The absolute thermoelectric power of polyvalent liquid metals

Results on the measurement of the absolute thermoelectric power of ten polyvalent liquid metals (Al, Bi, Cd, Ga, Hg, In, Pb, Sn, Tl, Zn) from their melting points to about 750°C are reported. The electrical resistivities and the absolute thermoelectric powers of these metals have been calculated using the latest available data on structure factor and Harrison and Animalu form factors. These are compared with the experimental values. It is seen that whereas the predicted and experimental values of the electrical resistivities are in reasonable agreement, those for the absolute thermoelectric power are not. It is suggested that the experimental data on the absolute thermoelectric powers and the resistivities of liquid metals may be used to find the magnitude of the form factor at K = 2k _F.     

A new scheme for calculation of effective pair potentials for liquid metals

A new scheme based on the Singwi et al. theory for an interacting electron gas is proposed for calculating pair potentials for liquid metals and applied to liquid sodium and rubidium. The resulting pair potentials are in much better agreement with the pseudopotential calculations than any of the three usual approximations, PY, HNC or BG used in the literature.     

Pair potentials and structure factors of liquid alkali metals

Summary Measured structure factors of liquid alkali metals are examined in the framework of screened pair potential theory. Information on the main attractive well in the effective pair potential is obtained from the structural data by an approximate method stemming from an optimized random-phase treatment of the indirect ion-ion attraction. The results are compared with a variety of theoretical pair potentials in the cases of sodium and potassium, after a test of the method against computer simulation data on a model for rubidium. Results for the other alkali metals are also given and discussed. The small-angle scattering region is then examined in considerable detail, with special attention to the possibility of a linear term in a series expansion of the structure factor at very small momentum transfer. Although sensitivity to both the bare electron-ion coupling and the local field factor in the screening function is demonstrated and analysed, no linear term of the magnitude reported in recent X-ray diffraction experiments is found in the present theoretical framework.

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Riassunto Il lavoro discute i fattori di struttura misurati nei metalli alcalini liquidi nell'àmbito della teoria di potentiziali di coppia schermati. L'inversione dei dati strutturali permette di ottenere informazioni sulla buca attrattiva nel potenziale, che è confrontata con potenziali teorici dopo un controllo del metodo d'inversione su dati di simulazione. Si analizza quindi il comportamento del fattore di struttura a piccoli numeri d'onda, in relazione all'osservazione di un termine lineare nella figura di diffrazione di raggi X.

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Резюме Измеренные структурные факторы жидких щелочных металлов исследуются в рамках теории экранированных парных потенциалов. Из структурных данных получается информация об основной яме притяжения в эффективном парном потенциале. Полученные результаты сравниваются с целым рядом теоретических парных потенциалов в случаях натрия и калия. Предложенный метод проверяется посредством компьютерного моделирования для рубидия. Также приводятся и обсуждаются результаты для других щело ных металлов. Подробно исследуется область малоуглового рассеяния, уделяя особое внимание возможности существования линейного члена в степенном разложении структурного фактора при очень малых передаваемых импульсах. Анализируется чувствительность предложенного подхода в связи с обнаружением линейного члена в экспериментах по дифракции рентгеновских лучей.

     

A relation between structure and pair potential for liquid metals

We emphasize the importance of considering the relationship between the structure of a liquid and the interatomic potential directly from the point of view of wave vector space (k space). Although the Ornstein-Zernike equation was not originally derived from this point of view, this equation when transformed into the k-space representation has direct physical content, when coupled with a normal mode representation according to the approaches of Pines and Bohm (1952), and Percus and Yevick (1958). These normal modes are defined isothermally, and the relation to the dynamical modes of the liquid is discussed. The use of a simple k-space relationship between the transform of the Ornstein-Zernike direct correlation function and the transform, V_k , of the interatomic potential is explored. This leads to a correspondingly simple relationship between the structure factor and the interatomic potential. It is equivalent to a generalized Debye-Hückel equation and is expected to be valid only under special circumstances; namely, where the potential is long range in a particular sense and the small k behaviour of V_k is dependent mainly upon this long-range behaviour and relatively insensitive to details of the potential at short distances. It is noted that these conditions appear to be met reasonably well for the liquid alkali metals. The comparison of theory and experiment is somewhat uncertain because of incomplete experimental data on the structure factor as well as unresolved theoretical issues.     

液态金属结构研究新进展

文章介绍了用内耗方法研究金属液态结构的新进展，发现了随温度变化金属液态结构发生不连续的变化，并经差热分析、X射线衍射等实验证实了这种变化．这对认知金属液态结构提供了新的实验依据。     

New pair potentials from an improved born-green integral equation: Application to liquid metals

With an improvement of the superposition approximation in the Born-Green integral equation recently proposed an attempt is made to extract new effective pair potentials from structure factors of simple liquids. The improvement is obtained by taking the first three terms of a hard-core density expansion of the triplet correlation function. The method of calculation is based on the solution of the integral equation in k-space. It is shown that the resulting potential of the improved Born-Green equation from a hard-core structure factor actually is hard-core like contrary to the Born-Green result. From measured structure factors of some simple liquid metals (Na-100°C, Al-670°C and Ni-1600°C) pair potentials are determined. With this application a significant improvement over the Born-Green theory can be achieved. In comparison to the old discrepancy between the Born-Green equation and theoretical models the results agree very well with theoretical calculations in the repulsive range of the potential.     

液态金属结构研究新进展

文章介绍了用内耗方法研究金属液态结构的新进展,发现了随温度变化金属液态结构发生不连续的变化,并经差热分析、X射线衍射等实验证实了这种变化.这对认知金属液态结构提供了新的实验依据.     

Liquid metal pair potentials from structure data

In linear screening theory, the zeroth order result is the equality of the potential of mean force and the pair potential. The Kirkwood superposition approximation holds to the same order.The next order yields an equation for the pair potential identical with the first order iteration of Johnson and March from the Born-Green equation.     

Construction of muffin-tin potentials for liquid metals

We propose a method of constructing muffin-tin potentials for liquid metals in which the structure of the liquid is explicitly incorporated through the pair-correlation function. It is shown that for the liquid alkalis, the structure has a significant effect on the potential, however, the muffin-tin potentials of liquid noble and transition metals like Cu, Fe, and Ni are insensitive to the structure. Our structure based potentials for the liquid alkalis give resistivities in much better agreement with experiment compared to those calculated from the conventionally constructed potentials.     

Electronic structure of liquid metals

A review is given of the electronic structure of liquid metals. The theoretical formalism is developed in terms of the density matrices of the system, and the conditions under which these can be obtained are described, and the limitations found at present. The experimental material is then reviewed and it is shown how experimental results are interpreted in terms of values and averages over the density matrices.     

Computer simulation of the structure of liquid cesium and determination of the pair potentials over a wide temperature range

Using diffraction data for liquid cesium structure over a wide temperature range, models of liquid cesium are constructed and the effective pair potentials are extracted using the theory of liquids. The iterative procedure proposed by L. Reatto is used. In the range 323-1923 K the pair potentials are weakly temperature-dependent. The potentials extracted from the diffraction data differ from the potentials calculated using the Animalu-Heine pseudopotential. The self-diffusion coefficients in liquid cesium are determined. Their temperature dependence is described satisfactorily by a power-law function. Zh. éksp. Teor. Fiz. 115, 50–60 (January 1999)     

碱基序列对DNA分子电子结构的影响

将DNA分子看成一维二元随机序列，利用负本征值理论计算其态密度，针对碱基对分布和相对含量等参量，讨论了DNA分子的电子结构.结果表明碱基对分布和相对含量都对电子能态结构影响较大，说明碱基序列对DNA分子的电子结构影响很大. 关键词： DNA分子 电子态密度 碱基对     

On the electronic structure of liquid metals

We consider the electronic structure of liquid metals as a problem of multiple scattering. The total scattering operator is developed in terms of the reaction operators of a single scattering event, having a ‘standing wave’ boundary condition. This method has several advantages with respect to the approach where the total scattering operator is developed in terms of the scattering operators of a single scattering. Since the reaction operators are hermitian, the occurring perturbation expansions have a real perturbation parameter, which is more easily handled. Furthermore, if in the expansion of the total scattering operator, only terms up to the second order are maintained, this approximate expression satisfies already the ‘optical theorem’, just as the exact total scattering operator. Finally, spurious damping terms are eliminated at the outset. For very dense systems we obtain practically non-attenuated waves and this can be understood as if the damping due to a single scattering event is compensated by the reaction of the surrounding scatterers.     

Interionic pair potentials and partial structure factors of compound-forming quaternary NaSn liquid alloy: First principle approach

In this paper formulae for partial structure factors have been used to study partial structure factors of compound-forming quaternary liquid alloys by considering Hoshino’s m-component hard-sphere mixture, which is based on Percus-Yevic equation of Hiroike. Formulae are applied to NaSn (Na, Sn, NaSn, Na₃Sn) which is considered as a quaternary liquid mixture with the formation of two compounds simultaneously. We have compared the total structure factors for ternary and quaternary alloys with experimental total structure factors which are found to be in good agreement. This suggests that, for suitable stoichiometric composition, two compounds are formed simultaneously. The hard-sphere diameters needed have been calculated using Troullier and Martins ab-initio pseudopotentials.      

The change in the structure of liquid metals at high temperatures

The structures of the models of the Lennard-Jones liquid and mercury, cesium, and rubidium melts have been investigated. According to the local order dominant in a system, three regions have been selected in the phase diagrams of the models. For the Lennard-Jones model, the transition between the selected regions corresponds to a change in the asymptotic behavior of the radial distribution function. For the Hg, Cs, and Rb models, the position of the boundaries between these regions correlates with the specific features of the physical properties of these materials.     

On the electronic structure of liquid transitional metals

The density of states of a narrow non-degenerate (s) band is studied in the tight binding approximation. In the first part, we relate its successive moments to correlation functions of increasing order, averaging over atomic pairs overlap integrals. This method could be, in principle, extended to the d band of liquid transitional metals. In a second part we discuss the values of the first moments and compare them to those of the solid. Then, using some approximations for the n atom correlation functions, we obtain different approximate forms of the density of states.     

On the electron band structure of liquid metals

The electronic structure and the density of states of simple liquid metals is discussed on the basis of a nonlocal and energy-dependent pseudopotential of the Phillips-Kleinman type. As an example we treat lithium. To calculate this pseudopotential we need to know the states and the eigenvalues of the liquid metal ion cores. For these quantities we use: first, the core data of the free atom; second, of the free ion; third, the data we have determined from the measured phonon dispersion curves. The deviations between the band structures, the density of states as calculated with these pseudopotentials and those of free electrons are considerable.