Relationship between Pair Potentials and Liquid Structure

1973 ◽  
Vol 51 (17) ◽  
pp. 1831-1839 ◽  
Author(s):  
L. E. Ballentine ◽  
J. C. Jones
Keyword(s):  
Structure Factor ◽  
Liquid Metals ◽  
Pair Potential ◽  
Liquid Structure ◽  
Main Peak ◽  
Repulsive Core ◽  
Pair Potentials ◽  
Eigenvector Analysis ◽  
Hypernetted Chain ◽  
Generalized Eigenvector

The Percus–Yevick and hypernetted chain theories are used to investigate the sensitivity of the pair potential [Formula: see text] to errors in the measured structure factor S(K) for several liquid metals and nonmetals. The linear relation between small errors, [Formula: see text], is studied by means of a generalized eigenvector analysis. Only those combinations of errors in S(K) which correspond to large eigenvalues lead to significant uncertainties in [Formula: see text]. The general form of the dominant eigenvectors was found to be the same for all liquids studied, except near the critical point. With this same exception, the following conclusions hold: Errors in S(K) for small K have by far the greatest effect on [Formula: see text]; the depth of the attractive portion of [Formula: see text] is most sensitive to errors in S(K); the repulsive core of [Formula: see text] is insensitive to errors in S(K); and the height of the main peak of S(K) has very little effect on [Formula: see text].

Structure and forces in liquid metals and alloys

1987 ◽  
Vol 65 (3) ◽  
pp. 219-240 ◽  
Author(s):  
N. H. March
Keyword(s):  
Structure Factor ◽  
Alkali Metals ◽  
Surface Segregation ◽  
Liquid Metals ◽  
Pair Potential ◽  
Liquid Structure ◽  
Cooperative Effects ◽  
Inversion Procedure ◽  
Chain Approximation ◽  
Three Body

The so-called force equation relating the pair function g(r), the three-body correlation function, and the assumed pair potential [Formula: see text] is first discussed from the standpoint of extracting force fields from diffraction measurements of the structure factor of liquid metals. Recent progress has been possible in this area by making use of the modified hypernetted-chain approximation, including the bridge function.A discussion is then given that relates the bridge function to vacancy-formation energy in hot close-packed metals, and also to the structure factor of the liquid. The possible role of cooperative effects in liquid metals on the inversion procedure is considered, as is the relation between three-body direct and total correlation functions.Pressing further the relation between liquid structure just above the melting point and the hot solid, advances in the theory of freezing are considered. The so-called Verlet rule on the height of the principal peak of the structure factor at melting is considered in relation to Lindemann's Law.After a brief discussion of the relation between structure and forces in liquid-metal alloys, the theory of inhomogeneous systems used to discuss freezing is applied to liquid surfaces, and in particular to surface segregation. The final topic treated is that of the critical constants of the fluid alkali metals, where it is argued that Coulomb forces are of decisive importance.

A theoretical study of the structure and dynamics of amorphous Fe

1992 ◽  
Vol 70 (8) ◽  
pp. 627-630 ◽  
Author(s):  
Neelam Gupta ◽  
Kamal C. Jain ◽  
Arun Pratap ◽  
N. S. Saxena
Keyword(s):  
Transition Metal ◽  
Theoretical Study ◽  
Liquid Metals ◽  
Pair Potential ◽  
Good Qualitative Agreement ◽  
Isothermal Bulk Modulus ◽  
Structure And Dynamics ◽  
Pair Potentials ◽  
Molecular Dynamics Results ◽  
Theoretical Results

The extended theory of transition-metal potential, which includes the transition-metal d states, is used to obtain the effective interatomic interactions in terms of pair potential for amorphous Fe. Pair potential for amorphous Fe is also computed using a simple approach for liquid metals given by de-Angelis and March. We employ the so obtained pair potentials to calculate the longitudinal- and transverse-phonon eigenfrequencies using the theory of phonons in amorphous solids. The results for the phonon eigenfrequencies obtained from these potentials are in good qualitative agreement with the molecular-dynamics results as well as with the theoretical results of Bhatia and Singh. Computation of the Debye temperature and the isothermal bulk modulus also shows a close agreement with other results.

Density Dependent Potentials in Simple Liquids

1972 ◽  
Vol 50 (20) ◽  
pp. 2461-2463 ◽  
Author(s):  
P. A. Egelstaff ◽  
S. S. Wang
Keyword(s):  
Density Dependence ◽  
Structure Factor ◽  
Liquid Structure ◽  
Real Space ◽  
Wave Number ◽  
Liquid Alkali Metal ◽  
Lennard Jones ◽  
Pair Potentials ◽  
Effective Pair ◽  
Fermi Wave Number

The density dependence of effective pair potentials may be studied through the density dependence of the liquid structure factor. For a liquid alkali metal (Rb) it is suggested that the ρ1/3 behavior of the Fermi wave-number of the electron gas explains the ρ1/3 behavior of the liquid structure factor recently discovered by Egelstaff et al. For the Lennard-Jones fluid and for liquid neon it is suggested that a near ρ-independent potential gives rise to ρ-dependent changes in the liquid structure factor corresponding to changes in the number of nearest neighbors in real space. This suggestion is tested by comparison with experiment.

scholarly journals Self Diffusion in Liquid Metals

1975 ◽  
Vol 30 (5) ◽  
pp. 619-622
Author(s):  
R. V. Gopala Rao ◽  
A. K. Murthy
Keyword(s):  
Liquid Metals ◽  
Soft Part ◽  
Pair Potential ◽  
Spherical Model ◽  
Liquid Structure ◽  
Self Diffusion ◽  
Mean Spherical Model ◽  
The Mean ◽  
Square Well ◽  
Theory And Experiment

AbstractSelf-diffusion coefficients of liquid metals have been calculated according to the linear trajectory prescription. The soft part of the pair potential is being represented by a square well potential. The theoretical liquid structure factor, S(q), calculated under the mean spherical model (MSM) approximation, has been employed in the present calculations. The agreement between theory and experiment is encouraging and shows that the representation of the attractive forces by the square well potential is quite satisfactory for liquid metals.

On the Fluctuation Model of Diffusion in Liquid Metals

1968 ◽  
Vol 23 (6) ◽  
pp. 805-813 ◽  
Author(s):  
R. A. Swalin
Keyword(s):  
Temperature Dependence ◽  
Liquid Metals ◽  
Pair Potential ◽  
Constant Volume ◽  
Liquid Sodium ◽  
Pair Potentials ◽  
Good Pair ◽  
Experimental Values ◽  
Fluctuation Model ◽  
Good Agreement

In this paper further considerations has been given to the fluctuation model of diffusion, and equations have been derived which express the self-diffusivity of liquid metals as a function of temperature and pressure. For liquid metals which are characterized by pair potentials which are relatively deep compared with k T, D is predicted to vary in a linear fashion with T at constant volume. At constant pressure, the apparent activation energy is predicted to be equial to R T+R(β/β)T2 where β is the isothermal compressibility and β' is its temperature derivative. Further, the variation in the logarithm of D with respect to pressure is predicted to be equal to [ (1/2.3)β] (∂β/∂P) T . A test of the equations for liquid mercury shows good correlation between theory and experiment. For liquid metals which are characterized by a shallow well in terms of the pair potential, no simple statements can be made concerning the nature of the temperature dependence, and simple approximations cannot be made. A test of the derived equations is made for liquid sodium which fits this case and for which good pair potential data exist, and good agreement is obtained at 373 °K. The temperature dependence of D as a function of T at constant volume is derived, but cannot be tested because of insufficient experimental data.The case of thermodiffusion is discussed, and it is shown that experimental values of the heat of transport are consistent with predictions of the theory.

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