Article Versions
Export Article
Cite this article
  • Normal Style
  • MLA Style
  • APA Style
  • Chicago Style
Research Article
Open Access Peer-reviewed

Structural, Electronic and Mechanical Properties of Re Doped FeMnP0.67A0.33 (A=Ga and Ge): A DFT Study

Gabriel Kipkemei Chirchir, Winfred Mueni Mulwa , Bamidele Ibrahim Adetunji
International Journal of Physics. 2022, 10(1), 70-78. DOI: 10.12691/ijp-10-1-6
Received December 01, 2021; Revised February 03, 2022; Accepted February 11, 2022

Abstract

The structural, electronic and mechanical properties of Re doped FeMnP0.67A0.33 (A= Ga and Ge) were examined by use of density functional theory (DFT) within the generalized gradient approximations as demonstrated in Quantum ESPRESSO code. The optimized structural parameters as well as derived lattice parameters are in consistent with other computational and achievable experimental results. The computed independent elastic constants confirm the mechanical stability of the investigated materials. The computed Poisson’s and Pugh’s ratios as well as Cauchy pressure, verify that FeMn0.67Re0.33P0.67Ga0.33 is the most ductile among the studied compounds. The calculated values of bulk modulus, shear modulus and Young’s modulus confirm high values of bond strength, hardness and stiffness of the investigated materials respectively. Therefore, the four compounds considered may be appropriate for industrial applications. The results report that FeMn0.67Re0.33P0.67Ga0.33 compound is more ductile and mechanically stable compared to other investigated compounds. This is the first qualitative computational prediction of the elastic properties of FeMnP0.67Ge0.33, FeMnP0.67Ga0.33, FeMn0.67Re0.33P0.67Ge0.33 and FeMn0.67Re0.33P0.67Ga0.33 compounds and this awaits experimental ratification. The calculated electronic density of states confirms that the Re_2p states are located in the conduction band (CB) in the unite cell while Re_3d dominate the CB in the supercell. Results from the doped compounds could not be compared with experimental or computational findings because to the best of our knowledge, this has not been done.

1. Introduction

Ferromagnets with first order conversion to the ordered state are scarce. P-type is an eminent example with curie temperature . Ferromagnetism in P-type materials fade away through first order phase transition at The origination of such abnormal Tc sensitivity is not clear. A distinctive property of P-type is an exceptionally heavy dependence of Tc on lattice parameter adjustments as a result of substitution/doping. P-type compounds also attract increasing attention due to their uncommon properties, that is, they exhibit a unique property of magnetocaloric effect (MCE). P-type compounds mimic magnetocaloric materials in that they are ductile and mechanically stable. These two properties manifest themselves in their function under repeated magnetic and thermal cycles. This unique combination of properties suits as magnetocaloric materials for near temperature refrigeration.

Research efforts have been made to study the properties of P-type materials both computationally 1 and experimentally 2 and a few of these compounds have been exhaustively investigated. The FeMn-based magnetocaloric materials of the form FeMnP0.67A0.33 (A = Ge and Ga) with hexagonal P-type structure are some of the compounds which have not yet been exhaustively investigated. FeMnP0.67A0.33 (A= Ga and Ge) which is an example of P-type compound crystalizes in a hexagonal structure belonging to the space group of P-6̄2m. The transition metals (Fe and Mn) occupy 3f and 3g sites and the phosphorous occupy 2c and (A= Ga and Ge) occupy the 1b site. It has been observed that close to the room temperature, this group of materials, undergoes first-order magneto-elastic transition 3 which leads to changes in the ratio of the lattice parameters (c/a) without significant changes in the volume. For P-type materials, first order conversion is expected to rise from an interaction between magnetic, structural and electronic properties 4, 5. This study addresses the structural, electronic and mechanical properties. For the purpose of tuning the curie temperature and reducing the thermal hysteresis while enhancing the mechanical stability in P-type materials, a lot investigations have been carried out 6. Balancing the Mn:Fe ratio 7 has been tried, not forgetting the introduction of nitrogen 8. Another option adopted in experiments was doping with elements such as (Co, Ni, Cu, Cr) 9, 10. This present study aims at obtaining the complementary knowledge on the influence of Re addition on the mechanical and ductility properties which is essential information that requires to be taken into consideration for practical applications.

Computational calculations on the structural, mechanical and electronic properties of FeMnP0.67A0.33 (A= Ga and Ge) are limited. Therefore, in this work, first principle calculations will be utilized to investigate the elastic properties of FeMnP0.67A0.33 (A= Ga and Ge) with the intention of determining optimal composition that combine fascinating machinability with improved ductility. Additionally, structural and electronic analysis will be carried out on the investigated alloys and compared with other DFT as well as experimental findings. These four compounds FeMnP0.67 Ge0.33, FeMnP0.67 Ga0.33, FeMn0.67Re0.33P0.67Ge0.33 and FeMn0.67Re0.33P0.67Ga0.33 have been chosen for this work due to their improved ductility and mechanical stability. Ma et al 11 confirms that substitution of the Si with Ge and Ga in the compound improves in ductility. Ductile compounds can withstand the strain during thermal hysteresis 12.

Si, Ga and Ge elements have a close atomic radius given as 1.46 Å,1.81 Å and 1.52 Å respectively, therefore structural distortion was not experienced. The atomic radius of the Ga and Ge elements compared to atomic radius of Phosphorus which is 1.23 Å ensures stability in the hexagonal Fe2-Ptype structure. Mechanical properties of solids are determined by their elastic constants. Ma et al 11 reports that, the weak mechanical stability across the phase transition of alloy restricts its applicability in practical devices. The mechanical stability of alloy can be improved by replacing Si atoms with other elements such as Ge and Ga 9, 13 atoms. The lattice parameters variations lead to large local strain in the alloy during the phase transition resulting in poor mechanical stability 11. This study investigates introduction of a group 13 element, Ga which replaces, group 14 element Ge, given that it is reported 14 that group 14 elements used as dopants, distorts the hexagonal structure of the compound to orthorhombic. From the analysis discussed above, it is clear that structural stability depends on the similarity in atomic radius of the dopant and host element. It also depends on the group of the element in the periodic table. From its properties, Re is a group 7 element which improves ductility and tensile strength. In this work Re has been used to substitute Mn given that they belong to the same group in the periodic table and their atomic radius are close that is, 1.79 Å for Mn and 1.97 Å for Re. From all the work reported in literature, to the best of our knowledge, perfect mechanical stability and ductility has not yet been addressed. In this study, we investigate the effects of Re (Rhenium) doping on Structural, Electronic and Mechanical stability of FeMnP0.67 Ge0.33 alloy. Ge0.33 is substituted with Ga0.33 element in order to improve the structural and mechanical stability of the Fe2 p-type compound. Re was introduced in the 3g site of the compounds, FeMn0.67Re0.33P0.67Ga0.33 and FeMn0.67Re0.33P0.67Ge0.33 compounds to substitute Mn which improves ductility.

2. Computational Details

Structural, electronic and mechanical properties of P-type compounds under investigation were analyzed by use of density functional theory 15 technique as implemented in the Quantum ESPRESSO (QE) code 16, 17, 18. Exchange correlation potentials for evaluating electron exchange and correlation results were approximated within the generalized gradient approximation (GGA) and parameterized by Perdew, Burke and Ernzerhof (PBE) 19. The ultrasoft pseudopotentials 20 were utilized for core electrons description. The Broyden-Flether-GoldFarb-Shanno (BFGS) quasi newton minimization scheme 21 was employed for the geometry optimization. The validity of computational findings depends on two parameters, that is the kinetic energy cutoff and the number of k-points utilized for the Brillouin Zone (BZ) integration. The value of kinetic energy cutoff dictates the number of plane waves in the calculation expansion. Electronic wave functions were expanded in plane waves up to a kinetic cut-off energy of 360 Ry which was achieved through an accurate convergence test. Convergence as a function of BZ sampling and intensity of the basis set was performed. Converged findings were realized with 3×3×2 k-point mesh 22 in the supercell and 3×3×5 in the unit cell. Vigilant convergence tests revealed that by use of these parameters, a self-consistent field (scf) 23 energy threshold converged at 10-6Ry. The forces converged below and also total stress converged below For reliability in our findings, exceptionally accurate computational technique, THERMO-PW technique 24, 25 was utilized in this study to compute the elastic constants as implemented in QE code. This technique has been proven to be successful in computational findings of elastic properties of various compounds 26. The computed equilibrium lattice constant was found to be, a = 6.11033 Å for the unit cell. A supercell of 18 atoms was constructed from optimized unit cell coordinates. Doping was via substitution, where Re was introduced to substitute 33% of Mn.

3. Results and Discussions

3.1. Structural Properties

Fe2P-type compounds crystallizes in hexagonal structure with space group p-62m no.189. The unit cell and supercell structures of FeMn0.67Re0.33P0.67Ga0.33 compounds are illustrated in Figure 1 and Figure 2 respectively. The unit cell comprises of 9 periodic atoms while the supercell comprises of 18 periodic atoms. The achieved equilibrium lattice parameters, that is, equilibrium cell volume and lattice constants of FeMn0.67Re0.33P0.67A0.33 (A= Ge and Ga) and FeMnP0.67A0.33 (A= Ge and Ga) are computed and tabulated in Table 4 and Table 3 respectively. The calculated bond lengths of the same compounds are presented in Table 2 and Table 1. All the findings are in conformity with other DFT results and the available experimental results as presented in Table 1, Table 2, Table 3 and Table 4. The computed results disparity from experimental results is by less than 3%. This disparity is attributed to the fact the DFT calculations are ab initio in nature, meaning that they are conducted at ground state while experimental work is at excited state. In Figure 1 and Figure 2, the green atoms represent the dopant which is Re.


3.1.1. Unit cell and Supercell Bond Lengths of FeMnP0.67A0.33 (A= Ga and Ge) Alloys

Table 1 results shows a correlation between bond lengths and atomic radius. The calculated bond lengths of FeMnP0.67Ge0.33 compound are Fe – Ge = 2.4364 Å in unit cell and 2.5012 Å in supercell. On substituting Ge with Ga, the bond lengths reduces to, Fe – Ga = 2.4318 Å in unit cell and 2.4719 Å in supercell. This is because Ga has a lager atomic radius compared to Ge. The atomic radius of Ge and Ga are 1.52 Å and 1.81 Å respectively.


3.1.2. Unit cell and Supercell Bond Lengths of FeMn0.67Re0.33P0.667A0.33 (A= Ga, Ge) Alloys

In Table 2, the calculated Fe - Mn bond length in the unit cell of FeMn0.67 Re0.33P0.67 Ga0.33 compound is 2.2060 Å while in its supercell it is, 2.3422 Å. This difference in bond lengths shows that there is a stronger covalent bonding between Fe and Mn in the unit cell as compared to the Fe-Mn covalent bonding in the supercell. In Fe-Re calculations, the bond length in unit cell of FeMn0.67 Re0.33P0.67 Ga0.33 alloy is 2.0980 Å while in the supercell it is 2.2069 Å. The difference between the unit and supercell bond lengths justifies the difference in covalent bonding. Similar trend is shown in Fe- Mn and Fe-Re calculated bond lengths of FeMn0.67Re0.33P0.67 Ge0.33 alloy both in unit cell and supercell structures as shown in Table 2. The results in Table 2 shows decreased bond lengths on introduction of Re into the compounds.


3.1.3. Unit cell and Supercell Lattice Parameters of FeMnP0.67Ax0.33 (A= Ge and Ga) Alloys

In Table 3, the calculated lattice parameters of unit cell FeMnP0.67Ge0.33 alloy are in agreement with experimental 27, 28 and other DFT 11 results, the calculated lattice constant being 6.0129 Å. When Ge was substituted with Ga, the calculated lattice parameters of unit cell FeMnP0.67Ga0.33 compounds confirmed the experimental 27 as well as DFT 11 findings. On introduction of Ga, the lattice constant became 6.4518 Å. Ga has a larger atomic radius of 1.81 Å while Ge has an atomic radius of 1.52 Å. This shows a strong correlation between lattice constant values and the atomic radius values. The supercell results were in agreement with the unit cell results in that, FeMnP0.67Ga0.33 alloy gave higher lattice constant of 6.5789 Å. The analyzed results confirm a direct proportionality between volume and atomic radius in both FeMnP0.67Ga0.33 and FeMnP0.67Ge0.33 alloys. Therefore, FeMnP0.67Ga0.33 alloys exhibits larger volume as compare to FeMnP0.67Ge0.33 alloys. The computed c/a ratio were in agreement with the available experimental findings 28.


3.1.4. Unit cell and Supercell Lattice Parameters of FeMn0.67Re0.33P0.67A0.33 (A= Ge and Ga) Alloys

We examine the effect of introduction of Re in the compounds FeMn0.67Re0.33P0.67Ga0.33 and FeMn0.67Re0.33P0.67Ge0.33 in both unit and supercell structures. In all these compounds Re (atomic radius 1.97 Å) substitutes Mn (atomic radius 1.79 Å). The results in Table 4 cannot be compared with other DFT findings or experimental results because to best of our knowledge, it has not been reported in literature. The results in Table 4 have a strong correlation with results in Table 3. In both Tables, the predicted lattice constant suggests that the alloys have stable hexagonal structures.

On substituting Mn with Re, the calculated lattice constant of the unit cell of FeMn0.67Re0.33P0.67Ga0.33 alloy is found to be a = 6.1429 Å. Re in the unit cell structure of FeMn0.67Re0.33P0.67Ge0.33 gives a lattice constant of 5.9722 Å. In the supercell structure, FeMn0.67Re0.33P0.67Ga0.33 and FeMn0.67Re0.33P0.67Ge0.33 have lattice constants of 6.1507 Å and 5.9194 Å respectively. These results shows that introduction of Re did not cause structural distortion in both compounds computed. These calculated results suggests that, an increase in atomic radius leads to increase in lattice constant.

On conclusion, all the compounds investigated in this work are of hexagonal structure. In this case, the ibrav used is 4 indicating the need for obtaining celldm(3), which is the c/a ratio. The results are shown in Table 3 and Table 4, where the values are in the range of 0.5 and 0.6 which is within the expected values. The computed volume results in Table 3 and Table 4 are directly proportional to the values of celldm(1) which is the length of the unit cell.

3.2. Electronic Properties

The electronic configuration of elements in FeMnP0.67A0.33 and FeMn0.67Re0.33P0.67A0.33 (A = Ga and Ge) alloys is analyzed as; P (3s23p3), Ga (3d10 4s 24p1), Mn (3d64s1), Fe (3d74s1), Re (4f 14 5d 5 6s 2) and Ge (3d104s 24p2), where electrons are treated as valence states 11. The electronic configuration is used to analyze band structure and projected density of states (PDOS).


3.2.1. FeMnP0.67 Ga0.33 Alloy

Figure 3 presents band structure and PDOS of unit cell FeMnP0.67 Ga0.33 alloy where Mn_4d and Fe_3d states are most projected states in VB and spread to CB. VB and CB overlaps, indicating that Figure 3 represents a metallic compound. It can be concluded that in Figure 3, only the d states contribute to the electronic properties of the compound. Figure 4 presents band structure and PDOS of supercell FeMnP0.67 Ga0.33 alloy has similar characteristics with Figure 3 in that, only the d states are responsible for the electronic properties. The Ef of Figure 3 is 118.3566 eV while Ef of Figure 4 is 17.1912 eV. The discrepancy in the Ef arise from dipole symmetry orientations of spins in unit and supercell structures.


3.2.2. FeMn0.67Re0.33P0.67 Ga0.33 Alloy

Figure 5 and Figure 6 introduces Re in unit and supercell structures of FeMnP0.67 Ga0.33. In Figure 5, Re_3d, Fe_3d and Mn_ 4d states shows dominance in VB and spreads to CB while the p states have no contribution in both CB and VB. Figure 6 reports the d states contribution in both VB and CB. Both Figure 5 and Figure 6 represents conducting compounds. The Efs of Figure 5 and Figure 6 are at 121.8706 eV and 17.9905 eV respectively, owing to difference in dipole symmetry. The increase in density of states in Figure 5 and Figure 6 compared to Figure 3 and Figure 4 is due to existence of 3d states of Re element in Figure 5 and Figure 6.


3.2.3. FeMnP0.67Ge0.33 alloy

Figure 7 represents Mn_4d and Fe_3d states dominating the VB and CB. The Ge_1d and the p states have insignificant contribution to the electronic properties of this compound. Figure 8 reports Mn_4d and Fe_3d having high contribution in CB and VB while P_2p and Mn_5p contributes only in the VB. Figure 7 and Figure 8 confirms metallic properties of the compounds.

The Ef of Figure 7 is found to be 117.7935 eV while that of Figure 8 is 16.9343 eV. Figure 8, reports high hybridization between the d and the p states.


3.2.4. FeMn0.67Re0.33P0.67 Ge0.33 Alloy

Figure 9 and Figure 10 reports introduction of Re in unit cell and supercell phases of FeMnP0.67Ge0.33. Figure 9 shows that Mn_4d, Fe_3d and Re_3d states dominates the VB as well as CB. Ge_1d and the p states have least contribution on electronic properties of the compound. In Figure 10, just like Figure 9, the d states are most projected in VB and CB. Compounds represented in Figure 9 and Figure 10 are metallic. The difference in dipole symmetry between unit and supercell places Ef of Figure 9 at 120.9112 eV and Ef of Figure 10 at 17.7881 eV. Hybridization between d and p states is witnessed in Figure 10. The increase in density of states in Figure 9 and Figure 10 compared to Figure 7 and Figure 8 is due to existence of 3d states of Re element in Figure 9 and Figure 10.

In this work, all supercell electronic Figures have a higher density of states compared to unit cell electronic Figures. This is because the supercell structures have 18 atoms while the unit cell structure is made up of 9 atoms. In conclusion, on introduction of Re in the Mn site, the electronic properties of the compound with group 13 element (FeMn0.67Re0.33P0.67 Ga0.33) are similar to electronic properties of compounds with group 14 elements (FeMn0.67Re0.33P0.67 Ge0.33). In both cases, Re_3d states have the highest contribution in the unit cell while Mn_4d states have the highest contribution in the supercells.

3.3. Mechanical Stability

The mechanical performance of solids is based on their elastic constants. Elastic constants describe the stability, ductility, brittleness and stiffness of a particular material. P-type materials have hexagonal structures and therefore they possess six elastic constants, that is, and The initial five constants are known as independent elastic constants while the final one takes into consideration; 29. A mechanically stable P-type compounds need to obey the following criteria for mechanical stability of hexagonal symmetry 30, 31, 32. and

Table 5 shows that the calculated elastic constants obey this stability condition. This confirms that the investigated compounds are mechanically stable. The achieved elastic constants are in agreement with other reported computational data 33, 34, 35. The elastic constants and represent the linear compression resistance along a and c orientations respectively. The values of and are high compared to other elastic constants. This implies that, P-type compounds are incompressible along both a and c orientations when subjected to stress. The elastic constant is large compared to which means that the incompressibility along the a-direction is higher than the one along c-direction. On introduction of Re in the unit and supercells of FeMnP0.67A0.33 (A=Ga and Ge), the estimated elastic constants still obeyed the above indicated Born stability conditions 36. The results are reported in Table 5.

  • Table 5. Calculated elastic constants Cij(GPa) for FeMnP1-XGeX, FeMnP1-XGaX, FeMn1-XReXP1-XGeX, and FeMn1-XReXP1-XGaX alloys obtained by use of QE code and compared with available computational data

Elastic moduli (Bulk modulus (B), Shear modulus (G), Young’s modulus (E)) and Poisson’s ratio (n) have been computed from the elastic constants using the Voigt-Reuss-Hill formula 37, 38, 39 and reported in Table 6. The bulk modulus illustrates an evaluate of resistance as a function of volume change and the averaged bond strength of a material. The value of bulk modulus increases with increase in bond strength. It is observed that, alloy has got the highest value of bulk modulus compared to other investigated compounds and therefore has the highest bond strength. Shear modulus predicts the hardness of a material. From Table 6, the shear modulus of alloy is realized to be the highest in comparison with other materials being studied. It is therefore expected that alloy is harder compared to other materials under investigation. Young’s modulus anticipates the stiffness of a material. The Young’s modulus values of the investigated materials have an increasing trend; alloys.

Investigations on failure mode, that is brittle or ductile nature of materials is important in investigations of mechanical properties of solids. A material may be termed as either ductile or brittle in several practical applications. To estimate the failure conditions of solids, Poisson’s and Pugh’s ratios as well as Cauchy pressure are powerful parameters to consider. Cauchy pressure 40, 41 given by identifies whether a material is ductile or brittle. When the Cauchy pressure is negative, the solid is likely to be brittle, but when it is positive, the solid is likely to be ductile. As per the Pugh’s ratio 42, <1.75 represents a brittle material while >1.75 represents a ductile material. Poisson’s ratio, discovered by Frantsevich et al 43 proposes that a solid with Poisson’s ratio greater than 0.26 will be ductile, otherwise the material is found to be brittle.

  • Table 6. Calculated elastic moduli B, G, E (GPa) and n for FeMnP1-XGeX, FeMnP1-XGaX, FeMn1-XReXP1-XGeX, and FeMn1-XReXP1-XGaX alloys obtained by use of QE code and compared with available computational data

From Table 6, the Cauchy pressure of alloy is positive, its Pugh’s ratio is 2.10 which is greater than 1.75 and its Poisson’s ratio n is 0.2946 which is greater than 0.26. Therefore compound is ductile.

Additional macroscopic property that relies on elastic constants is machinability 44. Machinability is described by the ratio of bulk modulus (B) to that is From Table 6, alloy has the highest value of suggesting that it is more machinable than the other investigated P-type compounds. A high value of means that a material has perfect lubricating properties. From the analysis among the studied compounds, it is realized that is the most ductile material while unit cell of alloy has the least ductility value.

4. Conclusion

In this work, the structural, electronic and mechanical mechanical stability of FeMnP0.67Ga0.33, FeMnP0.67Ge0.33, FeMn0.67Re0.33P0.67Ga0.33 and FeMn0.67Re0.33P0.67Ge0.33 compounds were investigated utilizing the first-principle calculations. The calculated lattice constants show perfect agreement with available calculated and experimental results. Mn_4d, Re_3d and Fe_3d had the highest contribution to the electronic properties in all the compounds analyzed. The mechanical stability was confirmed by elastic constants. The obtained elastic constants obey the mechanical stability conditions of hexagonal symmetry. The evaluated elastic moduli confirmed stiffness, hardness and bond strength of the studied compounds. The ratio and Poisson’s ratio n of FeMn0.67Re0.33P0.67Ga0.33 are higher than 1.75 and 0.26 respectively, both of which indicate that FeMn0.67Re0.33P0.67Ga0.33 is ductile. The obtained positive Cauchy pressure also confirmed ductility of FeMn0.67Re0.33P0.67Ga0.33. To conclude, we expect that this study will inspire further computational and experimental research work on this newly computed FeMn0.67Re0.33P0.67Ga0.33 compound.

Acknowledgements

This work is supported by Kenya climate smart agriculture project (KCSAP)/world bank. We acknowledge the Centre for High Performance Computing (CHPC) in South Africa for computer time in their clusters. This work is based on the research supported in part by the Kenya Education Network (KENET) Award No: CMMS2019/2020 in Nairobi - KENYA. This work is also based on the research supported in part by the Organization for Women in Science for the Developing World (OWSD), Award agreement No: 4500406550 in the International Centre for Theoretical Physics (ICTP), Trieste - ITALY. The grant holder acknowledges that opinions, findings and conclusions or recommendations expressed in any publication generated by the KENET and OWSD supported research are that of the author(s) and that the KENET and OWSD accepts no liability whatsoever in this regard. This work was carried out with the aid of a grant from UNESCO and the International Development Research Centre, Ottawa, Canada. The views expressed herein do not necessarily represent those of UNESCO, IDRC or its Board of Governors.

References

[1]  Roy, P., Brück, E., & de Groot, R. A. (2016). Latent heat of the first-order magnetic transition of MnFeSi 0.33 P 0.66. Physical Review. 93(16), 165101-165111.
In article      View Article
 
[2]  Ou, Z. Q., Dung, N. H., Zhang, L., Caron, L., Torun, E., Van Dijk, N. H., & Brück, E. (2018). Transition metal substitution in Fe2P-based MnFe0.95P0.50 Si 0.50 magnetocaloric compounds. Journal of Alloys and Compounds. 730, 392-398.
In article      View Article
 
[3]  Wurentuya, B., Yibole, H., Guillou, F., Ou, Z., Zhang, Z., & Tegus, O. (2018). First-order magnetic transition, magnetocaloric effect and moment formation in MnFe (P, Ge) magnetocaloric materials revisited by x-ray magnetic circular dichroism. Condensed Matter. 544, 66-72.
In article      View Article
 
[4]  Miao, X. F., Hu, S. Y., Xu, F., & Brück, E. (2018). Overview of magnetoelastic coupling in (Mn, Fe) 2 (P, Si)-type magnetocaloric materials. Rare Metals. 37(9), 723-733.
In article      View Article
 
[5]  He, A., Svitlyk, V., & Mozharivskyj, Y. (2017). Synthetic approach for (Mn, Fe) 2 (Si, P) magnetocaloric materials: purity, structural, magnetic, and magnetocaloric properties. Inorganic chemistry. 56(5), 2827-2833.
In article      View Article  PubMed
 
[6]  Trung, N. T., Ou, Z. Q., Gortenmulder, T. J., Tegus, O., Buschow, K. H., and Brück, E., (2010). Tunable thermal hysteresis in MnFePGe compounds. Journal of Physics Applied Physics. 670-676.
In article      
 
[7]  Liu, D., Yue, M., Zhang, J., McQueen, T. M., Lynn, J. W., Wang, X., & Altounian, Z. (2009). Origin and tuning of the magnetocaloric effect in the magnetic refrigerant Mn 1.1 Fe 0.9 (P 0.8 Ge 0.2). Physical Review. 79, 014435-014445.
In article      View Article
 
[8]  Su, L., Lei, S., Liu, L., Liu, L., Zhang, Y., Shi, S., & Yan, X. (2018). Sprinkling MnFe 2 O 4 quantum dots on nitrogen-doped graphene sheets: the formation mechanism and application for high-performance supercapacitor electrodes. Journal of Materials Chemistry A. 6(21), 9997-10007.
In article      View Article
 
[9]  Sepehri-Amin, H., Taubel, A., Ohkubo, T., Skokov, K. P., Gutfleisch, O., & Hono, K. (2018). Microstructural origin of hysteresis in Ni-Mn-In based magnetocaloric compounds. Acta Materialia. 147, 342-349.
In article      View Article
 
[10]  Ma, L., Guillou, F., Yibole, H., Miao, X. F., Lefering, A. J. E., Rao, G. H., & Brück, E. (2015). Structural, magnetic and magnetocaloric properties of (Mn, Co) 2 (Si, P) compounds. Journal of Alloys and Compounds. 625, 95-100.
In article      View Article
 
[11]  Ma, S., Wurentuya, B., Wu, X., Jiang, Y., Tegus, O., Guan, P., & Narsu, B. (2017). Ab initio mechanical and thermal properties of FeMnP1−x Gax compounds as refrigerant for room-temperature magnetic refrigeration. Royal Society Chemistry Advances. 7(44), 27454-27463.
In article      View Article
 
[12]  Brück, E., Trung, N. T., Ou, Z. Q., & Buschow, K. H. J. (2012). Enhanced magnetocaloric effects and tunable thermal hysteresis in transition metal pnictides. Scripta Materialia. 67(6), 590-593.
In article      View Article
 
[13]  Xu, H., Yue, M., Zhao, C., Zhang, D., & Zhang, J. (2012). Structure and magnetic properties of Mn 1.2 Fe 0.8 P 0.76 Ge 0.24 annealed alloy. Rare Metals. 31(4), 336-338.
In article      View Article
 
[14]  Cam Thanh, D.T., Brück, E., Trung, N.T., Klaasse, J.C.P., Buschow, K.H.J., Ou, Z.Q., Tegus, O., Caron, L (2008). Structure, magnetism, and magnetocaloric properties of MnFeP1−xSix compounds. Journal of Applied Physics. 103,318-323.
In article      View Article
 
[15]  W. Kohn & L. J. Sham (1964). Physics. Review. 385, 1133-1155.
In article      
 
[16]  Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., & Dal Corso, A. (2009). QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal of physics, Condensed matter. 21(39), 395502-395509.
In article      View Article  PubMed
 
[17]  Baroni, S., Dal Corso, A., De Gironcoli, S., Giannozzi, P., Cavazzoni, C., Ballabio, G., & Kokalj, A. (2005). Quantum ESPRESSO: open-source package for research in electronic structure, simulation, and optimization.
In article      
 
[18]  Baroni, S., Dal Corso, A., de Gironcoli, S., & Giannozzi, P. (2001). PWSCF and PHONON: Plane-wave pseudo-potential codes.
In article      
 
[19]  Perdew, J. P., Burke, K., & Ernzerhof, M. (1998). Perdew, Burke, and Ernzerhof reply. Physical Review Letters, 80(4), 891.
In article      View Article
 
[20]  Kresse, G., & Joubert, D., (1999). From ultrasoft pseudopotentials to the projector augmented-wave method. Physic. Review. 59, 1758-1775.
In article      View Article
 
[21]  Zhang, H., Li, R., Cai, Z., Gu, Z., Heidari, A. A., Wang, M., ... & Chen, M. (2020). Advanced orthogonal moth flame optimization with Broyden–Fletcher–Goldfarb–Shanno algorithm: Framework and real-world problems. Expert Systems with Applications, 159, 113617.
In article      View Article
 
[22]  Monkhorst, H.J., Pack, & J.D., (1976). Special points for Brillouin-zone integrations. Physics Review.
In article      View Article
 
[23]  Kohn, W., Sham, L.J., (1965). Self-Consistent Equations Including Exchange and Correlation Effects. Physics Review. 140, 1133-1138.
In article      View Article
 
[24]  Motornyi, O., Raynaud, M., Dal Corso, A., & Vast, N. (2018, December). Simulation of electron energy loss spectra with the TurboEELS and Thermo_PW codes. In Journal of Physics: Conference Series .11369(1).
In article      View Article
 
[25]  Dal Corso, A. (2016). Elastic constants of beryllium: a first-principles investigation. Journal of Physics: Condensed Matter. 28(7), 075401.
In article      View Article  PubMed
 
[26]  Adetunji, B. I., Adebambo, P. O., Bamgbose, M. K., Musari, A. A., & Adebayo, G. A. (2019). Predicting the elastic, phonon and thermodynamic properties of cubic HfNiX (X= Ge and Sn) Half Heulser alloys: a DFT study. The European Physical Journal B, 92(10), 1-7.
In article      View Article
 
[27]  Yue, M., Li, Z. Q., Xu, H., Huang, Q. Z., Liu, X. B., Liu, D. M., & Zhang, J. X. (2010). Effect of annealing on the structure and magnetic properties of Mn 1.1 Fe 0.9 P 0.8 Ge 0.2 compound. Journal of Applied Physics. 107(9), 939-950.
In article      View Article
 
[28]  Cam Thanh, D. T., Brück, E., Tegus, O., Klaasse, J. C. P., Gortenmulder, T. J., & Buschow, K. H. J. (2006). Magnetocaloric effect in MnFe (P, Si, Ge) compounds. Journal of Applied Physics. 99(8), 107.
In article      View Article
 
[29]  Fast, L., Wills, J. M., Johansson, B., & Eriksson, O. (1995). Elastic constants of hexagonal transition metals. Physical Review B. 51(24), 17431-17441.
In article      View Article  PubMed
 
[30]  Milman, V., Winkler, B., & Probert, M. I. J. (2005). Stiffness and thermal expansion of ZrB2: an ab initio study. Journal of physics. Condensed matter. 17(13), 2233.
In article      View Article
 
[31]  Milman, V., & Warren, M. C. (2001). Elastic properties of TiB2 and MgB2. Journal of Physics: Condensed Matter. 13(24), 5585.
In article      View Article
 
[32]  Birch, F. (1947). Finite elastic strain of cubic crystals. Physical review. 71(11), 809.
In article      View Article
 
[33]  Wallace, D. C. (1972). Thermodynamics of crystals. American Journal of Physics. 40(11), 1718-1719.
In article      View Article
 
[34]  Beckstein, O., Klepeis, J. E., Hart, G. L. W., & Pankratov, O. (2001). First-principles elastic constants and electronic structure of α− Pt 2 Si and PtSi. Physical Review B. 63(13), 134112.
In article      View Article
 
[35]  Christopoulos, S. R., Filippatos, P. P., Hadi, M. A., Kelaidis, N., Fitzpatrick, M. E., & Chroneos, A. (2018). Intrinsic defect processes and elastic properties of Ti3AC2 (A= Al, Si, Ga, Ge, In, Sn) MAX phases. Journal of Applied Physics. 123(2), 025103.
In article      View Article
 
[36]  Born, M. (1940, April). On the stability of crystal lattices. I. In Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University.36 (2)160-172.
In article      View Article
 
[37]  Voigt, W. J. T. L. (1928). A determination of the elastic constants for beta-quartz lehrbuch de kristallphysik. Terubner Leipzig, 40, 2856-2860.
In article      
 
[38]  Hill, R. (1952). The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society. Section A, 65(5), 349.
In article      View Article
 
[39]  Reuss, A. J. Z. A. M. M. (1929). Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals. Z. Angew. Math. Mech. 9, 49-58.
In article      View Article
 
[40]  Eberhart, M. E., & Jones, T. E. (2012). Cauchy pressure and the generalized bonding model for nonmagnetic bcc transition metals. Physical Review B. 86(13), 134106.
In article      View Article
 
[41]  Nguyen-Maxh, D., Pettifor, D. G., Znam, S., & Vitek, V. (1997). Negative Cauchy pressure within the tight-binding approximation. MRS Online Proceedings Library (OPL). 491, 1-4.
In article      View Article
 
[42]  Pugh, S. F. (1954). Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 45, 823-843.
In article      View Article
 
[43]  Frantsevich, I. N. (1982). Elastic constants and elastic moduli of metals and insulators. Reference book.
In article      
 
[44]  Korzhavyi, P. A., Vitos, L., Andersson, D. A., & Johansson, B. (2004). Oxidation of plutonium dioxide. Nature Materials. 3(4), 225-228.
In article      View Article  PubMed
 

Published with license by Science and Education Publishing, Copyright © 2022 Gabriel Kipkemei Chirchir, Winfred Mueni Mulwa and Bamidele Ibrahim Adetunji

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Cite this article:

Normal Style
Gabriel Kipkemei Chirchir, Winfred Mueni Mulwa, Bamidele Ibrahim Adetunji. Structural, Electronic and Mechanical Properties of Re Doped FeMnP0.67A0.33 (A=Ga and Ge): A DFT Study. International Journal of Physics. Vol. 10, No. 1, 2022, pp 70-78. http://pubs.sciepub.com/ijp/10/1/6
MLA Style
Chirchir, Gabriel Kipkemei, Winfred Mueni Mulwa, and Bamidele Ibrahim Adetunji. "Structural, Electronic and Mechanical Properties of Re Doped FeMnP0.67A0.33 (A=Ga and Ge): A DFT Study." International Journal of Physics 10.1 (2022): 70-78.
APA Style
Chirchir, G. K. , Mulwa, W. M. , & Adetunji, B. I. (2022). Structural, Electronic and Mechanical Properties of Re Doped FeMnP0.67A0.33 (A=Ga and Ge): A DFT Study. International Journal of Physics, 10(1), 70-78.
Chicago Style
Chirchir, Gabriel Kipkemei, Winfred Mueni Mulwa, and Bamidele Ibrahim Adetunji. "Structural, Electronic and Mechanical Properties of Re Doped FeMnP0.67A0.33 (A=Ga and Ge): A DFT Study." International Journal of Physics 10, no. 1 (2022): 70-78.
Share
  • Table 4. Calculated DFT- (PBE-GGA) lattice parameters of FeMn0.67Re0.33P0.67A0.33 (A = Ga and Ge) alloys
  • Table 5. Calculated elastic constants Cij(GPa) for FeMnP1-XGeX, FeMnP1-XGaX, FeMn1-XReXP1-XGeX, and FeMn1-XReXP1-XGaX alloys obtained by use of QE code and compared with available computational data
  • Table 6. Calculated elastic moduli B, G, E (GPa) and n for FeMnP1-XGeX, FeMnP1-XGaX, FeMn1-XReXP1-XGeX, and FeMn1-XReXP1-XGaX alloys obtained by use of QE code and compared with available computational data
[1]  Roy, P., Brück, E., & de Groot, R. A. (2016). Latent heat of the first-order magnetic transition of MnFeSi 0.33 P 0.66. Physical Review. 93(16), 165101-165111.
In article      View Article
 
[2]  Ou, Z. Q., Dung, N. H., Zhang, L., Caron, L., Torun, E., Van Dijk, N. H., & Brück, E. (2018). Transition metal substitution in Fe2P-based MnFe0.95P0.50 Si 0.50 magnetocaloric compounds. Journal of Alloys and Compounds. 730, 392-398.
In article      View Article
 
[3]  Wurentuya, B., Yibole, H., Guillou, F., Ou, Z., Zhang, Z., & Tegus, O. (2018). First-order magnetic transition, magnetocaloric effect and moment formation in MnFe (P, Ge) magnetocaloric materials revisited by x-ray magnetic circular dichroism. Condensed Matter. 544, 66-72.
In article      View Article
 
[4]  Miao, X. F., Hu, S. Y., Xu, F., & Brück, E. (2018). Overview of magnetoelastic coupling in (Mn, Fe) 2 (P, Si)-type magnetocaloric materials. Rare Metals. 37(9), 723-733.
In article      View Article
 
[5]  He, A., Svitlyk, V., & Mozharivskyj, Y. (2017). Synthetic approach for (Mn, Fe) 2 (Si, P) magnetocaloric materials: purity, structural, magnetic, and magnetocaloric properties. Inorganic chemistry. 56(5), 2827-2833.
In article      View Article  PubMed
 
[6]  Trung, N. T., Ou, Z. Q., Gortenmulder, T. J., Tegus, O., Buschow, K. H., and Brück, E., (2010). Tunable thermal hysteresis in MnFePGe compounds. Journal of Physics Applied Physics. 670-676.
In article      
 
[7]  Liu, D., Yue, M., Zhang, J., McQueen, T. M., Lynn, J. W., Wang, X., & Altounian, Z. (2009). Origin and tuning of the magnetocaloric effect in the magnetic refrigerant Mn 1.1 Fe 0.9 (P 0.8 Ge 0.2). Physical Review. 79, 014435-014445.
In article      View Article
 
[8]  Su, L., Lei, S., Liu, L., Liu, L., Zhang, Y., Shi, S., & Yan, X. (2018). Sprinkling MnFe 2 O 4 quantum dots on nitrogen-doped graphene sheets: the formation mechanism and application for high-performance supercapacitor electrodes. Journal of Materials Chemistry A. 6(21), 9997-10007.
In article      View Article
 
[9]  Sepehri-Amin, H., Taubel, A., Ohkubo, T., Skokov, K. P., Gutfleisch, O., & Hono, K. (2018). Microstructural origin of hysteresis in Ni-Mn-In based magnetocaloric compounds. Acta Materialia. 147, 342-349.
In article      View Article
 
[10]  Ma, L., Guillou, F., Yibole, H., Miao, X. F., Lefering, A. J. E., Rao, G. H., & Brück, E. (2015). Structural, magnetic and magnetocaloric properties of (Mn, Co) 2 (Si, P) compounds. Journal of Alloys and Compounds. 625, 95-100.
In article      View Article
 
[11]  Ma, S., Wurentuya, B., Wu, X., Jiang, Y., Tegus, O., Guan, P., & Narsu, B. (2017). Ab initio mechanical and thermal properties of FeMnP1−x Gax compounds as refrigerant for room-temperature magnetic refrigeration. Royal Society Chemistry Advances. 7(44), 27454-27463.
In article      View Article
 
[12]  Brück, E., Trung, N. T., Ou, Z. Q., & Buschow, K. H. J. (2012). Enhanced magnetocaloric effects and tunable thermal hysteresis in transition metal pnictides. Scripta Materialia. 67(6), 590-593.
In article      View Article
 
[13]  Xu, H., Yue, M., Zhao, C., Zhang, D., & Zhang, J. (2012). Structure and magnetic properties of Mn 1.2 Fe 0.8 P 0.76 Ge 0.24 annealed alloy. Rare Metals. 31(4), 336-338.
In article      View Article
 
[14]  Cam Thanh, D.T., Brück, E., Trung, N.T., Klaasse, J.C.P., Buschow, K.H.J., Ou, Z.Q., Tegus, O., Caron, L (2008). Structure, magnetism, and magnetocaloric properties of MnFeP1−xSix compounds. Journal of Applied Physics. 103,318-323.
In article      View Article
 
[15]  W. Kohn & L. J. Sham (1964). Physics. Review. 385, 1133-1155.
In article      
 
[16]  Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., & Dal Corso, A. (2009). QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal of physics, Condensed matter. 21(39), 395502-395509.
In article      View Article  PubMed
 
[17]  Baroni, S., Dal Corso, A., De Gironcoli, S., Giannozzi, P., Cavazzoni, C., Ballabio, G., & Kokalj, A. (2005). Quantum ESPRESSO: open-source package for research in electronic structure, simulation, and optimization.
In article      
 
[18]  Baroni, S., Dal Corso, A., de Gironcoli, S., & Giannozzi, P. (2001). PWSCF and PHONON: Plane-wave pseudo-potential codes.
In article      
 
[19]  Perdew, J. P., Burke, K., & Ernzerhof, M. (1998). Perdew, Burke, and Ernzerhof reply. Physical Review Letters, 80(4), 891.
In article      View Article
 
[20]  Kresse, G., & Joubert, D., (1999). From ultrasoft pseudopotentials to the projector augmented-wave method. Physic. Review. 59, 1758-1775.
In article      View Article
 
[21]  Zhang, H., Li, R., Cai, Z., Gu, Z., Heidari, A. A., Wang, M., ... & Chen, M. (2020). Advanced orthogonal moth flame optimization with Broyden–Fletcher–Goldfarb–Shanno algorithm: Framework and real-world problems. Expert Systems with Applications, 159, 113617.
In article      View Article
 
[22]  Monkhorst, H.J., Pack, & J.D., (1976). Special points for Brillouin-zone integrations. Physics Review.
In article      View Article
 
[23]  Kohn, W., Sham, L.J., (1965). Self-Consistent Equations Including Exchange and Correlation Effects. Physics Review. 140, 1133-1138.
In article      View Article
 
[24]  Motornyi, O., Raynaud, M., Dal Corso, A., & Vast, N. (2018, December). Simulation of electron energy loss spectra with the TurboEELS and Thermo_PW codes. In Journal of Physics: Conference Series .11369(1).
In article      View Article
 
[25]  Dal Corso, A. (2016). Elastic constants of beryllium: a first-principles investigation. Journal of Physics: Condensed Matter. 28(7), 075401.
In article      View Article  PubMed
 
[26]  Adetunji, B. I., Adebambo, P. O., Bamgbose, M. K., Musari, A. A., & Adebayo, G. A. (2019). Predicting the elastic, phonon and thermodynamic properties of cubic HfNiX (X= Ge and Sn) Half Heulser alloys: a DFT study. The European Physical Journal B, 92(10), 1-7.
In article      View Article
 
[27]  Yue, M., Li, Z. Q., Xu, H., Huang, Q. Z., Liu, X. B., Liu, D. M., & Zhang, J. X. (2010). Effect of annealing on the structure and magnetic properties of Mn 1.1 Fe 0.9 P 0.8 Ge 0.2 compound. Journal of Applied Physics. 107(9), 939-950.
In article      View Article
 
[28]  Cam Thanh, D. T., Brück, E., Tegus, O., Klaasse, J. C. P., Gortenmulder, T. J., & Buschow, K. H. J. (2006). Magnetocaloric effect in MnFe (P, Si, Ge) compounds. Journal of Applied Physics. 99(8), 107.
In article      View Article
 
[29]  Fast, L., Wills, J. M., Johansson, B., & Eriksson, O. (1995). Elastic constants of hexagonal transition metals. Physical Review B. 51(24), 17431-17441.
In article      View Article  PubMed
 
[30]  Milman, V., Winkler, B., & Probert, M. I. J. (2005). Stiffness and thermal expansion of ZrB2: an ab initio study. Journal of physics. Condensed matter. 17(13), 2233.
In article      View Article
 
[31]  Milman, V., & Warren, M. C. (2001). Elastic properties of TiB2 and MgB2. Journal of Physics: Condensed Matter. 13(24), 5585.
In article      View Article
 
[32]  Birch, F. (1947). Finite elastic strain of cubic crystals. Physical review. 71(11), 809.
In article      View Article
 
[33]  Wallace, D. C. (1972). Thermodynamics of crystals. American Journal of Physics. 40(11), 1718-1719.
In article      View Article
 
[34]  Beckstein, O., Klepeis, J. E., Hart, G. L. W., & Pankratov, O. (2001). First-principles elastic constants and electronic structure of α− Pt 2 Si and PtSi. Physical Review B. 63(13), 134112.
In article      View Article
 
[35]  Christopoulos, S. R., Filippatos, P. P., Hadi, M. A., Kelaidis, N., Fitzpatrick, M. E., & Chroneos, A. (2018). Intrinsic defect processes and elastic properties of Ti3AC2 (A= Al, Si, Ga, Ge, In, Sn) MAX phases. Journal of Applied Physics. 123(2), 025103.
In article      View Article
 
[36]  Born, M. (1940, April). On the stability of crystal lattices. I. In Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University.36 (2)160-172.
In article      View Article
 
[37]  Voigt, W. J. T. L. (1928). A determination of the elastic constants for beta-quartz lehrbuch de kristallphysik. Terubner Leipzig, 40, 2856-2860.
In article      
 
[38]  Hill, R. (1952). The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society. Section A, 65(5), 349.
In article      View Article
 
[39]  Reuss, A. J. Z. A. M. M. (1929). Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals. Z. Angew. Math. Mech. 9, 49-58.
In article      View Article
 
[40]  Eberhart, M. E., & Jones, T. E. (2012). Cauchy pressure and the generalized bonding model for nonmagnetic bcc transition metals. Physical Review B. 86(13), 134106.
In article      View Article
 
[41]  Nguyen-Maxh, D., Pettifor, D. G., Znam, S., & Vitek, V. (1997). Negative Cauchy pressure within the tight-binding approximation. MRS Online Proceedings Library (OPL). 491, 1-4.
In article      View Article
 
[42]  Pugh, S. F. (1954). Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 45, 823-843.
In article      View Article
 
[43]  Frantsevich, I. N. (1982). Elastic constants and elastic moduli of metals and insulators. Reference book.
In article      
 
[44]  Korzhavyi, P. A., Vitos, L., Andersson, D. A., & Johansson, B. (2004). Oxidation of plutonium dioxide. Nature Materials. 3(4), 225-228.
In article      View Article  PubMed