ISSN 2224087X (Print) ISSN 22240888 (Online)
Collected scientific papers "Electronics and information technologies"
(In 19662010 published under the title "Electrical engineering")
(Certificate of State Registration ÊÂ ¹176186468ÏÐ from February 11, 2011)
Issue 8, Pages: 143152 
DOI: https://doi.org/ 
The band structure and refractive parameters of potasium ammonium sulphate solid solution crystal 
V. Stadnyk, P. Shchepanskyi, M. Rudysh, R. Brezvin, ². Ìàtviishyn, L. Karpliuk, Z. Kohut 
In this work we present results of quantum chemistry calculations of the electronic and optical properties of the representative of potassium sulphate  ammonium sulphate system, K_{1.75}[NH_{4}]_{0.25}SO_{4} crystal. Current research was motivated by performed so far experimental study of refractive indices and birefringence dispersions of the crystal, which revealed the increase of optical indicatrix symmetry at room temperature, not detected in either K_{2}SO_{4} or (NH_{4})_{2}SO_{4} crystals. Thus we found interesting to investigate the peculiarities of electronic structure of specified compound along with comparison of theoretically deduced refractive parameters with experimental data. Ab initio calculations of the bandenergy structure, the distribution of the electronic density with contribution of individual atoms and dielectric function in this work are performed using ultrasoft pseudopotentials and generalized gradient approximation (GGA) in the framework of the density functional theory. As input parameters Xray analysis data served. Before the calculations the optimization of the structure was performed. Optimized structure was for about 9.3 % increased in volume; maximal deviation from the experimentally established lattice parameters is on the level of 5.4 %. The coordinates of special points were: Ã(0; 0; 0); F(0; 0.5; 0), Q(0; 0,5; 0.5) and Z(0; 0; 0.5). It is established that the band gap of the crystal is of a direct type and is equal Eg = 4.8 eV. The bottom of conduction band is formed mainly by the sstates of potassium atoms and the top of the valence band is formed by the oxygen pelectrons. Band structure of the crystal is characterized by a low dispersion of energy levels with an exception of lowest in conduction band in the vicinity of Brilluoin zone center which is rather typical for ABSO_{4}group crystals. The genesis of main bands of the crystal is established and contributions of individual atoms are discussed. Presence of NH_{4} complexes in the crystal leads to the decreasing of band gap value and insignificant changes in the band structure. Imaginary part of dielectric function is calculated from the momentum matrix elements between the occupied and unoccupied wavefunctions. From this, using KramersKronig relation its real part was obtained. Knowing the real and imaginary parts of dielectric function the spectral dependences of refractive indices were deduced. The crystal reveals normal dispersion for three crystal optics directions in a visible spectrum region and satisfy the relation n_{z} > n_{x} > n_{y}. Obtained results are in a good agreement with the experimental data. 

© Ivan Franko National University of Lviv, 2011
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