Generalized Gradient Approximation Calculations Research Articles

Central role of d-band energy level in Cu-based intermetallic alloys

Cu-Au intermetallic alloys are classic paradigms in the history of alloy theory for studying order-disorder transition, phase stability, and so on. However, density functional theory with a generalized gradient approximation (GGA) fails to describe their formation energies and Au-rich ground states, e.g., calculated formation energies are nearly 40% smaller than experimental values. In this work, we found that these discrepancies, which are also common in other Cu-transition metal (TM) intermetallic alloys, are actually caused by the fact that GGA produces Cu-3d bands with a shallower energy level than the experimental results, leading to incorrect d-d hybridizations. By using the Hubbard U correction to adjust the d-bands to the correct position, the discrepancies in GGA calculations are eliminated. Our finding that the correct d-bands position is the key to characterize Cu-TMs, which can be achieved efficiently by applying the Hubbard U correction.

First-principles calculations to investigate structural, electronic, and elastic properties of Fe3SnC ternary alloy

In this paper, the structural, electronic, and elastic properties of Fe3SnC were calculated based on local density approximation (LDA) and generalized gradient approximation (GGA) in density functional theory (DFT). Compared with GGA, LDA underestimates lattice constants and overestimates binding energy and elastic constants. The calculated lattice constants are 3.76 Å (LDA) and 3.83 Å (GGA), respectively, and the latter is closer to the experimental values. With U correction in GGA and LDA, the magnetic properties of the system are shown in the band structure. The GGA calculation results are more accurate, and the calculated magnetic moment of Fe3SnC is 5.74μB. The band structure indicates that Fe3SnC is a metallic compound. The elastic constants show that Fe3SnC has a large elastic constant and bulk modulus, in which the C11 calculated by GGA is as high as 463.81GPa, and the Young's modulus is as high as 350.72GPa. This indicates that Fe3SnC is a potential cermet due to a strong deformation resistance. At the same time, with the minimum thermal conductivity of 1.65 W/mK calculated by the Cahill model.

Physical properties of newly synthesized noncentrosymmetric TaIr2B2 and NbIr2B2 superconductors: an extensive comparison of GGA and LDA functional investigations.

In recent years, noncentrosymmetric (NCS) structural compounds have received much attention from the scientific community in the exploration for the unconventional nature of superconductivity with exciting physical properties. This study uses the comprehensive generalized gradient approximation (GGA) and local density approximation (LDA) to gain insights into the physical properties of two recently synthesized Ir-based NCS superconductors, TaIr2B2 and NbIr2B2. The structural parameters, mechanical performance, electronic structure, Debye temperature, melting temperature, electronic specific heat, and electron-phonon coupling constant of TaIr2B2 and NbIr2B2 are explored and discussed in detail. Density functional theory (DFT) optimized structural parameters of both NCS phases agree well with experimental observation. Both GGA and LDA calculations show that the compounds are ductile, machinable, mechanically stable, and anisotropic in nature. The elastic moduli and hardness calculations reveal that TaIr2B2 is harder than NbIr2B2. The calculation of the melting temperature reveals that TaIr2B2 is more suitable for high temperature technology applications compared to NbIr2B2. Both GGA and LDA functionals reveal that the optical functions are very similar. Both compounds display a significant amount of reflectivity spectra over a wide range of photon energies. The GGA functional reveals a somewhat higher density of states value compared to that of LDA. The present calculated values of the electron-phonon coupling constant of both compounds are consistent with values previously reported from experimental studies.

First-principles prediction of energy bandgaps in 18-valence electron semiconducting half-Heusler compounds: Exploring the role of exchange and correlation

The choice of exchange functional is a critical factor in determining the energy bandgap of semiconductors. Ab initio calculations using different exchange functionals, including the conventional generalized-gradient approximation (GGA) functionals, meta-GGA functionals, and hybrid functionals, show significant differences in the calculated energy bandgap for semiconducting half-Heusler compounds. These compounds, which have 18 valence electrons per unit cell, are of great interest due to their thermoelectric properties, making them suitable for energy conversion applications. In addition, accounting for electronic correlations using the GW method also affects the calculated energy bandgaps compared to standard GGA calculations. The variations in calculated energy bandgaps are specific to each material when using different functionals. Hence, a detailed investigation of the electronic properties of each compound is necessary to determine the most appropriate functional for an accurate description of the electronic properties. Our results indicate that no general rules can be established and a comparison with experimental results is required to determine the most appropriate functional.

Minority-spin conducting states in Fe substituted pyrite CoS2

There has been a longstanding debate whether the pyrite CoS2 or its alloys with FeS2 are half metallic. We argue using first principles calculations that there is a finite occupation of minority-spin states at the Fermi level throughout the series CoFe x S2. Although the exchange–correlation functional influences the specifics of the electronic structure, we observe a similar trend with increasing Fe concentration in both local density approximation and generalized gradient approximation calculations. Specifically, even as band filling is decreased through Fe substitution, the lowest-lying conduction band in the minority-spin channel broadens such that these states keep getting lowered relative to the Fermi level, which is contrary to the expectations from a rigid band picture. Furthermore, the exchange splitting decreases as more Co atoms are replaced by Fe, and this again brings the minority-spin states closer to the Fermi level. These two mechanisms, in conjunction with the experimental observation that minority-spin bands cross the Fermi level in stoichiometric CoS2, indicate that minority-spin charge carriers will always be present in CoFe x S2.

Synthesis, crystal and energy structure of the Ag8SnS6 crystal

The Ag8SnS6 crystal was synthesized by directly melting a high-purity stoichiometric mixture of elementary Ag, Sn, and S in a sealed quartz ampoule. This argyrodite crystallizes in the orthorhombic structure (Pna21 space group (No. 33)) at room temperature. The theoretical first-principle calculations of the electronic band structure and density of states of a αʹʹ-Ag8SnS6 crystal are estimated by the generalized gradient approximation (GGA) and local density approximation (LDA). A Perdew–Burke–Ernzerhof functional (PBE) and (PBEsol) were utilized for GGA calculation. All calculated parameters correlate well with known experimental data. Based on the electronic band structure, the effective mass of electrons and holes was calculated. The anisotropic behavior of electronic band structure is discussed.

Hardness of molecules and bandgap of solids from a generalized gradient approximation exchange energy functional.

The deviations from linearity of the energy as a function of the number of electrons that arise with current approximations to the exchange-correlation (XC) energy functional have important consequences for the frontier eigenvalues of molecules and the corresponding valence-band maxima for solids. In this work, we present an analysis of the exact theory that allows one to infer the effects of such approximations on the highest occupied and lowest unoccupied molecular orbital eigenvalues. Then, we show the importance of the asymptotic behavior of the XC potential in the generalized gradient approximation (GGA) in the case of the NCAPR functional (nearly correct asymptotic potential revised) for determining the shift of the frontier orbital eigenvalues toward the exact values. Thereby we establish a procedure at the GGA level of refinement that allows one to make a single calculation to determine the ionization potential, the electron affinity, and the hardness of molecules (and its solid counterpart, the bandgap) with an accuracy equivalent to that obtained for those properties through energy differences, a procedure that requires three calculations. For solids, the accuracy achieved for the bandgap lies rather close to that which is obtained through hybrid XC energy functionals, but those also demand much greater computational effort than what is required with the simple NCAPR GGA calculation.

A flexible and scalable scheme for mixing computed formation energies from different levels of theory

Computational materials discovery efforts are enabled by large databases of properties derived from high-throughput density functional theory (DFT), which now contain millions of calculations at the generalized gradient approximation (GGA) level of theory. It is now feasible to carry out high-throughput calculations using more accurate methods, such as meta-GGA DFT; however recomputing an entire database with a higher-fidelity method would not effectively leverage the enormous investment of computational resources embodied in existing (GGA) calculations. Instead, we propose here a general procedure by which higher-fidelity, low-coverage calculations (e.g., meta-GGA calculations for selected chemical systems) can be combined with lower-fidelity, high-coverage calculations (e.g., an existing database of GGA calculations) in a robust and scalable manner. We then use legacy PBE(+U) GGA calculations and new r2SCAN meta-GGA calculations from the Materials Project database to demonstrate that our scheme improves solid and aqueous phase stability predictions, and discuss practical considerations for its implementation.

Effect of External Electric Field Applied to Bilayer Graphene Bandgap: Density Functional Theory Study

Graphene is a prominent material in a wide range of applications, however, the gapless nature of graphene limits its great performance in certain applications, such as in optoelectronic and photocatalytic applications field. Opening the bandgap has become one of the focused studies on graphene material today. Here, we used density functional theory (DFT) calculation to investigate the bandgap opening of bilayer graphene by external electric field applying. The calculation was performed on hexagonal stacked bilayer graphene structure using three different approximations and functional DFT; that is generalized gradient approximation (GGA) PBE and PW-91, as well as Local-density approximations (LDA) -CAPZ. The external electric field varied from 0.0 to 0.5 eV/Å/e in various electric field directions. The calculations results shows that the external E-F applied in perpendicular direction open the bandgap almost 4-times than non-determined the electric field direction. The bandgap opening by LDA functional calculation perform smaller bandgap opening compared to GGA calculation results, while the PBE and PW-91 of GGA produced similar values at low electric field applied. The larger bandgap of 0.80 eV obtained at 0.3 eV/Å/e electric field applied calculated with both GGA functional At 0.5 eV/Å/e electric field applied, bandgap with GGA-PBE almost zero, and the crystal structure changed from cubic to triclinic with layer position become apart.

Fermi-Löwdin orbital self-interaction correction of adsorption energies on transition metal ions.

Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu+, Zn+, Zn2+, and Mn+ in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew-Zunger self-interaction correction (PZ-SIC) in the Fermi-Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1eV. Analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.

Structure and electronic properties of LnScO3 compounds: A GGA + U calculation

The lattice parameters, bond lengths, bond angles (octahedra tilt angles), Goldschmidt tolerance factor, density of states and electronic band structure of rare-earth scandates LnScO3 (Ln = Eu, La, Nd, Pr, Sm and Tb) in orthorhombic structure have been investigated in the generalized gradient approximation (GGA) + U method with the on-site Coulomb interaction parameter Ueff varying from 1 to 10 eV. The lattice constants, octahedra tilt angles (except for (Eu,Tb)ScO3 compounds), mean 〈Sc-O〉 and 〈Ln-O〉 bond lengths increased almost linearly with effective U parameter values. However, the tolerance factor has decreased (except for (Eu,Tb)ScO3 compounds). Density of states and electronic band structure computations show that LnScO3 compounds are insulator materials and have direct electronic band gap. The electronic band gap of the compounds first increases and then decreases with increasing Ueff. (GGA) + U calculation shows a strong hybridization between Sc-3d and O-2p states. Rare-earth (Ln)-5d states contribute somewhat to this hybridization. The electronic charge distribution and (P)DOS calculation results show that the bonding behavior of LnScO3 compound is a combination of covalent and ionic nature. Our results show that the structural and electronic properties are affected by the application of the Hubbard U term in GGA calculations and the computed lattice constants, bond distances and octahedra tilt angles deviate more from the experimental values. On the other hand, it was observed that the electronic band gap approached the experimental values at the optimal Ueff values determined for the compounds.

Effects of pseudopotentials and exchange-correlation functionals on phase transition of LaH10

To assess the effects of pseudopotentials and exchange-correlation functionals on trigonal to face-centered cubic phase transition of LaH10, we performed density functional theory based first-principles calculations by employing three-types of pseudopotentials with LDA (local density approximation) and GGA (generalized gradient approximation) exchange-correlation functionals. We found that the lattice parameters such as cell angle or cell volume and phase transition pressure exhibit a significant variation with LDA and GGA functionals whereas they exhibit a weak dependence on the pseudopotentials. In general, LDA calculations result in a lower phase transition pressure than GGA calculations. We also investigated the effects of pseudopotentials and exchange-correlation functionals on the electronic properties by calculating the total and partial density of state functions for face-centered cubic phase of LaH10 at 150 GPa. Computed electronic densities of states at the Fermi level are found to exhibit a weak dependence on the exchange-correlation functionals.

Assessment of the Accuracy of Density Functionals for Calculating Oxygen Reduction Reaction on Nitrogen-Doped Graphene.

Experimental studies of the oxygen reduction reaction (ORR) at nitrogen-doped graphene electrodes have reported a remarkably low overpotential, on the order of 0.5 V, similar to Pt-based electrodes. Theoretical calculations using density functional theory have lent support to this claim. However, other measurements have indicated that transition metal impurities are actually responsible for the ORR activity, thereby raising questions about the reliability of both the experiments and the calculations. To assess the accuracy of the theoretical calculations, various generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are employed here and calibrated against high-level wave-function-based coupled-cluster calculations (CCSD(T)) of the overpotential as well as self-interaction corrected density functional calculations and published quantum Monte Carlo calculations of O adatom binding to graphene. The PBE0 and HSE06 hybrid functionals are found to give more accurate results than the GGA and meta-GGA functionals, as would be expected, and for a low dopant concentration, 3.1%, the overpotential is calculated to be 1.0 V. The GGA and meta-GGA functionals give a lower estimate by as much as 0.4 V. When the dopant concentration is doubled, the overpotential calculated with hybrid functionals decreases, while it increases in GGA functional calculations. The opposite trends result from different potential-determining steps, the *OOH species being of central importance in the hybrid functional calculations, while the reduction of *O determines the overpotential obtained in GGA and meta-GGA calculations. The results presented here are mainly based on calculations of periodic representations of the system, but a comparison is also made with molecular flake models that are found to give erratic results due to finite size effects and geometric distortions during energy minimization. The presence of the electrolyte has not been taken into account explicitly in the calculations presented here but is estimated to be important for definitive calculations of the overpotential.

Relative stabilities of Si polytypes under biaxial stress: A first-principles study

We explore the possibility of the production of Si polytypes via the total energies and free energies obtained in the density-functional theory and the density-functional perturbation theory. We first calculate the total energies of three polytypes of the tetrahedrally coordinated $s{p}^{3}$ Si atoms having the two-layer, three-layer, and four-layer stacking periods in the hexagonal unit cell (``$2H$'', ``$3H$'', and ``$4H$'') as a function of the in-plane lattice constant $a$ using the local-density approximation (LDA) and generalized gradient approximation (GGA) comparatively. In the LDA calculation, the $4H$ phase is energetically the most favorable among three phases in the range of 3.55 \AA{} $\ensuremath{\le}$ $a$ $\ensuremath{\le}$ 3.73 \AA{}. While the $4H$ phase is found to be more stable than the $2H$ phase at a relatively wide range of the $a$ value we studied, the $2H$ phase is found to be more stable than the $3H$ ($3C$) phase in the range of 3.57 \AA{} $\ensuremath{\le}a\ensuremath{\le}$ 3.61 \AA{}. In the GGA calculation, on the other hand, the $4H$ phase becomes the most favorable phase for almost the same range as the LDA case, 3.57 \AA{} $\ensuremath{\le}a\ensuremath{\le}$ 3.73 \AA{}. The $2H$ phase also becomes as stable as the $3H$ phase as in the case of the LDA around the small $a$ value of 3.62 \AA{}, although the $3H$ phase energy is always lower than that of the $2H$ phase in the GGA calculation. Considering the chemical vapor deposition (CVD) growth process, we calculate the biaxial stress values to reduce the lattice constant of the substrate Si crystal to realize the small $a$ values, which can lead to the homoepitaxial growth of the $4H$ phase. The values obtained are 4.69 GPa and 8.14 GPa for the LDA and GGA, respectively. Next, we study the thermal effect on the relative stabilities of the 3 phases. We calculate the phonon dispersion, bulk modulus and thermal expansion including the vibrational and thermal effect. From the comparison with experimental values of the $3C$ phase, it is found that the LDA results show much better agreement with experiment than the GGA, indicating that the LDA calculation is reliable to predict thermal properties of the real systems. Finally, we derive the free energy as a function of $a$ under several designated temperatures. The relative stabilities of the $2H$ and $4H$ phases with respect to the $3H$ phase are found to be enhanced. At around $a=3.65$ \AA{}, stabilities of $2H$ and $4H$ phases relative to the $3H$ phase become most prominent. Although stabilities of the $2H$ and $4H$ phases relative to the $3H$ phase are reduced with increasing temperature at around $a$ = 3.60 \AA{}, $2H$ phase is found to be as stable as $3H$ and $4H$ phases at higher temperatures, indicating the possibility of the production of the $2H$ phase via high-temperature CVD process with the biaxial stress.

Sensitivity of the Fermi surface to the treatment of exchange and correlation

The group V and VI transition metals share a common Fermi surface feature of hole ellipsoids at the $N$ point in the Brillouin zone. In clear contrast to the other Fermi surface sheets, which are purely of $d$ character, these arise from a band that has a significant proportion of $p$ character. By performing local density approximation (LDA), generalized gradient approximation (GGA), strongly constrained and appropriately normed (SCAN) meta-GGA, and $GW$ approximation calculations, we find that the $p$ character part of this band (and therefore the Fermi surface) is particularly sensitive to the exchange-correlation approximation. LDA and GGA calculations inadequately describe this feature, predicting $N$ hole ellipsoid sizes that are consistently too large in comparison to various experimental measurements, whereas quasiparticle self-consistent $GW$ calculations predict a size that is slightly too small (and non-self-consistent $GW$ calculations that use an LDA starting point predict a size that is much too small). Overall, for the metals tested here, SCAN provides the most accurate Fermi surface predictions, mostly correcting the discrepancies between measurements and calculations that were observed when LDA calculations were used. However, none of the tested exchange-correlation approximations succeeds in simultaneously bringing all of the measurable properties of these metals into good experimental agreement, particularly where magnetism is concerned. The SCAN calculations predict antiferromagnetic moments for Cr that are 3 times larger than the experimental value ($1.90\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ compared to $0.62\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$).

Tuning the magnetic and electronic properties of strontium titanate by carbon doping

The magnetic and electronic properties of strontium titanate with different carbon dopant configurations are explored using first-principles calculations with a generalized gradient approximation (GGA) and the GGA+U approach. Our results show that the structural stability, electronic properties and magnetic properties of C-doped SrTiO3 strongly depend on the distance between carbon dopants. In both GGA and GGA+U calculations, the doping structure is mostly stable with a nonmagnetic feature when the carbon dopants are nearest neighbors, which can be ascribed to the formation of a C-C dimer pair accompanied by stronger C-C and weaker C-Ti hybridizations as the C-C distance becomes smaller. As the C-C distance increases, C-doped SrTiO3 changes from an n-type nonmagnetic metal to ferromagnetic/antiferromagnetic half-metal and to an antiferromagnetic/ferromagnetic semiconductor in GGA calculations, while it changes from a nonmagnetic semiconductor to ferromagnetic half-metal and to an antiferromagnetic semiconductor using the GGA+U method. Our work demonstrates the possibility of tailoring the magnetic and electronic properties of C-doped SrTiO3, which might provide some guidance to extend the applications of strontium titanate as a magnetic or optoelectronic material.

Study of some electronic and spectroscopic properties of ZnO nanostructers by density functional theory

The electronic and spectroscopic properties of ZnO nanostructures were evaluated by ab-initio density functional theory and generalized gradient approximation calculations combined with many-body, all calculations using Gaussian 09 program. These electronic properties including energy gap, density of state and bond length were calculated, also the spectroscopic properties like infrared and Raman scattering, force constant and reduced mass were calculated and compared with longitudinal optical mode of vibration. The geometrical structure of ZnO molecules and wurtzoids nanostructures were studied with the help of using Gauss view 05 program. The energy gaps of cyclohexane, Wurtzoid, wurtzoid2C and tri-wurtzoid are (4.48, 3.35, 3.4 and 3.096 eV) respectively, these values agreement with experimental values for ZnO wurtzite bulk (3.3 eV). As well as, the Spectroscopic study of IR and Raman scattering, force constant, and reduced mass as a function of frequencies showed an agreement with the experimental results.

Study geometrical, electronic and spectroscopic properties of BeO wurtzoids via DFT

The electronic and spectroscopic properties of BeO wurtzoids structure were investigated by using ab-initio density functional theory and generalized gradient approximation calculations combined with many-body. All calculations were carried out using Gaussian 09 program. Electronic properties including energy gap, density of state and bond length, as well as Spectroscopic properties of infrared and Raman scattering, force constant, reduce mass and longitudinal optical patterns. The geometrical structure of BeO molecules and wurtzoids nanostructure were studied with the help using Gauss view 05 program. The energy gap of Wurtzoid, wurtzoid2c and triwurtzoid was found to be (6.813, 7.13499 and 7.02669 eV) respectively. Those values agreed with theoretical values for BeO wurtzite (8.57 eV), and compare with the experimental value of BeO bulk (10.6 eV). The Spectroscopic study of IR and Raman scattering, force constant, and reduced mass and longitudinal optical modes as a function of frequencies are agreed with the experimental results.

First-principles study of intrinsic point defects and Xe impurities in uranium monocarbide

Based on density functional theory (DFT) calculations, we perform an extensive investigation of intrinsic point defects and Xe impurities in uranium monocarbide (UC). The DFT calculations involve both the conventional generalized gradient approximation (GGA) and the GGA+U approach with the Hubbard parametric term (U), using up to 5×5×5 supercells. GGA calculations for the formation energy of intrinsic defects demonstrate the significant effect of using larger supercells than in previous studies. Results confirm that the ⟨111⟩ and ⟨100⟩ dumbbell interstitials are the most stable interstitial configurations for U and C, respectively. The interstitial mechanisms are favored for self-diffusion of both uranium and carbon and diffusion of Xe under equilibrium conditions. Calculations also reveal that the Xe substitutional defect at the C lattice site tends to adopt an off-site configuration, which can be interpreted as a Xe interstitial–C vacancy complex. We also utilize GGA+U to assess the impact of effective U parameter (Ueff) on the results. Moreover, we introduce a method to estimate the carbon chemical potential by fitting the phase diagram composition data and propose a selection Ueff=1.25 eV based on the experimental Xe diffusion activation energy. With this approach, GGA+U calculations reproduce the available experimental data for the formation energy of the carbon Frenkel pair and can explain the stepwise recovery of intrinsic properties and burst Xe release behavior in UC observed in annealing experiments.

DFT – GGA calculations of magnetic, elastic, thermodynamic and thermoelectric properties of Co2YAl (Y = Ti, V) full Heusler alloy systems

This study used first principles calculations within the generalized gradient approximation (GGA) via plane-wave pseudo-potential scheme to extensively study the magnetic, elastic, thermodynamic and thermoelectric properties of Co2TiAl and Co2VAl Heusler alloys at their optimized lattice constants. Elastic properties of these alloys were obtained by fitting the stress-strain relationship via Voigt-Reuss-Hill approximations. Thermodynamic properties were calculated within the implementation of thermo_pw package while thermoelectric properties were estimated from non-spin polarized calculations via Boltzmann semi-classical approach as implemented in BoltzTraP package at temperatures between 0 and 800 K. Calculations reaffirmed the stable electronic and magnetic states for the alloys to be half metallic ferromagnetic (HMF) states. The estimated band gaps in the minority spin channels were 0.431 and 0.399 eV for Co2TiAl and Co2VAl alloys respectively and these were justified by their corresponding density of states. The calculated magnetic moments for the respective alloys were 0.949 and 1.978 μB, which agreed with experimental, theoretical and Slater-Pauling rule determined magnetic moments. Elastic constants (C11, C12 and C44) obtained for these cubic systems fulfilled Born-Huang mechanical stability criteria, from which other elastic related quantities were extracted. Elastic calculations predicted these alloys to be metallic bonded, extremely incompressible, highly anisotropic and ductile in nature. Thermodynamic calculations showed that Debye vibrational energies, entropies and constant volume heat capacities of the alloys increased remarkably as temperature increased whereas vibrational free energies decreased steadily with increased temperature. Thermoelectric properties were also determined, with Co2TiAl having higher figure of merit (ZT) than Co2VAl within the investigative temperatures.