Calculation of Lattice Parameters and Energy Band Structure and Density of States the β-zrncl with Ab Initio

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1 International Journal of Scientific Research in Knowledge (IJSRK), 1(8), pp , 2013 Available online at ISSN: ; 2013 IJSRPUB Full Length Research Paper Calculation of Lattice Parameters and Energy Band Structure and Density of States the βzrncl with Ab Initio Khatereh Sarvazad*, Soroosh Zarghani Department of Physics, Abadan Branch, Islamic Azad University, Abadan, Iran *Corresponding Author: Received 18 April 2013; Accepted 29 June 2013 Abstract. In this article we will compute structural parameters, band structure and density of for the β ZrNCl compound, based on the Density Functional Theory and the solution of the KouhanSham equations. The calculations have been done through PWscf software. In this study, soft pseudopotentials have been used for this compound. The volume of βzrncl unit cell decreases by increase of pressure. The pressure may cause different effects from various directions on the bonds. By increasing the pressure, the amount of decrease in c constant is 1.3 more than of a constant and the reason is that βzrncl is an anistropical structure. Since the compressibility is low, it can be said this compound is very hard. The band structure shows that this compound is a semiconductor with an indirect bandgap of 2.75 ev. By the partial density of, it is identified that the Nitrogen atom plays an important role in β ZrNCl properties and the electrons of P orbital in the N atoms are very effective. The calculations have a good correlation with the experimental results. Key words: density functional theory structural parameters pseudopotential lattice constant band structuredensity of. 1. INTRODUCTION Layered compounds have attracted a great deal of attention due to their structural flexibility and interesting physical properties including superconductivity. Zirconium nitride chloride have two forms: form α low temperature with layered structure type FeOC 1 and form β high temperature with layer structure type CdBr 2. The form α is very resistant in humidity while the form β which is considered in the research is stable even in the water. βzrncl has been found by Yamanaka in 1996 (Yamanaka, 1996). This compound is a special layered structure and is composed of structural slabs of {Cl Zr N N Zr Cl}. Three such slabs are stacked rhombohedrally along the caxis to build the unit cell (Chen, 2001). βzrncl was prepared by the reaction of Zr (99.9%,325 mesh) with NH 4 CI(99.5%)at C for 30 min under the flow of NH 3 gas(99.9,20 50cm 3 /min). Obtained samples were purified by a chemical vapor transport method (Kawaji, 1997; Yamanaka, 1998). This composition is an ntype semiconductor with an activation energy of 5060 mev and it has a band gap of 3.4 ev(ohashi, 1989). Upon Li intercalation, the system turns into a metal and superconducting at low temperatures. This is the first superconducting layered nitride (Taguchi, 2006; Takano, 2008). Figure (1) shows the crystal structure of βzrncl (Shamoto, 1998). According to the studies, very few theoretically studies have been done on this material. In this paper, calculations are performed on the structural and electronic properties of the βzrncl composition which include computing the lattice parameters, equilibrium volume V 0,total equilibrium energy E 0, bulk module B 0, its drive B 0`, compressibility, band structure, and density of the s which later,computation and comparing the results made by the other researcher will be studied. Fig. 1: The crystal structure βzrncl 2. MATERIALS AND METHODS The calculations have been done by using pseudo potential method in the framework of Density Functional Theory. In this study the method of 245

2 energy(ry) Sarvazad and Zarghani Calculation of Lattice Parameters and Energy Band Structure and Density of States the βzrncl with Ab Initio instability (uspp) was used, therefore, it is very important to determine the pseudopotential exactly. βzrncl has the trigonal structure with the space group R3m and the lattice constants that have been measured experimentally, are a= A and c= A and used in the calculations (Adelmann, 2000). The calculations have been done with or without considering spiny interactions. To implementation energy convergence program is considered that with 10 cycles. The kinetic energy cutting the electronic wave functional based on plane waves 40 ridberg are elected which a lattice of 12*12*14 kmesh is created. 3. RESULTS AND DISCUSSION measured and is available; however, it should be calculated in order to be conically. After optimization k points and cut energy, there is need to draw an energy graph the lattice parameters and the smallest volume is obtained which is the optimum volume and regarding to the studied structure, the lattice parameters can be extracted. To do this, convergence eigenvalue of structure energy for the different parameters have been calculated. Due to being selfequations, we can calculate the amount of energy to arbitrary precision. Energy changes based on volume is given by Mvrnagan, s equation; the minimum energy is obtained for this compound by using this equation. One of these results is shown in figure (2) Calculation of lattice parameters One of the most important parameters in the calculations is the lattice constant.it is experimentally volume((a.u)^3) Fig. 2: Energy diagram in terms of volume βzrncl. Following these calculations, other parameters such as lattice constant, bulk module, derivate of the bulk module to the pressure and compressibility has been calculated. The results are given in table (1) and compared with the both experimental and theoretical data made by others. In this table a&c are lattice constants, V 0 is optimum volume, B is bulk module, B` is derivative of bulk module, k is compressibility and E min is the minimum energy. According to researches, very few studies have done on this compound and no theoretical results have been obtained. The result show considering spiny interactions have a little effect on the structural parameters and improves the volume. Compressibility is defined converse to the bulk module and the bulk module represents the stability of the crystal, in other words, the more module volume means the more crystal stability. Now we will study effect of pressure on βzrncl. The graph of dependency of volume on the pressure for the combination has been shown in figure (3). The graph clears that the volume of unit cell decreases by increasing pressure. Since the compressibility is low, it can be said this compound is very hard. Graph of lattice parameters changes of a/a 0 and c/c 0 based on the pressure were shown in figure (4). According to the figure the lattice parameters decreases by increasing pressure, and it also can be seen that the amount of decrease in c constant is 1.3 more than of a constant and the reason is that β ZrNCl is anistropical structure and this is due to the difference in the type of bonds along with a,c. 246

3 a/a.,c/c. V((a.u.)^3) International Journal of Scientific Research in Knowledge (IJSRK), 1(8), pp , 2013 Table 1: The structural parameters calculated The calculated parameters Regardless of the spin interactions In view of the interaction of spin Experimental results(istomin, 1999) V (A ) a ( A 0 ) c ( A 0 ) c / a B (kbar) B K ( kbar) * *10 3 E min ( Ry) P(kbar) Fig. 3: Diagram of dependency of volume on the pressure βzrncl Series1 Series P(kbar) Fig. 4: Diagram of βzrncl lattice parameters changes based on the pressure 3.2. Band structure calculations Another important result that can be derived from simulation of crystal properties is the graph of band structure. Nature of the crystal whether it is metal or not, measure of energy gap, if there is and its type whether it is direct or not, also method of distribution of the electron s in the different energies can be derived from this graph. Accordance of this graph to density curve of the s could be a reason to accuracy of the calculations. Structures of the energy band βzrncl along with different symmetric lines are shown in figure (5). 247

4 Sarvazad and Zarghani Calculation of Lattice Parameters and Energy Band Structure and Density of States the βzrncl with Ab Initio Energy L Γ X Fig. 5: Diagram structure of the energy band βzrncl regardless of the spin interactions. In this curve Fermi energy is located in the coordinate system origin, as it is clear from the figure (5) the levels of energy did not cut the Fermi level.it shows that βzrncl compound has indirect band gap of 2.75 ev in the point of. Table (2) shows the calculated band structure of this method with other methods. The structure of energy band of βzrncl combination regarding to spiny interaction shows that this spiny interaction has no effect on the structure and the calculated gap has a good agreement with other results. Band gap No interaction of spin Table2: Band gap compared with the results obtained by others Experimental Experimental results(ohashi, 1984) results(ohashi, 1989) The interaction of spin Theoretical results(hase, 1999) (ev ) E g Type of gap in point Γ indirect indirect 3.3. Density of s Electron distribution in energy spectrum is described by density of s. Density of diagram βzrncl has been drawn based on energy at the range 10 ev to 10 ev in figure (6). 248

5 International Journal of Scientific Research in Knowledge (IJSRK), 1(8), pp , 2013 Fig. 6: The βzrncl total density of s diagram In the density of diagram, zero energy scale presents Fermi level that it has been shown with vertical line. As it is clear from figure, maximum of the density of s is expanded from 4.5 ev to 0eV and approximately density of s is zero from 4.5 ev to later. For more accurate investigation about different orbitals participation, partial density of of atoms energy has been shown in the next figures. According to these figures, it can be seen that N atoms share to Zr and Cl is more in dos of all compound. Therefore it can be concluded that N atoms have a basic role to determine the electronic properties of βzrncl. In figure (7) dos share of each Zr atom orbitals were compared to each other. As it is clear from figure, in Fermi level, density of s s orbital in the Zr atom is almost zero. For d orbital N (E f ) is about 3 /ev and for p orbital is about 0.3/eV. share of s and p orbitals in the N atom are compared in figure (8), for s orbital of N atom, peaks of energy have been located in limits 1eV to 4eV. Density of s for s orbital in Fermi level is almost 0.1 /ev. It shows that s orbital of N atom has a small role in compound properties determining. Energy peaks for P orbital in the N atom are almost expanded from 3eV to 0eV. The P orbital of Nitrogen atom has basic role in electronic properties of all compound βzrncl. The N(E f ) for p orbital of N atom is about 4.5 /ev. ) (ev energy (a) 249

6 Sarvazad and Zarghani Calculation of Lattice Parameters and Energy Band Structure and Density of States the βzrncl with Ab Initio (b) (c) Fig. 7: The zirconium partial density of s diagram for a) d orbitals b)s orbitals c)p orbitals ) (ev energy (a) 250

7 International Journal of Scientific Research in Knowledge (IJSRK), 1(8), pp , 2013 (b) Fig. 8: The partial density of s diagram of nitrogen atom for a) s orbitals b) p orbitals Curve of partial density of s of s and p orbitals for Cl atom is shown in figure (9). As it is clear from figure N (E f ) of s orbital of the chlorine atom is about 0.1/eV. Therefore s electrons of Cl atom have little share in total density of and it basically shows unoccupied s also the N(E f ) of p orbital of Cl atom is about 2.5 /ev. The p orbital of Cl atom in fact has a greater role in the electronic properties of total compound. 4. CONCLUSION Calculation has been done by using Ab initio method and looking at spiny interaction and obtained structural parameter have good compatibility with experimental consequences. Obtained consequences determine that spiny interaction has insignificant effect on structural parameters and the consequences are an emphasis on the more difficulty and less compressibility of βzrncl compound. According to compound band structure, it is distinguished that energy levels have not been cut fermi level, this expresses that βzrncl is a semiconductor with band gap of 2.75eV. By looking at to the partial density of s diagram, it is distinguished that N atoms have important role to determine electronic properties of β ZrNCl. The partial density of of N atom shows that s orbital of N atom has an insignificant role, and p orbital of Nitrogen atom has basic role in electronic properties of all compound βzrncl. ) (ev energy (a) 251

8 Sarvazad and Zarghani Calculation of Lattice Parameters and Energy Band Structure and Density of States the βzrncl with Ab Initio (b) Fig. 9: The partial density of s diagram of chlorine atom for a) s orbitals b) p orbitals ACKNOWLEDGEMENT This article is adapted from the research projects Calculation of lattice parameters and energy band structure and density of s the βzrncl with Ab initio which is supported by Islamic Azad Universit (IAU), Abadan BranchIran. REFERENCES Adelmann P, Renker B, Schober H, Braden M, FernandezDiaz F (2000).Structural Study of Superconducting Lidoped betazrncl. J of Low Temp. Phys., 117: 449. Chen X, Koiwasaki T, Yamanaka S (2001).High Pressure Synthesis and Crystal Structures of β MNCl (M=Zr and Hf). Hiroshima University, Hase I, Nishihara Y (1999). Electronic Band Structure of βzrnclbased nanotubes. Phys. Rev. B 60, 1573 Hase I, Nishihara Y (2000). Electronic Band Structure of βzrnclbased nanotubes. Physica B 281 & 282, 788. Istomin SY, Kohler J, Simon A (1999). HighPressure Synthesis and Crystal Structures of βmncl (M=Zr and Hf). Physica C, 319: Kawaji H, Hotehama K, Yamanaka S (1997).Valenceband Photoemission Study of βzrncl and the Quasitwodimensional superconductor Na x ZrNCl. Chem. Mater., 9: Ohashi M, Nakano H, Yamanaka S, Hattori M (1989). Valenceband Photoemission Study of βzrncl and the Quasitwodimensional superconductor Na x ZrNCl. Solid State Ionics, 33/32,97. Ohashi M, Yamanaka S, Hattori M (1989). Valenceband Photoemission Study of βzrncl and the Quasitwodimensional superconductor Na x ZrNCl. Ceram, J., Soc. Jpn., 97: Ohashi M, Yamanaka S, Sumihara M, Hattori MJ (1984). Superconductivity of Alkali Metal Intercalated βzirconium Nitride Chloride, A x ZrNCl(A=Li,Na,K). Inclusion Phenom., 2: 289. Shamoto S, Kato T, Miyazaki Y, Ohoyama K, Ohashi M, Yamaguchi Y, Kajitani T (1998). Electronic Band Structure of βzrnclbased nanotubes. Physica C306, 714. Takano T (2008).Effects of Molecule Intercalation In The Layered Nitride Li x ZrNCl Superconductor. Phys. Rev. B77, Taguchi Y (2006).Optical Properties of Layered Superconductor Li x ZrNCl. Phys. Rev. Lett. 97, Yamanaka S (1996). Isotope Effect In Li x ZrNCl Superconductors. Adv.Mater. 8,77. Yamanaka S, Hotehama K, Kawaji H (1998). High Pressure Synthesis and Crystal Structures of β MNCl (M=Zr and Hf). Nature (London), 392,

9 International Journal of Scientific Research in Knowledge (IJSRK), 1(8), pp , 2013 Khatereh Sarvazad is faculty member of physics department of Islamic Azad University, Abadan Branch, Iran. She holds MSc in Physics from IAU, Khouzestan Science and Research Branch. She is interested in research on her educational field; she organized a research project in Physics field. She has written the present article based on her research project s findings on Energy Band Structure and Density of States. She wrote this manuscript as corresponding author with the assistant of Dr. Soroosh Zarghani. Dr. Soroosh Zarghani is faculty member of Physics department of Islamic Azad University of Abadan, Iran. He holds MSc in Physics from Tehran Science and Research Branch. Iran. Then He was recruited by Islamic Azad University of Abadan, Iran as a course instructor in Physics department since 2007; and now he is student of physical occanography in University of Khoramshahr. He is interested in research on his educational field, he organized a research project in Physics area. He has written the present article based on his research project s findings on Calculation of lattice parameters and energy band structure and density of s the βzrncl with Ab initio. He wrote this manuscript with the assistant of Khatereh Sarvazad, faculty member of Physics department of Islamic Azad University of Abadan, Iran. 253