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Understanding the energy characteristics at the metal-organic interface is of great importance for the development of equipment and technologies in various industries. In this regard, there is a great interest in studying the processes occurring at this interface. Particularly noteworthy is the rapid growth of studies on the properties of metal-organic framework structures, which is associated with the possibility of synthesizing these structures with the desired properties by varying the lengths of the organic molecules connecting the atoms of metals or their oxides, as well as by selecting the chemical composition. In this paper, the values of the interfacial energy at the boundaries of the faces of an aluminum crystal with organic liquids are obtained within the framework of the electron-statistical method, taking into account the polarization of metal ions and molecules of the organic liquid, as well as the dispersion interaction of Wigner-Seitz cells on the interface. The dependence of the interfacial energy and corrections to the interfacial energy on the permittivity of the liquid and the orientation of the metal crystal is obtained. It is found that the dispersion correction makes a positive contribution while the polarization correction reduces the interfacial energy.

The active implementation of devices based on the use of the properties of the metal-organic interface makes it important to study characteristics of such interfaces, especially of the metal-organic framework structures. The creation of these structures with the necessary properties is possible since one can vary the elemental composition in the active metal centers as well as the organic ligands binding these centers. In this regard, understanding the properties and nature of the interaction at the interface of a metal with organic substances becomes of primary interest. In this work, within the framework of the electron-statistical method, a correction to the interfacial energy of cobalt at the interface with non-polar organic liquids for the dispersion interaction of the Wigner-Seitz cells is obtained. The dependences of the dispersion correction on the orientation of the metal crystal and the permittivity of the organic liquid are determined. It is shown that the contribution of the dispersion correction to the interfacial energy is positive and decreases with an increase of the permittivity of the liquid.

Calculations of the interphase energy of low-temperature modification of titanium at the boundary with nonpolar organic liquids are carried out within the framework of the electron-statistical method, corrections to the interphase energy for the dispersion interaction of Wigner-Seitz cells and the electron density oscillation in the transition layer, the polarization of surface metal ions and organic liquid in the field of a semi-infinite metal are obtained. When calculating the interphase energy, changes in all components of the metal bond energy in the transition layer are considered – the eigenenergies of the electron gas, the energies of the interaction of the electron gas with ions. The effect of an organic liquid on the orientational dependence of the interphase energy of alpha-titanium and the corrections to the interphase energy taking into account the permittivity of the organic liquid is established. It is shown that the dispersion and oscillation corrections increase the interphase energy, and the polarization correction reduces the interphase energy. A sharp anisotropy of the interphase energy and corrections is obtained for this titanium structure.

On the basis of the electronic-statistical method, a relationship is obtained and the surface energy and the work function of the electron of the faces of lithium crystals are estimated, taking into account the dispersion, polarization, and oscillatory interactions of the atoms of the surface layer. It was assumed that the crystal lattice has no defects. The expressions for the corrections and an analytical relationship between the work function of the electron and the surface energy are modified taking into account the type of the crystal lattice and the orientation of the faces. The work function of the electron and the surface energy of smooth faces are calculated at the limiting temperatures of the existence of polymorphic lithium phases. The influence of polymorphic transformations and temperature on the anisotropy is established. The temperature coefficient of the work function of an electron in a defect-free crystal is positive and amounts to about 0,1-1 meV. The calculation results are in good agreement with the experimental data for polycrystals.

The melting and crystallization temperatures have been calculated and the phase diagram of Pd — Pt metal particles of 10 nm in size has been constructed. The surface and interfacial energies, their temperature and size dependences were estimated by a modified electron-statistical method. It was found that the form of the phase diagram for Pd — Pt nanoparticles has significant differences from the diagram of bulk phases, including the melting-crystallization hysteresis.

On the basis of the electronic statistical method, expressions for the dispersion and polarization corrections to the surface energy of the crystal faces IA of metals at the boundary with vacuum are obtained and their value are calculated. Both corrections are highly anisotropic. The dispersion correction increases the surface energies of the faces (from 3 to 23 %), the polarization correction reduces them by less than 1 %. Taking into account these interactions improves the agreement between the calculated surface energy and the experimental data of the melts.

A method we developed for determining anisotropy of the interfacial energy in a solid system was used to investigate nickel nanocrystals on an oriented silicon substrate. Nickel particles were obtained by the vapor-liquid-solid mechanism, i.e. by vacuum deposition on a substrate. The surface of the sample was visualized by the atomic force microscopy in the tapping mode. A analysis of AFM images made it possible to establish the geometric characteristics of nickel crystals and to investigate the relief. Based on the data obtained, the model shape and position of the Wulf point of the equilibrium crystals on the substrate are determined. The dependences of the characteristic value A/V^(2/3) on the effective contact angle in two directions are constructed and it is shown that in this system the interfacial energy of the crystal-substrate interface is highly anisotropic.

We propose a technique for estimating the wetting and anisotropy of the interfacial energy at the interface between the metal particles (indium) with a substrate based on the construction of the Winterbottom equilibrium shape of the crystal. The effective contact angle and the ratio of interfacial energies at the particle-substrate interface are calculated from the experimental data of the geometric characteristics of the particles obtained by analyzing the AFM images of the samples. The obtained dependences are qualitatively consistent with thermodynamic states and known data for other systems.

Expressions have been obtained for estimating the interfacial energy of metallic thin films at the interface with an organic dielectric coating. The case of the boundary of the contact of cobalt films with polyatomic alcohols (diols) is considered. Comparison with the experimental data shows a good agreement between the theoretical model and real objects.

In this paper we have obtained polarization and dispersion corrections to the interfacial energy of the faces at the boundary between calcium and barium crystals of low-temperature modifications and nonpolar organic liquids using the electron-statistical method. We have shown orientation dependence of the corrections and interfacial energy of the crystals in view of polarization and dispersion corrections.

The interfacial energy of uranium boundary with alkali and alkaline-earth metals has been estimated by the electron-statistical method. It has been shown that alkali and alkaline-earth metals are strong surfactants relative to uranium. Formulas for polarization correction, external and temperature terms, have been obtained which take into account change of density at the contact boundary. The temperature contribution in the interfacial energy of crystal faces of three allotropic modification of uranium has been estimated. The influence of s-metal melts on the profile of electron density has been analysed.

Within the frames of a modified version of the electronic statistical theory, an amendment to the interfacial energy at the metal-nonpolar organic liquid interface on the polarization of metal ions of the transition layer in the field of a semi-infinite metal is obtained. An effect of the correction on the macroscopic dielectric permeability of the liquid and orientation of the metallic crystal is established.

Dependence of the surface energy of metal thin films on the monoaxies deformation of compression and stretching has been qualitatively described. Calculations made for films of tantalum and niobium by modified electron-statistical method. The influence of deformation on the electron density of the system and the Gibbs coordinate has been demonstrated. A weak nonlinear change of the surface energy with the monoaxies deformation has been determined.

The contribution of the dispersion interaction into the interfacial energy of lithium and sodium BCC-crystals has been found on the boundaries with non-polar organic liquids on the grounds of the electron-statistical method as well as the E.M. Lifshits theory.

We developed a modified version of the electron - statistical method of calculation of the temperature contribution to the interfacial energy of the metal on the boundary with non-polar organic liquids. The dependence of the temperature contribution to the interfacial energy of Sc , α- Ti and α- Co metal on the orientation of the crystal and the dielectric permeability of the liquid has been obtained.

On the bases of thermodynamic model we have obtained the ratio for the bond energy of alloy crystals. The modified electron-statistical method has reproduced size and concentration dependences of the surface energy of thin films of the transitional metal alloys.

The method to calculate the interfacial energy on the boundary with non-polar organic liquids has been developed within the electron-statistical theory. The dependence of interfacial energy of faces of alkali metal crystals bounding to hexane on the atomic number of the element has been obtained. The anisotropy of the interfacial energy has been found.

Electron-statistical method by Frenkel-Gambos-Zadumkin has been modified to determine the temperature dependence of interface energy of low dimensional metallic system on the interface with different surrounding. The temperature contribution of interface energy, which caused by changing the Fermi energy, has been estimated. The temperature and the dimensional dependences of temperature contribution of rhodium have been shown for the interfaces thin films – vacuum and nanopartical – self-melt.

The electron-statistical method is used to determine the dimensional dependences of the interfacial energy of the rhodium small particles on the boundary with self-melting. Interface energy was calculated for spherical and cubic particles. The oscillation and dispersion corrections were taken into account. The formulas for polarization correction and temperature contribution were modified.