BIBECHANA Vol. 22, No. 2, August 2025, 188-195 ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher:Dept. of Phys., Mahendra Morang A. M. Campus (Tribhuvan University)Biratnagar First Principles Calculations of Mechanical, Electronic, Thermoelectric and Thermal Properties of ZnCu Shashit Kumar Yadav∗, Subash Dahal, Bhupal Guragain , Department of Physics, Mahendra Morang Adarsh Multiple Campus Tribhuvan University,Biratnagar, Nepal ∗Corresponding author. Email: sashit.yadav@mmamc.tu.edu.np Abstract The structural, mechanical, electronic and thermoelectric properties of ZnCu were investigated using Density Functional Theory (DFT). The Perdew–Burke–Ernzerhof (PBE) exchange- correlation functional within the Generalized Gradient Approximation (GGA) was employed in the Quantum ESPRESSO package for the purpose. The ZnCu compound was found to be both mechanically and dynamically stable. Analysis of its elastic and electronic properties reveals that ZnCu is mechanically stable, anisotropic, and exhibits metallic behavior. Further- more, thermoelectric property analysis indicates that ZnCu achieves its highest power factor at 300 K. The study of thermodynamic properties suggests that ZnCu retains mechanical stability at elevated temperatures. Keywords ZnCu compound, Quantum Espresso, electronic properties, phonon, thermoelectric properties. Article information Manuscript received: January 10, 2025; Revised: April 12, 2025; Accepted: May 26, 2025 DOI https://doi.org/10.3126/bibechana.v22i2.79223 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons. org/licenses/by-nc/4.0/ 1 Introduction Alloying materials serve an important role in im- proving the qualities of materials for a variety of applications by increasing their strength, durabil- ity, and corrosion resistance. The material can be alloyed to achieve the qualities that alloy com- ponents lack for practical application [1]. There are enormous possibilities for alloying the material, but copper alloy has gained its own importance in the fields of machinery, electrical industry, and construction over the past year [2, 3]. Among the different possible alloys of copper, the ZnCu al- loy stands out due to its potential application in diverse domains. The unique combination of zinc and copper provides promising characteristics [4–8]. Different research has been conducted to study the properties of the ZnCu alloy. For example, Iwaoka and Hirosawa used first principles method to calcu- late elastic properties of three different complex of Cu-Zn system to improve the stiffness of aluminum alloy [4]. Similarly, Liu et al. studied the struc- tural, elastic, and electronic properties of Cu-X (X = Al, Be, Mg, Sn, Zn, and Zr) by the first-principles calculations [8]. Furthermore, Tang et al. used a modified quasi-chemical model (MQM) to describe the Gibbs energy of the liquid phase [9]. 188 http://nepjol.info/index.php/BIBECHANA sashit.yadav@mmamc.tu.edu.np https://doi.org/10.3126/bibechana.v22i2.79223 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 189 Despite significant progress in material science, comprehensive studies that integrate structural, electronic, elastic, thermoelectric, and thermal properties of ZnCu crystal structure are still sparse. Therefore, this work attempts to explain these properties of the ZnCu compound using the first principles calculations employing Quantum Espresso codes [10]. 2 Computational Details The first principles calculation of ZnCu structure was performed using the Quantum Espresso soft- ware package [10]. The crystal structure was first optimized by performing the VC-relax calculation using Perdew-Burke-Ernzerhof (PBE) of scalar rel- ativistic exchange-correlation functional and ionic potentials described by ultrasoft pseudopotential (USPP) for Zn and Cu downloaded from the ma- terial cloud website [11]. The plane wave cutoff energy was set to 40 Ry and 320 Ry was set for the wave function and charge density. The Bril- louin zone was determined using Monkhorst-Pack for self-consistent field calculation and for den- sity of state (DOS) calculation. The electronic band structure was calculated along the high- symmetry point in the Brillouin zone using the path Γ−X −M − Γ−R−X|R−M . The bulk modulus was calculated using the Mur- naghan equation of state using the ev.x utility of Quantum Espresso [12]. Furthermore, the Thermo_pw [13] postprocessing tool was used to cal- culate the elastic constant, which allowed for the calculation of mechanical properties such as bulk modulus, young modulus, shear modulus, and Pois- son ratio of the material. Electronic transport prop- erties were calculated with the help of the Boltz- trap code [12, 14]. The output information of non- self-consistent field calculation was used as input for boltztrap software, which solves the Boltzmann transport equation to determine electrical conduc- tivity, Seebeck coefficient, and thermal conductiv- ity. The phonon calculation was executed in the Phonopy package [15] using the finite displacement method on a supercell. Finally, thermal properties such as heat capacity at constant volume, free en- ergy, and entropy were calculated. 3 Results and Discussion 3.1 Structural properties Figure 1 shows the ZnCu crystal structure which is a tetraauricupride cubic structure in space group Pm3m with all bond lengths of 2.53 Å. Zn is bonded with eight Cu atoms in body centered geometry [16]. Figure 1: Crystal structure of ZnCu. Using the first principles calculations in Quantum Espresso software, the total energies were mini- mized as a function of the lattice parameter for the material. The lattice parameter (a), bulk modulus( B0 = −V ∂P ∂V ) , and pressure derivative (B′) of the ZnCu crystal structure are derived by fitting the Murnaghan equation of state as [17] P (V ) = B0 B′ [( V0 V )B′ − 1 ] (1) where V0 is the equilibrium volume and B′ = dB/dP . The Murnaghan equation of state is fitted using the ev.x tool of Quantum Espresso to calculate total energy as a function of unit cell volume. The ob- tained value of the lattice parameter is 2.96628 Å, which is consistent with the experimental value of 2.959 Å [4]. Similarly, bulk modulus (B0) and its pressure derivative (B′) are found to be 115.00 GPa and 5.02, respectively. The obtained value of bulk modulus is in good agreement with the value in the materials project database, which is 116.00 GPa [18]; validating the present computational ap- proaches. 3.2 Vibrational properties The phonon serves as a medium for understanding transmission of vibrational energy in the material. Utilizing the phonopy algorithm [15], the phonon frequency of ZnCu was calculated. A 2×2×2 super- cell was created to collect force sets for analyzing the phonon band structures and phonon density of states (DOS). The phonon dispersion curves and the corresponding phonon density of states (DOS) of ZnCu are shown in Figure 2. These calculations Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 190 were performed to assess the dynamical stability and lattice vibrational behavior of the compound. The phonon dispersion curve displays the vibra- tional frequencies along high-symmetry directions in the Brillouin zone. Importantly, no imaginary frequencies (i.e., frequencies below zero) are ob- served throughout the entire Brillouin zone, indicat- ing that the ZnCu structure is dynamically stable in its equilibrium configuration. The phonon spec- trum features both acoustic and optical branches. The acoustic modes originate from the Γ- point and extend up to about 4 THz, while the opti- cal modes span from about 4 THz to over 6.5 THz. The separation between the acoustic and optical branches suggests a moderate mass differ- ence between Zn and Cu atoms and indicates poten- tial phonon scattering behavior relevant to thermal transport. The phonon density of state (DOS) ex- hibits multiple sharp peaks, especially in the high- frequency region (4–7 THz), corresponding to lo- calized optical modes. The lower-frequency region shows a more gradual increase in DOS, associated with acoustic phonons. This distribution of vi- brational states implies that optical phonons sig- nificantly contribute to the vibrational properties, while acoustic phonons dominate low-temperature specific heat and thermal conductivity. he phonon DOS achieved is consistent with the findings of a previous study by Peter et al. for β-ZnCu [7]. Figure 2: Phonon band structures and phonon DOS of ZnCu. 3.3 Elastic properties The elastic constant matrices (Cij) were calcu- lated using Thermo_pw utility of Quantum Espresso. Three independent elastic constants; C11, C12, and C44 for cubic structure of ZnCu were obtained. These elastic constants were further used to calcu- late the elastic property through Voigt–Reuss–Hill (VRH) methods [19–22]. The relation of shear modulus (G) and bulk modulus (B) are expressed as [12,19,23] GV = C11 − C12 + 3C44 5 (2) GR = 5C44(C11 + C12) 4C44 + 3(C11 − C12) (3) G = GV +GR 2 (4) BV = BR = C11 + 2C12 3 (5) B = BV +BR 2 (6) Similarly, Young’s modulus (Y ), Poisson’s ratio (ν), and universal elastic anisotropy index (AU ) can be calculated using the relations as [19,20,23] Y = 9BG 3B +G (7) ν = 3B − 2G 2(3B +G) (8) AU = 5 ( GV GR ) + ( BV BR ) − 6 (9) Table 1 shows the calculated values of these elas- tic parameters. Born criteria for mechanical stabil- ity of the cubic system, i.e., C11 > 0, C44 ≥ 0, C11 ≥ |C12| and C11 + 2C12 ≥ 0 are satisfied by the calculated value of elastic constants [12,22,23]. This shows that ZnCu crystal is mechanically sta- ble. Furthermore, the value of bulk modulus (B0) calculated using Murnaghan equation of state in the Section 3.1 and Voigt-Reuss-Hill methods using Equation (3.3) are comparable with the value pre- dicted in the material project database [18] and ref. Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 191 [4]. The small discrepancy in the calculated values of elastic parameters with material project database may be due to the use of different pseudopotentials. We have used PBE type pseudopotential whereas the later, ref. [18], have used PBESol type pseu- dopotential. Table 1: Calculated values of elastic parameters for ZnCu complex Parameter This work Material project [18] Other [4] C11 (GPa) 152.692 134.8 – C12 (GPa) 102.697 104.7 – C44 (GPa) 96.992 75.4 – B (GPa) 119.362 116 117.4 G (GPa) 56.632 46 40.1 Y (GPa) 145.975 107.7 – ν 0.295 0.33 0.34 AU 2.565 3.57 3.87 Figure 3: Spatial dependence and 3D visualization of Young’s Modulus (Y ), linear compressibility (β), shear modulus (G) and Poisson’s ratio (ν) of ZnCu. Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 192 The bulk modulus (B) characterizes the material’s resistance to uniform compression and is intrinsi- cally linked to its crystal structure, including the nature and length of chemical bonds . The shear modulus (G), or modulus of rigidity, quantifies the material’s response to shear stress, reflecting its ability to resist deformation caused by tangential forces that induce relative motion between adjacent atomic layers. Young’s modulus (Y ) represents the stiffness of the material under uniaxial tensile stress and provides a comprehensive measure of its elas- tic rigidity [16, 24, 25]. Its higher values indicate greater resistance to deformation. The calculated value of Y = 145.975 GPa, indicating moderately high stiffness, consistent with metallic bonding. Additional mechanical parameters derived from the elastic moduli, namely Pugh’s ratio (k = B/G), Poisson’s ratio (ν), and the universal anisotropy index (AU ) offer valuable insight into the bonding characteristics, mechanical behavior, and elastic anisotropy of crystalline materials [26]. According to Pugh’s criterion, materials with k > 1.75a re typ- ically classified as brittle, while those with k > 1.75 are considered ductile [19]. The calculated value of k = 2.11, indicating the material to be ductile. The calculated value of ν = 0.295 corresponding that the material exhibits metallic ductility, as predicted by k. Furthermore, a universal anisotropy index of AU = 1 denotes a mechanically isotropic material, whereas any deviation from this value indicates the presence of elastic anisotropy [19]. The obtained value of AU = 2.565 corresponding that te material to be significantly anisotropic, which may affects its mechanical behaviour under directional stress. The directiona dependence of the elastic properties was also analyzed using the ELATE software [27], which processes the second-order elastic constants (Cij) in Voigt notation. Based on the calculated values of C11, C12 and C44, Table 1. The software then generated 2D and 3D plots of mechanical properties, including Young’s modulus (Y ), linear compressibility β, shear modulus (G) and Poisson’s ratio (ν). The obtained results are summarized in Table 2, and their 2D and 3D plots are visualized in Figure 3. The uniform shapes of the respective plots indicate isotropy, while deviations reflect elas- tic nisotropy. The software utilizes distinct color schemes to rep- resent elastic properties in 2D and 3D visualiza- tions [27]. For Y and β, green indicates positive values and red denotes negative values. In the case of G and ν, up to three colors are employed: solid green and translucent blue for positive values, and translucent red for negative values, particularly rel- evant for Poisson’s ratio, which may become nega- tive in specific crystallographic directions. It can be observed that the spatial dependence of Y , β and G are found to be positive for the material with finite and non-negative values of respective anisotropy. Figure 3. But the value of ν is found to be negative (there is presence of red colour) with infinite value of anisotropy indicating its directional dependence. Table 2: Variations of Young’s modulus (Y ), linear compressibility (β), shear modulus (G), and Poisson’s ratio (ν), along with their corresponding anisotropy ratios for ZnCu Parameter Y (GPa) β (TPa−1) G (GPa) ν Min Max Min Max Min Max Min Max Value 70.009 228.960 2.7926 2.7926 24.998 96.992 -0.24656 0.83841 Anisotropy 3.266 1.000 3.880 ∞ 3.4 Electronic properties The electronic properties of the material were inves- tigated using DFT within the PBE scalar relativis- tic approximation. The calculated electronic band structures, density of states (DOS), and partial density of states (PDOS) are presented in Figure 4(a,b). The band structures of te material shows multi- ple bands crossing the Fermi level (EF ), consistent with its metallic character, as shown in Figure 4(a). Notably, several highly dispersive bands are observed near EF along the Γ-X, R-X, and M–Γ directions, indicating the presence of high carrier mobility in these directions. In contrast, the pres- ence of relatively flat bands around −3 eV to −2 eV corresponds to localized Cu-d states, as supported by the PDOS in Figure 4(b). The absence of a band gap and the significant overlap of conduction and valence bands near EF suggest that ZnCu can ex- hibit good electrical conductivity. The availability of partially filled conduction states also implies the possibility of tuning thermoelectric performance through appropriate doping or carrier concentra- tion adjustment. The PDOS plot reveals that the Cu-3d orbitals dominate the valence region, particularly within the energy range from approximately −4 eV to −2 eV, Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 193 as shown in Figure 4(b). The Zn-3d states con- tribute mainly at deeper energies (−6 eV to −3 eV), whereas the s and p orbitals of both Zn and Cu ex- hibit relatively minor contributions. The non-zero density of states at the Fermi level confirms the metallic nature of ZnCu, which further supports the results of band structures. Figure 4: Electronic band structures, density of states and partial density of states (PDOS) of ZnCu. 3.5 Thermoelectric properties The thermoelectric properties of the ZnCu were investigated using Boltzmann transport equation implemented in BoltzTrap2 codes [12, 14]. The calculations were basically focusing on the See- beck coefficient (S), electrical conductivity (σ/τ0), thermal conductivity (ke/τ0), and power factor (PF = S2σ/τ). The calculated values of these pa- rameters are plotted as a function of temperature in Figure 5. The Seebeck coefficient exhibits a nonlinear trend, starts slightly positive from about 200 K and be- comes strongly negative around/at 300 K. With further increase in the temperature of the sam- ple, plot of Seebeck coefficient gradually increases towards zero as temperature approaches 850 K. The change in sign of the coefficient indicates a crossover in carrier type dominance. Its posi- tive value indictes hole-like or p-type behaviour whereas negative value indicates electron-like or n- type behaviour. The sharp negative peak suggests dominant n-type conduction at intermediate tem- peratures. The plot of electrical conductivity decreases with temperature (top right panel of Figure 5). This behaviour is expected for metallic semiconduct- ing materials, in which increased phonon scattering takes place at higher temperatures thereby reducing the conductivity of material. Further, the thermal conductivity of the material increases linearly with temperature (bottom left panel of Figure 5). This behaviour is typical as thermal conductivity due to electrons generally increases with temperature in metallic system. The power factor combines Seebeck and conduc- tivity, which is a key quantity in thermoelectric performance. The plot of power factor stars from zero at/about 200 K and then gradually increases attaining peak value around 300 K. It decreases sharply then after with further increase in temper- ature (bottom right panel of Figure 5). The peak near 300 K indicates optimal thermoelectric perfor- mance at room temperature. 4 Conclusions The structural, mechanical, electronic, and thermo- electric properties of ZnCu have been systemati- cally investigated using the first principles calcula- tions employing Quantum Espresso codes. Elastic constant calculations confirm the mechanical sta- bility of the compound, satisfying the Born sta- bility criteria for cubic systems. Pugh’s ratio and Poisson’s ratio indicate that ZnCu is ductile, while the universal anisotropy index and ELATE visual- izations reveal significant elastic anisotropy. Elec- tronic band structure analysis demonstrates that ZnCu exhibits metallic behavior, with no band gap across the Fermi level. This metallic nature sup- ports good electrical conductivity, which is a critical factor in thermoelectric performance. Thermoelec- tric calculations show that ZnCu achieves its high- est power factor at 300 K, highlighting its poten- tial for energy conversion applications. Thus, ZnCu Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 194 Figure 5: Temperature dependence of Seebeck coefficient (S), electrical conductivity (σ/τ0), thermal conductivity (ke/τ0), and power factor (PF = S2σ/τ) of ZnCu. combines mechanical robustness, metallic conduc- tivity, and promising thermoelectric performance, making it a potential candidate for multifunctional applications in structural and energy-related tech- nologies. References [1] Sah D, Adhikari D, Yadav S. Temperature- Dependence of Mixing Properties of Cu-Ti Liq- uid Alloy. Adhyayan Journal. 2023;10(10):1– 10. [2] Yadav S, GautamM, Adhikari D. Mixing prop- erties of Cu–Mg liquid alloy. AIP Advances. 2020;10(12). [3] Godbole R, Jha S, Milanarun M, Mishra A. Thermodynamics of liquid Cu–Mg alloys. Journal of alloys and compounds. 2004;363(1- 2):187–193. [4] Iwaoka H, Hirosawa S. First-principles calcula- tion of elastic properties of Cu-Zn intermetallic compounds for improving the stiffness of alu- minum alloys. Computational Materials Sci- ence. 2020;174:109479. [5] Liu Q, Cheng L. Structural evolution and elec- tronic properties of Cu-Zn alloy clusters. Jour- nal of Alloys and Compounds. 2019;771:762– 768. [6] Li L, zhou Wang Y, Liu Q, Wang K, Bao Y, Zhao B, et al. The thermodynamic properties of disorder CuZn solid solution and nonstoi- chiometric Cu-Zn alloy: Pseudo-atomic lattice inversion potential method. Journal of Solid State Chemistry. 2020;289:121488. [7] Peter M, Potzel W, Steiner M, Schäfer C, Karzel H, Schiessl W, et al. Lattice-dynamical effects and hyperfine interactions in Cu-Zn al- loys. Physical Review B. 1993;47(2):753. [8] Liu Y, Wang J, Gao Qn, Du Y. Struc- tural, elastic and electronic properties of Cu- X compounds from first-principles calcula- Shashit Kumar Yadav et al./ BIBECHANA 22 (2025) 188-195 195 tions. Journal of Central South University. 2015;22(5):1585–1594. [9] Tang Y, Ma J, Han D, Wang J, Qi H, Jin L. Critical evaluation and thermodynamic opti- mization of the Cu-Zn, Cu-Se and Zn-Se binary systems. Metals. 2022;12(9):1401. [10] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, et al. QUANTUM ESPRESSO: a modular and open-source soft- ware project for quantumsimulations of mate- rials. Journal of physics: Condensed matter. 2009;21(39):395502. [11] Talirz L, Kumbhar S, Passaro E, Yakutovich AV, Granata V, Gargiulo F, et al. Materials Cloud, a platform for open computational sci- ence. Scientific data. 2020;7(1):299. [12] Yadav S, Dahal S, Khadka R, Guragain B, Pokharel P, Oli P, et al. First Principles Study of Electronic, Vibrational, Elastic, and Thermodynamic Properties of Sc-X (X= P, S, Se) Compounds. Engineering Reports. 2025;7(1):e13115. [13] Dal Corso A. Elastic constants of beryl- lium: a first-principles investigation. Journal of Physics: Condensed Matter. 2016;28(7):075401. [14] Madsen GK, Singh DJ. BoltzTraP. A code for calculating band-structure dependent quan- tities. Computer Physics Communications. 2006;175(1):67–71. [15] Togo A, Chaput L, Tadano T, Tanaka I. Implementation strategies in phonopy and phono3py. Journal of Physics: Condensed Matter. 2023;35(35):353001. [16] Jain A, Ong SP, Hautier G, Chen W, Richards WD, Dacek S, et al. Commentary: The Mate- rials Project: A materials genome approach to accelerating materials innovation. APL mate- rials. 2013;1(1). [17] Bhardwaj P, Singh S. First principle calcula- tion of structural, electronic and elastic prop- erties of rare earth nitride. Mater Sci-Poland. 2016;34(4):715. [18] Project M. mp-987: Material Properties; 2025. Accessed: 2025-05-27. Available from: https://next-gen.materialsproject.org/ materials/mp-987. [19] Pokharel P, Yadav S, Pantha N, Adhikari D. Strain-dependent electronic, mechani- cal and piezoelectric properties of ZrSiO3 2D monolayer: A first principle approach. Journal of Physics and Chemistry of Solids. 2024;193:112198. [20] Pokharel P, Yadav SK, Pantha N, Sharma B, Adhikari D. Structural, electronic, opti- cal, magnetic, and mechanical properties of SmMnO3 perovskite with europium and yt- trium doping: A first-principles study. AIP Advances. 2024;14(12). [21] Gupta PC, Adhikari R. Structural, Elas- tic, Electronic and Optical Properties of Be_2X(X = C, Si,Ge, Sn): First Principle Study. arXiv preprint arXiv:211210521. 2021;. [22] Chaudhary U, Chaudhary S, Yadav DK, Kaphle GC, Yadav SK. First-Principles In- vestigation of Structural, Elastic, Electronic, and Optical Properties of AcMO3 (M= B, Sc) Perovskites. physica status solidi (b). 2025;262(5):2400574. [23] Gao J, Liu QJ, Tang B. Elastic stability cri- teria of seven crystal systems and their ap- plication under pressure: Taking carbon as an example. Journal of Applied Physics. 2023;133(13). [24] Cao Y, Zhu J, Liu Y, Nong Z, Lai Z. First- principles studies of the structural, elastic, electronic and thermal properties of Ni3Si. Computational Materials Science. 2013;69:40– 45. [25] Hadi MA, Christopoulos SR, Chroneos A, Naqib SH, Islam AKMA. DFT insights into the electronic structure, mechanical behaviour, lattice dynamics and defect processes in the first Sc-based MAX phase Sc2SnC. Scientific Reports. 2022;12(1):14037. [26] Jamal M, Asadabadi SJ, Ahmad I, Aliabad HR. Elastic constants of cubic crystals. Com- putational Materials Science. 2014;95:592–599. [27] Gaillac R, Pullumbi P, Coudert FX. ELATE: An open-source online application for anal- ysis and visualization of elastic tensors. Journal of Physics: Condensed Matter. 2016;28(27):275201. https://next-gen.materialsproject.org/materials/mp-987 https://next-gen.materialsproject.org/materials/mp-987 Introduction Computational Details Results and Discussion Structural properties Vibrational properties Elastic properties Electronic properties Thermoelectric properties Conclusions