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

References

• L. Schlapbach, Technology: Hydrogen-fuelled vehicles, Nature 460 (2009), pp. 809–811. doi: 10.1038/460809a
   PubMed Web of Science ®Google Scholar
• B.D. Adams and A. Chen, The role of palladium in a hydrogen economy, Mater. Today 14 (2011), pp. 282–289. doi: 10.1016/S1369-7021(11)70143-2
   Web of Science ®Google Scholar
• R.K. Joshi, S. Krishnan, M. Yoshimura, and A. Kumar, Pd nanoparticles and thin films for room temperature hydrogen sensor, Nanoscale Res. Lett. 4 (2009), pp. 1191–1196. doi: 10.1007/s11671-009-9379-6
   PubMed Web of Science ®Google Scholar
• G. Sandrock and R.C. Bowman, Gas-based hydride applications: recent progress and future needs, J. Alloy. Compounds 356–357 (2003), pp. 794–799, proceedings of the Eighth International Symposium on Metal-Hydrogen Systems, Fundamentals and Applications (MH2002).
   Google Scholar
• F. Cuevas, J.M. Joubert, M. Latroche, and A. Percheron-Guégan, Intermetallic compounds as negative electrodes of Ni/MH batteries. Appl. Phys. A 72 (2001), pp. 225–238. doi: 10.1007/s003390100775
   Web of Science ®Google Scholar
• J.M. Joubert, M. Latroche, and A. Percheron-Guégan, Metallic hydrides ii: Materials for electrochemical storage, MRS Bull. 27 (2002), pp. 694–698. doi: 10.1557/mrs2002.224
   Web of Science ®Google Scholar
• J. Worsham, M. Wilkinson, and C. Shull, Neutron-diffraction observations on the palladium-hydrogen and palladium-deuterium systems, J. Phys. Chem. Solids 3 (1957), pp. 303–310. doi: 10.1016/0022-3697(57)90033-1
   Web of Science ®Google Scholar
• E.O. Wollan, J.W. Cable, and W.C. Koehler, The hydrogen atom positions in face centered cubic nickel hydride, J. Phys. Chem. Solids 24 (1963), pp. 1141–1143. doi: 10.1016/0022-3697(63)90028-3
   Web of Science ®Google Scholar
• N. Bourgeois, J.C. Crivello, P. Cenedese, and J.M. Joubert, Systematic first-principles study of binary metal hydrides, ACS. Comb. Sci. 19 (2017), pp. 513–523. doi: 10.1021/acscombsci.7b00050
   PubMed Web of Science ®Google Scholar
• O. Blaschko, P. Fratzl, and R. Klemencic, Model for the structural changes occurring at low temperatures in PdDx, Phys. Rev. B 24 (1981), pp. 277–282. doi: 10.1103/PhysRevB.24.277
   Google Scholar
• O. Blaschko, Structural features occurring in PdDx within the 50 K anomaly region, J. Less-Common Met. 100 (1984), pp. 307–320. doi: 10.1016/0022-5088(84)90071-7
   Google Scholar
• I. Anderson, D. Ross, and C. Carlile, The structure of the γ phase of palladium deuteride, Phys. Lett. A 68 (1978), pp. 249–251. doi: 10.1016/0375-9601(78)90819-8
   Web of Science ®Google Scholar
• I.S. Anderson, D.K. Ross, and C.J. Carlile, The 50 K transition in β-phase palladium deuteride observed by neutron scattering. J. Phys. C: Solid State Phys. 11 (1978), pp. L381–L384. doi: 10.1088/0022-3719/11/9/005
   Google Scholar
• T.E. Ellis, C.B. Satterthwaite, M.H. Mueller, and T.O. Brun, Evidence for H (D) ordering in PdHx (PdDx), Phys. Rev. Lett. 42 (1979), pp. 456–458. doi: 10.1103/PhysRevLett.42.456
   Google Scholar
• D. Ross, M. McKergow, D. Witchell, and J. Kjems, Neutron diffraction studies of domain growth associated with the 50 K anomaly in Pd–D, J. Less-Common Met. 172 (1991), pp. 169–182. doi: 10.1016/0022-5088(91)90445-A
   Google Scholar
• E. Wu, S.J. Kennedy, E.M.A. Gray, and E.H. Kisi, The ordered structure of PdD0.78 at 70–75 K. J. Phys.: Condens. Matter 8 (1996), pp. 2807–2813.
   Web of Science ®Google Scholar
• J.R. Lacher and R.H. Fowler, The statistics of the hydrogen-palladium system, Math. Proc. Cambridge Philos. Soc. 33 (1937), pp. 518–523. doi: 10.1017/S0305004100077641
   Google Scholar
• A. Harasima, T. Tanaka, and K. Sakaoku, Cooperative phenomena in Pd-H system. J. Phys. Soc. Jpn. 3 (1948), pp. 208–213. doi: 10.1143/JPSJ.3.208
   Google Scholar
• H. Brodowsky, Das system palladium/wasserstoff, Z. Phys. Chem. 44 (1965), pp. 129–142. doi: 10.1524/zpch.1965.44.3_4.129
   Google Scholar
• W. Oates, Thermodynamic properties of the Pd–H system, J. Less-Common Met. 88 (1982), pp. 411–424. doi: 10.1016/0022-5088(82)90250-8
   Google Scholar
• J.W. Cahn, On spinodal decomposition, Acta Metall. 9 (1961), pp. 795–801. doi: 10.1016/0001-6160(61)90182-1
   Google Scholar
• G. Alefeld, Wasserstoff in Metallen als Beispiel für ein Gittergas mit Phasenumwandlungen. Phys. Status Solidi 32 (1969), pp. 67–80. doi: 10.1002/pssb.19690320109
   Web of Science ®Google Scholar
• G. Alefeld, Phase transitions of hydrogen in metals due to elastic interaction, Ber. Bunsenges. Phys. Chem. 76 (1972), pp. 746–755.
   Google Scholar
• R.A. Bond and D.K. Ross, The use of Monte Carlo simulations in the study of a real lattice gas and its application to the α' Pd-D system, J. Phys. F Met. Phys. 12 (1982), pp. 597–609. doi: 10.1088/0305-4608/12/4/003
   Google Scholar
• D. Picton, R. Bond, B. Bowerman, D. Ross, D. Witchell, I. Anderson, and C. Carlile, The influence of H–H interactions on the phase diagram of Pd–H, J. Less-Common Met. 88 (1982), pp. 133–140. doi: 10.1016/0022-5088(82)90023-6
   Google Scholar
• T. Mohri and W.A. Oates, CVM–based calculation of the Pd–H phase diagram in the high temperature region, Mater. Trans. 43 (2002), pp. 2656–2661. doi: 10.2320/matertrans.43.2656
   Web of Science ®Google Scholar
• T. Mohri and W.A. Oates, Theoretical investigation of Pd–H phase equilibria by the cluster variation method, J. Alloy. Compd. 330-332 (2002), pp. 14–19. doi: 10.1016/S0925-8388(01)01663-2
   Web of Science ®Google Scholar
• D.E. Nanu and A.J. Böttger, Phase stabilities of Pd-based alloys for membranes for hydrogen gas separation: A statistical thermodynamics approach, J. Alloy. Compd. 446–447 (2007), pp. 571–574. doi: 10.1016/j.jallcom.2006.11.071
   Web of Science ®Google Scholar
• J.M. Joubert and S. Thiébaut, A thermodynamic description of the system Pd-Rh-H-D-T, Acta Mater. 59 (2011), pp. 1680–1691. doi: 10.1016/j.actamat.2010.11.035
   Web of Science ®Google Scholar
• J. Ågren, Y. Brechet, C. Hutchinson, J. Philibert and G. Purdy, Thermodynamics and Phase Transformations: the Selected Works of Mats Hillert, EDP Sciences, Les Ulis Cedex A, 2006.
   Google Scholar
• H.L. Lukas, S.G. Fries, and B. Sundman, Computational Thermodynamics: the Calphad Method, Vol. 131, Cambridge, Cambridge University Press, 2007.
   Google Scholar
• N. Bourgeois, J.C. Crivello, A. Saengdeejing, Y. Chen, P. Cenedese, and J.M. Joubert, Thermodynamic modeling of the Ni–H system, J. Phys. Chem. C 119 (2015), pp. 24546–24557. doi: 10.1021/acs.jpcc.5b06393
   Web of Science ®Google Scholar
• R. Kikuchi, A theory of cooperative phenomena, Phys. Rev. 81 (1951), pp. 988–1003. doi: 10.1103/PhysRev.81.988
   Web of Science ®Google Scholar
• A. Pelizzola, On three new cluster variation approximations, Physica. A. 211 (1994), pp. 107–123. doi: 10.1016/0378-4371(94)90072-8
   Web of Science ®Google Scholar
• J. Sanchez, F. Ducastelle, and D. Gratias, Generalized cluster description of multicomponent systems, Phys. A 128 (1984), pp. 334–350. doi: 10.1016/0378-4371(84)90096-7
   Web of Science ®Google Scholar
• M. Minoux, Programmation mathématique. Théorie et algorithmes, Dunod, 1983. ISBN: 2040154876 9782040154875. https://www.worldcat.org/search?q=no%3A491729873.
   Google Scholar
• R. Kikuchi, Superposition approximation and natural iteration calculation in cluster -- variation method, J. Chem. Phys. 60 (1974), pp. 1071–1080. doi: 10.1063/1.1681115
   Web of Science ®Google Scholar
• N.I.M. Gould, D. Orban, and P.L. Toint, Galahad, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization, ACM Trans. Math. Softw. 29 (2003), pp. 353–372. doi: 10.1145/962437.962438
   Web of Science ®Google Scholar
• HSL, A collection of fortran codes for large scale scientific computation, A collection of Fortran codes for large scale scientific computation, (2013). Available at http://www.hsl.rl.ac.uk.
   Google Scholar
• H. Flyvbjerg and H.G. Petersen, Error estimates on averages of correlated data, J. Chem. Phys. 91 (1989), pp. 461–466. doi: 10.1063/1.457480
   Web of Science ®Google Scholar
• A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108 (2015), pp. 1–5. doi: 10.1016/j.scriptamat.2015.07.021
   Web of Science ®Google Scholar
• J.W.D. Connolly and A.R. Williams, Density-functional theory applied to phase transformations in transition-metal alloys, Phys. Rev. B 27 (1983), pp. 5169–5172. doi: 10.1103/PhysRevB.27.5169
   Web of Science ®Google Scholar
• A. van de Walle, M. Asta, and G. Ceder, The alloy theoretic automated toolkit: A user guide, Calphad 26 (2002), pp. 539–553. doi: 10.1016/S0364-5916(02)80006-2
   Web of Science ®Google Scholar
• A. van de Walle, Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit, Calphad 33 (2009), pp. 266–278. doi: 10.1016/j.calphad.2008.12.005
   Web of Science ®Google Scholar
• A. van de Walle and G. Ceder, Automating first-principles phase diagram calculations, J. Phase Equilib. 23 (2002), pp. 348–359. doi: 10.1361/105497102770331596
   Web of Science ®Google Scholar
• J.P. Perdew, M. Ernzerhof, and K. Burke, Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys. 105 (1996), pp. 9982–9985. doi: 10.1063/1.472933
   Web of Science ®Google Scholar
• J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 78 (1997), pp. 1396–3868. doi: 10.1103/PhysRevLett.78.1396
   Web of Science ®Google Scholar
• G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996), pp. 11169–11186. doi: 10.1103/PhysRevB.54.11169
   PubMed Web of Science ®Google Scholar
• G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999), pp. 1758–1775. doi: 10.1103/PhysRevB.59.1758
   Web of Science ®Google Scholar
• H.J. Monkhorst and J.D. Pack, Special points for brillouin-zone integrations, Phys. Rev. B 13 (1976), pp. 5188–5192. doi: 10.1103/PhysRevB.13.5188
   Web of Science ®Google Scholar
• Y. Wang, S.N. Sun, and M.Y. Chou, Total-energy study of hydrogen ordering in PdHx(0≤x≤1), Phys. Rev. B 53 (1996), pp. 1–4. doi: 10.1103/PhysRevB.53.1
   Google Scholar
• P. Vajda, Hydrogen in rare-earth metals, including RH2+x phases, in Handb. Phys. Chem. Rare Earths, Vol. 20, Elsevier, Amsterdam, 1995, pp. 207–291.
   Google Scholar
• N. Bourgeois, J.-C. Crivello, P. Cenedese, V. Paul-Boncour, and J.-M Joubert, Vibration analysis of hydrogen, deuterium and tritiumin metals: consequences on the isotope effect. J. Phys.: Condens. Matter 30 (2018), pp. 335–402. https://doi.org/10.1088/1361-648X/aad259.
   Web of Science ®Google Scholar
• C. Demangeat and M. Khan, Chemical binding energies of point defects in palladium doped with hydrogen and d impurities, J. Phys. 41 (1980), pp. 1001–1007. doi: 10.1051/jphys:019800041090100100
   Web of Science ®Google Scholar
• Y. Yamada, and T. Mohri, Lattice statistics and dynamics within cluster variation method, Mater. Trans. 57 (2016), pp. 481–487. doi: 10.2320/matertrans.MBW201504
   Web of Science ®Google Scholar