Super Abundant Vacancies, or Fukai Vacancies

This study is being split into two pages. A list of all papers cited, with abstracts, is being created on the subpage, Abstracts.This page will then become a summary review.

See subpage, McKubre and Staker (2018), “NAE = SAV = SPD + D”. As well, see  the ICCF-21 abstract, “Coupled Calorimetry and Resistivity Measurements, in Conjunction with an Emended and More Complete Phase Diagram of the Palladium – Isotopic Hydrogen System,” Michael Staker, and there is audio of the Staker presentation. A preprint is linked below.

One of the major unresolved issues in research into the Anomalous Heat Effect is the location of the reactions. Much early research assumed that the reaction would be taking place generally in the bulk of the palladium metal, loaded with deuterium, used in the Fleischmann-Pons experiment. Eventually, it became quite clear, with many evidences, that the heat, and associated helium, was coming from a surface effect. Where on the surface, the whole surface? Not likely. Different theories propose different sites. Storms’ hydroton theory proposes nanocracks, formed when repeated loading and deloading stresses the metal. There have been other proposals, most notably vacancies, empty locations within the lattice, which might then host reactions. However, ordinary vacancies are just that, ordinary. Whatever is causing the FP Heat Effect is not ordinary. Something special must happen first.

Recently, I became aware of concepts that were first published in the 1990s, but which were not necessarily widely noticed and understood. This page will collect sources on what are called “Fukai phases” or “super abundant vacancies.” The “vacancies” name could be seen as misleading, because these are not simply vacancies, they are phases of an alloy, palladium hydride/deuteride, phases not ordinarily seen because they do not form under ordinary conditions. This is getting quite interesting, and I will be able to write more about this soon. I started with sources.

Then I have a document from a LENR researcher critical of SAV theory. Permission to quote was given, but there were unclear restrictions. I will report the ideas here, absent clear permission to quote with attribution.

(I have just received copies of many of these papers and have uploaded them. It may take a little time before Google responds, but I’m entering the search terms now.

Sources relating to SAVs 

Flanagan, T.B. and W.A. Oates, The Palladium-Hydrogen System. Annu. Rev. Mater. Sci., 1991. 21: p. 269. Britz, P.Flan1991

In this review an attempt is made to highlight some of the important properties of the palladium-hydrogen system. (The term hydrogen will be used as a collective term when referring to all three isotopes, but otherwise the names of the specific isotopes, protium, deuterium, and tritium, will be used.) Most of the data in the literature are for the palladium-protium  system; generally the three isotopes behave similarly, however, the thermodynamic and kinetic (diffusion) behavior of the isotopes differ quantitatively and these differences are discussed below. 

Y. Fukai, The Metal–Hydrogen System: Basic Bulk Properties, Second, Revised and Updated Edition, Springer, 2005, Britz Fukai2005

Metal hydrides are of inestimable importance for the future of hydrogen energy. This unique monograph presents a clear and comprehensive description of the bulk properties of the metal-hydrogen system. The statistical thermodynamics is treated over a very wide range of pressure, temperature and composition. Another prominent feature of the book is its elucidation of the quantum mechanical behavior of interstitial hydrogen atoms, including their states and motion. The important topic of hydrogen interaction with lattice defects and its materials-science implications are also discussed thoroughly. This second edition has been substantially revised and updated.

Y. Fukai, N. Okuma, Evidence of copious vacancy formation in Ni and Pd under a high hydrogen
pressure. Jpn. J. Appl. Phys. 32, L1256-1259 (1993).Britz Fukai1993

From in situ observation of X-ray diffraction of Ni and Pd under a high hydrogen pressure (sime5 GPa) and temperatures (≤800°C), anomalous lattice contraction of the hydride was found to occur in 2~3 h. This contraction, amounting to ~0.5 Å3 per a metal atom, remained in the recovered specimen even after the hydrogen was removed by heating to 400°C, but was annealed out at 800°C. The concentration of vacancies responsible for this effect is estimated at ~20% of metal-atom sites. Anomalous concentration dependence of the hydrogen-induced volume and enhanced diffusion of metal atoms are explained in terms of this effect.

Y. Fukai, N. Okuma, Formation of superabundant vacancies in Pd hydride under high hydrogen
pressures. Phys. Rev. Lett. 73, 1640-1643 (1994). Britz Fukai1994

In situ x-ray diffraction on Pd hydride under 5 GPa of hydrogen pressure show that lattice contraction due to vacancy formation occurs in 2-3 h at 700-800 °C, and two-phase separation into PdH and a vacancy-ordered phase of Cu3Au structure (Pd3VacH4) on subsequent cooling. After recovery to ambient conditions and removal of hydrogen, the vacancy concentration in Pd metal was determined by measuring density and lattice parameter changes to be 18 ± 3 at.%. This procedure provides a new method of introducing superabundant vacancies in metals.

Y. Fukai, Formation of superabundant vacancies in M–H alloys and some of its consequences: a
review. J. Alloys and Compounds 356-357, 263-269 (2003).  Britz Fukai2003a

Superabundant vacancies (SAVs) are the vacancies of M atoms formed in M-H alloys, of concentrations as large as 30 at.%. After presenting some results of SAV formation as revealed by X-ray diffraction (XRD) at high temperatures and high hydrogen pressures, its mechanism in terms of vacancy-hydrogen (Vac-H) cluster formation is described, including the underlying information of Vac-H interactions. One of the most important conclusions of the theory is that defect structures containing SAVs are in fact the most stable structure of M-H alloys, and therefore SAVs should be formed whenever the kinetics allow. It is shown subsequently that SAVs can be formed in the process of electrodeposition. Some of the consequences of SAV formation including the enhancement of M-atom diffusion and creep are described, and its possible implication for hydrogen embrittlement of steels is mentioned.

Y. Fukai, Y. Shizuku, Y. Kurokawa, Superabundant vacancy formation in Ni–H alloys. J. Alloys
Compds. 329, 195-201 (2001). Britz Fukai2001

X-ray diffraction measurements on the Ni–H system were made using synchrotron radiation at high hydrogen pressures p(H2)=3∼5 GPa and high temperatures T≲1000°C. Gradual lattice contraction occurring over several hours at high temperatures revealed the formation of superabundant vacancies (vacancy-hydrogen clusters). Superlattice reflections due to ordered arrangements of Vac-H clusters were also observed. The concentration of Vac-H clusters (xcl≅0.30), deduced from the magnitude of the lattice contraction, was very nearly independent of pressure and temperature, and indicates the maximum possible cluster concentration to be accommodated by the metal lattice. A simple enlightening description of the physics of superabundant vacancy formation is given in Appendix A.

S. Miraglia, D. Fruchart, E. K. Hill, S. S. M. Tavares, D. Dos Santos, Investigation of the vacancy ordered
phases in the Pd–H system. J. Alloys and Compounds 317, 77-82 (2001). Britz Mira2001

It has been shown that hydrogen–metal reactions operated at high pressures (3–5 GPa) may lead to hydrogen-induced lattice migration. The occurrence of fast diffusion processes that take place within the metal lattice has been established. Under these conditions, modifications of the diffusion kinetics and of the phases equilibria allow to produce vacancy-ordered phases with high vacancy concentrations (20%). An alternative route which leads to such phases that are stable at ambient pressure and temperature is presented. The structural properties of the Pd-(vacancy, H) system which have been studied by means of X-ray diffractionscanning electron microscopy and transmission electron microscopy will be discussed. In the case of palladium, the vacancy-ordered state is characterized by the loss of superconductivity with respect to the Pd hydride. This spectacular modification of the physical properties will be presented and discussed in the light of band structure calculations that have been performed modeling different types of decorated vacancies with octahedral coordination.

D. S. dos Santos, S. Miraglia, D. Fruchart, A high pressure investigation of Pd and the Pd–H
system. J. Alloys and Compd. 291, L1-L5 (1999). Britz dSan1999

The effect of high pressure (3.5 GPa) on the Pd and Pd–H systems has been investigated. We have been able to induce a cubic–monoclinic structural transformation in the case of pure Pd treated at 450°C for 5 h. Hydrogen has been introduced at high pressures using an alternative hydrogen source (C14H10). It is shown that such a route can be operated to produce vacancy-ordered phases that are stable at ambient pressure and temperature.

H. Osono, T. Kino, Y. Kurokawa, Y. Fukai, Agglomeration of hydrogen-induced vacancies in
nickel. J. Alloys and Compd. 231, 41-45 (1995). Britz Oson1995

Scanning electron microscope observations of Ni samples annealed after recovery from high temperature heat treatment in the hydride phase showed the presence of numerous holes 20–200 nm in size. From various features of the holes they are identified as voids formed by agglomeration of supersaturated vacancies (about 5 at.% in concentration) which have diffused from the surface to the interior of the sample during heat treatment.

M. Tsirlin, Comment on the article ‘Simulation of Crater Formation on LENR Cathodes Surfaces’.
J. Cond. Matter Nucl. Sci. 14, 1-4 (2014).

Formation of small craters on the surface of Pd cathode during electrolysis in electrolytes based on heavy water is sometimes interpreted as a consequence of low-temperature nuclear reactions. In this note we discuss the validity of these statements.

E. K. Storms, C. Talcott-Storms, The effect of hydriding on the physical structure of palladium
and on the release of contained tritium. Fusion Technol. 20, 246 (1991). Britz Stor1991a

The behavior of tritium released from a contaminated palladium cathode is determined and compared with the pattern found in cells claimed to produce tritium by a cold fusion reaction. Void space is produced in palladium when it is subjected to hydrogen absorption and desorption cycles. This void space can produce channels through which hydrogen can be lost from the cathode, thereby reducing the hydrogen concentration. This effect is influenced, in part, by impurities, the shape of the electrode, the charging rate, the concentration of hydrogen achieved, and the length of time the maximum concentration is present.

Y. Fukai, M. Mizutani, S. Yokota, M. Kanazawa, Y. Miura, T. Watanabe, Superabundant
vacancy–hydrogen clusters in electrodeposited Ni and Cu. J. Alloys and Compd. 356-357, 270-273
(2003). Britz Fukai2003b

Superabundant vacancies (SAVs) are the vacancies of M atoms formed in M–H alloys, of concentrations as large as ≲30 at.%. After presenting some results of SAV formation as revealed by X-ray diffraction (XRD) at high temperatures and high hydrogen pressures, its mechanism in terms of vacancy-hydrogen (Vac-H) cluster formation is described, including the underlying information of Vac-H interactions. One of the most important conclusions of the theory is that defect structures containing SAVs are in fact the most stable structure of M–H alloys, and therefore SAVs should be formed whenever the kinetics allow. It is shown subsequently that SAVs can be formed in the process of electrodeposition. Some of the consequences of SAV formation including the enhancement of M-atom diffusion and creep are described, and its possible implication for hydrogen embrittlement of steels is mentioned.

Nazarov, R. and Hickel, T. and Neugebauer, J., Ab initio study of H-vacancy interactions in fcc metals: Implications for the formation of superabundant vacancies, Phys. Rev. B 89, 144108 (2014). Britz Naza2014

Hydrogen solubility and interaction with vacancies and divacancies are investigated in 12 fcc metals by density functional theory. We show that in all studied fcc metals, vacancies trap H very efficiently and multiple H trapping is possible. H is stronger trapped by divacancies and even stronger by surfaces. We derive a condition for the maximum number of trapped H atoms as a function of the H chemical potential. Based on this criterion, the possibility of a dramatic increase of vacancy concentration (superabundant vacancy formation) in the studied metals is discussed.

See below, Nazarov.

L.E. Isaeva, D.I. Bazhanov, E.I. Isaev, S.V. Eremeev, S.E. Kulkova, I.A. Abrikosov, Dynamic stability of palladium hydride: An ab initio study, International Journal of Hydrogen Energy 36, 1254 (2011). (copy)

We present results of our ab initio studies of electronic and dynamic properties of ideal palladium hydride PdH and its vacancy ordered defect phase Pd3VacH4 (“Vac” – vacancy on palladium site) with L12 crystal structure found experimentally and studied theoretically. Quantum and thermodynamic properties of these hydrides, such as phonon dispersion relations and the vacancy formation enthalpies have been studied. Dynamic stability of the defect phase Pd3VacH4 with respect to different site occupation of hydrogen atoms at the equilibrium state and under pressure was analyzed. It was shown that positions of hydrogen atoms in the defect phase strongly affect its stability and may be a reason for further phase transitions in the defect phase.

A. Houari, A., S. Matar, V. Eyert, Electronic structure and crystal phase stability of palladium hydrides, arXiv (2014).

The results of electronic structure calculations for a variety of palladium hydrides are presented.
The calculations are based on density functional theory and used different local and semilocal
approximations. The thermodynamic stability of all structures as well as the electronic and chemical
bonding properties are addressed. For the monohydride, taking into account the zero-point energy
is important to identify the octahedral Pd-H arrangement with its larger voids and, hence, softer
hydrogen vibrational modes as favorable over the tetrahedral arrangement as found in the zincblende
and wurtzite structures. Stabilization of the rocksalt structure is due to strong bonding of the 4d
and 1s orbitals, which form a characteristic split-off band separated from the main d-band group.
Increased filling of the formerly pure d states of the metal causes strong reduction of the density
of states at the Fermi energy, which undermines possible long-range ferromagnetic order otherwise
favored by strong magnetovolume effects. For the dihydride, octahedral Pd-H arrangement as
realized e.g. in the pyrite structure turns out to be unstable against tetrahedral arrangement as found
in the fluorite structure. Yet, from both heat of formation and chemical bonding considerations
the dihydride turns out to be less favorable than the monohydride. Finally, the vacancy ordered
defect phase Pd3H4 follows the general trend of favoring the octahedral arrangement of the rocksalt
structure for Pd:H ratios less or equal to one.

M.R. Staker, Coupled Calorimetry and Resistivity Measurements, in Conjunction with an Emended and More Complete Phase Diagram of the Palladium – Isotopic Hydrogen System, ICCF-21 (2018) (preprint).

Results of a calorimetric study established the energy produced, over and above input energy, from electrolytic loading of deuterium into Pd was 150 MJ/cc of Pd (14000 eV/Pd atom) for a 46 day period. High fugacity of deuterium was developed in unalloyed palladium via electrolysis (0.5 molar electrolyte of lithium deuteroxide, LiOD) with the use of an independent electromigration current. In situ resistivity measurements of Pd were used to assay activity of D in the Pd lattice (ratio of D/Pd) and employed as an indicator of phase changes. During this period, two run-away events were triggered by suddenly increasing current density resulting in 100 percent excess power (2.4 watts output with 1.2 watts input) and necessitating temporary cut back in electrolysis current. The average excess power (excluding run-away) ranged from 4.7 +/- 0.15 to 9.6 +/- 0.30 percent of input power while input power ranged from 2.000 to 3.450 watts, confirming the Fleischmann-Pons effect. The precision was: Power In = +/-.0005 W; ∆T = +/- .05oC; Power Out = +/-.015 W for an overall precision of +/- 0.5%. High fugacity was required for these results, and the triggered run-away events required even higher fugacity. Using thermodynamic energy balance, it was found that the energy release was of such magnitude that the source of the energy is from a nuclear source, however the exact reaction was not determined in this work. X-ray diffraction results from the recent literature, rules for phase diagram construction, and thermodynamic stability requirements necessitate revisions of the phase diagram, with addition of three thermodynamically stable phases of the superabundant vacancy (SAV) type. These phases, each requiring high fugacity, are: γ (Pd7VacD6-8), δ (Pd3VacD4 – octahedral), δ’ (Pd3VacD4 – tetrahedral). The emended Palladium – Isotopic Hydrogen phase diagram is presented. The excess heat condition supports portions of the cathode being in the ordered δ phase (Pd3VacD4 – octahedral), while a drop in resistance of the Pd cathode during increasing temperature and excess heat production strongly indicates portions of the cathode also transformed to the ordered δ’ phase (Pd3VacD4 – tetrahedral). A dislocation mechanism is presented for creation of vacancies and mobilizing them by electromigration because of their attraction to D+ ions which aids the formation of SAV phases. Extending SAV unit cells to the periodic lattice epiphanates δ as the nuclear active state. The lattice of the decreased resistance phase, δ’, reveals extensive pathways of low resistance and a potential connection to the superconductivity phase of PdH/PdD.

Nazarov (2014)

This paper begins with a review of SAV studies. The introductory paragraph here I want to copy.

The desired or unwanted presence of hydrogen in metals is a long-standing research topic in materials science. One of the astonishing implications of this presence can be an increase of the vacancy concentration in a material by several orders of magnitude, the so-called superabundant vacancy (SAV) formation. The physical picture behind this effect is a trapping of hydrogen in vacancies, yielding an overall reduction of the vacancy energy of formation. Despite the straightforwardness of such an explanation, it took until 1993 before the SAV phenomenon was first discovered experimentally by Fukai and co-workers in Pd [1] and Ni [2]. Since then, however, it has been observed in many metallic systems such as Cu [3], Ti [4], Pd and Pd alloys [5–8], Al [9], Mn [10], Fe [10,11], Mo [12], Cr [13], Co [10], Ni [14], Ni-Fe alloy [15], Nb [16–18], some hydrogen storage alloys [19], some metal hydrides [20], and stainless steels [21,22]. There are now examples available that the concentration of vacancies can become as large as 10% and more [10,23,24]. Even vacancy-ordered phases have been detected in Pd [1,5,25–27], Mn [28], Ni [14], and Fe [29]. These high-vacancy concentrations are typically not formed immediately, but only after hydrogen loading for several hours at sufficiently high temperatures [23]. However, recent investigations [10] have shown that large concentrations of vacancies (up to 10−4) can be generated at internal sources of pure metals in less than 1 s. Further, hydrogen-induced vacancy formation can be substantially promoted by deformation in mechanical loading experiments [9,30–32] or strain due to phase transformations [8,33,34].

The references:

[1] Y. Fukai and N. Okuma, Phys. Rev. Lett. 73, 1640 (1994). 
[2] Y. Fukai and N. Okuma, Jpn. J. Appl. Phys., Part 2 32, L1256 (1993). 
[3] Y. Fukai, M. Mizutani, S. Yokota, M. Kanazawa, Y. Miura, and T. Watanabe, J. Alloys Compd. 356, 270 (2003)
[4] K. Nakamura and Y. Fukai, J. Alloys Compd. 231, 46 (1995). [paper needed]
[5] D. dos Santos, S. Miraglia, and D. Fruchart, J. Alloys Compd. 291, L1 (1999)
[6] Y. Fukai, Y. Ishii, T. Goto, and K. Watanabe, J. Alloys Compd. 313, 121 (2000). [paper needed]
[7] K. Watanabe, N. Okuma, Y. Fukai, Y. Sakamoto, and Y. Hayashi, Scr. Mater. 34, 551 (1996)[paper needed]
[8] K. Sakaki, R. Date, M. Mizuno, H. Araki, and Y. Shirai, Acta Mater. 54, 4641 (2006)[paper needed]
[9] H. Birnbaum, C. Buckley, F. Zaides, E. Sirois, P. Rosenak, S. Spooner, and J. Lin, J. Alloys Compd. 253, 260 (1997)[paper needed]
[10] Y. Fukai, T. Haraguchi, E. Hayashi, Y. Ishii, Y. Kurokawa, and J. Yanagawa, Defect Diffus. Forum 194, 1063 (2001)[paper needed]
[11] Y. Fukai, K. Mori, and H. Shinomiya, J. Alloys Compd. 348, 105 (2003)[paper needed]
[12] Y. Fukai, Y. Kurokawa, and H. Hiraoka, J. Jpn. Inst. Met. 61, 663 (1997). [paper needed][reference obscure, no vol 61, paper not at page in 1997. About Mo, see this 2003 paper]
[13] Y. Fukai and M. Mizutani, Mater. Trans. 43, 1079 (2002). (copy)  Britz Fukai2003b
[14] Y. Fukai, Y. Shizuku, and Y. Kurokawa, J. Alloys Compd. 329, 195 (2001).  Britz Fukai2001
[15] Y. Fukai, T. Hiroi, N. Mukaibo, and Y. Shimizu, J. Jpn. Inst. Met. 71, 388 (2007)[paper needed]
[16] H. Koike, Y. Shizuku, A. Yazaki, and Y. Fukai, J. Phys.: Condens. Matter 16, 1335 (2004)[paper needed]
[17] T. Iida, Y. Yamazaki, T. Kobayashi, Y. Iijima, and Y. Fukai, Acta Mater. 53, 3083 (2005)[paper needed]
[18] J. Cızek, I. Prochazka, F. Becvar, R. Kuzel, M. Cieslar, G. Brauer, W. Anwand, R. Kirchheim, and A. Pundt, Phys. Rev. B 69, 224106 (2004)[paper needed]
[19] Y. Shirai, H. Araki, T. Mori, W. Nakamura, and K. Sakaki, J. Alloys Compd. 330, 125 (2002).  [paper needed]
[20] Y. Fukai and H. Sugimoto, J. Phys.: Condens. Matter 19, 436201 (2007).  [paper needed]
[21] V. Gavriljuk, V. Bugaev, Y. Petrov, A. Tarasenko, and B. Yanchitski, Scr. Mater. 34, 903 (1996).  [paper needed]
[22] Y. Yagodzinskyy, T. Saukkonen, S. Kilpelinen, F. Tuomisto, and H. Hnninen, Scr. Mater. 62, 155 (2010).  [paper needed]
[23] Y. Fukai, J. Alloys Compd. 356, 263 (2003)
[24] Y. Fukai, Phys. Scr. T103, 11 (2003)[paper needed]
[25] S. Semiletov, R. Baranova, Y. Khodyrev, and R. Imamov, Kristallografiya 25, 1162 (1980) ,[Sov. Phys.–Crystallogr. 25, 665 (1980)]. [paper needed]
[26] Y. Fukai, J. Alloys Compd. 231, 35 (1995) [paper needed]
[27] S. Miraglia, D. Fruchart, E. Hlil, S. Tavares, and D. D. Santos, J. Alloys Compd. 317-318, 77 (2001).
[28] Y. Fukai, Computer Aided Innovation of New Materials (Elsevier, Amsterdam, 1993), Vol. II, pp. 451–456. [the Fukai paper appears to be in Vol I?] [paper needed]
[29] Y. Fukai, M. Yamakata, and T. Yagi, Z. Phys. Chem. 179, 119 (1993). [paper needed] bad doi, corrected:
[30] M. Nagumo, M. Takamura, and K. Takai, Metall. Mater. Trans. A 32, 339 (2001)[paper needed]
[31] K. Sakaki, T. Kawase, M. Hirato, M. Mizuno, H. Araki, Y. Shirai, and M. Nagumo, Scr. Mater. 55, 1031 (2006)[paper needed]
[32] Y. Z. Chen, G. Csiszar, J. Cizek, C. Borchers, T. Ung ´ ar, S. Goto, and R. Kirchheim, Scr. Mater. 64, 390 (2011)[paper needed]
[33] Y. Shirai, F. Nakamura, M. Takeuchi, K. Watanabe, and M. Yamaguchi, in Eighth International Conference on Positron Annihilation, edited by V. Dorikens, M. Drikens, and D. Seegers (World Scientific, Singapore, 1989), p. 488. [paper needed]
[34] P. Chalermkarnnon, H. Araki, and Y. Shirai, Mater. Trans. JIM 43, 1486 (2002). [copy

Another SAV paper has been pointed out to me:

Yoshiki FukadaTatsumi HiokiTomoyoshi MotohirobMultiple phase separation of super-abundant-vacancies in Pd hydrides by all solid-state electrolysis in moderate temperatures around 300 °C, Journal of Alloys and Compounds, Volume 688, Part B, 15 December 2016, Pages 404-412. DOI * ResearchGate


The dynamics of hydrogen-induced vacancies are the key for understanding various phenomena in metal–hydrogen systems under a high hydrogen chemical potential. In this study, a novel dry-electrolysis experiment was performed in which a hydrogen isotope was injected into a Pd cathode and time-resolved in situ monochromatic X-ray diffraction measurement was carried out at the Pd cathode. It was found that palladium-hydride containing vacancies forms multiple phases depending on the hydrogen chemical potential. Phase separation into vacancy-rich, vacancy-poor, and moderate-vacancy-concentration phases was observed when the input voltage was relatively low, i.e., ∼0.5 V. The moderate-vacancy-concentration phase may be attributed to Ca7Ge or another type of super-lattice Pd7VacH(D)8. Transition from the vacancy-rich to the moderate-vacancy-concentration phase explains the sub-micron void formations without high temperature treatment that were observed at the Pd cathode but have never been reported in previous anvil experiments.

“Graphical Abstract”|

The researchers are also working on Leading the Japanese Gvt NEDO project on anomalous heat effect of nano-metal and hydrogen gas interaction

For comparison, the sources from Fukada:

(all these sources have links in the paper found on ResearchGate)

[1] Y. Fukai, N. Okuma, Evidence of Copious Vacancy Formation in Ni and Pd under a High Hydrogen Pressure, Jpn.J.Appl.Phys., 32 (1993) L1256–L1259.
[2] Y. Fukai, N.Okuma, Formation of Superabundant Vacancies in Pd Hydride under High Hydrogen Pressures, Phys.Rev.Lett., 73 (1994) 1640.
[3] S. Harada, S. Yokota, Y. Ishii, Y. Shizuku, M. Kanazawa, Y. Fukai, A relation between the vacancy concentration and hydrogen concentration in the Ni–H, Co–H and Pd–H systems, J. Alloys Compd., 404–406 (2005) 247–251.
[4] Y. Tateyama and T. Ohno, Stability and clusterization of hydrogen–vacancy complexes in α-Fe: An ab initio study, Phys. Rev., B67 (2003) 174105.
[5] M. Nagumo, M. Nakamura, K. Takai, Hydrogen thermal desorption relevant to delayed-fracture susceptibility of high-strength steels, Metal.Mater.Trans. A, 32A (2001) 339–347.
[6] M. Nagumo, Hydrogen related failure of steels—a new aspect, Mater.Sci.Tech., 20 (2004) 940–950.
[7] Y. Fukai, M. Mizutani, S. Yokota, M. Kanazawa, Y. Miura, T. Watanabe, Superabundant vacancy–hydrogen clusters in electrodeposited Ni and Cu, J. Alloys Compd., 356–357 (2003) 270–273.
[8] N. Fukumuro, T. Adachi, S. Yae, H. Matsuda, Y. Fukai, Influence of hydrogen on room temperature recrystallisation of electrodeposited Cu films: thermal desorption spectroscopy, Trans. Inst. Met. Finish., 89 (2011) 198–201.
[9] N. Hisanaga, N. Fukumuro, S. Yae, H. Matsuda, Hydrogen in Platinum Films Electrodeposited from Dinitrosulfatoplatinate(II) Solution, ECS Trans., 50(48) (2013) 77–82.
[10] K. Watanabe, N. Okuma, Y. Fukai, Y. Sakamoto and Y. Hayashi, Superabundant vacancies and enhanced diffusion in Pd–Rh alloys under high hydrogen pressures, Scripta Materialia, 34(4) (1996) 551–557.
[11] E. Hayashi Y. Kurokawa and Y. Fukai, Hydrogen-Induced Enhancement of Interdiffusion in Cu–Ni Diffusion Couples, Phys.Rev.Lett., 80(25) (1998) 5588.
[12] N. Fukumuro, M. Yokota, S. Yae, H. Matsuda, Y.Fukai, Hydrogeninduced enhancement of atomic diffusion in electrodeposited Pd films, J. Alloys Compd., 580 (2013) s55–s57.
[13] Y. Fukai, Formation of superabundant vacancies in metal hydrides at high temperatures, J. Alloys Compd., 231 (1995) 35–40.
[14] Y. Fukai, Y. Kurokawa, H. Hiraoka, Superabundant Vacancy Formation and Its Consequences in Metal–Hydrogen Alloys, J. Japan Inst. Metals, 61 (1997) 663–670 (in Japanese).
[15] Y. Fukai, Y. Shizuku, Y. Kurokawa, Superabundant vacancy formation  in Ni–H alloys, J. Alloys Compd., 329 (2001) 195–201.
[16] Y. Fukai, Y. Ishii, Y. Goto, K. Watanabe, Formation of superabundant vacancies in Pd–H alloys, J. Alloys Compd., 313 (2000) 121–132.
[17] Y. Fukai, H. Sugimoto, Formation mechanism of defect metal hydrides containing superabundant vacancies, J. Phys.: Condens. Matter, 19 365 (2007) 436201. [paper needed]
[18] Y. Fukai, H. Sugimoto, The defect structure with superabundant vacancies to be formed from fcc binary metal hydrides: Experiments and simulations, J. Alloys Compd., 446–447 (2007) 474–478. [paper needed]
[19] C. Zhang, Ali Alavi, First-Principles Study of Superabundant Vacancy Formation in Metal Hydrides, J. Am. Chem. Soc., 127(27) (2005) 9808–9817.
[20] S.Yu. Zaginaichenko, Z.A. Matysina, D.V. Schur, L.O. Teslenko, A. Veziroglu, The structural vacancies in palladium hydride. Phase diagram, Int. J. Hydrogen Energy, 36 (2011) 1152–1158.
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