Crystals total energy

Fig. 37. Distribution of energies of water molecules about bovine pancreatic trypsin inhibitor in the crystal. Total energy ( ) partitioned into contribution from water-water (D) water-protein (O) interactions. From Hermans and Vacatello (1980).

Figure 7 illustrates the changes in the crystal total energy as a function of the amplitude for a k = 0 optical phonon frozen... 

There was proposed a classification of one-sided phases, the composition of a phase at T=0 being chosen as a main criterion. "Genuine NS phases" remain one-sided in the entire temperature range, even at T—>0. The formation of such phases can be connected with a decrease in the crystal free energy under deviation from stoichiometiy due to an increase in the contribution of the electron subsystem to the crystal total energy and defect ordering. 

Feibelman P J 1987 Force and total-energy calculations for a spatially compact adsorbate on an extended, metallic crystal surface Phys. Rev. B 35 2626... 

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development... 

In crystals with the LI2 structure (the fcc-based ordered structure), there exist three independent elastic constants-in the contracted notation, Cn, C12 and 044. A set of three independent ab initio total-energy calculations (i.e. total energy as a function of strain) is required to determine these elastic constants. We have determined the bulk modulus, Cii, and C44 from distortion energies associated with uniform hydrostatic pressure, uniaxial strain and pure shear strain, respectively. The shear moduli for the 001 plane along the [100] direction and for the 110 plane along the [110] direction, are G ooi = G44 and G no = (Cu — G12), respectively. The shear anisotropy factor, A = provides a measure of the degree of anisotropy of the electronic charge... 

FIGURE 5.16 Crystal-field pictures for the low-spin d5 system in deformed octahedra. (a) relative energy of d-orbitals for an octahedron with strong crystal field (b) d-orbitals of the T2s set in a rhombically distorted octahedron (c) three possible electron configurations of increasing total energy (d) the term scheme for the configurations in (c). 

We have already mentioned that for sodium chloride approximately 1.78 times as much energy is released when the crystal lattice forms as when ion pairs form. This value, the Madelung constant (A) for the sodium chloride lattice, could be incorporated to predict the total energy released when 1 mole of NaCl crystal is formed from the gaseous Na+ and Cl- ions. The result would be... 

The adequacy of the spin-averaged approach has been confirmed in self-consistent spin-density-functional calculations for H in Si by Van de Walle et al. (1989). The deviation from the spin-averaged results is expected to be largest for H at the tetrahedral interstitial (T) site, where the crystal charge density reaches its lowest value. For neutral H at the T site, it was found that inclusion of spin polarization lowered the total energy of the defect only by 0.1 eV. The defect level was split into a spin-up and a spin-down level, which were separated by 0.4 eV. These results are consistent with spin-polarized linearized-muffin-tin-orbital (LMTO) Green s-function calculations (Beeler, 1986). 

The total energy of the system is one of the most important results obtained from any of the calculational techniques. To study the behavior of an impurity (in a particular charge state) in a semiconductor one needs to know the total energy of many different configurations, in which the impurity is located at different sites in the host crystal. Specific sites in the diamond or zinc-blende structure have been extensively studied because of their relatively high symmetry. Figure 1 shows their location in a three-dimensional view. In Fig. 2, some sites are indicated in a (110) plane... 

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