Lambda transitions in materials science: Recent advances in CALPHAD and first‐principles modelling

Körmann, Fritz; Breidi, A.; Dudarev, S. L.; Dupin, N.; Ghosh, Gautam; Hickel, Tilmann; Korzhavyi, Pavel A.; Muñoz, J. A.; Ohnuma, Ikuo

doi:10.1002/pssb.201350136

Cited by 84 publications

(73 citation statements)

References 168 publications

(219 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This remains then an unquantified potential inaccuracy in our calculations. If needed, it should be possible to capture the effect of this phenomenon on the FE perturbatively at each temperature, starting from the results developed here and using emerging methods for quantifying combined electronic-magnetic-vibrational effects [81][82][83] . The computational framework developed here can be used as a basis for calculation of regions of stability for various phases of iron at high pressure and temperature, solely based on ab initio methods.…”

Section: Discussionmentioning

confidence: 99%

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

et al. 2017

View full text Add to dashboard Cite

A framework for computing the anharmonic free energy (FE) of metallic crystals using BornOppenheimer ab initio molecular dynamics (AIMD) simulation, with unprecedented efficiency, is introduced and demonstrated for the hcp phase of iron at extreme conditions (up to ≈ 290 GPa and 5000 K). The advances underlying this work are: (1) A recently introduced harmonically-mapped averaging temperature integration (HMA-TI) method reduces the computational cost by order(s) of magnitude compared to the conventional TI approach. The TI path starts from zero Kelvin, where it assumes the behavior is given exactly by a harmonic treatment; this feature restricts application to systems that have no imaginary phonons in this limit. (2) A Langevin thermostat with the HMA-TI method allows use of a relatively large MD time step (4 fs, which is about eight times larger than the size needed for the Andersen thermostat) without loss of accuracy. (3) AIMD sampling is accelerated by using density functional theory (DFT) with a low-level parameter set, then the measured quantities of selected configurations are robustly reweighted to a higher level of DFT. This introduces a speedup of about 20-30× compared to directly simulating the accurate system. (4a) The temperature (T ) dependence of the hcp equilibrium shape (i.e. c/a axial ratio) is determined (including anharmonicity), with uncertainty less than ±0.001. (4b) Electronic excitation is included through Mermin's finite-temperature extension of the T = 0 K DFT. A simple FE perturbation method is introduced to handle the difficulty associated with applying the TI method with a Tdependent geometry and (due to electronic excitation) potential-energy surface. (5) The FE in the thermodynamic limit is attained through extrapolation of only the (computationally inexpensive) quasiharmonic FE, because the anharmonic FE contribution has negligible finite-size effects. All methods introduced here do not affect the AIMD sampling -results are obtained through postprocessing -so established AIMD codes can be employed without modification. Analytical formulas fitted to the results for the variation of the equilibrium c/a ratio and FE components with T are provided. Notably, effects of magnetic excitations are not included, and may yet prove important to the overall FE; if so, it is plausible that such contributions can be added perturbatively to the FE values reported here. Notwithstanding these considerations, FE values are obtained with an estimated accuracy and precision of 2 meV/atom, suggesting that the capability to compute the phase diagram of iron at Earth's inner core conditions is within reach.

show abstract

Section: Discussionmentioning

confidence: 99%

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Force-constant calculations and spin simulations have indeed been performed for decades [10,13]. However, most studies have been restricted to separate investigations of the two effects, whereas their mutual coupling could only be addressed in recent years [1,[14][15][16].…”

mentioning

confidence: 99%

Temperature Dependent Magnon-Phonon Coupling in bcc Fe from Theory and Experiment

et al. 2014

View full text Add to dashboard Cite

An ab initio based framework for quantitatively assessing the phonon contribution due to magnonphonon interactions and lattice expansion is developed. The theoretical results for bcc Fe are in very good agreement with high-quality phonon frequency measurements. For some phonon branches, the magnonphonon interaction is an order of magnitude larger than the phonon shift due to lattice expansion, demonstrating the strong impact of magnetic short-range order even significantly above the Curie temperature. The framework closes the previous simulation gap between the ferro-and paramagnetic limits. DOI: 10.1103/PhysRevLett.113.165503 PACS numbers: 63.20.K-, 63.20.dd, 63.20.dk, 75.50.Bb An understanding of the mutual interaction between different temperature-induced excitations in solids is a pivotal challenge for the simulation of thermodynamic properties of many materials. Experimental studies of phonons at elevated temperatures can help elucidate magnon-phonon coupling. Neutron scattering experiments of phonon dispersions have provided important data at selected temperatures [11]. Nuclear resonant inelastic x-ray scattering measurements are more amenable for showing thermal trends with measurements at many temperatures, and we have recently performed nuclear resonant inelastic x-ray scattering measurements of the phonon density of states of bcc Fe at 38 temperatures through the Curie transition [12]. Nonharmonic changes in the phonon DOS and vibrational entropy were found to track the change in magnetization with temperature. Since experimental analysis of phonon DOS broadening suggests explicit anharmonic contributions from phonon-phonon interactions to be an order of magnitude smaller, these new results are suggestive of large magnon-phonon interactions in bcc Fe.Parameter-free electronic structure calculations like density functional theory (DFT) in principle provide access to interatomic forces, spin-polarized energetics, and their interactions. Force-constant calculations and spin simulations have indeed been performed for decades [10,13]. However, most studies have been restricted to separate investigations of the two effects, whereas their mutual coupling could only be addressed in recent years [1,[14][15][16]. The T ¼ 0 K limit of a ferromagnetic system like Fe is the most straightforward case [17] since calculating force constants for a single magnetic configuration with all spins pointing in the same direction is sufficient ("FM limit" in Fig. 1). The infinite-temperature limit of a paramagnetic system with fully disordered spins ("PM limit") is significantly more challenging due to the large magnetic phase space that needs to be sampled for an accurate prediction of the coupling. Significant progress has been made only very recently with techniques based on DLM and spin molecular dynamics [1,18], a spin-spiral approach [15], dynamical mean field theory [14], and a spin-space averaging procedure [16].Given the complexity of the problem, present day methods are currently applied only at very low temperat...

show abstract

“…116,117 The magnetic entropy is interpreted as the orientational disorder of the spin alignments for a Heisenberg-like system in which the spins are collinear, and is used here as a first approximation for the case of CrN. Including only the electronic and magnetic contributions to the free energy, the orthorhombic phase is stable at low temperatures.…”

Section: 22 C H R O M I U M N I T R I D Ementioning

confidence: 99%

Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

Shulumba¹

2015

Linköping Studies in Science and Technology. Dissertations

View full text Add to dashboard Cite

In this thesis I introduce a new method for calculating the temperature dependent vibrational contribution to the free energy of a substitutionally disordered alloy that accounts for anharmonicity at high temperatures. This method exploits the underlying crystal symmetries in an alloy to make the calculations tractable. The validity of this approach is demonstrated by constructing the phase diagram via direct minimization of the Gibbs free energy of a notoriously awkward and technologically important system, Ti 1-x Al x N. The vibrational entropy including anharmonic effects is shown to be large and comparable to the configurational entropy at high temperatures, and with its inclusion, the theoretical miscibility gap of Ti 1-x Al x N is reduced from 6560 K to 2860 K, in line with atom probe experiments. A similar treatment of Zr 1-x Al x N and Hf 1-x Al x N alloys suggests that mass disorder has a minimal effect on phase stability compared with chemical ordering. My method is also capable of demonstrating that Hf 1-x Al x N, which is dynamically unstable at room temperature, is stabilised at high temperatures. Moreover I develop a new method of computing temperature dependent elastic constants for alloys from their phonon spectra, and show that for Ti 1-x Al x N, the elastic anisotropy is found to increase with temperature, helping to explain the spinodal decomposition.The effects of lattice dynamics on phase stability, mechanical, magnetic and transport properties on other materials are also examined. Four specific systems are discussed in detail. Firstly, in the case of CrN, lattice vibrations are shown to decrease the antiferromagnetic to paramagnetic phase transition temperature from 500 K to 380 K, in line with experimental evidence. Secondly, a temperature/pressure induced phase transition in AlN becomes much more facile than in the quasiharmonic approximation, and the thermal conductivity of the rocksalt phase is shown to be much lower than that of the wurtzite phase, as a result of the increased anharmonicity in the rocksalt structure. Thirdly, the temperature dependence of elastic constants of TiN becomes more isotropic as the temperature increases. Finally, iron carbides are evaluated as potentially important phases at the Earth's core; specifically, calculating the Gibbs free energy of a recently discovered orthorhombic phase of Fe 7 C 3 demonstrates that it is not stable relative to the known hexagonal phase at extreme pressure and temperatures.V Popular science summary Solid materials can be described using a simple mathematical model from the theory of lattice dynamics. In a solid, atoms are arranged in a regular and repeating structure (a lattice), and the forces between them can essentially be modelled as springs. Despite the simplicity of this model, it is possible to derive a surprising amount of information on materials from it. One can determine which arrangements of atoms, or phases, form the stable microscopic structures that we encounter in the real world, their mechanical properti...

show abstract

Lambda transitions in materials science: Recent advances in CALPHAD and first‐principles modelling

Cited by 84 publications

References 168 publications

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

Temperature Dependent Magnon-Phonon Coupling in bcc Fe from Theory and Experiment

Vibrations in solids : From first principles lattice dynamics to high temperature phase stability

Contact Info

Product

Resources

About