Exact Muffin-tin Orbitals Method Research Articles

Exact muffin tin orbital based first-principles method for electronic-structure and electron-transport simulation of device materials

The exact muffin tin orbital (EMTO) method features high efficiency and accuracy for first-principles simulations with density functional theory. In this paper we report our implementation of the EMTO method for electronic-structure and quantum transport simulation of device materials. We consider a device-material structure with a central device region in contact with different semi-infinite electrodes. Based on the Green's function method, the infinite device, nonperiodic in transport direction, is transformed into a calculable finite material system by treating the semi-infinite electrodes with electrode self-energies, and the Green's function of the device region is calculated with an efficient recursive technique. In the present implementation we adopt the spherical cell approximation to treat the electrostatics, and we solve the electrostatic potential of the finite device region by enforcing the boundary conditions to the known potential of electrode materials. The coherent potential approximation is incorporated for treating the atomic disorders inevitable in realistic materials, and the effects of multiple disorder scattering on electron transport are accounted for by vertex correction for simulating disordered electronic devices. To demonstrate the capability of the present implementation, we calculate the monolayer two-dimensional material MoS2 and black phosphorus, and study the spin-dependent tunneling in the Fe/MgO/Fe magnetic tunneling junction. We find the EMTO electronic structures of the calculated systems agree well with the results of the projector augmented wave method. The EMTO transport simulation produces the important spin-filtering effect of the Fe/MgO/Fe junction and the important influence of the interfacial disorders on the spin-dependent tunneling, agreeing well with previous theoretical and experimental studies. The implementation of the EMTO based device simulator provides an effective simulation tool for simulating both ordered and disordered device materials, extending the capability for theoretical design of electronic devices from first principles.

Elastic Parameters of Paramagnetic Fe–20Cr–20Ni-Based Alloys: A First-Principles Study

The single-crystal and polycrystalline elastic parameters of paramagnetic Fe0.6−xCr0.2Ni0.2Mx (M = Al, Co, Cu, Mo, Nb, Ti, V, and W; 0 ≤ x ≤ 0.08) alloys in the face-centered cubic (fcc) phase were derived by first-principles electronic structure calculations using the exact muffin-tin orbitals method. The disordered local magnetic moment approach was used to model the paramagnetic phase. The theoretical elastic parameters of the present Fe–Cr–Ni-based random alloys agree with the available experimental data. In general, we found that all alloying elements have a significant effect on the elastic properties of Fe–Cr–Ni alloy, and the most significant effect was found for Co. A correlation between the tetragonal shear elastic constant C′ and the structural energy difference ΔE between fcc and bcc lattices was demonstrated. For all alloys, small changes in the Poisson’s ratio were obtained. We investigated the brittle/ductile transitions formulated by the Pugh ratio. We demonstrate that Al, Cu, Mo, Nb, Ti, V, and W dopants enhance the ductility of the Fe–Cr–Ni system, while Co reduces it. The present theoretical data can be used as a starting point for modeling the mechanical properties of austenitic stainless steels at low temperatures.

Density Functional Theory description of the order-disorder transformation in Fe-Ni

The thermodynamic ordering transformation of tetragonal FeNi system is investigated by the Exact Muffin-Tin Orbitals (EMTO) method. The tetragonal distortion of the unit cell is taken into account and the free energy is calculated as a function of long-range order and includes the configurational, vibrational, electronic and magnetic contributions. We find that both configurational and vibrational effects are important and that the vibrational effect lowers the predicted transformation temperature by about 480 K compared to the value obtained merely from the configurational free energy. The predicted temperature is in excellent agreement with the experimental value when all contributions are taken into account. We also perform spin dynamics calculations for the magnetic transition temperature and find it to be in agreement with the experiments. The present research opens new opportunities for quantum-mechanical engineering of the chemical and magnetic ordering in tetrataenite.

Elastic Properties of FeCr20Ni8Xn (X = Mo, Nb, Ta, Ti, V, W and Zr) Austenitic Stainless Steels: A First Principles Study

Austenitic stainless steels suffer from intergranular corrosion and stress corrosion cracking when exposed to elevated temperature (500–800 °C). Under these environments, Cr-carbides and Cr-carbontrides precipitate at the grain boundaries, which results in the formation of Cr-depleted zone. In practice, alloying elements could be added into austenitic stainless steels to modify the precipitation processes. Besides the precipitation processes, the elastic properties of the iron matrix would be influenced. Using the exact muffin-tin orbitals (EMTO) method, the solute effects on the elastic properties of FeCr20Ni8 austenitic stainless steels were studied. Based on the simulated shear modulus (G) and bulk modulus (B), we proposed a design map for FeCr20Ni8 based alloys, aiming to provide a basis for the design of high-performance austenitic stainless steels.

Generalized stacking fault energy of carbon-alloyed paramagnetic -Fe

Generalized stacking fault energy (GSFE) is an important parameter for understanding the underlying physics governing the deformation mechanisms in face-centred cubic (fcc) materials. In the present work, we study the long-standing question regarding the influence of C on the GSFE in austenitic steels at paramagnetic state. We calculate the GSFE in both -Fe and Fe–C alloys using the exact muffin-tin orbitals method and the Vienna Ab initio Simulation Package. Our results show that the GSFE is increased by the presence of interstitial C, and the universal scaling law is used to verify the accuracy of the obtained stacking fault energies. The C-driven change of the GSFE is discussed considering the magnetic contributions. The effective energy barriers for stacking fault, twinning and slip formation are employed to disclose the C effect on the deformation modes, and we also demonstrate that the magnetic structures as a function of volume explain the effect of paramagnetism on the C-driven changes of the stacking fault energies as compared to the hypothetical non-magnetic case.

Composition and temperature dependence of phase stability and elastic properties of Co2Cr(Ga1−xSix ) shape memory alloys from first principles

The composition and temperature dependence of the phase stability and elastic properties of ${\mathrm{Co}}_{2}\mathrm{Cr}({\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Si}}_{x}$) ($0.0\ensuremath{\le}x\ensuremath{\le}1.0$) alloys are investigated by using the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation. The calculated equilibrium properties and Curie temperature of the ground FM $L{2}_{1}$ phase are in good agreement with the available experimental and theoretical results. Separating the thermal effects into volume expansion, phonon-smearing, and magnetic terms, we find that dominated by the magnetic excitations in each FM alloy upon cooling, the free-energy difference ($\mathrm{\ensuremath{\Delta}}F$) between the $D{0}_{22}$ and $L{2}_{1}$ phases increases from negative to become positive, and the tetragonal shear elastic constant (${C}^{\ensuremath{'}}$) of the $L{2}_{1}$ phase stiffens, whereas that (${C}_{s}$) of the $D{0}_{22}$ phase softens even to become negative, resulting in the reentrant martensitic transformation (RMT) from $D{0}_{22}$ to $L{2}_{1}$. Nevertheless, with contributions from all three thermal effects, the contrary trends of $\mathrm{\ensuremath{\Delta}}F\ensuremath{\sim}T$, ${C}^{\ensuremath{'}}\ensuremath{\sim}T$, and ${C}_{s}\ensuremath{\sim}T$ are found in each PM alloy, promoting the normal martensitic transformation (MT) from $L{2}_{1}$ to $D{0}_{22}$ upon cooling. From both the energetic and mechanical points of view, the evaluated critical temperature (${T}_{M}$) of the RMT decreases whereas that of the MT is supposed to increase with increasing $x$. The MT and RMT are further attributed to the Jahn-Teller instability of the PM $L{2}_{1}$ and FM $D{0}_{22}$ phases, respectively, caused by the relatively weak covalent bond between Co and Ga (or Si) in them.

Elastic properties of 4d transition metal alloys: Values and trends

Using the Exact Muffin-Tin Orbitals method within the Perdew-Burke-Ernzerhof exchange-correlation approximation for solids and solid surfaces (PBEsol), we study the single crystal elastic constants of 4d transition metals (atomic number Z between 39 and 47) and their binary alloys in the body centered cubic (bcc) and face centered cubic (fcc) structures. Alloys between the first neighbors Z(Z + 1) and between the second neighbors Z(Z + 2) are considered. The lattice constants, bulk moduli and elastic constants are found in good agreement with the available experimental and theoretical data. It is shown that the correlation between the relative tetragonal shear elastic constant C′fcc-2C′bcc and the structural energy difference between the fcc and bcc lattices ΔE is superior to the previously considered models. For a given crystal structure, the equiatomic Z(Z + 2) alloys turn out to have similar structural and elastic properties as the pure elements with atomic number (Z + 1). Furthermore, alloys with composition Z1−x(Z + 2)x possess similar properties as Z1−2x(Z + 1)2x. The present theoretical data on the structural and the elastic properties of 4d transition metal alloys provides consistent input for coarse scale modeling of material properties.

First-principles study of the structural and elastic properties of AuxV1–x and AuxNb1–x alloys

Ab initio total energy calculations, based on the Exact Muffin-Tin Orbitals (EMTO) method in combination with the coherent potential approximation (CPA), are used to calculate the total energy of AuxV1–x and AuxNb1–x random alloys along the Bain path that connects the body-centred cubic (bcc) and face-centred cubic (fcc) structures as a function of composition x (0 ≤ x ≤ 1). The equilibrium Wigner–Seitz radius and the elastic properties of both systems are determined as a function of composition. Our theoretical prediction in case of pure elements (x = 0 or x = 1) are in good agreement with the available experimental data. For the Au–V system, the equilibrium Wigner–Seitz radius increase as x increases, while for the Au–Nb system, the equilibrium Wigner–Seitz radius is almost constant. The bulk modulus B and C44 for both alloys exhibit nearly parabolic trend. On the other hand, the tetragonal shear elastic constant C′ decreases as x increases and correlates reasonably well with the structural energy difference between fcc and bcc structures. Our results offer a consistent starting point for further theoretical and experimental studies of the elastic and micromechanical properties of Au–V and Au–Nb systems.

Effect of Magnetic Ordering on the Stability of Ni–Mn–Ga(–Co–Cu) Alloys Along the Tetragonal Deformation Path

The influence of magnetic ordering on the stability of Ni–Mn–Ga(–Co–Cu) Heusler alloys is investigated using the first-principles exact muffin-tin orbital method in combination with the coherent-potential approximation. The paramagnetic (PM) state is described by disordered local moment approach. In stoichiometric Ni2MnGa alloy, the total energy profile along the tetragonal deformation path differs between ferromagnetic (FM) ground state and PM state with high energy, where cubic structure of austenite exhibits lower total energy than tetragonally distorted structure of martensite. Martensitic structure is stabilized in ground state by FM interaction. In PM state it can be stabilized by partial substitution of Ni by Co or by partial substitution of Mn/Ga by Cu. Energy difference between PM and FM state $\Delta E_{\mathrm {PM{-}FM}}$ can be used for qualitative estimation of Curie temperature $T_{C}$ . Since Co doping to Ni sublattice slightly increases $\Delta E_{\mathrm {PM{-}FM}}$ , the $T_{C}$ should also increase, which corresponds to experimental findings. Analogically, Cu doping to Mn sublattice strongly decreases $\Delta E_{\mathrm {PM{-}FM}}$ , which corresponds to strong decrease of $T_{C}$ , also confirmed experimentally. For Cu doping in Ga sublattice the decrease in $T_{C}$ is weaker.

Effect of Mo on the phase stability and elastic mechanical properties of Ti–Mo random alloys from ab initio calculations

Ti–Mo alloys are promising materials for shape memory alloys and biomedical materials. Whereas, the appearance of metastable ω phase can cause embrittlement and destroy the shape memory effect. In order to avoid the ω phase, the effect of Mo on the temperature dependent lattice parameters, phase stability and elastic mechanical properties of β, α, and ω Ti1−xMox (x = 0–2.0) random alloys was systematically investigated by using the exact muffin-tin orbitals method in combination with the coherent potential approximation. The theoretical predictions for the lattice parameters are in good agreement with the available experiments. Results show that β Ti0.96Mo0.04 can almost transform to ω phase without lattice deformation and volume change, which suggests that the athermal ω phase is easier to precipitate and grow near 4 at.% Mo content in the β Ti1−xMox alloys. The critical content of Mo for the competed stabilization of β phase at T = 300 K is ~11.2 at.%. Its valence electron concentration of 4.224 is viewed as a necessary criterion for the competed phase stability. The calculations of formation energy are used to explain successfully why the partitioning of Mo can be found in Ti0.91Mo0.09 alloy after annealing. Through the analysis of formation energy, both Mo addition and increasing temperature can stabilize the β phase. The calculated Cauchy pressure, Pugh’s ratio, Poisson ratio, and Young’s modulus suggests that ω phase is intrinsically brittle and has large Young’s modulus compared with β and α phases.

Thermal Expansion, Elastic and Magnetic Properties of FeCoNiCu-Based High-Entropy Alloys Using First-Principle Theory

The effects of V, Cr, and Mn on the magnetic, elastic, and thermal properties of FeCoNiCu high-entropy alloy are studied by using the exact muffin-tin orbitals method in combination with the coherent potential approximation. The calculated lattice parameters and Curie temperatures in the face-centered-cubic structure are in line with the available experimental and theoretical data. A significant change in the magnetic behavior is revealed when adding equimolar V, Cr, and Mn to the host composition. The three independent single-crystal elastic constants are computed using a finite strain technique, and the polycrystalline elasticity parameters including shear modulus, Young’s modulus, Pugh ratio, Poisson’s ratio, and elastic anisotropy are derived and discussed. The effects of temperature on the structural parameters are determined by making use of the Debye–Grüneisen model. It is found that FeCoNiCuCr possesses a slightly larger thermal expansion coefficient than do the other alloys considered here.

An ab initio and experimental studies of the structure, mechanical parameters and state density on the refractory high-entropy alloy systems

The refractory high-entropy alloys (TiZrVMo, TiZrVMoTa, TiZrVMoTaNb, TiZrVMoTaNbCr and TiZrVMoTaNbCrW) possess a single phase solid solutions to the body centered cubic crystal structure. We showed the X-ray diffractograms of the calculation and experimental for refractory high-entropy alloys. However, the results of calculation are basically in agreement with the experimental. The equilibrium volume, thermodynamic stability, elastic constants and anisotropic elastic properties, electronic structures of the refractory high-entropy alloys were employed by the ab initio exact muffin-tin orbitals method. Formation enthalpy and cohesive energy were calculated and used to estimate the stability of the refractory high-entropy alloys. The elastic constants and modulus were obtained by the stress-strain method and the Voigt-Reuss-Hill approximation. Meanwhile, all the alloys showed different mechanical anisotropy for bulk modulus and Young's modulus. The total density and partial density of states were analyzed in physical properties of the refractory high-entropy alloys.

Tuning the plasticity of Ni-Mo solid solution in Ni-based superalloys by ab initio calculations

The generalized stacking fault energies of face centered cubic Ni-Mo solid solutions are calculated using the exact muffin-tin orbital method in combination with coherent potential approximation. The alloying of Mo in Ni is found to decrease the intrinsic stacking fault energy of the solid solution from 150mJ/m2 (pure Ni) to 50mJ/m2 (17.5at.% Mo) almost linearly. At the same time, the unstable stacking fault energy (the unstable twin fault energy) of the Ni-based solid solution increases (decreases) in a small extent with increasing Mo concentration. Three different twinnability measures are adopted and all indicate a substantially enhanced twinning mechanism in Ni-Mo solid solutions with increasing concentration of Mo. The weaker Ni-Ni bonding at high Mo concentrations is considered to be the main mechanism behind the disclosed phenomena. Segregation of Mo to the fault plane is proved to have strong effect on the generalized stacking fault energy of Ni-based solid solution.

Assessing the Exact Muffin-Tin Orbitals method for the Bain path of metals

We scrutinise the muffin-tin approximation and the screening within the framework of the Exact Muffin-Tin Orbitals method in the case of cubic and tetragonal crystal symmetries. Systematic total energy calculations are carried out for the Bain path including the body-centred cubic and face-centred cubic structures for a set of simple and transition metals. The present converged results in terms of potential sphere radius (S) and hard sphere radius (b) are in good agreement with previous theoretical calculations. We demonstrate that for all structures considered here, potential sphere radii around and slightly larger than the average Wigner–Seitz radius (w) yield accurate total energy results whereas S values smaller than w give large errors. It is shown that for converged total energies hard spheres with radii b = 0.7–0.8w should be used for an efficient screening within real space clusters consisting typically of 70–90 lattice sites. The less efficient convergence of the total energy in the case of small hard spheres is ascribed to the delocalisation of the screened spherical waves, which leads to inaccurate interstitial overlap matrix. The above conclusions are not significantly affected by the volume of the system.

Composition-dependent elastic properties in TiNi-Nb from first principle calculations

Abstract In this work, site-preference and elastic properties of TiNi-Nb austenite were investigated for various compositions, by using Exact Muffin-Tin Orbitals method in conjunction with Coherent Potential Approximation (EMTO-CPA). Moreover, composition-dependent elastic constants were calculated and used to explain the relation between composition and martensitic transition temperature. Our calculations suggested that Nb atoms prefer to occupy either Ni sites or Ti sites, depending strongly on composition. Variation of TiNi-Nb compositions is achieved through the formation of four sorts of defects: substituting Ti by Nb, substituting Ni by Nb, Ti anti-sites and Ni anti-sites. Our results suggested that c ′increases when Ni is substituted by Nb, while c 44 increases when Ni is substituted by Nb or Ni anti-sites form. Moreover, the maps of composition-dependent elastic constants were presented. TiNi-Nb with high c ′and c 44 could be obtained in Ni-deficient area. However, in Ni-excess area, only high c 44 could be obtained. Changing of martensitic transition temperature is sensitive to the variation of c 44 , rather than c ′. With the variation of c 44 , we explained the composition-dependent martensitic transition temperature for TiNi-Nb.

Elastic anharmonicity of bcc Fe and Fe-based random alloys from first-principles calculations

We systematically investigate elastic anharmonic behavior in ferromagnetic body-centered cubic (bcc) Fe and ${\mathrm{Fe}}_{1\ensuremath{-}x}{M}_{x}$ ($M=\mathrm{Al}$, V, Cr, Co, or Ni) random alloys by means of density-functional simulations. To benchmark computational accuracy, three ab initio codes are used to obtain the complete set of second- and third-order elastic constants (TOECs) for bcc Fe. The TOECs of ${\mathrm{Fe}}_{1\ensuremath{-}x}{M}_{x}$ alloys are studied employing the first-principles alloy theory formulated within the exact muffin-tin orbital method in combination with the coherent-potential approximation. It is found that the alloying effects on ${C}_{111},\phantom{\rule{0.28em}{0ex}}{C}_{112}$, and ${C}_{123}$, which are governed by normal strains only, are more pronounced than those on ${C}_{144},\phantom{\rule{0.28em}{0ex}}{C}_{166}$, and ${C}_{456}$, which involve shear strains. Remarkably, the magnitudes of all TOECs but ${C}_{123}$ decrease upon alloying with Al, V, Cr, Co, or Ni. Using the computed TOECs, we study compositional effects on the pressure derivatives of the effective elastic constants ($d{B}_{ij}/dP$), bulk ($dK/dP$), and shear moduli ($dG/dP$) and derive longitudinal acoustic nonlinearity parameters ($\ensuremath{\beta}$). Our predictions show that the pressure derivatives of $K$ and $G$ decrease with $x$ for all solute elements and reveal a strong correlation between the compositional trends on $dK/dP$ and $dG/dP$ arising from the fact that alloying predominantly alters $d{B}_{11}/dP$. The sensitivity of $d{B}_{11}/dP$ to composition is attributed to intrinsic alloying effects as opposed to lattice parameter changes accompanying solute addition. For Fe and the considered Fe-based alloys, $\ensuremath{\beta}$ along high-symmetry directions orders as $\ensuremath{\beta}[111]g\ensuremath{\beta}[100]g\ensuremath{\beta}[110]$, and alloying increases the directional anisotropy of $\ensuremath{\beta}$ but reduces its magnitude.

Elastic and thermal properties of refractory high-entropy alloys from first-principles calculations

We present a study of the elastic and thermal properties of single-phase ternary and quaternary Al-Ti-V-Cr-Nb-Mo refractory high-entropy alloys based on the first-principles calculations. The exact muffin-tin orbitals (EMTO) method in combination with the coherent potential approximation (CPA) is employed to calculate the equilibrium bulk properties and elastic parameters. The calculated Young’s moduli are in good agreement with the available experiments. Based on the thermal equation of state we use the quasi-harmonic Debye model to study the thermal properties such as the Gibbs free energy, Debye temperature, thermal expansion coefficient, and specific heat capacity. The elastic moduli at finite temperature are also discussed.

Different <i>Ab Initio</i> Approaches for Doping Descriptions: Tetragonal Deformation of Ni-Mn-Ga Alloys

The influence of Co and Cu doping on Ni-Mn-Ga alloy is investigated using the different ab initio methods for description of chemical disorder. The exact muffin-tin orbital method in combination with the coherent-potential approximation provides almost identical profiles of total energies along the tetragonal deformation path compared to the supercell approach used within the projector-augmented wave method. On the other hand, the simple virtual crystal approximation exhibits different results and thus it is not able to describe doping in Ni-Mn-Ga alloy properly.

Spinodal decomposition in ternary Fe-Cr-Co system

Using the exact muffin-tin orbitals method in conjunction with the coherent potential approximation we have studied the tendency towards spinodal decomposition of solid solution in ternary Fe-Cr-Co system. In addition, we have estimated the Curie temperature of the alloys, and considered the influence of the magnetic state on the decomposition thermodynamics of the ternary alloys. Using the mean field approximation, we have estimated the finite temperature effects on the alloys free energy. We predict that an increase Co and Cr content in the ternary Fe-Cr-Co system increases the tendency of the bcc (α)-FexCryCoz alloys towards the spinodal decomposition. Because of this, high magnetic properties and high thermal stability of these properties can be expected in the Fe-Cr-Co alloys with high Co content.

Order–disorder transition of alloys

Ab initio total-energy calculations, based on the exact muffin-tin orbitals method, are used to determine the equilibrium chemical configuration of alloy as a function of disorder and temperature. The transition from a substitutionally disordered face-centred-cubic crystallographic phase to an ordered phase is monitored using the coherent potential approximation which allows us to continuously scan the order parameter and thermodynamics of the alloy. We find signs of a first-order phase transition from a substitutionally disordered state to a partially ordered state around 210 K temperature and the completely ordered state is predicted around 90 K.