a chain, while the new island position is influenced by depletion of the wetting layer around the island.

Critical thermodynamic assessment and modeling of the Fe-Ni-S system

A thorough review and critical evaluation of phase equilibria and thermodynamic data for phases in the iron-nickel-sulfur ternary system at 1 bar pressure has been made over the entire composition range for temperatures from 25°C to above the liquidus. The Gibbs energies of system phases have been modeled, and optimized model parameters have been obtained which reproduce all data simultaneously within experimental error limits. The modeling is based on the recent evaluations by the authors of the Fe-S and Ni-S binary subsystems. For the liquid phase, the recently extended modified quasichemical model for short-range ordering is applied for the first time to a liquid metal-sulfur phase. Although the binary Fe-S and Ni-S liquid solutions were modeled with the extended modified quasichemical model, while the binary Fe-Ni liquid solution was modeled with a simple random-mixing model, it is shown, for the first time, that these can be combined into a consistent model of the ternary liquid phase. Two-sublattice models, within the framework of the compound-energy formalism, are used for the solid solutions: pyrrhotite, pentlandite, pyrite, vaesite, and high-temperature heazlewoodite. The ternary-solution model for iron-nickel pyrrhotite permits very good prediction of thermodynamic properties solely on the basis of binary-model parameters.

Thermodynamic evaluation and optimization of the (NaCl + KCl + AlCl 3) system

All available phase equilibrium and thermodynamic data for the (NaCl + KCl + AlCl 3) system were collected and critically evaluated. An optimization was performed to obtain the parameters of one set of model equations for each phase (solids, liquid, gas) in order to best reproduce all the data simultaneously. In this way the data are rendered self-consistent, discrepancies among the data are identified, and extrapolations and interpolations can be performed. For the molten phase the Modified Quasichemical Model for short-range ordering was used, with monomeric Al 3+ ions (corresponding to AlCl 4 − complexes in earlier models) predominating in alkali-rich melts, and dimeric aluminum species (corresponding to Al 2Cl 7 − complexes in previous models) predominating in AlCl 3-rich melts. No ternary model parameters were required for the liquid phase; the binary parameters suffice. The models can be used with Gibbs free energy minimization software to calculate phase diagram sections, vapor pressures, and all thermodynamic properties at all compositions and over extended ranges of temperature and pressure.

The aging effect in Au-Cd alloys: A Mössbauer spectroscopy study

The martensite aging effect, observed in a number of alloy systems and through which fundamental properties for particular materials are altered by aging in the martensite state, has attracted considerable interest in recent years. It is important to understand and control the effect, particularly in shape-memory alloys for which stability of properties is fundamental to applications. The most likely model, at least for the Au-Cd system in which it has been most critically tested, is the symmetry conforming short-range order (SC-SRO) model first proposed by Ren and Otsika. 197 Au Mossbauer spectroscopy offers the possibility to observe the nature of defects associated with the gold sites. The spectra for single crystal and polycrystalline Au-Cd in both the aged martensite and quenched austenite conditions are presented and discussed. While some uncertainty in interpretation of the spectra remains, particularly in relation to any quadrupole splitting to be expected from either Au atoms on Cd-nearest-neighbour sites or the martensite lattice distortion, the best single-line fits provide evidence for two defect types.

First-principles investigations of ordering in binary α-Ti solid solutions

The ordering tendency in binary f-Ti solid solution containing 3sp or 4sp simple-metal (SM) or 3d transition-metal (TM) solute is investigated systematically by the linear muffin-tin orbital (LMTO) method within the atomic sphere approximation (ASA). We demonstrated that the effective pairwise interaction (EPI) energy in a solid solution is equal to half the solute-solute interaction energies and can be evaluated by a supercell total energy approach. The calculations of EPI energy both with and without volume relaxation of the supercells and local density of states (LDOS) show that the EPI energies of Ti-SM and Ti-TM solutions are dominated by different factors. For Ti-SM solutions, the EPI energies are of large absolute values with a negative sign, indicating strong ordering tendency in these solutions. The volume relaxation does not alter the EPI energy substantially. The calculated LDOS shows that the ordering tendency in Ti-SM solutions may be related to the hybridization between the electrons of the SM atoms when they are close to each other. For most Ti-TM solutions, if calculated without relaxation, the absolute EPI energies are very small; however, if calculated with relaxation, they are of relatively large positive values, indicating a clustering tendency in these solutions. By combining the calculated EPI energy and Flinn's model for short-range order (SRO) strengthening, the increase in critical shear stress sro due to SRO is estimated for Ti-SM alloys, and the results qualitatively agree with experiment.

X-ray scattering in liquid β-naphthalene derivatives

This paper reports results of the X-ray diffraction structural studies of liquid β-chloronaphthalene C10H7–Cl and β-methylnaphthalene C10H7–CH3 performed at 333 and 353K, respectively. The mean angular distributions of intensity were determined by diffraction of monochromatic X-ray radiation MoKα(λ=0.71069Å). Then, the electron density radial distribution functions 4πr2∑j,knK̄j[ρk(r)−ρ0] were numerically found using Fourier analysis. Interpretation of the results was carried out using the reduction method of Blum and Narten. For the proposed model of short-range order in the liquids studied, the molecular structure functions were calculated and compared to the experimental ones. A good agreement between the theoretical and experimental functions i(S)=[Ieu(S)/N−∑ucfj2(S)]/g2(S), was obtained on assuming the statistically most probable models of the molecules studied. The structural data obtained by X-ray analysis for liquids were discussed. The mean distances between the neighbouring molecules and the mean coordination numbers were found. In liquid β-naphthalene derivatives, the presence of the coordination spheres of intermolecular ordering were established. X-ray structural analysis was applied to determine the packing coefficient of β-naphthalene derivatives molecules.

Thermodynamic evaluation and optimization of the LiCl-NaCl-KCl-RbCl-CsCl-MgCl2-CaCl2 system using the modified quasi-chemical model

A complete critical evaluation of all available phase-diagram and thermodynamic data has been performed for all condensed phases of the LiCl-NaCl-KCl-RbCl-CsCl-MgCl2-CaCl2 system, and optimized model parameters have been found. The model parameters obtained for binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The modified quasi-chemical model for short-range ordering was used for the molten salt phase. Particularly in solutions with MgCl2 and KCl, RbCl, or CsCl, the calculations indicate a large dregree of ordering on the cationic sublattice, with Mg-Alkali second-nearest-neighbor pairs being favored.

Thermodynamic evaluation and optimization of the LiF-NaF-KF-MgF2-CaF2 system using the modified quasi-chemical model

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the LiF-NaF-KF-MgF2-CaF2 system and optimized model parameters have been found. The model parameters obtained for binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The modified quasi-chemical model for short-range ordering (SRO) was used for the molten salt phase. For solutions with NaF or KF together with MgCl2 or CaCl2, the calculations indicate a large degree of ordering on the cationic sublattice, with Mg-alkali and Ca-alkali second-nearest-neighbor (SNN) pairs being favored.

Simulation of diffuse scattering: Interlayer short-range order in Cu2Gd2/3S2 and Ti1.43S2 and two-directional positional disorder in composite crystals M1-pCr2S4-p

Diffuse streaks in electron and X-ray diffraction patterns of Cu2Gd2/3S2 and Ti1.43S2 were simulated using the matrix method for stacking disorder based on the models of intralayer order and interlayer short-range order of metal vacancies. Diffuse scattering planes observed by electron diffraction of composite crystals M1-pCr2S4-p (M=Sn, Pb, Sr, Ba; p-0.3) were simulated using the extended matrix method based on the two-directional positional disorder model of the M6Cr2S6 columns.

Hydrogen occupancy, 1H NMR spectrum and second moment of Zr xNi 1− x–H metallic glasses

The paper presents the results of an experimental investigation of rigid-lattice proton magnetic resonance (PMR) spectra and second moments in Ni 0.67Zr 0.33–H, Ni 0.50Zr 0.50–H, Ni 0.33Zr 0.67–H binary glassy alloy–hydrogen systems in the range of hydrogen-per-metal ( H/ M) ratio of 0.14≤ H/ M≤1.9. The line shape can be described by the empirical Harper-Barnes function with exponent values ranging from 1.45 to 2.95 in the whole hydrogen concentration range. The generally assumed Gaussian form is valid in a narrow H/ M interval only. The second moment as a function of H/ M can be fitted by a power function of an exponent 3/4. The exponent is independent of the composition of the alloy. We found that a simple lattice gas model based on a homogeneous hydrogen distribution contradicts the experimental results. Instead, a short-range order model has been proposed in which the hydrogen atoms are located in the centres of distorted tetrahedra of metal atoms, that is in the basic building blocks of the amorphous alloys. The Switendick criterion was also taken into consideration. We have shown that few proton first neighbours (0–2) and a small number of second neighbours (1–8), that is, a cluster of hydrogen is sufficient to account for the measured value of the second moment. Ternary Zr 0.5Ni 0.5− x Cu x –H alloys have been investigated, too. The addition of Cu nuclei did not lead to the second moment enhancement expected for a homogeneous distribution of components.