Journal of Molecular Modeling (2018) 24:131 https://doi.org/10.1007/s00894-018-3666-z
ORIGINAL PAPER
Electronic structure, mechanical and thermodynamic properties of BaPaO3 under pressure Shakeel Ahmad Khandy 1,2 & Ishtihadah Islam 3 & Dinesh C. Gupta 2 & Amel Laref 4 Received: 16 February 2018 / Accepted: 17 April 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract Density functional theory (DFT)-based investigations have been put forward on the elastic, mechanical, and thermo-dynamical properties of BaPaO3. The pressure dependence of electronic band structure and other physical properties has been carefully analyzed. The increase in Bulk modulus and decrease in lattice constant is seen on going from 0 to 30 GPa. The predicted lattice constants describe this material as anisotropic and ductile in nature at ambient conditions. Post-DFT calculations using quasiharmonic Debye model are employed to envisage the pressure-dependent thermodynamic properties like Debye temperature, specific heat capacity, Grüneisen parameter, thermal expansion, etc. Also, the computed Debye temperature and melting temperature of BaPaO3 at 0 K are 523 K and 1764.75 K, respectively. Keywords Electronic structure . Perovskite . Mechanical and thermal properties
Introduction Topical advances in bulk and atomic-scale simulations endowed with the technical progress in synthesis of perovskite oxides and their heterostructures have bestowed a productive and new opinion for producing novel, superlative structures with intriguing properties. The designing of structures with promising phenomena can be obtained via different symmetry constraints. Also, the understandings of fundamental physical aspects behind these characteristic properties are liable to be explained by the customary advanced simulative codes available with diverse and appropriate degrees of freedom [1]. Owing to the multifaceted and technologically important properties, perovskites turned out to be an active area of research and therefore symbolize a distinguished class of
* Shakeel Ahmad Khandy
[email protected] 1
Department of Physics, Islamic University of Science and Technology, Awantipora, Jammu, Kashmir 192122, India
2
Condensed Matter Theory Group, School of Studies in Physics, Jiwaji University, Gwalior, MP 474011, India
3
Department of Physics, Jamia Millia Islamia, New Delhi 110025, India
4
Department of Physics, College of Science, King Saud University, Riyadh, Saudi Arabia
materials. The various properties for which these oxides are known include superconductivity, charge and spin ordering, ferroelectricity, colossal magnetoresistance, thermoelectricity, and photoconduction, which henceforth make them promising candidates for efficient energy management and other applications [2–5]. Perovskite oxides with actinide element constituents have been principally studied for their chemical instability and structural analysis. Among this family, BaUO3 [6], BaNpO3 [7, 8], and BaAmO3 [9] are reported to be ferromagnetic halfmetals. In our previous work, BaPaO 3 , an important byproduct of fission produce, was studied for structural, electronic, and transport properties [10] and optical properties by Erum et al. [11]. It was therefore found that BaPaO3 can be a potential material for micro as well as nano-electronic devices. However, its experimental study is limited only to structure, thereby a gap for mechanical stability and elastic and thermodynamic properties in the available literature needs to be filled. For that reason, the present work has been undertaken to investigate the undecided elastic response and thermal properties of this material and the effect of pressure on its half-metallic character as well as mechanical properties.
Methods Density functional theory (DFT) has proven to be the most influential and acceptable and approximate method for
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describing the physical properties of solids [12–15]. Especially, it paved the way to determine these properties at elevated temperatures and pressures, which are very difficult to predict in normal lab conditions. Full-potential linearized augmented plane wave (FPLAPW) method, as embedded in Wien2k, is used to simulate the crystal properties of the present oxide [16]. To optimize the crystal structure, generalized gradient approximation (GGA) [17] has been engaged for the present calculations. Tetrahedral method for Brillion zone integration within the dense mesh of 3500 k points was utilized. The convergence criteria for the largest wave vector, RMTKmax, equal to 7.0, is chosen to control the size of the basis set for the present calculations. The consistency of the present calculations was assured only when the charge difference is less than 0.001e/a.u.3 per unit cell and the total energy is stable within 0.001 Ry. The elastic constants at 0 K and 0 GPa and 30 GPa are computed by the Jamal’s cubic elastic code [18].
Structural and electronic properties The structural and electronic properties and their variation due to applied pressure compressions are investigated within the pressure range of 0–30 GPa, keeping in view the intactness of cubic structure. The ground-state stable structure at 0 GPa pressure with the corresponding atomic position of Ba at (0, 0, 0); O at (1/2, 1/2, 0), (1/2, 0, 1/2), (0, 1/2, 1/2) and Pa at (1/2, 1/2, 1/2) in its cubic Pm-3m structure is considered for the present set of calculations. The energy-volume optimization was achieved by Birch–Murnaghan equation to find the necessary lattice parameters, which in turn were utilized to calculate the thermodynamic properties of the present oxide within the quasi-harmonic Debye model [19]. The effect of compression on the observed lattice parameters, like lattice constant (a0), minimum volume (V0), and bulk modulus (B′), is shown in Table 1. Usually, the increase in pressure makes the volume and lattice constant of a crystal to decrease accordingly. On moving from 0 GPa to 40 GPa, the lattice constant of BaPaO3 decreases with the increasing pressure while as the reverse is observed for the bulk moduli of this material. This phenomenon could be attributed to the Table 1 Variation of the equilibrium lattice constant (a0), minimum volume (V0), and bulk modulus (B′) within the pressure gradient (0– 30 GPa) Pressure (GPa)
a0 (Å)
B (GPa)
V0 (Å)
0 10 20 30 40
4.51 4.47 4.43 4.39 4.37
114.80 116.99 126.55 140.27 162.67
327.16 318.55 310.21 303.29 300.23
strong binding forces present in this material and incompressible nature of the material. From Table 1, the bulk modulus of BaPaO3 increases as we move from 0 to 40 GPa. This means that the resistance of this material increases towards external compressions. Under normal conditions (0 GP and 0 K), this compound is found to be a ferromagnetic half-metal. As discussed in our previous work, the spin up state of this material is conducting, while as the down spin is semiconducting in nature [10]. The electronic structure at 0, 20, and 40 GPa pressures of the present material has been studied to estimate the variation of the band structure under compressions. The corresponding band structures are shown in Fig. 1, and it is clearly seen that the half-metallic nature decreases accordingly. It can be seen from the obtained plots at various pressures that the few bands in spin down phase shift across the Fermi level. Therefore, the effect of pressure on the electronic structure of this oxide is clearly implicated from the crossover of conduction band minima through the Fermi level in the spin down state. Hence, the applied compressions on this system lead to loosening of the half-metallic character of this material and thereafter at high pressures the metallic nature of this compound is observed.
Mechanical stability and elastic properties Elastic constants have been extensively manipulated to establish the stability of the crystal structures by applying the stress in different directions. As we know that all the compliance constants Sij’s of the single crystal are utilized to calculate the elastic constants and for cubic symmetry, these constants reduce only to three in number, i.e., C11, C12, and C44 [20]. The elastic parameters for the present material have been evaluated at two different pressures (0 and 40 GPa) to establish the stability under different pressure conditions as well as the effect on the overall mechanical parameters. The calculated lattice constants for BaPaO3 strictly follow the generalized stability criteria; C 12 < B < C 11 , (C 11 -C 12 ) ˃ 0, (C 11 + 2C12) > 0 and C44 > 0 [21]. To obtain the bulk and shear moduli from these constants, Viogt–Reuss–Hill method is employed within the following equations [22].
GV ¼
ðC 11 −C 12 þ 3C 44 Þ 5ðC 11 −C 12 ÞC 44 GV þ GR ;G ¼ ; GR ¼ 4C 44 þ 3ðC 11 −C 12 Þ 2 5
BV ¼ BG ¼ B ¼
ðC 11 þ 2C 12 Þ 3
The obtained values of Bulk’s and shear moduli, as depicted in Table 2, establish the strength of BaPaO3 compound towards the external strain. The observed values of B and G at 0 GPa are 114.59 and 42.14 and at 40 GPa; these values are 162.67 and 39.45, respectively. The Poisson’s ratio
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Fig. 1 Band structures calculated at different pressures in both spin up and spin down states
Table 2 Calculated values of elastic (C11, C12, C44), bulk (B), shear (G), Young’s (Y) moduli (in GPa), Poisson’s ratio (υ), Zener anisotropy factor (A), B/G ratio, Cauchy’s pressure (C″ = C 12 -C 44 ) and melting temperature (Tm) in K for BaPaO3 Parameter
0 GPa
40 GPa
C11 C12 C44 B GV GR G Y υ A B/G C″ Tm
205.60 67.58 29.94 114.59 113.59 38.70 42.14 112.51 0.67 0.43 2.67 37.64 1764.75 ± 300
300.39 87.44 17.29 162.67 52.96 25.94 39.45 109.49 0.38 0.16 4.12 70.15 2328.60 ± 300
states about the plasticity of the material and its critical value is: 0 < υ < 0.5. The lower value of Poisson’s ratio signifies the higher plastic performance of a material and vice versa; the obtained value of υ designates this material as elastic at 0 GPa and plastic at higher pressures [20]. Y¼
9BG 3B−Y ;υ ¼ 3B þ G 6B
Likewise, the Zener’s anisotropy factor calculated by the equation A = 2C44/(C11-C12) clearly designates this oxide as anisotropic at ambient pressure and temperature; however, it tends to achieve isotropy at elevated pressures. Because A = 1, means that the material perfectly isotropic and A, less or greater than unity claims the anisotropic nature of the material. If the value of Pugh’s ratio, B/G > 1.75 and Cauchy pressure, C12-C44 > 0 characterizes the ductile nature of the material; otherwise the material is brittle in nature [21]. Therefore, from the calculated values of B/G and C12-C44, BaPaO3 is found to be ductile. The ductile nature is observed to increase on seeing the corresponding values at 30 GPa.
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Fig. 2 Pressure variation of a thermal expansion coefficient (α) and b Debye temperature (θD) for BaPaO3
T m ðK Þ ¼ ½553ðK Þ þ ð5:911Þc11 GPa 300K Besides, the melting temperature (Tm) of this compound has been calculated by the empirical equation depicted elsewhere [8, 23]. The observed value of Tm is 1764.75 ± 300 K, which is greater than the BaNpO3 [9] compound of the same family.
Thermal properties Thermodynamic properties of BaPaO3 oxide have been calculated via quasi-harmonic Debye model [17], in which the Gibbs function G∗ (V;P,T) is operated as:
Θ 9Θ −Θ=T þ 3ln 1−e −D Avib ðΘ; T Þ ¼ nkT 8T T where D(Θ/T) is the Debye integral, n the number of atoms per formula unit, and Θ is specified as [25]. rffiffiffiffiffiffiffi h i1=3 KS 2 1=2 Θ ¼ ħk 6π V n f ðσ Þ M where M represents the molecular mass per formula unit, σ is the Poisson ratio and KS, the adiabatic bulk modulus under static compressibility approximation takes the form: [19].
G* ðV; P; T Þ ¼ EðV Þ þ PV þ Avib ðΘðV Þ; T Þ here E(V) is the total energy per unit perovskite cell, PV represents the constant hydrostatic pressure condition, Avib the vibrational Helmholtz free energy and Θ(V) is the Debye temperature. Phonon density of states are exploited via the Debye model and applying quasi-harmonic approximation, Avib becomes [24, 25].
K S ≈ K ðV Þ ¼ V
d 2 E ðV Þ dV 2
Using the Poisson ratio σ = 0.25 [26], f (σ) takes the form given elsewhere [27, 28]. Hence, the minimization of non-
Fig. 3 a Thermal expansion coefficient (α) and b Debye temperature (θD) for BaPaO3 under pressure
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equilibrium Gibbs function G∗(V;P,T) as a function of (V;P,T) w.r.t volume V is as follows: * ∂G ðV; P; T Þ ¼0 ∂V P;T On solving the above equation, we obtain the required thermal equation of state. The heat capacity at constant volume CV, the thermal expansion coefficient α and the entropy S are given as [28]. Θ 3Θ=T C V ¼ 3nk 4D − Θ=T T e −1 α¼
γC V KT V
where γ is the Grüneisen parameter expressed as γ = −dlnΘ(V)/dlnV. Θ S ¼ nk 4D −3ln 1−e−Θ=T T Thermal expansion coefficient (α) and Debye temperature (θD) plots amid their pressure variation are displayed in Fig. 2a, b. The observed influence of pressure on α can been seen from Fig. 2a, which clearly shows the declining trend; at the same time its values increase from 0.7 × 10−5/K at 0 K to 3.47 × 10−5 at 500 K. Also, the Debye temperature displays a substantial increase with increasing pressure (0–35 GPa) while a slight decrease is observed along the temperature gradient (0–500 K). The θD value calculated from quasiharmonic model at ambient conditions for BaPaO3 is 523 K. In Fig. 3a, b, the effect of pressure on the Grüneisen parameter (γ) and specific heat capacity (CV) are displayed. A gradual decrease is visualized in γ with increasing pressure, while it increases with increasing temperature. Such type of results for other compounds of the same family have been reported in our previous works [7, 8]. Moreover, the specific heat capacity at constant volume in the pretext of pressure and temperature variation has also been included in adherence to the agreement of Debye model [29] at lower temperatures. From Fig. 3b, CV is observed to decrease with increasing pressure, and increases along the temperature gradient. Due to unavailable, experimental, or theoretical data regarding these physical properties, the comparison of our results is not achieved; at the same time, this data could serve as guide/reference data to further the experimental or theoretical investigations which are still unattended.
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been predicted in this report. The electronic band structures calculated at various pressures are predicted. Structural parameters, like lattice constant, bulk modulus, and volume within the constraints of pressure conditions, are calculated. The elastic parameters and mechanical properties suggest the ductile and elastic behavior of this oxide at 0 K and 0 GPa. Further, the thermodynamic properties via the quasi-harmonic Debye model are presented to enhance the basic understandings of the physical principles behind them. Acknowledgements One of the authors, A. Laref, wants to acknowledge the BResearch Center of Female Scientific and Medical Colleges^, Deanship of Scientific Research, King Saud University for financial support.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
17. 18. 19. 20. 21. 22. 23. 24. 25.
Conclusions Full-potential linearized augmented plane wave computations on the electronic, mechanical, and thermal properties of BaPaO3 and the effect of pressure on these properties have
26. 27. 28. 29.
Hwang HY, Iwasa Y, Kawasaki M, Keimer B, Nagaosa N, Tokura Y (2012). Nat. Mater. 11:103 Reshak AH (2014). Phys. Chem. Chem. Phys. 16:10558 Bristowe NC, Varignon J, Fontaine D, Bousquet E, Ghosez P (2015). Nat. Commun. 6:6677 Abbad A, Benstaali W, Bentounes HA, Bentata S, Benmalem Y (2016). Solid State Commun. 228:36 Reshak AH (2014). RSC Adv. 4:39565 Ali Z, Ahmad I, Reshak AH (2013). Physica B 410:217 Dar SA, Khandy SA, Islam I, Gupta DC, Srivastava V, Sakalle UK, Parrey K (2017). Chin. J. Phys. 55:1769 Khandy SA, Gupta DC (2017). Mater. Chem. Phys. 198:380 Dar SA, Srivastava V, Sakalle UK, Khandy SA, Gupta DC, Supercond J. Nov. Magn. https://doi.org/10.1007/s10948-017-4181-7 Khandy SA, Gupta DC (2017). J. Electron. Mater. 46:5531 Erum N, Iqbal MA (2017). Mater. Res. Express 4:025904 Reshak AH, Stys D, Auluck S, Kityk IV (2011). Phys. Chem. Chem. Phys. 13:2945 RSC AH (2014). Adv. 4:63137 Reshak AH (2016). Phys. Chem. Chem. Phys. 6:92887 Souidi A, Bentata S, Benstaali W, Bouadjemi B, Abbad A, Lantri T (2016). Mater. Sci. Semicond. Process. 43:196A Blaha P, Schwarz K, Madsen GKH, Kvasnicka D, Luitz J, WIEN2k (2001) An augmented plane wave plus local orbitals program for calculating crystal properties. Vienna University of Technology, Vienna Perdew JP, Burke K, Ernzerhof M (1996). Phys. Rev. Lett. 77:3865 M. Jamal, Cubic-elastic, http://www.WIEN2k.at/reg_user/ unsupported/cubic-elast/, 2012 Flórez M, Recio JM, Francisco E, Blanco MA, Martín Pendás A (2002). Phys. Rev. B 66:144112 Khandy SA, Gupta DC (2016). RSC Adv. 6:48009 Khandy SA, Gupta DC (2017). J. Magn. Magn. Mater. 441:166 Khandy SA, Gupta DC (2016). RSC Adv. 6:97641 Khandy SA, Gupta DC (2017). Int. J. Qua. Chem. 117(8):1–6. https://doi.org/10.1002/qua.25351 Poirier P (2000) Introduction to the physics of the Earth’s interior, 2nd edn. Cambridge University Press, Cambridge Francisco E, Recio JM, Blanco MA, Martín Pendás A (1998). J. Phys. Chem. 102:1595 Francisco E, Sanjurjo G, Blanco MA (2001). Phys. Rev. B 63:094107 Yakoubi A, Baraka O, Bouhafs B (2012). Results Phys 2:58 Khandy SA, Islam I, Ganai ZS, Gupta DC, Parrey KA (2018). J. Electron. Mater. 47:436 Sahnoun O, Benziane HB, Sahnoun M, Driz M, Daul C (2013). Comput. Mater. Sci. 77:316
