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Coherent phase decomposition in the PdH system

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Abstract

We have used molecular dynamics and Monte Carlo methods to simulate the structure and phase stability of a Pd crystal in thermodynamic equilibrium with molecular hydrogen gas at temperature T and pressure \( P_{g}^{H2} \). The pressure–composition–temperature (PCT) curves were deduced under the extreme conditions of an open system (Pd crystal in equilibrium with a large-volume H2 gas reservoir) and a closed system (Pd crystal in equilibrium with H2 gas reservoir of infinitesimal volume). The PCT curves from the open simulations reproduce the experimental observations, including the ubiquitous hysteresis. The PCT curves from the closed-system simulations are continuous curves. Below a tri-critical point, the Pd–H system decomposes into two coherent phases. We find excellent agreement between the present simulation results and the predictions of the Schwarz–Khachaturyan theory for the decomposition of a Pd–H alloy into two coherent hydride phases.

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References

  1. 1

    Manchester FD, San-Martin A, Pitre JM (1994) The H–Pd (Hydrogen–Palladium) system. J Phase Equilibria 15:62–83

  2. 2

    Ubbelohde AR (1937) Some properties of the metallic state: I-metallic hydrogen and its alloys. Proc R Soc London Ser A 159:295–306

  3. 3

    Scholtus NA, Hall WK (1963) Hysteresis in the palladium–hydrogen system. J Chem Phys 39:868–870

  4. 4

    Lundin CE, Lynch FE (1978) A new rationale for the hysteresis effects observed in metal-hydrogen systems. In: Andersen AF, Maeland AJ (eds) Hydrides for energy storage. Elsevier, London, pp 395–405

  5. 5

    Wicke E, Blaurock J (1987) New experiments on and interpretations of the hysteresis effects of Pd–D2 and Pd–H2. J Less Common Metals 130:351–363

  6. 6

    Flanagan TD, Clewley JD, Kuji T, Park Ch-N, Everett DH (1986) Isobaric and isothermal hysteresis in metal hydrides and oxides. J Chem Soc Faraday Trans 1(82):2589–2604

  7. 7

    Quian S, Northwood DO (1988) Hysteresis in metal-hydrogen systems: a critical review of the experimental observations and theoretical models. Int J Hydrogen Energy 13:25–35

  8. 8

    Flanagan TB, Clewley JD (1982) Hysteresis in metal hydrides. J Less Common Metals 83:127–141

  9. 9

    Flanagan TB, Oates WA (1988) Thermodynamics of Intermetallic compound-hydrogen systems. In: Schlapbach L (ed) Hydrogen in intermetallic compounds I, topics in applied physics, vol 63. Springer, Berlin, pp 49–85

  10. 10

    Jamieson HC, Weatherly GC, Manchester FD (1976) The β → α phase transformation in palladium-hydrogen alloys. J Less Common Metals 50:85–102

  11. 11

    Ho E, Goldberg HA, Weatherly GC, Manchester FD (1979) An in situ electron microscopy study of precipitation in palladium–hydrogen alloys. Acta Metall 27:841–853

  12. 12

    Kirchheim R (1986) Interaction of hydrogen with dislocations in palladium. In: Ashby MF, Hirth JP (eds) Perspectives in hydrogen in metals. Pergamon, Oxford, pp 355–374

  13. 13

    Chandra D, Bagchi S, Lambert SW, Cathey WN, Lynch FE, Bowman RC Jr (1993) Long-term thermal cycling studies on LaNi5.2. J Alloys Compd 199(1–2):93–100

  14. 14

    Nakamura H, Nakamura Y, Fujitani S, Yonezu I (1996) Cycle performance of a hydrogen-absorbing La0.8Y0.2Ni4.8Mn0.2 Alloy. Int J Hydrogen Energy 21:457–460

  15. 15

    Schwarz RB, Khachaturyan AK (1995) Thermodynamics of open two-phase systems with coherent interfaces. Phys Rev Lett 74:2523–2526

  16. 16

    Schwarz RB, Khachaturyan AK (2006) Thermodynamics of open two-phase systems with coherent interfaces: application to metal-hydrogen systems. Acta Mater 54:313–323

  17. 17

    Eshelby JD (1956) The continuum theory of lattice defects. In: Seitz F, Turnbull D (eds) Solid state physics, vol 3. Academic Press, New York, pp 79–144

  18. 18

    Wolf RJ, Lee MW, Davis RC, Fay PJ, Ray JR (1993) Pressure-composition isotherms for palladium hydride. Phys Rev B 48:12415–12418

  19. 19

    Lee MW, Wolf RJ, Ray JR (1995) Atomistic calculations of hydrogen loading in palladium. J Alloys Compd 231:343–346

  20. 20

    Murray SD, Baskes MI (1984) Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys Rev B 29:6443–6453

  21. 21

    Wolf RJ, Mansour KA, Lee MW, Ray RJ (1992) Temperature dependence of elastic constants of embedded-atom models of palladium. Phys Rev B 46:8027–8035

  22. 22

    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1–19

  23. 23

    Zhou XW, Zimmerman JA, Wong BM, Hoyt JJ (2008) An embedded-atom method interatomic potential for Pd–H alloys. J Mater Res 23:704–718

  24. 24

    Emin D, Baskes MI, Wilson WD (1979) Small-polaronic diffusion of light interstitials in bcc metals. Phys Rev Lett 42:791–794

  25. 25

    Schwarz RB, unpublished results, Los Alamos National Laboratory (2018) These measurements are sufficiently detailed to enable us to construct the experimental coherent phase diagram of Pd–D, shown in Fig. 10

  26. 26

    Carrillo-Bucio JL, Tena-Garcia JR, Armenta-Garcia EP, Hernandez-Silva O, Cabañas-Moreno JG, Suárez-Alcántara K (2018) Low-cost Sieverts-type apparatus for the study of hydriding/dehydriding reactions, HardwareX e00036

  27. 27

    We use the name “load line” in analogy to the electrical engineering use of a resistor (with linear current-voltage dependence) added in series to a transistor or vacuum tube (with non-linear current-voltage dependence) to force the device to operate at a prescribed current-voltage point

  28. 28

    Feenstra R, Griessen R, de Groot DG (1986) Hydrogen induced lattice expansion and effective H–H interaction in single phase PdHc. J Phys F Metals Phys 16:1933–1952

  29. 29

    Schwarz RB, Bach HT, Harms U, Tuggle D (2005) Elastic properties of Pd–hydrogen, Pd–deuterium, and Pd-tritium single crystals. Acta Meter 53:569–580

  30. 30

    ELASTIC_T is a computer code developed by Aidan Thompson (Sandia Natl. Labs), included in the LAMMPS depository, which uses MD to calculate the elastic constants of solids

  31. 31

    Krueger F, Gehm G (1933) Lattice constants and electrical conductivity of electrolytically loaded palladium-silver alloys as a function of hydrogen loading. Ann Phys 16:174–189

  32. 32

    Huang W, Pálsson GK, Brischetto M, Droulias SA, Hartmann O, Wolff M, Hjörvasson B (2017) Experimental observation of hysteresis in a coherent metal-hydride phase transition. J Phys Condens Matter 29:495701

  33. 33

    Slater JC (1939) Introduction to chemical physics. Dover Publications, New York, pp 130–149

  34. 34

    de Darwent BB (1970) Bond dissociation energies in simple molecules. National Bureau of Standards Publication NSRDS-NBS, St Paul, p 31

  35. 35

    Lässer R, Klatt KH (1983) Solubility of hydrogen isotopes in palladium. Phys Rev B 28:748–758

  36. 36

    Khachaturyan AG (1983) Theory of structural transformations in solids. Willey, New York

  37. 37

    Bitter F (1931) On impurities in metals. Phys Rev 37:1527–1547

  38. 38

    Crum MM, Private communication cited in Nabarro FRN (1940) The strains produced by precipitation in alloys. Proc R Soc A 125:519–538

  39. 39

    Crespo EA, Ruda M, de Debiaggi SR, Bringa EA, Braschi FU, Bertolino G (2012) Hydrogen absorption in Pd nanoparticles of different shapes. Int J Hydrogen Energy 37:14831–14837

  40. 40

    Frazier GA, Glosser R (1980) Characterization of thin films of the palladium-hydrogen system. J Less Common Metals 74:89–96

  41. 41

    Feenstra R, de Groot DG, Rector JH, Salomons E, Griessen R (1986) Gravimetrical determination of pressure composition isotherms of thin PdHc films. J Phys F Metals Phys 16:1953–1963

  42. 42

    Pundt A, Sachs C, Winter M, Reetz MT, Fritsch D, Kirchheim R (2016) Hydrogen sorption in elastically soft stabilized Pd-clusters. J Alloys Compd 293–295:480–483

  43. 43

    Griessen R, Strohfeldt N, Giessen H (2016) Thermodynamics of the hybrid interaction of hydrogen with palladium nanoparticles. Nat Mater 15:311–317

  44. 44

    Shtaya-Suleiman MAM (2003) Size-selective synthesis of nanometer-sized palladium clusters and their hydrogen solvation behavior. Ph.D. dissertation, Georg-August-University Göttingen, Germany

  45. 45

    Nelson DR, Spaepen F (1989) Polytetrahedral order in condensed matter. In: Ehrenreich H, Turnbull D (eds) Solid state physics, vol 42. Academic Press, Cambridge, pp 1–90

  46. 46

    Baldi A, Narayan T, Koh AL, Dionne JA (2014) In situ detection of hydrogen-induced phase transitions in individual palladium nanocrystals. Nat Mater 13:1143–1148

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Acknowledgements

This research used resources provided by the Los Alamos National Laboratory Institutional Computing Program, which is supported by the US Department of Energy National Nuclear Security Administration under Contract No. DE-AC52-06NA25396.

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Correspondence to R. B. Schwarz.

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Schwarz, R.B., Khachaturyan, A.K., Caro, A. et al. Coherent phase decomposition in the PdH system. J Mater Sci 55, 4864–4882 (2020) doi:10.1007/s10853-019-04179-z

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