It is certified that the work contained in the thesis entitled "First-principles electronic structure based research of Mn2NiX magnetic alloys with Inverse Heusler structure" by Mr. spin bands as the mechanism behind the martensitic transformation.
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Shape Memory Alloys (SMAs)
- Martensitic Transformation (MT)
- Shape Memory Effect (SME)
- Pseudoelasticity
- Applications of Shape Memory Alloys
However, it is possible for shape memory alloys to remember the shape of the martensitic phase under certain conditions [37, 38]. The stress level corresponding to the start and end of the transformation and the size of the hysteresis loop depend on the shape memory materials.
Magnetic Shape Memory Alloys (MSMAs)
Ni-Mn based Magnetic Shape Memory Alloys (MSMAs)
The symmetric octahedral positions, i.e., the last two sublattices, are occupied by Ni atoms and. The wave vector corresponding to the pronounced phonon anomaly is related to the periodicity of the rearrangement.
The role of first-principles electronic structure calculations in understanding
An excellent shape memory effect that can be controlled in the field up to 4% has been observed in this material. These results predict Mn2NiGa as a new promising shape memory material with functional parameters such as TM and TC superior to Ni2MnGa.
Outline of the thesis
Overview of the thesis 19 landscapes (energy versus (c/a) plot, where (c/a) determines the tetragonal deformation) as in all four cases, global minima are obtained for (c/a), 1. So the physical properties of these materials may be related to the relative sizes of the sp constituents.
Density Functional Theory (DFT)
They are solutions of the Kohn-Sham equations 2.5 for the same effective potential as above, with the only change occurring in the exchange correlation part. The solution of equation 2.5 requires certain approximations for the exchange and correlation terms because these are not precisely known except for the free (homogeneous) electron gas.
Pseudopotential method
The Phillips-Kleinman Construction
Norm-Conserving Pseudopotentials (NCPP)
Ultrasoft Pseudopotentials (USPP)
The triple complications associated with the construction of the ultrasoft pseudopotential are: (i) since the wavefunctions are not necessarily normalized, they introduce a non-trivial overlap into the secular equation, (ii) the pseudo-charge density cannot be easily determined. obtained only by calculating X. Nevertheless, the use of these pseudopotentials over the years in large-scale calculations has proven their reliability in condensed matter calculations, and most importantly, the cost of generating such pseudopotentials is negligible compared to the cost of calculations where they are used.
Projector Augmented Wave (PAW) method
On the contrary, a term must be added in the core region, (iii) relaxation of the norm conservation leads to a less transferable pseudopotential. Since the transformation operator T is linear, the coefficients must be linear functionals of the smooth wave function.
Linearized Augmented Plane Wave (LAPW) method
Therefore, the radial functions no longer represent exact solutions inside the sphere, while the potential correction does not affect the choice of basis functions in the interstices. Inside the muffin tin-shaped sphere, the APW augmentation is replaced by uℓ and its energy derivatives ˙uℓ evaluated at a fixed linearization energy Eℓ.
Korringa, Kohn and Rostoker (KKR) Green’s Function method
Korringa, Kohn and Rostoker (KKR) Green's function method 35 This method introduces errors of order (ε−Eℓ)2 in the wavefunctions and (ε−Eℓ)4 in the band. The second term, in equation 2.48, represents the contribution of the multiple or backscatter to the Green's function and produces the band structure. The zeros of the KKR matrix give the poles of the Green function; each pole corresponds to its own state of the Hamiltonian.
Exact Muffin-Tin orbital (EMTO) method
In the interstitial region, where the potential approaches v0, the basis functions can be described as solutions of the wave equation. Finally, the exact muffin tin orbitals are constructed as a superposition of screened spherical waves, partial waves, and the free electron solution, i.e. These solutions can be obtained from the poles of the path operator gR′′L′′RL defined. for a complex energy z from.
Modeling of the chemical or substitutional disorder
Coherent Potential Approximation (CPA)
The Green's function g and the Palloy alloy potential are used to describe the above system. Then, the Green's functions of the gis alloy components are determined by replacing the coherent potential of the CPA medium with the real atomic potential Pi, which is given by. Finally, the average of the individual Green's functions should reproduce the single part of the coherent Green's functions, i.e.
Special Quasirandom Structure (SQS)
Summary
Introduction
Such a study is necessary for two reasons: first, to check the usefulness of the alloys in the series for magnetic shape memory applications, that is, whether martensitic transformation can be realized around room temperature and whether the other key parameters such as the magnetizations are substantial. and second, any trends regarding their properties related to magnetic shape memory effects would shed enough light to understand the physics of these materials and then help tune their properties to make them functional. Comparisons of their energies with respect to the martensitic phase transformations, magnetic properties and details regarding the electronic structures have been carried out. The chapter is organized as follows: details of the calculations are given in section 3.2, followed by the results and detailed discussions in section 3.3.
Computational Details
Generalized Gradient Approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) [186] parametrization was used for the exchange-correlation part of the Hamiltonian. Perdew-Wang (PW-91) generalized gradient approximation (GGA) functionals [193] were used in this case for the exchange correlation part of the Hamiltonian. For calculations with PAW pseudopotentials, PBE [186] parameterization of the GGA exchange correlation functional was used.
Results and Discussions
Structural properties and energetics related to martensitic transforma-
F 3.1: Total energy as a function of tetragonal deformations (c/a) for Mn2NiX alloys. The energies calculated by a) the FP-LAPW method and b) the PW-USPP method are plotted with reference to the energy of the cubic phase (c/a)= 1. Analysis of the energy surfaces calculated by the PW-USPP method (F 3.1(b)), we find that the positions of the global and the local minima are almost identical to those calculated by the FP-LAPW method for Mn2NiGa and Mn2NiAl, while there are some discrepancies in two others cases. The energy differences between the tetragonal (c/a)> 1 phase and the cubic phase as calculated by the PW-USPP method show identical trends as obtained with the results of the FP-LAPW calculations.
Magnetic moments
In the martensitic phases, the total moment of each alloy is reduced relative to its moment in the austenitic phase. However, their moments in the martensitic phase are for (c/a)= 0.97 and the values are very close to those obtained in the austenitic phase. Our results, on the other hand, are consistent with the trends obtained in the other alloys.
Electronic structures and analysis of the trends in phase stabilities and
In general, there are fewer structures in the DOS of Mn2NiIn and Mn2NiSn compared to the other two alloys. The appearance of fewer structures in the DOS is due to the weak hybridization between Ni and Mn atoms. This is clear from the representations of well-separated partial contributions from Ni and Mn atoms to the PDOS.
Summary
However, the near compensations of Mn moments and small Ni moments in the case of Mn2NiSn and Mn2NiIn are due to weak hybridizations between Ni and Mn atoms. Therefore, the physical properties of these materials are affected by the relative sizes of the sp elements. Complete softening of the TA2 acoustic branch with imaginary frequencies along the [ξξ0] direction of Ni2MnAl was reported [204].
Computational details
The Fourier component of the increased charge density with cutoffenergy up to 6530 eV was taken after convergence test. Such convergence tests ensured accuracies in elastic constants as they are calculated from the slopes of the phonon scattering curves. It can be noted that the strength of the phonon anomaly is extremely sensitive to temperature.
Results and Discussions
- Phonon dispersion
- Vibrational Density of States (VDOS)
- Inter-atomic force constants
- Fermi surfaces
- Elastic constants
Ni modes also occur at lower frequencies, similar to the cases of the other three. They related this anomalous mode inversion to the instability of the TA2 modes of Ni2MnGa. To understand the features in VDOS, we analyze the behavior of real-space interatomic force constants.
Summary
In the early 1990s, the existence of spin-spiral structures is theoretically investigated in the context of high-Tc superconductors, using the framework of the Hubbard model, where the stabilizations of the spin-spiral states are realized within a wide range of the parameters. 254] calculated the energies of the noncollinear spin spirals in Ni2MnAl and Ni2MnGa within the framework of DFT. It also becomes important to investigate the role of crystal structure, that is, whether a particular arrangement of magnetic atoms plays a role in maintaining non-collinear magnetic states.
Computational Details
From a careful convergence test against Brillouin zone (BZ) sampling and basis set size, we find that the plane wave limit for the basis set is RMTKmax= 9, where RMT is the radius of the muffin pan and Kmax is the largest reciprocal lattice vector, which is nearly 350 straight waves. Magnetic pair exchange interactions were calculated within the Green's function multiple scattering formalism as implemented in the EMTO code [154–158] . The indices µ and ν represent different sublattices, i and j denote the atomic positions and eµi is the unit vector along the direction of the magnetic moments at site i belonging to the sublattice µ.
Results and Discussions
Spin wave spectra of Mn 2 NiX materials in inverse Heusler structure . 87
F 5.1: Total energies of Mn2NiX systems as a function of spin spiral vectors q in the inverse Heusler phases. F 5.2: Total energies of Mn2NiX systems as a function of spin spiral vectors q in the inverse Heusler phases. The black and red lines indicate spin majority and spin minority band structure in the collinear (q= 0) state respectively.
Exchange interactions
The results of F5.4 thus show that the nesting of the up and down spin bands is a necessary condition for the stabilization of the non-collinear spin helical state and that features in the band structure together with the topology of the Fermi surfaces can explain the observed trends in the Mn2NiX series. Panels (b) and (d) present the same information but for the case of the MnII sublattice. In the case of Mn2NiIn (panel (d)), we see that for lattice constants starting at 5.91 Å and higher, the MnII interactions within the sublattice are all ferromagnetic.
The role of chemical composition and crystal structure
F 5.6: Total energies of Ni2MnX systems as a function of spin vectors q in the usual Heusler structure. F 5.7: Total energies of Mn2NiX systems as a function of spin vectors q in the usual Heusler structure. F 5.8: Total energies of Ni2MnX systems as a function of spin vectors q in the inverse Heusler structure.
Summary
In the earlier chapters we stated that few experimental results on the total moments in the austenite phase are available for Mn2NiGa [103–107] and Mn2NiSn [102]. A large ∆M between the two phases in the presence of moderate external magnetic field H, that is, the Zeeman term ∆M.H, was found to drive the motions of the martensitic domains facilitating the martensitic transformation [56]. For the reverse magnetocaloric effect, the magnetization in the martensitic phase must be lower than that in the austenite phase.
Computational Details
Computational details 101 Inspired by the above facts, in this chapter we have investigated the properties of the four. In the case of OC and OT, the sublattices with octahedral symmetries are occupied by the X element and one of the Mn atoms (named MnII), while the sublattices with tetrahedral symmetries are occupied by Ni and the other Mn atom (named MnII). to as MnI). In materials with chemical disorder, especially in systems where constituents have large size differences, such as Mn2NiIn and Mn2NiSn, there can be significant relaxations of the local bonds.
Results and Discussions
Understanding the origin of discrepancy between theory and experi-
We find that ∆EstrD> 0 for Mn2NiAl, which means that it is in “disordered site vs. site”. Significant changes in the density of states in DC configurations occur due to anti-site interference between MnI and Ni sites. It is expected that large changes in the electronic structure come from the densities of states of MnI and Ni.
The density of states in the minority generations, although it still retains some of the structure, but generally becomes quiet. In general, the calculated Tc in DC configurations agrees quite well with the experimental trends.
