Structural energies of solids

As a paradigm for the type of work that has been done to determine the internal energy contribution to the free energy, fig. 6.6 shows the classic work of Yin and Cohen (1982) in which some of the possible competing crystal structures for Si 

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Abstract. This paper provides an overview of the title paper by Yin and Cohen. I will briefly review some of the background for this work, provide some details of the calculations and discuss how this paper has influenced the field. In particular, this paper led to the development of the first realistic calculations for the structural energies of solids. It was the origin of the pseudopotential density functional method applied to the solid state. 

The total structural energy of a solid using the model above has the form... 

We have developed a model to study the basic structural properties of solid C<,q. The model consists of two distinct types of intermolecular interactions. The dominant one is the van der Waals-type interactions between carbon atoms on different Cm molecules. A secondary short-range Coulomb interaction is modeled by a small charge transfer between the two types of bonds in the C60 molecule. In contrast to early calculations [6] which include the van der Waals interactions only, our model predicts correctly the observed cubic ground-state structure Pa3. Many structural properties calculated, such as the compressibility, cohesive energy, and specific heat, are in good agreement with experiments l7l. 

Solid solutions can form in metals if the atoms of which they are composed.are similar also, compounds can form. In such cases, expressions for the excess Gibbs energy of solid mixtures should contain a strain or mechanical energy term (which results from distorting the crystal structure to accommodate an atom of different size), a valence or coiilombic term to account for the difference in charge between the solute atom and the atoms of the host crystal, the noncoulombic interactions of the type we considered in discussing molecular fluids in Sec. 9.5, and perhaps a chemical reaction term to account for compound formation. Alloys, amalgams, and intermetallic compounds can occur in solids these more complicated situations will not be considered here. 

The carbon monoxide molecule is isoelectronic and isobaric with the nitrogen molecule, and has a very small dipole moment. The densities of the solid forms of the two are nearly the same. Assuming that they have the same crystal structure, calculate a value of the binding energy of solid carbon monoxide from that of nitrogen (Table 4.1) for comparison with the experimental value 2 09 kcal per mole. The polarizability of a CO molecule is 2-21 x 10" 40 F m2,and its ionization potential is 329 kcal per mole. 

An elementary approach for determining the structural energies of a solid is to eonstruct an algebraic representation of the interatomic force field. There are numerous obstacles to constructing such potentials. For example, changes in coordination, re-hybridization, charge transfer, and Jahn-Teller distortions are very difficult to incorporate in classical potentials. However, if the Coulomb forces play a dominant role in the chemical bonds present, it may be possible to obtain some useful results with interatomic potentials. This may be the case for materials subjected to high pressure situations. 

Theoretical work concerning structure and energy of solids could not represent major achievements until the advent of high power computers (supercomputers). 

The influence of the thermal and chemical history on the active state of powdered iron(III) oxide was assessed from values of the activation energy of radon diffusion, determined from the experimental results of DSA at temperatures below 0.5Tm, where is the melting point in Kelvin [16]. In this temperature range the activation energy of radon diffusion reflects the concentration and type of non-equilibrium defects remaining in the structure of iron(III) oxide after the decomposition of initial iron salts used for the preparation of the oxide samples. Hedvall [18] called this phenomenon the structure memory of solids . 

The development of plane-wave pseudopotential methods for electronic structure calculations of solids (e.g., Payne et al. 1992) has also opened the door to real first-principles molecular dynamics simulations using the algorithm of Car and Parinello (1985). Here, we let the wavefimctions become part of the dynamics of the system. To do this, we introduce a fictitious kinetic energy associated with a dynamical motion of the wavefunction ... 

A review of the applications of the pseudopotential method and total energy techniques to the electronic and structural properties of solids is presented. With this approach, it has recently become possible to determine with accuracy crystal structures, lattice constants, bulk moduli, shear moduli, cohesive energies, phonon spectra, solid-solid phase transformations, and other static and dynamical properties of solids. The only inputs to these calculations, which are performed either with plane wave or LCAO bases, are the atomic numbers and masses of the constituent atoms. Calculations have also been carried out to study the atomic and electronic structure of surfaces, chemisorption systems, and interfaces. Results for several selected systems including the covalent semiconductors and insulators and the transition metals are discussed. The review is not exhaustive but focuses on specific prototype systems to illustrate recent progress. 

As mentioned earlier, vegetable oils, because of their amphiphilicity, can adsorb onto surfaces and change various surface properties. Properties that can be modified due to adsorption of vegetable oils onto surfaces include surface tension of liquids, surface energy of solids, interfacial tension, boundary friction, adhesion, wettability, etc. The extent to which these properties are modified depends on a variety of factors, including the properties of the surfaces and the structure of the vegetable oil. Thus,... 

Good, R.J., 1977. Surface free energy of solids and liquids thermodynamics, molecular forces, and structure. J. Colloid Interface Sci. 59, 398-419. 

Structural Characterization of Solids 5.5.2. Inelastic Scattering of Low-Energy Neutrons... 

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