Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [M. L. Glasser, J. Math. Phys. 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [M. A. Stremler, J. Math. Phys. 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation

On the Structure of ZnI2{\rm ZnI_2}

A new structure for ${\rm ZnI_2}$ is proposed which it exists in tetragonal state. In this structure the ${\rm ZnI_2}$ molecule exists in a nonlinear array and forms the basis of the tetragonal unit cell with one basis per unit cell. The structural analysis based on the reflections listed in ASTM 30-1479 shows that the proposed structure is correct.Comment: six pages and four figures. Manuscript prepared in RevTe

Raoult's Formalism in Understanding Low Temperature Growth of GaN Nanowires using Binary Precursor

Growth of GaN nanowires are carried out via metal initiated vapor-liquid-solid mechanism, with Au as the catalyst. In chemical vapour deposition technique, GaN nanowires are usually grown at high temperatures in the range of 900-1100 ^oC because of low vapor pressure of Ga below 900 ^oC. In the present study, we have grown the GaN nanowires at a temperature, as low as 700 ^oC. Role of indium in the reduction of growth temperature is discussed in the ambit of Raoult's law. Indium is used to increase the vapor pressure of the Ga sufficiently to evaporate even at low temperature initiating the growth of GaN nanowires. In addition to the studies related to structural and vibrational properties, optical properties of the grown nanowires are also reported for detailed structural analysis.Comment: 24 pages, 7 figures, journa

Effective way to sum over long range Coulomb potentials in two and three dimensions

I propose a method to calculate logarithmic interaction in two dimensions and coulomb interaction in three dimensions under periodic boundary conditions. This paper considers the case of a rectangular cell in two dimensions and an orthorhombic cell in three dimensions. Unlike the Ewald method, there is no parameter to be optimized, nor does it involve error functions, thus leading to the accuracy obtained. This method is similar in approach to that of Sperb [R. Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably simpler and physically appealing. An important aspect of the proposed method is the faster convergence of the Green function for a particular case as compared to Sperb's work. The convergence of the sums for the most part of unit cell is exponential, and hence requires the calculation of only a few dozen terms. In a very simple way, we also obtain expressions for interaction for systems with slab geometries. Expressions for the Madelung constant of CsCl and NaCl are also obtained.Comment: To appear in Phy. Rev.