Liquid Noble Metals Research Articles

Hard-to-recover reserves of gas, liquid petroleum hydrocarbons, bituminous components, rare, rare-earth and noble metals of the gas-saturated part of oil and gas condensate and gas condensate fields at the late stage of development

Many oil and gas condensate and gas condensate fields discovered in the ‘60s and ‘70s of the last century are now at the late stage of development. Research of the Laboratory for Hard-to-Recover Hydrocarbon Reserves of the Oil and Gas Research Institute of the Russian Academy of Sciences has been devoted to justify an increase in the resource potential and attain a maximum of recovery efficiency for long-developed fields using the evidence from the Orenburg and the Vuktyl oil and gas condensate fields. The involvement of the unique reserves of hard-to-recover oil will help to enhance declining production in old oil and gas producing regions.

Effective Pair Interactions and Structure in Liquid Noble Metals within Wills-Harrison and Bretonnet-Silbert Models

Recently, for calculating the effective pair interactions in liquid transition metals, we have developed an approach which includes the Wills-Harrison and Bretonnet-Silbert models as limit cases. Here, we apply this approach to noble liquid metals. The dependencies of pair potentials and corresponding MD-simulated pair correlation functions in pure liquid Cu, Ag and Au on the portion of the non-diagonal (with respect to the magnet quantum number) d-d-electron couplings in the metal under consideration are studied. The model provides a good agreement with experimental and ab initio data for pair correlation functions, structure factors and velocity autocorrelation functions.

Verification of the Stokes-Einstein relation in liquid noble metals over a wide range of temperatures

The validity of Stokes-Einstein (SE) relations in liquid noble metals namely Cu, Ag and Au over a wide temperature range has been studied using Dzugutov's scaling scheme and Faber's hard-sphere (HS) theory of transport coefficients. Basic ingredients of those theories are the temperature-dependent effective HS diameter and excess entropy. To determine them, we have applied variational modified hypernetted chain theory in conjunction with effective interionic interaction derived from embedded atomic method (EAM) with both temperature-dependent and independent adjustable parameters α and b. Obtained ingredients using α(T) and b(T) are close to the available experimental data than those obtained using fixed α and b with an empirical relation. Calculated transport coefficients are in good agreement with experimental data when scaling scheme with α(T) and b(T) has been considered. Simplified SE relations from transport coefficients hold when scaling scheme has been applied with α(T) and b(T) and lies around the slip boundary line.

Test of the universal scaling law for square well liquid metals

A universal scaling law relating the dimensionless diffusion coefficient with excess entropy of a liquid [M. Dzugutov, Nature (London), 381 (1996), 137] is tested for liquid noble metals due to their fundamental importance both in society and industry. The square well form of interatomic potential is used to study liquid noble metals because it possesses the basic nature of real liquids. The radial distribution function (RDF), g(r) and self diffusion coefficient, D of liquid noble metals were derived using statistical mechanical square well (SW) model under random phase approximation, which was proposed by Rao and Murthy [R. V. Gopala Rao and A. K. Murthy, Physics Letters A, 51 (1975), 3]. g(r) and D data of liquid noble metals were employed to compute excess entropy, SE using scaling law, surface entropy, SV through temperature derivative of D under linear trajectory principle and microscopic reducing parameter; Enskog collision frequency, Γ. Further new equations have been derived from equation of state (EOS) for the SW potential and verified them to compute structure factor in the long wavelength limit. The results obtained were compared with available experimental results and we find there is fair agreement between theoretical and experimental values. Present study shows the applicability of the Dzugutov scaling law for square well liquids.

Surface entropy of liquid transition and noble metals

Abstract Surface entropy of liquid transition and noble metals has been investigated using an expression obtained from the hard-sphere (HS) theory of liquid. The expression is developed from the Mayer's extended surface tension formula [Journal of Non-Crystalline Solids 380 (2013) 42–47]. For interionic interaction in metals, Brettonet–Silbert (BS) pseudopotentials and embedded atom method (EAM) potentials have been used. The liquid structure is described by the variational modified hypernetted chain (VMHNC) theory. The essential ingredient of the expression is the temperature dependent effective HS diameter (or packing fraction), which is calculated from the aforementioned potentials together with the VMHNC theory. The obtained results for the surface entropy using the effective HS diameter are found to be good in agreement with the available experimental as well as other theoretical values.

Atomic transport for liquid noble and transition metals using scaling laws

We have studied the atomic transport coefficients namely diffusion coefficients and shear viscosities of liquid transition metals of the 3d, 4d and 5d series by applying universal scaling laws proposed by Dzugutov [Nature (London) 381, 137 (1996)] and Rosenfeld [Phys. Rev. A 15, 2545 (1977)]. The embedded atom method is used in order to describe interionic interaction in metals; and the liquid state theory is described by variational modified hypernetted chain integral equation theory. We have finally calculated excess entropy for each system, which is the main ingredient in the universal scaling law. Our results for atomic transport coefficients calculated with true excess entropy provide better agreement and also confirm the claim of Hoyt et al. [Phys. Rev. Lett 85, 594 (2000)].

Surface tension of liquid transition and noble metals

We have studied the surface tension of all liquid transition and noble metals using extended Mayer's empirical formula. For interionic interaction in metals, Bretonnet and Silbert (BS) pseudopotentials and the embedded atom method (EAM) potentials are chosen. Self-consistent variational modified hypernetted chain (VMHNC) integral equation theory is used to describe liquid state. The premier ingredients of the extended Mayer's formula are the effective hard sphere (HS) diameter and packing fraction. We calculated HS diameter using both BS and EAM potentials in conjunction with the VMHNC theory. We have found that the surface tension obtained using EAM potentials are in very good agreement with the available experimental data.

Thermodynamical Properties of Equiatomic Liquid Noble Metal Alloys by A Pseudopotential

Thermodynamical Properties of Equiatomic Liquid Noble Metal Alloys by A Pseudopotential

Molecular dynamics prediction of density for metastable liquid noble metals

Abstract The thermophysical properties of metastable liquid noble metals are not readily available due to the great experimental difficulties. Here the densities of liquid Pd, Pt, Ag, and Au are predicted by molecular dynamics method. The pair distribution functions are computed to monitor the atomic structure of these noble metals, which indicate that the systems remain in liquid state in the process of simulation. The calculated densities exhibit nonlinear temperature dependences and prove to have a high accuracy. The density data are obtained in a much broader temperature range, especially in the undercooled regime. Moreover, the molar volumes and the thermal expansion coefficients are also derived from the density predictions.

Calculation of surface entropy of liquid transition and noble metals

The surface entropies of liquid transition and noble metals Fe, Co, Ni, Cu, and Ag have been investigated. Surface entropy expression involving hard–sphere (HS) interaction in closed form is used. Since the HS diameter depends on metallic properties and temperature, the temperature dependent effective HS diameter is determined from a well-known perturbation theory, linearized Weeks–Chandler–Andersen (LWCA) and integral equation theory, variational modified hypernetted chain (VMHNC). Theoretical calculations are compared with the available experimental data, and found good agreement for some concerned systems.

Electronic properties of liquid noble metal–Si alloys

The electrical resistivity, ρ, of liquid noble metal–Si alloys (M1−cSic, M=Cu, Ag, Au) increases rapidly with the addition of Si to liquid noble metals. The composition dependence of ρ exhibits a maximum at the composition c=0.3, 0.4 and 0.4 for liquid Cu–Si, Ag–Si and Au–Si, respectively. A positive to negative transition of thermoelectric power, S, is observed at c=0.3, 0.15 and 0.1 for liquid Cu–Si, Ag–Si and Au–Si, respectively. Their composition dependence of S reaches a minimum value in the composition range c=0.6–0.8. The experimental results of ρ and S have been analyzed using the Faber–Ziman theory. The composition dependence of χ for liquid Cu–Si and Au–Si alloys exhibits a clear deviation from a straight line on the noble metal-rich side. As a result, liquid Cu–Si and Au–Si alloys have a minimum in the composition dependence of paramagnetic susceptibility.

Study of diffusion coefficients in liquid noble metals

Molecular dynamic simulation technique is employed to determine self-diffusion coefficients and activation energies in liquid noble metals due to their importance in the industrial applications. The embedded atom method (EAM) potentials for silver and gold, developed for solid-state simulations, are shown to produce plausible results for liquid state. The simulated values of diffusion coefficients in the liquid state compare very well with the experimental and the calculated reported results. The calculated diffusion data follows Arrhenius equation which enables to find the prefactor and the activation energy for liquid state diffusion. The deduced activation energies of self-diffusion are found close to the experimental values.

APPLICATION OF THE EAM POTENTIALS TO THE STUDY OF DIFFUSION COEFFICIENTS OF LIQUID NOBLE AND TRANSITION METALS

The embedded atom method (EAM) potentials, originally proposed for solid state calculations, have been applied to investigate the atomic transport property namely the diffusion coefficients of liquid Ni, Cu, Ag and Au. Two different liquid state theories, specifically the linearized Weeks–Chandler–Andersen (LWCA) theory and the Gibbs–Boguliubov variational method (GB) are used to evaluate the packing fraction near melting temperature. Calculated values for the diffusion coefficients are compared with the available experimental data. Results of variational calculations are found to be better in agreement. Results of calculations also allow us to conclude that the concerning EAM potentials are transferable to the study of atomic transport properties of liquid transition and noble metals.

Correlation entropy and its relation to properties of simple liquid metals

In this paper we will provide a prescription for evaluating properties of liquid metals from measured diffraction data. This is investigated for liquid alkali, noble and typical polyvalent metals near the melting point. First, we have calculated the pair and triplet correlation entropies. Then, we have calculated the self-diffusion coefficient D using the excess entropy (ion configurational entropy). By means of D, we estimate the viscosity coefficient η and the surface tension γ. Predicted values of D, η and γ are reasonable in size in comparison with available experimental data.

Excess Entropy, Diffusion Coefficient, Viscosity Coefficient and Surface Tension of Liquid Simple Metals from Diffraction Data

In this paper we will provide a prescription for evaluating properties of liquid metals from measured diffraction data. When a liquid metal structure factor is of hard-sphere form, there is a correlation between structure factor and entropy. This is investigated for liquid alkali, noble and typical polyvalent metals. First of all, we calculate the pair and triplet correlation entropies (S(2) and S(3)) from the measured diffraction data. To evaluate the triplet correlation entropy S(3), we do not use the superposition approximation of Kirkwood. Next, assuming that the excess entropy (i.e., ion configurational entropy) SE is given as S(2)+S(3)+S(x), where S(x) denotes an entropy contribution arising from the four-body and higher-order terms of correlations, we calculate the self-diffusion coefficient D based on Dzugutov’s scaling law. By means of D, we estimate the viscosity coefficient η and the surface tension γ for these liquid metals using the Stokes-Einstein relation, the Born-Green equation and Fowler’s formula for the surface tension. We can find there exists a clear relationship between SE, D, η and γ. Predicted values of D, η and γ are reasonable in size in comparison with the available experimental data.

Formation of nano-scale icosahedral quasicrystalline phase in amorphous Zr60Ni25Ti15 alloy

The precipitation of icosahedral quasicrystalline phases (I-phase) from Zr-based amorphous alloys was reported initially by Koster et al. [1]. Recently, much attention has been paid to amorphous Zr–Al–TM– M (TM = Co, Ni, Cu, M = Ag, Pd, Au, or Pt) system [2–4] and Zr–TM–M system [5–7] for the formation of I-phases from amorphous phases by crystallization. A typical alloy composition for the Zr–Al–TM–M system is Zr65Al7.5Ni10Cu12.5M5. In these alloys, noble metals (Pd, Pt, Au and Ag) are added to the wellknown good metallic glass former Zr65Al7.5Ni10Cu17.5 [8] in order to stabilize I-phases. For the Zr–TM– M system, the noble metals also play an important role in the formation of I-phases. It is noticed that most of the above amorphous alloys exhibit a large supercooled liquid region, Tx(=Tx − Tg), where Tx and Tg are the crystallization and glass transition temperature, respectively. Such a large supercooled region means good glass-forming ability for an amorphous alloy. It also seems that the addition of noble metals is essential for the formation of I-phases in these Zr-based amorphous alloys. For example, no icosahedral phase was observed in the Zr70(Ni, Cu)30 amorphous alloy, while I-phases could be acquired in the quaternary, ternary, and even binary Zr70(Ni, Cu, Pd)30 amorphous alloys [7]. In order to determine the possibility of getting an I-phase from a Zr-based amorphous alloy without a significant supercooled liquid region and noble metals, a study was undertaken on the formation of a nano-scale I-phase in amorphous Zr60Ni25Ti15 alloy. The Zr60Ni25Ti15 alloy ingot was prepared by arc melting a mixture of pure Zr, Ni and Ti. From the alloy ingot, a ribbon with a cross section of 0.03 × 1 mm2 was produced by a single roller melt-spinning method in an argon atmosphere. Annealing of the specimen was performed in a differential scanning calorimetry (DSC) at a heating rate of 0.67 K/s. The microstructure was examined by a transmission electron microscope (TEM). The sample for TEM observation was prepared by the ion milling technique. The XRD pattern of the melt-spun Zr60Ni25Ti15 ribbon is shown in Fig. 1. The existence of a broad peak indicates the formation of an amorphous state. It is very clear that the as-quenched ribbon only contains a single amorphous phase. The DSC curve of the melt-spun Zr60Ni25Ti15 ribbon is shown in Fig. 2. We can see from this figure that the crystallization proceeds through two Figure 1 XRD patterns of the Zr60Ni25Ti15 ribbon: (a) melt-spun, (b) annealed to 685 K, and (c) annealed to 900 K at a heating rate of 0.67 K/s and then cooled rapidly in the DSC cell.

A molecular dynamics study of the transport coefficients of liquid transition and noble metals using effective pair potentials obtained from the embedded atom model

Using effective pair potentials obtained from the Voter and Chen version of the embedded atom model, we carried out molecular dynamics simulations to compute the diffusion coefficients and shear viscosities of liquid Ni, Pd, Pt, Cu, Ag, and Au. The results obtained agree satisfactorily with those derived in previous studies using the full Voter and Chen potentials.

Structural, Thermodynamic and Transport Troperties of Liquid Noble and Transition Metals

We have investigated a number of structural, thermodynamic and atomic transport properties of various liquid noble and transition metals. The underlying theory combines a simple form of the N-body potential and the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquid. The static structure factors calculated by using the VMHNC resemble, as expected, the hard sphere (HS) values. Consequently the HS model is used to calculate thermodynamic properties, viz. the specific heat, entropy, isothermal compressibility and the shear viscosity of liquid Ni, Cu, Ag, and Au. The results are in reasonable accord with the experimental values.

Liquid state structure of some noble and transition metals

The static structure factors, S( q), for a number of liquid noble and transition metals are calculated. The underlying theory combines together a simple form of the N-body potential and the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquid. The static structure factors calculated by using the VMHNC resemble the hard sphere (HS) and these are consistent with experiments.

Calculations of g(r) for Liquid Cu and Ni Using Many-Body

The pair distribution function, g(r), for Ni and Cu at various temperatures above melting are investigated by using the Finnis-Sinclair (FS) many-body potentials and the thermodynamically self-consistent Variational Modified Hypernetted Chain (VMHNC) theory. The overall agreement with experiment is reasonably good. The calculations indicate that the many-body interactions, precisely taken care of by the FS potentials, are important for the study of g(r) for the liquid transition and noble metals. The results also permit us to examine the applicability of the temperature independent approximation of the FS potentials.