Calculation of Sound Velocities of Liquid Metals at their Melting Point via the Percus-Yevick Theory of Melting

Abstract

In this brief note, we utilize the 3N collective coordinate theory of liquids of Percus and Yevick¹ as applied to the phenomenon of melting by Omini² to calculate the sound Velocities in various simple liquid metals at their melting temperatures. We perform this calculation by taking derivatives of Omini's² calculated Percus-Yevick dispersion relations for their “liquid phonon” collective coordinate elementary excitations of the liquid. We compare these calculated sound velocities with experimental data, where possible, to ascertain the validity of the liquid phonon dispersion relation as a source of sound velocities.     

Virtual Crystal Model of Melting and the Structure Factor of Liquid Alloys

Abstract

In this paper, we extend the theory of melting entropy of metals, of Omini, based on the Percus-Yevick collective coordinate theory of liquids, to binary liquid alloys. We reformalate Omini's use of the Percus-Yevick theory to include binary liquid alloys and calculate the long wavelength limit of the binary liquid alloy structure factor as a function of solute concentration for the systems: Li-Na, K-Rb. Rb-Cs, Al-Zn, Zn-Ca and AI-Ga which are the most nearly equi-valent and equi-volumeatom pairs Omini worked with.     

Additivity of Sound Velocity in Binary Liquid Mixtures

Ideality and additivity of sound velocity in liquid mixtures are discussed. The methods of calculation of deviations of sound velocity from theoretically predicted values are analyzed using literature data for 24 different binary liquid systems. Calculations of such deviations, assuming linearity with mole fraction of a component, were found to be wrong. It is also shown that the Nomoto relation predicting the sound velocity in liquid mixtures yields results similar to those of the equation of Ernst et al., while the Van Dael model often fails. The validity of Rao's hypothesis on additivity of molar sound velocities (Rao constant) has been confirmed.     

Excess molar volumes and ultrasonic studies of dimethylsulphoxide with ketones at T = 303.15 K

Excess molar volumes (V^E) and ultrasonic sound velocities at T = 303.15 K and ambient pressure have been measured as a function of composition for the binary liquid mixtures of dimethylsulphoxide (DMSO) with ketones. The ketones studied in the present investigation include ethyl methyl ketone (EMK), diethylketone (DEK), methyl propyl ketone (MPK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The V^E values were measured using a dilatometer and were positive over the entire mole fraction range for all systems except in the binary system DMSO with EMK where the V^E exhibits an inversion in sign. The experimental V^E values have been correlated using Redlich–Kister and Hwang et al. equations. The ultrasonic sound velocities for the above systems have been measured with a single crystal interferometer at a frequency of 3 MHz. The sound velocity (u) data have been used to calculate isentropic compressibility (K_s) and deviation in isentropic compressibility (ΔK_s) over the entire range of volume fraction. The sound velocity data have been predicted in terms of free length theory (FLT), collision factor theory (CFT), and Nomoto relation. The results reveal that all the theories gave a satisfactory estimate of the sound velocity. The deviations in values of isentropic compressibility (ΔK_s) were negative over the entire range of volume fraction in all the binary liquid mixtures. The results are interpreted with respect to possible molecular interactions between components.     

Entropy of Mixing of Compound Forming Liquid Binary Alloys Using Flory's Formula

Abstract

We demonstrate how the formula we proposed recently for the effective volume can be applied to improve Flory's formula so that the entropy of mixing of liquid binary alloys can be determined theoretically with good accuracy. The results are distinctly better than in the hard sphere system for compound forming alloys.     

Liquid phase separation of ternary Al–In–Sn/Ge monotectic type alloys investigated with calorimetric method

The phase equilibrium, thermodynamic properties and liquid demixing patterns for binary Al_100−xIn_x, ternary (Al_100−xIn_x)₉₀Sn₁₀ and (Al_100−xIn_x)₉₀Ge₁₀ (x = wt.%) alloys are investigated by differential scanning calorimetry (DSC) method. The corresponding phase diagrams are experimentally established, and it is found that both monotectic temperature and critical temperature for immiscibility gap decrease when either Sn or Ge is added to binary Al_100−xIn_x alloys. The enthalpy of fusion for binary Al–In alloys, ternary Al–In–Sn and Al–In–Ge alloys shows linear functions with In content, and the introduction of Sn and Ge elements decreases the enthalpy of fusion. The liquid phase separation mechanism is discussed in relation to the DSC curves and solidified microstructures. It is demonstrated that the core and shell phases can be altered by the addition of Ge element in (Al_100−xIn_x)₉₀Ge₁₀ alloys as compared with those in binary Al_100−xIn_x and ternary (Al_100−xIn_x)₉₀Sn₁₀ alloys. This provides an effective way to switch the inner and outer phases for core–shell structure.     

Study of molecular interaction in binary liquid mixtures of ethyl acetoacetate with chloroform and dimethylsulphoxide using excess acoustic parameters and spectroscopic methods

Densities and ultrasonic velocities were measured for binary liquid mixtures of ethyl acetoacetate (EAA) with chloroform (CHCl₃) and dimethylsulphoxide (DMSO) over the entire composition range. These experimental values were used to calculate the adiabatic compressibility (βs), intermolecular free length (L_f), excess molar volume (V^E), excess adiabatic compressibility (β_s^E) and excess intermolecular free length (L_f^E) for the liquid mixtures under consideration. In all the excess parameters, a positive deviation was observed in CHCl₃–EAA binary mixture, whereas a slight negative deviation was found for EAA–DMSO binary liquid mixture. These deviations were explained in terms of molecular interactions between like and unlike molecules and further affirmed by UV–Vis spectroscopic measurements in terms of polar and non-polar environment in the close proximity of solvatochromic dye. Fourier transform infrared spectroscopy (FT-IR) and proton-nuclear magnetic resonance (H¹ NMR) measurements have also been done to explain the molecular interaction in the binary liquid mixtures.     

A Model of Resonance Scattering in Liquid Na[sbnd]Pb Alloys

Abstract

The curve of the electrical resistivity of liquid Na[sbnd]Pb alloys has a large maximum around the composition of Na₄Pb corresponding to a minimum value of the concentration-concentration fluctuation in the long wavelength limit, S_cc (0). The maximum in the resistivity curve is interpreted in terms of a resonance scattering of the conduction electrons by the short range ordered ‘complex’, based on the t-matrix formulation and with the help of thermodynamic data of these alloys.     

Excess molar volumes and ultrasonic studies of N-methyl-2-pyrrolidone with ketones at T = 303.15 K

Excess molar volumes (V^E) and ultrasonic studies at T = 303.15 K and atmospheric pressure have been measured over the whole composition range for the binary mixtures of N-methyl-2-pyrrolidone (NMP) with ketones. The ketones studied in the present investigation include methyl ethyl ketone (MEK), diethylketone (DEK), methyl propyl ketone (MPK), methyl isobutyl ketone (MIBK), and cyclohexanone (CH). The V^E values were measured using a dilatometer and were negative over the entire mole fraction range for NMP with MEK, DEK, MPK, and MIBK and were positive for NMP with CH. The ultrasonic sound velocities for the above systems were measured with a single crystal interferometer at a frequency of 3 MHz. The sound velocity (u) results have been used to calculate isentropic compressibility (K_s) and deviation in isentropic compressibility (ΔK_s) over the entire range of volume fraction. The sound velocity results have been predicted in terms of free length theory (FLT), collision factor theory (CFT), and Nomoto relation. The results reveal that all the theories gave a satisfactory estimate of the sound velocity. The deviation values of the isentropic compressibilities (ΔK_s) were negative over the entire range of volume fraction in all the binary liquid mixtures except in the binary system NMP with CH, where we observed positive ΔK_s values. The results are interpreted on possible molecular interactions between components.     

Physicochemical Methods Used to Study Internal Structures of Liquid Binary Mixtures

Abstract

Different methods, based on application of studies of intensive physicochemical properties of liquid binary mixtures and ¹H-NMR spectral measurements, used in the analysis of intermolecular interactions and estimation of the internal structure of these mixtures and here reviewed.     

Thermodynamic properties of binary mixtures containing 1-alkanols

Densities (ρ) of pure liquids and their mixtures have been measured at 303.15 and 313.15 K and atmospheric pressure over the entire composition range for the binary mixtures of benzylalcohol with 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol by using Rudolph Research Analytical digital densitometer (DDM-2911 model). Further, the ultrasonic sound velocities for the above said mixtures were also measured at 303.15 and 313.15 K. The measured density data were used to compute excess molar volumes (V ^E) and these were compared with the values obtained by Hwang equation. Isentropic compressibility (κ _S) and excess isentropic compressibilities (κ _S ^E ) were evaluated from experimental sound velocity and density data. Moreover, the experimental sound velocities were analyzed in terms of theoretic models namely, collision factor theory and free length theory. The experimental results were discussed in terms of intermolecular interactions between component molecules.     

Volumetric, Ultrasonic and Transport Properties of Binary Liquid Mixtures Containing Dimethyl Formamide at 303.15 K

Excess volumes （v^E）, ultrasonic velocities （u）, isentropic compressibility （△Ks） and viscosities （η） for the binary mixtures of dimethyl formamide （DMF） with 1,2-dichlorobenzene, 1,3-dichlorobenzene, 1,2,4-trichlorobenzene, o-chlorotoluene, m-chlorotoluene, p-chlorotoluene, o-nitrotoluene and m-nitrotoluene at 303.15 K were studied. Excess volume data exhibit an inversion in sign for the mixtures of dimethyl formamide with 1,2- and 1,3-dichlorobenzenes and the property is completely positive over the entire composition range for the mixtures of dimethyl formamide with 1,2,4-trichlorobenzene, o-nitrotoluene and m-nitrotoluene. On the other hand, the quantity is negative for the mixtures of dimethyl formamide with chlorotoluenes. Isentropic compressibility （Ks） has been computed for the same systems from precise sound velocity and density data. Further, deviation of isentropic com- pressibility （△Ks） from ideal behavior was also calculated. AKs values are negative over the entire volume fraction range in all the binary mixtures. The experimental sound velocity data were analysed in terms of Free Length Theory （FLT） and Collision Factor Theory （CFT）. The viscosity data were analysed on the basis of corresponding state approach. The measured data were discussed on the basis of intermolecular interactions between unlike molecules.     

Excess Acoustical and Volumetric Properties and Theoretical Estimation of Ultrasonic Velocities in Binary Liquid Mixtures of 2-Chloroaniline with Acrylic Esters at 308.15 K

The ultrasonic velocities (u) and densities (??) for three binary mixture systems of 2-chloroaniline (CA) with ethyl acrylate (EA), butyl acrylate (BA), and 2-ethylhexyl acrylate (EHA) were measured over the entire mole fraction range at the temperature 308.15?K, including those of pure liquids. From these data, the deviations in ultrasonic velocity (??u), the excess molar volumes ( $V_{\mathrm{m}}^{\mathrm{E}}$ ), deviations in excess molar volume ( $\delta V_{\mathrm{m}}^{\mathrm{E}}$ ), deviations in isentropic compressibility (??k _S), excess intermolecular free lengths ( $L_{\mathrm{f}}^{\mathrm{E}}$ ), and excess acoustic impedances (Z ^E) have been calculated. The variations of these properties with solution composition are discussed in terms of molecular interactions among unlike molecules of the mixtures. The excess and deviation functions have been fitted to Redlich-Kister type polynomials and the corresponding standard deviations ??(Y ^E) have been calculated. The deviations and excess values were plotted against the mole fraction of CA over the whole composition range. The $V_{\mathrm{m}}^{\mathrm{E}}$ and ??k _S values are negative in the EA + CA and BA + CA systems but are positive in the EHA + CA system, which indicates the presence of specific interactions between unlike molecules. Further, theoretical values of the sound velocity in these mixtures have been evaluated using various theories and have been compared with experimental sound velocities to verify the applicability of such theories to the investigated systems. Two types of polynomial equations, f(x) and g(x), have been fitted to experimental values of ultrasonic velocities. The sound velocities obtained by these polynomials have extremely small deviations from the experimental values.     

Theoretical investigation of the viscosity of some liquid metals and alloys

The viscosities of some liquid metals and liquid binary alloys have been determined using the theoretical model developed by Morioka et al. (Z. Metallkd. 93, 4 (2002)). The model was applied successfully to the liquid mono-component metals Hg and Na and to the liquid binary alloys Hg–Na, Ag–Cu, Bi–Sn and Ag–Sb. The model successfully described the temperature dependence of viscosity for Hg and Na for a wide range of temperatures. The values of the adjustable parameters k and z were obtained for Hg and Na. For the liquid binary alloys, calculations were done at a particular temperature for each alloy and our results show that for Hg–Na and Ag–Cu there are both qualitative and quantitative agreements between calculated and experimental viscosity data. However, Bi–Sn and Ag–Sb manifested significant levels of quantitative discrepancies between calculated and experimental viscosity data.     

Improved Flory Formula for the Entropy of Mixing of Binary Liquids

Abstract

A simple model for the entropy of mixing of the compound forming binary alloys is proposed. It is shown that the entropy of the associates is proportional to the relative volume contraction of the liquid alloys.     

Chemical potentials,concentration fluctuations,etc., in binary metal alloys

Abstract

Relationships among transport parameters and the mean square composition fluctuations as determined by measurements of the chemical potentials are described for a variety of binary liquid metal alloys. The measurement of the chemical potential is described and the thermodynamic basis for the analysis given in terms of the concentration correlation functions as well as more traditional thermodynamic parameters. Alloys involving group III_A metals with Te are used as an example     

室温离子液体FeCl3-BPC体系的研究

利用差示扫描量热法(DSC)建立了无水三氯化铁和氯化正丁基吡啶(BPC)二元体系相图. 依据相图, FeCl₃和BPC形成室温离子液体的窗口是x＝0.26～0.58; 室温离子液体的深度是80 ℃. 利用UHF/6-31G^*对FeCl₃, FeCl₄^－, Fe₂Cl₇^－等配合物的几何结构、键长、能量和Raman频率进行优化, 从头算和Raman光谱证实了相图中FeCl₃摩尔分数x＝0.50处有稳定化合物存在, FeCl₄^－是主要阴离子; x＝0.67处, FeCl₄^－, Fe₂Cl₇^－是主要阴离子.     

Structure of Liquid Pb-Bi Alloys by X-ray Diffraction

Abstract

X-ray diffraction measurement were made at temperatures about 50°C above liquidus in the Pb-Bi system. Three partial structure factors S_ij(Q) were evaluated from the observed X-ray intensities assuming that each S_ij(Q) is independent on the relative abundance of the constituent elements in the alloys. The partial reduced distribution functions G_ij(r) were also calculated. The functions S_ij(Q) and G_ij(r) have maxima which lie between those of the pure elements. The radii of the first coordination sphere show a linear dependence on the concetration as expected from random distribution of the atoms in liquid Pb-Bi alloys. A comparison was made between the partial and total structure factors obtained in this work and those calculated from the hard sphere model. Adequate agreement was obtained on the first peak, but good agreement of the damping behaviour and phase was not necessarily found.     

Non-monotonic behaviour with concentration of the surface tension of certain binary liquid alloys

The surface tension σ(c) of most liquid binary alloys usually varies with concentration c in a monotonic way between the values σ₁ and σ₂ of the two pure metals, and this behaviour is well explained by current models. Some alloys show deviations from this ideal behaviour. One of those is Fe–B. The surface tension of this liquid alloy shows a minimum at 17 atomic % B, which corresponds well with the composition of the eutectic point in the phase diagram, followed by a maximum at a concentration of 24 atomic % B or higher. The usual models for the surface tension of liquid binary alloys do not explain those exceptional features, and we propose that a model involving the concentration fluctuations in the liquid alloy has the proper ingredients to account for the features in Fe–B and similar alloys.