Crystals cohesion energy

The crystal cohesive energy, E, in Fig. 21 could also be plotted along an ionicity axis, q, normal to the paper. The crystal electrostatic (Madelung) energy of mixed stacks clearly increase with q, so that the second valley may deepen with increasing q. The first valley for segregated stacks may initially deepen but becomes far less favorable... 

By atomic characteristics we imply some crystal characteristics which are determined by the total energy of the electron-nuclear system of the crystal, its bulk derivatives and interatomic spacing. These include, for example, the crystal cohesive energy, lattice spacings, various elastic moduli, etc. In the theory of the electron density functional, the expression for the total energy is of the form... 

The joint effect of multiple fields on the cohesive energy of nanocrystals can be integrated based on the rule of energy superposition [20]. Variation in these external stimuli provides perturbations in the crystal cohesive energy, based on the core-shell configuration. 

First, the stability of the fitted Llo structure relative to other crystal structure with the same composition can be studied. In the present case we calculated the cohesive energies of fully relaxed B2 and structure 40 compounds and found 4.41eV and 4.50 eV, respectively. These are both lower than the cohesive energy of the Llo structure. Structure B19 was also investigated but relaxation always transformed this structure into Llo. 

We will limit ourselves here to transition metals. It is well known that in these metals, the cohesive properties are largely dominated by the valence d electrons, and consequently, sp electrons can be neglected save for the elements with an almost empty or filled d valence shelP. Since the valence d atomic orbitals are rather localized, the d electronic states in the solid are well described in the tight-binding approximation. In this approximation, the cohesive energy of a bulk crystal is usually written as ... 

Morita, A., and Takahashi, K., Progr. Theoret. Phys. [Kyoto) 19, 257, Theory of cohesive energy of LiH crystal—the method of semilocalized crystalline orbitals."... 

One may expect that with increasing temperature the thermal expansion in the crystalline regions will lead to an enlargement of the chain cross-section in the crystalline phase which in turn will induce a decrease in the cohesion energy of the crystals thus causing a gradually lower resistance to plastic deformation. In order to minimize the effect of the surface layer, the influence of temperature on microhardness has been investigated in PE crystallized at 260 °C under a pressure of 5 Kbar 28). The decrease of MH with temperature for the above chain extended PE material is depicted in Fig. 11. The hardness decrease follows an exponential law... 

The materials for solid solutions of transition elements in -rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by crystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (VT ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, Co, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V, . Boron is a brittle material, indicating the accommodation of transition-element atoms in the /3-rh boron structure is associated with an increase in the cohesion energy of the solid. 

The interaction between particle and surface and the interaction among atoms in the particle are modeled by the Leimard-Jones potential [26]. The parameters of the Leimard-Jones potential are set as follows pp = 0.86 eV, o-pp =2.27 A, eps = 0.43 eV, o-ps=3.0 A. The Tersoff potential [27], a classical model capable of describing a wide range of silicon structure, is employed for the interaction between silicon atoms of the surface. The particle prepared by annealing simulation from 5,000 K to 50 K, is composed of 864 atoms with cohesive energy of 5.77 eV/atom and diameter of 24 A. The silicon surface consists of 45,760 silicon atoms. The crystal orientations of [ 100], [010], [001 ] are set asx,y,z coordinate axes, respectively. So there are 40 atom layers in the z direction with a thickness of 54.3 A. Before collision, the whole system undergoes a relaxation of 5,000 fsat300 K. 

There is a rough correlation between the hardnesses and the cohesive energies of molecular crystals as shown by Roberts et al. (1995). These authors studied crystals of 11 pharmaceutical compounds and found a linear correlation between their hardnesses and their cohesive energies. However, the data scatter substantially. The hardnesses range from about 1.0 (aspirin), through 5.0 (sucrose), to 10.0 (anthracene) kg/mm2. 

R. J. Roberts, R. C. Rowe, and P. York, The Relationship Between Hardness and Cohesive Energy for Some Organic Crystals, Pharmeceutical Sdiences, 1, 501 (1995). 

The crystal field effect is due primarily to repulsive effects between electron clouds. As we have already seen, the repulsive energy is of opposite sign with respect to coulombic attraction and the dispersive forces that maintain crystal cohesion. An increase in repulsive energy may thus be interpreted as actual destabilization of the compound. 

Table XI gives the room-temperature, atmospheric pressure crystal structures, densities, and atomic volumes, along with the melting points and standard enthalpies of vaporization (cohesive energies), for the actinide metals. These particular physical properties have been chosen as those of concern to the preparative chemist who wishes to prepare an actinide metal and then characterize it via X-ray powder diffraction. The numerical values have been selected from the literature by the authors.

---