Bhatia-Thornton Partial Structure Factor Research Articles

Computer simulation of thermodynamic factors in Ni-Al and Cu-Ag liquid alloys

In this paper, thermodynamic factors of two liquid alloys, Ni-Al and Cu-Ag, are studied by means of molecular dynamics simulation (with the most reliable embedded-atom method potentials) over both wide composition and temperature ranges. For the first time, a comparison is possible between Ni-Al (with a strong ordering tendency) and Cu-Ag (with a strong phase separation tendency). The calculations were performed based on the evaluation of pair correlation functions and mean square thermal fluctuations in composition (the thermodynamic limit of one of the Bhatia-Thornton partial structure factors, SCC). A novel but straightforward computational approach is developed and successfully applied to these calculations. In order to ensure reliability of the employed model description of Ni-Al liquid alloys, the calculated partial and total structure factors are verified by data from neutron scattering experimental measurements (performed as part of this work as well as also being available in the literature). Good agreement is observed for the structure factor SCC for all values of q including the thermodynamic limit q→0. On the other hand, for the total and Faber-Ziman partial structure factors, good agreement is observed only for q values outside the limit q→0. In addition, a similarity between the shapes of the thermodynamic factor composition dependence and the shape of the liquidus lines in both Ni-Al and Cu-Ag liquid alloys is noted. We highlight the significance of the presented computational and experimental study for developing and testing various models and frameworks.

Accurate determination of the radii and order parameter of the layers of a binary alloy, liquid or amorphous, from the eigenstates of the exchange operator of its components

In this work, a rigorous mathematical method to calculate the order parameter in a binary amorphous or liquid alloy, is established even when the alloy is made up of very differently sized atoms. This method, based on the study of the eigenstates of the exchange operator of the alloy components, allows revealing different spherical layers whose inner and outer radii are solutions of a certain equation. These layers have no constant thickness but contain numbers of atoms of each species that are exactly in the ratio of the concentrations of these two species. Thus, each layer has exactly the average concentration of the alloy, allowing to properly formalize the order parameter. Thus the order parameter is formalized in each of these layers. This method makes possible to retrieve the subtle Bhatia-Thornton formalism [Phys. Rev., B2, 3004 (1970)] used for the description of binary alloys. We discuss the link between the zero q value of concentration-concentration Bhatia-Thornton partial structure factor and the numbers of neighbours. We apply our method to study the order in the Bi0.3Ga0.7 liquid alloy. We are able to determine eight layers and their order parameter on the interatomic distance-range [0, 15 Å].

Structure of sticky-hard-sphere random aggregates: The viewpoint of contact coordination and tetrahedra.

We study more than 10^{4} random aggregates of 10^{6} monodisperse sticky hard spheres each, generated by various static algorithms. Their packing fraction varies from 0.370 up to 0.593. These aggregates are shown to be based on two types of disordered structures: random regular polytetrahedra and random aggregates, the former giving rise to δ peaks on pair distribution functions. Distortion of structural (Delaunay) tetrahedra is studied by two parameters, which show some similarities and some differences in terms of overall tendencies. Isotropy of aggregates is characterized by the nematic order parameter. The overall structure is then studied by distinguishing spheres in function of their contact coordination number (CCN). Distributions of average CCN around spheres of a given CCN value show trends that depend on packing fraction and building algorithms. The radial dependence of the average CCN turns out to be dependent upon the CCN of the central sphere and shows discontinuities that resemble those of the pair distribution function. Moreover, it is shown that structural details appear when the CCN is used as pseudochemical parameter, such as various angular distribution of bond angles, partial pair distribution functions, Ashcroft-Langreth and Bhatia-Thornton partial structure factors. These allow distinguishing aggregates with the same values of packing fraction or average tetrahedral distortion or even similar global pair distribution function, indicative of the great interest of paying attention to contact coordination numbers to study more precisely the structure of random aggregates.

Measurements of structural and chemical order inZr80Pt20andZr77Rh23liquids

The short-range order (SRO) and medium-range order of electrostatically levitated $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ and $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquids are presented based on a combination of high-energy x-ray diffraction and time-of-flight neutron diffraction studies. The atomic structures of the $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ liquids were determined as a function of temperature from constrained reverse Monte Carlo simulations using x-ray and elastic neutron scattering measurements and two partial pair-distribution functions obtained from molecular dynamics (MD) simulations. Analysis of both the Faber-Ziman and Bhatia-Thornton partial structure factors shows that the $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$ and $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquids have similar topological SRO. Interestingly, the chemical SRO appears to be much more strongly tied to the topological order in the $\mathrm{Z}{\mathrm{r}}_{77}\mathrm{R}{\mathrm{h}}_{23}$ liquid than in the $\mathrm{Z}{\mathrm{r}}_{80}\mathrm{P}{\mathrm{t}}_{20}$. These results demonstrate that the combination of experimental scattering measurements with MD results provides a powerful approach for obtaining details of chemical and topological ordering in metallic glasses and liquids.

The Bhatia–Thornton structure factor "concentration – concentration" for hard-core fluid in the random phase approximation

The expression for the Bhatia-Thornton partial structure factor “concentration concentration” for an arbitrary two-component hard-core fluid in the random phase approximation is obtained.

The Bhatia–Thornton structure factor "number density – concentration" for hard-core fluid in the random phase approximation

The expression for the Bhatia-Thornton partial structure factor “number density – concentration” for arbitrary two-component hard-core fluid in the random phase approximation is obtained.

The Bhatia–Thornton structure factor "number density – number density" for the hard-core fluid in random phase approximation

The expression for the Bhatia-Thornton partial structure factor “number density – number density” for arbitrary two-component hard-core fluid in the random phase approximation is obtained.

Local order and dynamic properties of liquid and undercooledCuxZr1−xalloys byab initiomolecular dynamics

We report the results of first-principles molecular-dynamics simulations for liquid and undercooled ${\text{Cu}}_{x}{\text{Zr}}_{1\ensuremath{-}x}$ alloys at four different compositions. The local structure as defined by the partial pair-correlation functions and the Bhatia-Thornton partial structure factors is found to display a strong evolution as a function of composition. In addition, a structural analysis using three-dimensional pair-analysis techniques evidences an icosahedral short-range order much more pronounced around ${x}_{\text{Cu}}=0.64$. In examining the dynamic properties of these alloys, we show a strong interplay between the structural changes and the evolution of the viscosity as a function of composition.

An experimentally consistent atomistic structural model of silica glass

Empirical potential structure refinement is used to build an atomistic model of silica glass based on neutron scattering data. This model is tested against X-ray diffraction and extended X-ray absorption fine structure (EXAFS) spectroscopy data to establish its local and intermediate range structural veracity. The chemical specificity of the silicon and oxygen K-edge spectroscopic information allows us to confirm that the neutron scattering derived model represents a reasonable representation of the three partial structure factors that are required to characterise this binary glass and subsequently give confidence in the Faber–Ziman and Bhatia–Thornton partial structure factors and pair distribution functions that are extracted from the model.

Structure of liquids and glasses in the Ge–Se binary system

A summary is given of the partial structure factors that have been measured for liquids and glasses in the Ge–Se binary system by using diffraction methods. Information is presented on the pair correlation functions describing the atomic species and use is made of the Bhatia–Thornton formalism to separate those pair correlation functions describing the system topology from those that describe the chemical ordering. The information made available by the measured Bhatia–Thornton partial structure factors on the thermodynamic properties of Ge–Se mixtures is briefly summarized. The properties of the network structures formed in liquid and glassy Ge–Se compounds are investigated as a function of composition, temperature and pressure. For GeSe2 at ambient pressure it is shown that the so-called first sharp diffraction peak, which appears in the measured diffraction patterns at a small scattering wavevector value of ≈1Å−1 and which is associated primarily with Ge–Ge correlations, does account for discernable features of the observed intermediate range order in both the liquid and glassy phase. The first sharp diffraction peak in the measured Ge–Ge partial structure factor for both phases is described by comparable parameters suggesting communality in the underlying intermediate range order which survives the glass transition. Homopolar bonds are found to be a feature in the structure of liquid GeSe and both liquid and glassy GeSe2 with Ge–Ge and Se–Se distances in the ranges 2.33(3)–2.42(2) and 2.30(2)–2.34(2)Å, respectively.

Modeling the structural, dynamical, and magnetic properties of liquidAl1−xMnx(x=0.14, 0.2, and 0.4): A first-principles investigation

We report the results of first-principles molecular dynamics simulations of liquid ${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}$ alloys at three different compositions. The local structure as defined by the Bhatia-Thornton partial structure factors is found to display significant changes at $x=0.4$. In addition, a structural analysis using three-dimensional pair-analysis techniques evidences a fivefold symmetry around $x=0.14$, in agreement with the experimental quasicrystal-forming range, and an increasing complexity of the Frank-Kasper polytetrahedral symmetry around Mn atoms at $x=0.4$. We also examine the time evolution of the configurations at the three compositions in terms of the mean-square displacements and self-diffusion coefficients. Finally, we show a strong interplay between the structural changes and the evolution of the magnetic properties of the Mn atoms as a function of composition.

Decay of the pair correlations and small-angle scattering for binary liquids andglasses

The origin of extended-range ordering in binary liquids and glasses is investigated. Thestarting point is a simple model pair potential which includes both Coulomb and dispersionforces. For this model, the behaviour of the Bhatia–Thornton partial structure factors at smallscattering vector values is examined and also the asymptotic behaviour of the associatedpartial pair correlation functions in real space. The results are compared with the observedreal space pair correlation functions for a range of liquid and glassy systems for whichaccurate partial structure factors have been measured by using neutron diffraction. It isfound that the extended range ordering can often be accounted for by using anexponentially damped oscillatory function with a wavelength of oscillation given by≈2π/kPP,where kPP is the position of the principal peak in the measured partial structure factors.Sometimes this exponentially damped oscillatory function also accounts for theobserved behaviour of the real space data at relatively small distances as in thecase of the concentration–concentration pair correlation function for moltenAg2Se and forglassy GeSe2, ZnCl2 and GeO2. For these glasses, all of the Bhatia–Thornton pair correlation functions in real spaceeventually decay with a common wavelength of oscillation and a common decay length. Thelimitations associated with the use of simple model pair potentials to analyse theexperimental data sets are discussed. In addition, the effect on the small-angle scatteringand asymptotic decay of the real space pair correlation functions of including a termcorresponding to ion-induced dipole interactions in the pair potential is briefly considered.An analytical expression is also given for the real space manifestation of the Lorchmodification function.

Intermediate Range Order in Model Liquid Binary Alloys

Abstract We study the nature of intermediate range order (IRO) in a 2:1 model liquid binary mixture as the range of the potentials is changed from short to long range. The calculations were carried out within the Mean Spherical Approximation, and the study focuses on the Bhatia-Thornton partial structure factors. We find evidence of IRO when there is size difference between the atoms in the mixture. However, at the level of description of this work, there appears no way of distinguishing between the IRO in a compound forming or an ionic system.

Atomic structure of melt-spun amorphous Ni 56Dy 44 studied by neutron diffraction

The atomic structure of a melt-spun amorphous Ni 56Dy 44 alloy was studied by neutron diffraction using the isotopic substitution technique with nickel isotopes. The three Faber-Ziman partial structure factors as well as the Bhatia-Thornton partial structure factors together with the corresponding correlation functions were evaluated. The short-range order parameter, calculated from the partial coordination numbers, reflects a chemical ordering effect in amorphous Ni 56Dy 44.

Ab initio molecular dynamics study of liquid Li 12Si 7

A report is given on the progress of an ab initio molecular dynamics simulation of liquid Li 12Si 7. This material has been extensively investigated experimentally (e.g., neutron diffraction). Some structural properties (partial pair distribution functions, angle distribution, Bhatia-Thornton partial structure factors) are discussed and it is demonstrated that elements of the solid state structure (low Si coordination, a preferred SiSiSi angle) are preserved in the liquid state. Also some first results on diffusion coefficients are presented.

Short Range Structure of Amorphous Ni50Ta50-Alloys by Means of X-Ray- and Neutron-Diffraction

Abstract Amorphous Ni50Ta50-samples with their high crystallization temperature of 985 K were investigated. To evaluate the three partial structure factors of amorphous Ni50Ta50 one X-ray diffraction experiment was performed with Ni50Ta50 and two neutron diffraction experiments with Co10Ni40Ta50 and with Ni50Ta50, respectively. The Bhatia-Thornton partial structure factor SCC(Q) indicates rather strong chemical short range order which also explains the premaximum observed in the Faber-Ziman partial SNiNi(Q)-function. The nearest neighbor distance is 2.82 Å for Ni-Ni, 2.91 Å for Ta-Ta, and is shortest for Ni-Ta, 2.44 Å. The coordination numbers are NNiNi = 4.9, NTaTa = 8.2, and NNiTa = 6.0. We report on the chemical short range order and the possible binding behavior in a-Ni50Ta50 and compare the present results with those reported in the literature on a-Ni40Ti60 as well as on a-Ni55Ta45

Modified Mean Spherical Model for a Binary System of Interacting Hard Spheres with Factorizable Coupling Strength

The solution of the Ornstein-Zernike equation is investigated in the modified meanspherical approximation for a binary system consisting of equal-size hard spheres interacting with each other via a pairwise tail potential such as a i a j ϕ( r ), with a i a j and ϕ( r ) being the coupling strength between i - and j -species of hard spheres and an arbitrary potential function, respectively. For the Bhatia-Thornton partial structure factors S NN ( q ), S NC ( q ) and S CC ( q ), this solution produces a relationship like [ S NN - S 0 ][ S CC - c 1 c 2 ]= S NC 2 , where S 0 ( q ) equals S NN ( q ) at a 1 = a 2 =0 and c i , is the concentration. It is also shown that this relationship is in reasonably good agreement with the experimental results on thermodynamic properties of liquid Li–Pb alloy.

The Bhatia-Thornton Partial Structure Factors of Polyelectrolyte Solutions

Abstract We have calculated the Bhatia-Thornton partial structure factors for a two component system of charged hard spheres in solution, using the mean spherical approximation for the computation of the Ashcroft-Langreth structure factors. Our results show that for electrolytes which are highly asymmetrical in size and charge, the charge-number partial structure factor SNQ(q) is very sensitive to the distribution of the ions. The Bhatia-Thornton structure factors exhibit clearly the effects of charge ordering and condensation of the small ions around the large ions in concentated solutions.

Electronic theory of the chemical short-range order in liquid and amorphous transition-metal alloys.

We present microscopic calculations of the chemical short-range order in amorphous and liquid alloys of two transition metals. Our approach is based on a model one-band tight-binding Hamiltonian and a thermodynamic variational technique founded on the Gibbs-Bogolyubov inequality and a hard-sphere Yukawa fluid as a reference system. We calculate the Bhatia-Thornton partial structure factors of ${\mathrm{Ni}}_{\mathrm{x}}$${\mathrm{Ti}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ and ${\mathrm{Ni}}_{\mathrm{x}}$${\mathrm{Zr}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ alloys and find good agreement with experiment.