Calculation of the lattice constant of hexagonal compounds with two dimensional search of equation of state and with semilocal functionals a new package (2D-optimize)
Highlights
► A new package for calculating lattice constants and equation of state is released. ► The package called 2D-optimize, it is part of commercial WIEN2k code. ► It is compatible with [FP-(L)APW+lo] method implemented in WIEN2k code. ► Several hexagonal compounds were used to test the new package. ► Results from 2D-optimize show good agreement with experiment.
Introduction
density functional theory (DFT) is one of the most important and powerful method to solve the quantum many body problem. Kohn–Sham (KS) equations [1], [2] is used to solve the quantum mechanical equations within Density Functional Theory (DFT) [3], [4]. By using the Kohn–Sham equations we map an interacting many body system to non-interacting hypothetical system which has the same electron density. The price that we have to pay is definition a new functional that called exchange–correlation functional. Unfortunately exact form of exchange–correlation functional is unknown [5]. Therefore the accuracy of our results will be sensitive to selection of the exchange–correlation functional and it can play a major role for the accuracy of our results and this is one of the main questions in DFT. WHICH EXCHANGE–CORRELATION CAN DESCRIBE THE PROPERTIES OF THE MATERIALS? For the exchange–correlation we have used different approximations [6], [7], [8], [9], [10]. Thus, we need to choose an approximate and suitable functional [11] because the exact functional is unknown [5].
On the other hand, there are two degrees of freedom for finding equation of state (EOS) for some crystal such as hexagonal compounds [12]. Usually for hexagonal compounds EOS calculates with constant c/a ratio or constant volume, we call it one Dimensional (1D) search of EOS. In this work we are interested to calculate two Dimensional (2D) search of EOS within five exchange–correlations for several hexagonal compounds.
Section snippets
Exchange–correlation functional
The functional of the Local Density Approximation (LDA) [13], [14] that roots into the uniform electron gas approximation and Generalized Gradient Approximation (GGA) [15], [16], by adding gradient terms of the electron density to the exchange correlation energy of LDA, can be the first choice for ab initio calculation of materials. Perdew et al. (1992) (PW91) [15] have obtained the first GGA functional and then it replaced by the functional of Perdew, Burke, and Ernzerhof (PBE) [16] which is
Two dimensional search
In this work, we have performed a convenient volume and c/a structure optimization by using 2D-optimize package [29]. First, we find the best value of c/a and therefore the energy for each volume, and then for those volumes and energies the equation of state (EOS) will obtained, and after that the value of c/a calculates within optimal volume.
To test the new 2D-optimize package, we have done 1D and 2D search of EOS for MnAs and Mg within PBE functional and compared the results with experimental
Details of calculations
A new package for calculating lattice constants and equation of state of hexagonal and tetragonal structure is released. We call it as 2D-optimize [29]. This package is compatible with the highly accurate all-electron full-potential (linearized) augmented plane-wave plus local orbital [FP-(L)APW+lo] method implemented in WIEN2k code. This is an implementation of the density functional theory (DFT) with different possible approximation for the exchange correlation (XC) potentials. This package
Results and discussion
Using the new package the cell parameters of twenty hexagonal structure compounds were calculated and compared with the available experimental data. These results were listed in Table 2, Table 3, Table 4. In Table 2, we have listed our calculated a-lattice constants in unit of Angstrom within different exchange correlation (XC) potentials namely; AM05, LDA, PBEsol, WC and PBE in comparison with experimental data [33], [35], [36], [37] and the previous theoretical results obtained from different
Conclusions
A new package for calculating lattice constants and equation of state of hexagonal and tetragonal structure is released. We call it as 2D-optimize. This package is available with WIEN2k code and compatible with the highly accurate all-electron full-potential (linearized) augmented plane-wave plus local orbital [FP-(L)APW+lo] method implemented in WIEN2k code. This is an implementation of the density functional theory (DFT) with different possible approximation for the exchange correlation (xc)
Acknowledgements
This work was supported from the institutional research concept of the project CENAKVA (No. CZ.1.05/2.1.00/01.0024), the Grant No. 152/2010/Z of the Grant Agency of the University of South Bohemia. School of Material Engineering, Malaysia University of Perlis, Malaysia.
In this manuscript a NEW package for calculating lattice constants and equation of state for hexagonal and tetragonal structure is released. The Package now online as part of the commercial code WIEN2K. http://www.wien2k.at/.
References (38)
- et al.
J. Magn. Magn. Mater.
(2010) - et al.
Phys. Rev.
(1964) - et al.
Phys. Rev.
(1965) - et al.
Density-Functional Theory of Atoms and Molecules
(1989) Science
(2002)- et al.
Phys. Rev. B
(2009) - et al.
Phys. Rev. B
(2004) - et al.
Phys. Rev. B
(1995) - et al.
Phys. Rev. B
(1996)
Model. Simul. Mater. Sci. Eng.
J. Phys. Condens. Matter
Proc. Camb. Philos. Soc.
Phys. Rev. B
Phys. Rev. B
Phys. Rev. Lett.
Phys. Rev. B
Phys. Rev. B
ibid.
ibid.
Phys. Rev. B
Cited by (41)
Exchange-correlation effects on the structural, electronic, and optical properties of Sr<inf>2</inf>RuO<inf>4</inf> using DFT calculations
2024, Journal of Alloys and CompoundsThe effect of oxygen atom substitution in the sulphur sites of the bulk ZnS: A DFT study
2024, Chemical PhysicsPhase stability, phonon, electronic, and optical properties of not-yet-synthesized CsScS<inf>2</inf>, CsYS<inf>2</inf>, and APmS<inf>2</inf> (A= Li, Na, K, Rb, Cs) materials: Insights from first-principles calculations
2022, Materials Science in Semiconductor ProcessingCitation Excerpt :Local density approximation (LDA) and generalized gradient approximation (GGA) are the oldest and the largest used functionals, as well as cheaper computational cost, despite their success in many cases, they suffered from some flaws. Often they fail to determine the correct lattice parameters (LDA underestimates and GGA overestimates) [22–26], predict the exact band gap of semiconductors and insulators [27,28], define the transition pressure [29–31], confirmed that ice is less dense than water [32–36]. Recently, a new appropriately normed functional with very low computational cost compared to hybrid functionals, so-called (SCAN) [37], which belongs to the meta GGA family of functionals, was suggested.
Study on properties of single-phase high entropy alloys with FCC structure based on the empirical electron theory
2022, Journal of Alloys and CompoundsCu<inf>2</inf>XSnS<inf>4</inf> (X = Mn, Fe, Co) semiconductors: Boltzmann theory and DFT investigations
2021, Solid State Communications