Total Pair Correlation Functions Research Articles

Thermodynamic metric geometry and the Fisher-Widom line of simple fluids.

Two boundary lines are frequently discussed in the literature, separating state regions dominated by repulsion or attraction. The Fisher-Widom line indicates where the longest-range decay of the total pair correlation function crosses from monotonic to exponentially damped oscillatory. In the context of thermodynamic metric geometry, such a transition exists where the Ricci curvature scalar vanishes, R=0. To establish a possible relation between these two lines, R is worked out for four simple fluids. The truncated and shifted Lennard-Jones, a colloid-like and the square-well potential are analyzed to investigate the influence of the repulsive nature on the location of the R=0 line. For the longer-ranged Lennard-Jones potential, the influence of the cutoff radius on the R=0 line is studied. The results are compared with literature data on the Fisher-Widom line. Since such data are rare for the longer-ranged Lennard-Jones potential, dedicated simulations are carried out to determine the number of zeros of the total correlation function, which may provide approximate information about the position of the Fisher-Widom line. An increase of the repulsive strength toward hard sphere interaction leads to the disappearance of the R=0 line in the fluid phase. A rising attraction range results in the nonexistence of the Fisher-Widom line, while it has little effect on the R=0 line as long as it is present in the fluid state.

Designing Magnetic Semiconductors From a Ferromagnetic Metallic Glass

Utilizing both charge and spin degrees of freedom of electrons simultaneously in magnetic semiconductors promises new device concepts by creating an opportunity to realize data processing, transportation and storage in one single spintronic device. Unlike most of the traditional diluted magnetic semiconductors, which obtain intrinsic ferromagnetism by adding magnetic elements to non-magnetic semiconductors, we attempt to develop new magnetic semiconductors via a metal-semiconductor transition by introducing oxygen into a ferromagnetic Co-Fe-B metallic glass. The atomic structure and electronic structure of the Co-Fe-B-O sample are explored by using first-principles calculations. The total pair correlation functions of both the Co-Fe-B and Co-Fe-B-O samples evidence their glass structures. The bond pair and coordination number analysis together demonstrate that the oxygen addition enables the bond types to change from the dominant metallic bonding in the Co-Fe-B metallic glass to the mixture of metallic, ionic and covalent bonding in the Co-Fe-B-O oxide glass. This results in the localization of electron charge density and the opening of the band gap in the Co-Fe-B-O oxide glass. The density of states suggests the Co-Fe-B-O oxide glass is semiconducting with a band gap of about 1.7 eV, but there are intermediate energy levels in the band gap. Meanwhile, the Co-Fe-B-O oxide glass remains to be ferromagnetic. These results indicate that the Co-Fe-B-O oxide glass is a magnetic semiconductor transferred from a ferromagnetic Co-Fe-B metallic glass, which is further verified by the experimental realization of a Co-Fe-B-O magnetic semiconductor. Furthermore, our calculation results reveal that a hybridization of the 4s/4p, 3d electrons of ferromagnetic Co and Fe atoms and O 2p electrons exists. Such s, p-d exchange interaction is essential to bridge the mutual interaction between the electrical conduction arising from s-like electrons and ferromagnetism supported by 3d electrons in magnetic semiconductors, thereby enabling the control of ferromagnetism by electrical means. Our calculation results represent an important step to gain a deeper understanding of the oxygen addition induced metal-semiconductor transition in an amorphous alloy Co-Fe-B system. We anticipate that our calculation results provide theoretical fundamentals for experimentally transferring many other ferromagnetic amorphous alloys into ferromagnetic semiconductors with attractive magnetoelectric coupling properties.

Atomic Structure of Glassy GeTe4 as a Playground to Assess the Performances of Density Functional Schemes Accounting for Dispersion Forces.

The atomic structure of glassy GeTe4 is obtained in the framework of first-principles molecular dynamics (FPMD) by considering five different approaches for the description of the electronic structure within density functional theory (DFT). Among these schemes, one is not corrected by accounting for the dispersion forces and it is based on the BLYP exchange-correlation (XC) functional, while all of the others consider the dispersion forces according to different theoretical strategies. In particular, by maintaining the BLYP expression for the XC functional, two of them (BLYP-D2 and BLYP-D3) exploit the Grimme expressions for the dispersion forces, while the fourth scheme is based on the maximally localized Wannier functions (MLWFs). Finally, we also considered the rVV10 functional constructed to include seamlessly the dispersion part. Our results point out the better performances of BLYP-D3 and MLWF in terms of comparison with experimental data for the total pair correlation functions, with BLYP-D2 and rVV10 being closer to the uncorrected BLYP data. The implications of such findings are discussed by considering the overall limited impact of dispersion forces on the atomic structure of glassy GeTe4.

An enhanced core–shell interatomic potential for Te–O based oxides

We present a new parametrization of the core–shell Buckingham interatomic potential (IAP) of Te–O oxides which allows to accurately reproduce experimental structural properties of various Te–O based systems including α-, β-, and γ-TeO2. Based on this IAP, we generate a high temperature model of TeO2 and find that it features a liquid-like dynamical behaviour in contrast to previous models. Furthermore, we generate an amorphous TeO2 model by quenching from the melt and study its structural properties in comparison with those available in the literature. We find that our model improves upon existent data and leads to a total pair correlation function in close agreement with the one measured through x-ray diffraction. These results open the way to systematic studies of binary and ternary complex Te–O based oxides by relying on a cheap, yet transferable and accurate IA potentials.

Spin-resolved pair-correlation functions of quasi one dimensional electron gas at finite temperature

In a recent paper [Phys. Status Solidi B 255, 1800174 (2018)], we found that the total contact pair-correlation function g(r = 0, T) of an unpolarized quasi one dimensional electron gas (Q1DEG) exhibits non-monotonous dependence on temperature T, initially decreasing with rise in T and then increasing beyond a critical T for a fixed electron number density. Here, we calculate the spin-resolved pair-correlation functions i.e., g↑↑(r, T) [= g↓↓(r, T)] and g↑↓(r, T) of the unpolarized Q1DEG for different values of T at a fixed wire width and electron number density. To this endeavor, we are using the celebrated theory given by Singwi, Tosi, Land and Sjölander developed for an interacting three-dimensional many-electron system. Our present study reveals that with rise in T, g↑↑(r, T) at small electron separation becomes stronger in complete contrast to g↑↓(r, T) and the non-monotonic T-dependence of g(r = 0, T) is governed by the cumulative behaviour of g↑↑(r, T) and g↑↓(r, T).

Transport properties and abnormal breakdown of the Stokes-Einstein relation in computer simulated Al72Ni16Co12 metallic melt

Molecular dynamic simulations were performed for liquid Al72Ni16Co12 to study the transport properties and the Stokes-Einstein relation (SER). It was observed that the self-diffusion coefficient for Co is much lower and α-relaxation time is much longer than the other two elements. The viscosity as a function of temperature was obtained with a method of reversed non-equilibrium molecular dynamics simulation. The SER in terms of viscosity and α-relaxation time for all elements was evaluated. It is found that the effective diameter for Co increases abnormally with the decrease of the temperature. The breakdown of SER for Co between self-diffusion coefficient and viscosity or α-relaxation time happens in the whole temperature range covered in this work, whereas the breakdowns of SER for both Al and Ni occur respectively at 1500 K and 1200 K in term of viscosity and α-relaxation time, which are far above the critical temperature of mode coupling theory, Tc, around 814 K according to transport properties, and 797 K based on the α-relaxation time. The decoupling of element dynamics and the dynamic heterogeneity are studied by calculating the ratio of the two diffusivities for different elements, D1/D2, and the non-Gaussian parameter. To check the structural-dynamics correlation, the total and partial pair correlation functions are calculated. It is proposed that for Co the decoupling of self-diffusion coefficient and viscosity or α-relaxation time persists at all temperatures due to the strong interactions between Co atoms. And the sudden increase of the dynamic heterogeneity, accompanied by a subtle change of liquid structure, is supposed to be the reason for the abnormal breakdown of SER for Al and Ni at a temperature far above Tc.

Local structures and optical properties of As-Se-Te(S) chalcogenide glasses

The partial, total and average coordination number of atoms and, their neighbor distributions have been determined by the neutron diffraction method and application of the Reverse Monte Carlo modeling for experimental data in As40Se60, As40Se30S30 and As40Se30Te30 chalcogenide glasses. The total coordination number of the arsenic and chalcogen atoms is 3 and 2 for all compounds. The average coordination number is 2.4, i.e. the 8-N rule is performed and main structural element is AsSe3 type pyramids, where depending on the chemical composition Se atom is replaced by S or Te atoms. The proportion of homopolar bonds is significant in As40Se60 and As40Se30S30 compositions, but sharply decreases in As40Se30Te30. In all compositions the neighbor distances between arsenic and selenium atoms are the same within error: 2.35 Å (SeSe); 2.45 Å (AsAs) and 2.40 Å (AsSe). The existence of medium range order (MRO) is proved by the analysis of the total and partial pair structural factors and correlation functions in above mentioned compositions. The geometric dimensions of the MRO area, i.e. the quasi-periodicity of density fluctuations in the MRO area and the size of nano-voids have determined within Elliott's void-based model. The change of the optical parameters by variation of the chemical composition has been established from the analysis of the optical transmission spectra.

Generalized Stealthy Hyperuniform Processes: Maximal Rigidity and the Bounded Holes Conjecture

We study translation invariant stochastic processes on $\mathbb{R}^d$ or $\mathbb{Z}^d$ whose diffraction spectrum or structure function $S(k)$, i.e. the Fourier transform of the truncated total pair correlation function, vanishes on an open set $U$ in the wave space. A key family of such processes are stealthy hyperuniform point processes, for which the origin $k=0$ is in $U$; these are of much current physical interest. We show that all such processes exhibit the following remarkable maximal rigidity : namely, the configuration outside a bounded region determines, with probability 1, the exact value (or the exact locations of the points) of the process inside the region. In particular, such processes are completely determined by their tail. In the 1D discrete setting (i.e. $\mathbb{Z}$-valued processes on $\mathbb{Z}$), this can also be seen as a consequence of a recent theorem of Borichev, Sodin and Weiss; in higher dimensions or in the continuum, such a phenomenon seems novel. For stealthy hyperuniform point processes, we prove the Zhang-Stillinger-Torquato conjecture that such processes have bounded holes (empty regions), with a universal bound that depends inversely on the size of $U$.

Statistics-Based Analysis of the Evolution of Structural and Electronic Properties of Realistic Amorphous Alumina During the Densification Process: Insights from First-Principles Approach

On the basis of the melt and quench strategy, over 3000 structurally different AlOx structures have been generated using ab initio molecular dynamics. Unlike other previous studies where defects were introduced into some crystalline polymorph of Al2O3, a variety of defects emerged directly from this approach. A new way to probe the short (distances between first neighbors and coordination numbers) and medium (atom rings, bond angles, and distances between second neighbors) range structural properties of H- and/or O-rich AlOx has been defined. The evolution of such structural properties during the densification process with mass loss has been studied using averaged data at a fixed chemical composition. A good agreement is observed between experimental and theoretical structural data, validating the methodology. In particular, the profile of the total experimental neutron pair correlation function has been rationalized. At fixed composition, the Spearman correlations have been calculated in order to reveal monotonic relationships between properties: a correlation between the structure and band gap energy of different stoichiometries of AlOx could not be clearly inferred. Finally, we may speculate that the O22– and Al–H defects could explain the origin of negative fixed charges in AlOx because of their effects on electronic properties of AlOx and their structural characteristics.

Structure and properties of liquid Al–Cu alloys: Empirical potentials compared

We report on the structure and mass transport properties of liquid Al–Cu alloys predicted by two recently-developed empirical many-body potentials: MEAM (Jelinek et al., 2012) and EAM-ADP (Apostol and Mishin, 2011), and by the well-known Gupta potential. Total and partial pair correlation functions, angular distribution functions, densities, coordination numbers and self-diffusion coefficients are compared with published experimental and ab initio results for a number of temperatures above the liquidus. Prevalent local orderings are characterized by means of Voronoi analysis. Densities and the temperature coefficient of density are compared with experiment for different compositions of the alloy. All three studied potentials, and EAM-ADP and MEAM in particular, display marked difficulty in describing mixed (Al–Cu) interactions. EAM-ADP mispredicts Cu-rich alloys to re-solidify at all temperatures studied, while MEAM’s predictions for the density and its temperature dependence are poor for Al-rich compositions. Overall, the best description of liquid Al–Cu is offered by the Gupta potential, which is found to give a reasonable picture of short-range order and predicts mass transport coefficients and densities in moderately good agreement with experiment.

Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassyGeTe4

The structural properties of amorphous ${\mathrm{GeTe}}_{4}$ are studied within the framework of first-principles molecular dynamics combined with density functional theory. Four different theoretical schemes are considered, each one intended to correspond to a distinct structural model. These are obtained by selecting either the PBE (Perdew, Burke, and Ernzerhof) or the BLYP (Becke, Lee, Yang, and Parr) exchange-correlation functionals and, for each one of the two, by disregarding or including van der Waals dispersion forces. Based on the comparison with experimental total structure factor $S(k)$ and total pair correlation function $g(r)$, one can infer the quantitative character of such models, thereby extracting information on the underlying structures. We found that the inclusion of the vdW forces improves the predictive power of our approach for the PBE and (to a smaller extent) the BLYP exchange-correlation functionals. Overall, BLYP performs better than PBE in reproducing the available experimental quantities, providing a tetrahedral atomic-scale network profoundly different from the one predicted by PBE, in which tetrahedral and octahedral motifs do coexist. Our work demonstrates that a careful choice of the exchange-correlation functional, combined with the account of van der Waals forces, is crucial to achieve realistic structural predictions for glassy ${\mathrm{GeTe}}_{4}$.

Structural evolution and thermophysical properties of ZrxNi100 − x metallic liquids and glasses

The results of high-energy X-ray scattering studies over a wide temperature range for equilibrium and supercooled ZrxNi100−x (x=36, 57, 76) liquids and the corresponding glasses are presented. The results of liquid density and viscosity measurements are also shown. All of the liquid studies were made on containerlessly processed liquids using the technique of electrostatic levitation. The scattering data were used to determine the temperature-dependent total structure factor, S(q), and pair-correlation function, g(r). A discontinuity is observed between the magnitude of the first peak in S(q) of the liquid when extrapolated to the glass transition temperature, Tg, and the value determined for the structurally relaxed glass at Tg. This indicates that the structural ordering in the liquid accelerates upon approaching Tg, consistent with the behavior expected for a fragile liquid. An asymmetry in the first peak in the pair correlation function develops with decreasing temperature for all alloy liquids and glasses, suggesting that chemical ordering accompanies the structural ordering.

Communication: Integral equation theory for pair correlation functions in a crystal.

A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two-particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving parts are calculated using the integral equation theory of homogeneous fluids. The symmetry broken part of the direct pair correlation function is calculated from a series written in powers of order parameters and that of the total pair correlation function from the Ornstein-Zernike equation. The results found for a two-dimensional hexagonal lattice show that the method provides accurate and detailed informations about the pair correlation functions in a crystal.

Anomalous structural evolution and liquid fragility signatures in Cu–Zr and Cu–Hf liquids and glasses

The results of high energy X-ray scattering studies of equilibrium and supercooled Cu100−xZrx (x=46 and 54) and CuxHf100−x (x=55 and 60.8) liquids and the corresponding glasses are presented. The liquid data were obtained in a containerless environment using the beamline electrostatic levitation (BESL) technique. The total structure factor and total pair correlation functions were measured as a function of temperature for the liquids, and for the glasses at room temperature. A developing asymmetry in the peak of the first coordination shell in the total pair correlation function suggests chemical ordering in the liquids with cooling. This asymmetry takes the form of two prominent peaks, suggesting two prominent ordering length scales. When the magnitudes of these peaks are extrapolated to the glass transition temperature a discontinuity is observed, indicating that an abrupt increase in the magnitude is required to match the observed peak heights in the glass. This suggests that the structure of the supercooled liquid orders more rapidly near the glass transition temperature, a conclusion that is supported by molecular dynamics simulations. This observed structural evolution of the liquid indicates that the concept of fragility, typically defined from the behavior of viscosity with temperature, has a measurable structural signature as well, which can be observed in X-ray diffraction studies.

Anomalous structural evolution in Cu50Zr50 glass-forming liquids

The structural evolution of the Cu50Zr50 liquid and glass was determined from in situ high-energy X-ray diffraction measurements. The temperature dependence of the static X-ray structure factor for the glass was measured from room temperature to above the glass transition temperature. Data were obtained for equilibrium and supercooled liquids in a containerless environment using electrostatic levitation. The structure factors and the total pair correlation functions display an anomalous evolution, indicating a rapid acceleration of short-range atomic order in the liquid above, but near the glass transition temperature. This behavior contrasts sharply with that observed in high glass forming ability metallic liquids.

Structural evolution in Ni–Nb and Ni–Nb–Ta liquids and glasses — A measure of liquid fragility?

The structures of Ni59.5Nb40.5, Ni62Nb38, and Ni60Nb30Ta10 liquids and glasses were studied using synchrotron high-energy X-ray diffraction. To avoid reactions between the liquids and their containers and to deeply supercool them below their equilibrium liquidus temperatures, the liquids were processed without a container using the beamline electrostatic levitation (BESL) technique. The total static structure factor, S(q), and the total pair-correlation function, g(r), were obtained for all liquid compositions over a temperature range of approximately 250°C; S(q) and g(r) were measured for the corresponding glasses at room temperature. All of the S(q)s have a shoulder on the high-q side of the second peak; this becomes more pronounced as the liquid is supercooled, and is most prominent in the glass. Based on a Honeycutt–Andersen analysis of the atomic configurations obtained from Reverse Monte Carlo fits to the total structure factors obtained from the scattering data, icosahedral short-range order (ISRO) is dominant in all liquids and becomes particularly pronounced in the glasses. No correlation is noted, however, between the amount of ISRO and easy glass formability. Structural features show evidence for an acceleration of ordering in the supercooled liquid above the glass transition temperature, consistent with the behavior expected for fragile liquids. This suggests that scattering data can provide a new method to assess liquid fragility, which is typically obtained from the temperature behavior of the viscosity near the glass transition temperature.

The Atomic Structure of a Metal‐Supported Vitreous Thin Silica Film

Clear as glass: The atomic structure of a metal-supported vitreous thin silica film was resolved using low-temperature scanning tunneling microscopy (STM). Based on the STM image, a model was constructed and the atomic arrangement of the thin silica glass determined (see picture). The total pair correlation function of the structural model shows good agreement with diffraction experiments performed on vitreous silica.

Structure and electric resistance of Sn–Cu(Ag) solders in the precrystallization temperature range

We investigate the atomic structure of tin-based solders by X-ray diffraction methods and the reverse Monte Carlo method. Total and partial structural factors and pair correlation functions are calculated. It is shown that Sn 0.987 Cu 0.013 , Sn 0.962 Ag 0.038 , and Sn 0.949 Ag 0.038 Cu 0.013 liquid alloys are characterized by a microinhomogeneous structure with Cu(Ag)–Sn clusters distributed in the tin-based matrix.

Atomic structure of the two intermediate phase glassesSiSe4andGeSe4

The microscopic origin of the intermediate phase in two prototypical covalently bonded AxB1-x network glass forming systems, where A=Ge or Si, B=Se, and 0=x=1, was investigated by combining neutron diffraction with first-principles molecular-dynamics methods. Specifically, the structure of glassy GeSe4 and SiSe4 was examined, and the calculated total structure factor and total pair-correlation function for both materials are in good agreement with experiment. The structure of both glasses differs markedly from a simple model comprising undefective AB4 corner-sharing tetrahedra in which all A atoms are linked by B2 dimers. Instead, edge-sharing tetrahedra occur and the twofold coordinated Se atoms form three distinct structural motifs, namely, Se-Se2, Se-SeGe (or Se-SeSi), and Se-Ge2 (or Se-Si2). This identifies several of the conformations that are responsible for the structural variability in GexSe1-x and SixSe1-x glasses, a quantity that is linked to the finite width of the intermediate phase window.

Ion–ion interaction in room temperature ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate studied by large angle X-ray scattering experiment and molecular dynamics simulations

Large angle X-ray scattering (LAXS) experiment for 1-ethyl-3-methylimidazolium tetrafluoroborate [EMI +][BF 4 −] ionic liquid was carried out at 298 K, to reveal the closest ion–ion interaction in the ionic liquid. The intra-molecular atom–atom correlations based on the molecular geometries in crystals were subtracted from the total pair correlation function to yield the inter-molecular pair correlation function. In the inter-molecular pair correlation function, peaks of 3.4, 4.4 and 5.5 Å were successfully extracted as the closest ion–ion interactions. Molecular dynamics simulations based on the effective pair potentials were also performed to ascribe the peaks found in the experimentally evaluated inter-molecular pair correlation function at an atomistic level. The X-ray interference function derived from MD simulations and thus Fourier transferred X-ray weighted pair correlation function were reasonably agreement with those obtained by the experiment, the extracted peaks in the experimental inter-molecular pair correlation function can be appropriately attributed to the C (EMI +) - F (BF 4 −) atom–atom correlations. In addition, artificial MD simulations employed rigid models for the nonplanar and the planar EMI + isomers were performed to obtain further insight into the effect of the conformational isomerism on the ion–ion interactions in the ionic liquid. It turned out that the ion–ion interaction, namely the anion orientation around the cation, depends on the conformational isomerism of the cation from the artificial MD simulations.