Pd–H and Ni–H phase diagrams using cluster variation method and Monte Carlo simulation

Bourgeois, Natacha; Cénédèse, Pierre; Crivello, Jean-Claude; Joubert, Jean-Marc

doi:10.1080/14786435.2019.1628367

Cited by 6 publications

(3 citation statements)

References 53 publications

(60 reference statements)

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“…These differences are likely related to both the (in)accuracy of the underlying DFT calculations and the treatment of temperaturedependent properties, notably the neglect of vibrations. Similar results for the incoherent phase diagram have previously been obtained in CE studies [48,49]. Interestingly these studies, which did not include a special treatment of strain, yielded a more pronounced underestimation of the critical temperature.…”

Section: B the Pd-h Phase Diagramsupporting

confidence: 84%

Quantitative predictions of thermodynamic hysteresis: Temperature-dependent character of the phase transition in Pd-H

Rahm,

Löfgren,

Erhart

2021

Preprint

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The thermodynamics of phase transitions between phases that are size-mismatched but coherent differs from conventional stress-free thermodynamics. Most notably, in open systems such phase transitions are always associated with hysteresis. In spite of experimental evidence for the relevance of these effects in technologically important materials such as Pd hydride, a recipe for first-principles-based atomic-scale modeling of coherent, open systems has been lacking. Here, we develop a methodology for quantifying phase boundaries, hysteresis, and coherent interface free energies using density-functional theory, alloy cluster expansions, and Monte Carlo simulations in a constrained ensemble. We apply this approach to Pd-H and show that the phase transition changes character above approximately 400 K, occurring with an at all times spatially homogeneous hydrogen concentration, i.e., without coexistence between the two phases. Our results are consistent with experimental observations but reveal aspects of hydride formation in Pd nanoparticles that have not yet been accessible in experiment.

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Section: B the Pd-h Phase Diagramsupporting

confidence: 84%

Quantitative predictions of thermodynamic hysteresis: Temperature-dependent character of the phase transition in Pd-H

Rahm,

Löfgren,

Erhart

2021

Preprint

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“…Zhang et al [48]. For the last developments of the Cluster Variation Method, we refer to [49][50][51]. However, in our case, we have utilised the possibility to divide the system into subsystems with energetically equivalent lattice positions.…”

Section: Discussionmentioning

confidence: 99%

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

Svoboda

Holec

Popov

et al. 2020

Philosophical Magazine

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Short-range ordering as the formation of couples and pairs between solutes is affected by their formation energies. This is not reflected in the standard regular solution model. Here, we present a new thermodynamic model which accounts for the dependence of the molar Gibbs energy on the concentrations of couples and pairs and their formation energies. The model treats kinetics of couples and pairs formation controlled by diffusion. This new model uses tracer diffusion coefficients of solutes and bond formation energies, which can be taken from ab initio calculations. Insofar, the current concept bridges the gap between ab initio methods and non-equilibrium thermodynamics. The reliability of the model is checked by comparison with kinetic Monte Carlo simulations. The model is applied to an Al-Mg-Si-Cu system. Finally, the configurational entropy for a binary system evaluated with the current model is compared with Bethe's approximation, which allows estimating of applicability limits of the current model.

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“…To this end, we use alloy cluster expansions (CEs) fitted to DFT to describe the energetics of the system ranging from 0% to 50% Au in Pd and in the full range from no hydrogen to 100% hydrogen (i.e., 1 H atom per 1 Au or Pd atom). This approach, which has been successfully applied to similar materials in the past [30][31][32][33][34], allows for very fast evaluation of the energy of a system with hundreds of atoms with an accuracy approaching that of DFT. Using Monte Carlo (MC) simulations, we can elucidate the thermodynamics and, in particular, study how chemical order evolves under different circumstances.…”

Section: Introductionmentioning

confidence: 99%

A tale of two phase diagrams: Interplay of ordering and hydrogen uptake in Pd-Au-H

Rahm,

Löfgren,

Fransson

et al. 2021

Preprint

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Due to their ability to reversibly absorb/desorb hydrogen without hysteresis, Pd-Au nanoalloys have been proposed as materials for hydrogen sensing. For sensing, it is important that absorption/desorption isotherms are reproducible and stable over time. A few studies have pointed to the influence of short and long range chemical order on these isotherms, but many aspects of the impact of chemical order have remained unexplored. Here, we use alloy cluster expansions to describe the thermodynamics of hydrogen in Pd-Au in a wide concentration range. We investigate how different chemical orderings, corresponding to annealing at different temperatures as well as different external pressures of hydrogen, impact the behavior of the material with focus on its hydrogen absorption/desorption isotherms. In particular, we find that a long-range ordered L12 phase is expected to form if the H2 pressure is sufficiently high. Furthermore, we construct the phase diagram at temperatures from 250 K to 500 K, showing that if full equilibrium is reached in the presence of hydrogen, phase separation can often be expected to occur, in stark contrast to the phase diagram in para-equilibrium. Our results explain the experimental observation that absorption/desorption isotherms in Pd-Au are often stable over time, but also reveal pitfalls for when this may not be the case.

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Pd–H and Ni–H phase diagrams using cluster variation method and Monte Carlo simulation

Cited by 6 publications

References 53 publications

Quantitative predictions of thermodynamic hysteresis: Temperature-dependent character of the phase transition in Pd-H

Quantitative predictions of thermodynamic hysteresis: Temperature-dependent character of the phase transition in Pd-H

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

A tale of two phase diagrams: Interplay of ordering and hydrogen uptake in Pd-Au-H

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