Abstract
A comprehensive assessment of interstitial hydrogen on the elastic behavior across different metals (Al, Ni, Fe, Nb, Ti, and Zr) was carried out using first-principles calculations. The volumetric strain introduced by interstitial hydrogen had a key role in the observed variation in elastic constants. However, in Nb, Ti, and Zr, the host and hydrogen atoms interact strongly which had a significant contribution towards the variation in elastic response due to the presence of hydrogen. The addition of hydrogen reduced the resistance to shear deformation along respective active slip systems for all the metals, except Nb. Similarly, the homogenized macroscopic approximation of Young’s and shear moduli also demonstrated a drop with increasing hydrogen concentration across all the metals, apart from Nb. Finally, these findings accurately quantify the variation in elastic behavior of various metals when exposed to a hydrogen rich environment.
Issue Section:
Research Papers
References
1.
Robertson
, I. M.
, Sofronis
, P.
, Nagao
, A.
, Martin
, M. L.
, Wang
, S.
, Gross
, D. W.
, and Nygren
, K. E.
, 2015
, “Hydrogen Embrittlement Understood
,” Metall. Mater. Trans.
, 46
(6
), pp. 2323
–2341
. 2.
Dwivedi
, S. K.
, and Vishwakarma
, M.
, 2018
, “Hydrogen Embrittlement in Different Materials: A Review
,” Int. J. Hydrog. Energy
, 43
(46
), pp. 21603
–21616
. 3.
Birnbaum
, H. K.
, 1984
, “Mechanical Properties of Metal Hydrides
,” J. Less-Common Met.
, 104
(1
), pp. 31
–41
. 4.
Barrera
, O.
, Bombac
, D.
, Chen
, Y.
, Daff
, T. D.
, Galindo-Nava
, E.
, Gong
, P.
, Haley
, D.
, et al, 2018
, “Understanding and Mitigating Hydrogen Embrittlement of Steels: A Review of Experimental, Modelling and Design Progress From Atomistic to Continuum
,” J. Mater. Sci.
, 53
(9
), pp. 6251
–6290
. 5.
Lynch
, Stan
, 2011
, Stress Corrosion Cracking
, Vol. 30
, Elsevier
, New York
, pp. 90
–130
.6.
Louthan
, M. R.
, Caskey
, G. R.
, Donovan
, J. A.
, and Rawl
, D. E.
, 1972
, “Hydrogen Embrittlement of Metals
,” Mater. Sci. Eng.
, 10
, pp. 357
–368
. 7.
Nelson
, H. G.
, 1983
, “Hydrogen Embrittlement,” Treatise on Materials Science & Technology
, C. L.
Briant
, and S. K.
Banerji
, eds., Elsevier
, New York
, pp. 275
–359
.8.
Dadfarnia
, M.
, Nagao
, A.
, Wang
, S.
, Martin
, M. L.
, Somerday
, B. P.
, and Sofronis
, P.
, 2015
, “Recent Advances on Hydrogen Embrittlement of Structural Materials
,” Int. J. Fract.
, 196
(1–2
), pp. 223
–243
. 9.
Westlake
, D. G.
, 1969
, “Generalized Model for Hydrogen Embrittlement
,” Trans. Amer. Math. Soc.
, 62
, pp. 1000
–1006
. Accessed August 16, 2021.10.
Harris
, Z. D.
, Lawrence
, S. K.
, Medlin
, D. L.
, Guetard
, G.
, Burns
, J. T.
, and Somerday
, B. P.
, 2018
, “Elucidating the Contribution of Mobile Hydrogen-Deformation Interactions to Hydrogen-Induced Intergranular Cracking in Polycrystalline Nickel
,” Acta Mater.
, 158
, pp. 180
–192
. 11.
Demetriou
, V.
, Robson
, J. D.
, Preuss
, M.
, and Morana
, R.
, 2017
, “Study of the Effect of Hydrogen Charging on the Tensile Properties and Microstructure of Four Variant Heat Treatments of Nickel Alloy 718
,” Int. J. Hydrog. Energy
, 42
(37
), pp. 23856
–23870
. 12.
Su
, H.
, Toda
, H.
, Masunaga
, R.
, Shimizu
, K.
, Gao
, H.
, Sasaki
, K.
, Bhuiyan
, M. S.
, Uesugi
, K.
, Takeuchi
, A.
, and Watanabe
, Y.
, 2018
, “Influence of Hydrogen on Strain Localization and Fracture Behavior in AlZnMgCu Aluminum Alloys
,” Acta Mater.
, 159
, pp. 332
–343
. 13.
Takano
, N.
, 2008
, “Hydrogen Diffusion and Embrittlement in 7075 Aluminum Alloy
,” Mater. Sci. Eng. A
, 483–484
, pp. 336
–339
. 14.
Rajagopalan
, M.
, Tschopp
, M. A.
, and Solanki
, K. N.
, 2014
, “Grain Boundary Segregation of Interstitial and Substitutional Impurity Atoms in Alpha-Iron
,” JOM
, 66
(1
), pp. 129
–138
. 15.
Rajagopalan
, M.
, Adlakha
, I.
, Tschopp
, M. A.
, and Solanki
, K. N.
, 2017
, “Energetics of Hydrogen Segregation to α-Fe Grain Boundaries for Modeling Stress Corrosion Cracking
,” JOM
, 69
(8
), pp. 1398
–1403
. 16.
Adlakha
, I.
, and Solanki
, K. N.
, 2016
, “Atomic-Scale Investigation of Triple Junction Role on Defects Binding Energetics and Structural Stability in α-Fe
,” Acta Mater.
, 118
, pp. 64
–76
. 17.
Coleman
, C. E.
, and Hardie
, D.
, 1966
, “The Hydrogen Embrittlement of α-Zirconium—A Review
,” J. Less-Common Met.
, 11
(3
), pp. 168
–185
. 18.
Hsu
, H.-H.
, and Tsay
, L.-W.
, 2011
, “Effect of Hydride Orientation on Fracture Toughness of Zircaloy-4 Cladding
,” J. Nucl. Mater.
, 408
(1
), pp. 67
–72
. 19.
Marshall
, R. P.
, and Louthan
, M. R.
, 1963
, “Tensile Properties of Zircaloy With Oriented Hydrides
,” Trans. ASME.
, 56
, pp. 693
–700
.20.
Sudarshan
, T. S.
, Pruitt
, N. C.
, Louthan
, M. R.
, Jr., and Place
, T. A.
, 1985
, “Susceptibility of a Dual Phase Steel to Hydrogen Embrittlement
,” ASME J. Eng. Mater. Technol.
, 107
(4
), pp. 343
–345
. 21.
Myers
, S. M.
, Baskes
, M. I.
, Birnbaum
, H. K.
, Corbett
, J. W.
, DeLeo
, G. G.
, Estreicher
, S. K.
, Haller
, E. E.
, et al, 1992
, “Hydrogen Interactions With Defects in Crystalline Solids
,” Rev. Mod. Phys.
, 64
(2
), pp. 559
–617
. 22.
Adlakha
, I.
, and Solanki
, K. N.
, 2016
, “Critical Assessment of Hydrogen Effects on the Slip Transmission Across Grain Boundaries in α-Fe
,” Proc. R. Soc. A.
, 472
(2185
), p. 20150617
. 23.
Lu
, G.
, and Kaxiras
, E.
, 2005
, “Hydrogen Embrittlement of Aluminum: The Crucial Role of Vacancies
,” Phys. Rev. Lett.
, 94
(15
), p. 155501
. 24.
Robertson
, I.
, and Birnbaum
, H.
, 1986
, “An HVEM Study of Hydrogen Effects on the Deformation and Fracture of Nickel
,” Acta Metall.
, 34
(3
), pp. 353
–366
. 25.
Shih
, D. S.
, Robertson
, I. M.
, and Birnbaum
, H. K.
, 1988
, “Hydrogen Embrittlement of α Titanium: In Situ Tem Studies
,” Acta Metall.
, 36
(1
), pp. 111
–124
. 26.
Ferreira
, P. J.
, Robertson
, I. M.
, and Birnbaum
, H. K.
, 1998
, “Hydrogen Effects on the Interaction Between Dislocations
,” Acta Mater.
, 46
(5
), pp. 1749
–1757
. 27.
Depover
, T.
, and Verbeken
, K.
, 2018
, “The Detrimental Effect of Hydrogen at Dislocations on the Hydrogen Embrittlement Susceptibility of Fe-C-X Alloys: An Experimental Proof of the HELP Mechanism
,” Int. J. Hydrog. Energy
, 43
(5
), pp. 3050
–3061
. 28.
Sofronis
, P.
, Liang
, Y.
, and Aravas
, N.
, 2001
, “Hydrogen Induced Shear Localization of the Plastic Flow in Metals and Alloys
,” Eur. J. Mech. A-Solid.
, 20
(6
), pp. 857
–872
. 29.
Beachem
, C. D.
, 1972
, “A New Model for Hydrogen-Assisted Cracking (Hydrogen “Embrittlement”)
,” Metall. Mater. Trans. B
, 3
(2
), pp. 441
–455
. 30.
Lee
, D.-H.
, Lee
, J.-A.
, Seok
, M.-Y.
, Baek
, U. B.
, Nahm
, S. H.
, and Jang
, J.
, 2014
, “Stress-Dependent Hardening-to-Softening Transition of Hydrogen Effects in Nanoindentation of a Linepipe Steel
,” Int. J. Hydrog. Energy
, 39
(4
), pp. 1897
–1902
. 31.
Hou
, S.
, Lei
, H.
, and Zeng
, Z.
, 2016
, “Hydrogen Influence on Generalized Stacking Fault Energies of Zr {0001} Basal Plane: A First-Principles Study
,” RSC Adv.
, 6
(59
), pp. 54371
–54376
. 32.
Kumar
, P.
, Garg
, P.
, Solanki
, K. N.
, and Adlakha
, I.
, 2021
, “Effect of Hydrogen on the Ideal Shear Strength in Metals and Its Implications on Plasticity: A First-Principles Study
,” Int. J. Hydrog. Energy
, 46
(50
), pp. 25726
–25737
. 33.
Meng
, F.-S.
, Du
, J.-P.
, Shinzato
, S.
, Mori
, H.
, Yu
, P.
, Matsubara
, K.
, Ishikawa
, N.
, and Ogata
, S.
, 2021
, “General-Purpose Neural Network Interatomic Potential for the α-Iron and Hydrogen Binary System: Toward Atomic-Scale Understanding of Hydrogen Embrittlement
,” Phys. Rev. Mater.
, 5
(11
), p. 113606
. 34.
Zhao
, Y.
, and Lu
, G.
, 2011
, “QM/MM Study of Dislocation—Hydrogen/Helium Interactions in α-Fe
,” Modell. Simul. Mater. Sci. Eng.
, 19
(6
), p. 065004
. 35.
Dwivedi
, S. K.
, and Vishwakarma
, M.
, 2018
, “Hydrogen Embrittlement in Different Materials: A Review
,” Int. J. Hydrog. Energy
, 43
(46
), pp. 21603
–21616
. 36.
Koyama
, M.
, Akiyama
, E.
, Lee
, Y.-K.
, Raabe
, D.
, and Tsuzaki
, K.
, 2017
, “Overview of Hydrogen Embrittlement in High-Mn Steels
,” Int. J. Hydrog. Energy
, 42
(17
), pp. 12706
–12723
. 37.
Scully
, J. R.
, Young
, G. A.
, and Smith
, S. W.
, 2012
, “Hydrogen Embrittlement of Aluminum and Aluminum-Based Alloys,” Gaseous Hydrogen Embrittlement of Materials in Energy Technologies
, RP
Gangloff
, and BP
Somerday
, eds., Woodhead Publishing
, UK
, pp. 707
–768
.38.
Louthan
, M. R.
, Jr., 2008
, “Hydrogen Embrittlement of Metals: A Primer for the Failure Analyst
,” J. Fail. Anal. Preven.
, 8
(3
), pp. 289
–307
. 39.
Kirchheim
, R.
, 2010
, “Revisiting Hydrogen Embrittlement Models and Hydrogen-Induced Homogeneous Nucleation of Dislocations
,” Scr. Mater.
, 62
(2
), pp. 67
–70
. 40.
Kirchheim
, R.
, 2007
, “Reducing Grain Boundary, Dislocation Line and Vacancy Formation Energies by Solute Segregation. I. Theoretical Background
,” Acta Mater.
, 55
(15
), pp. 5129
–5138
. 41.
Metsue
, A.
, Oudriss
, A.
, and Feaugas
, X.
, 2014
, “Displacement Field Induced by a Vacancy in Nickel and Some Implications for the Solubility of Hydrogen
,” Philos. Mag.
, 94
(34
), pp. 3978
–3991
. 42.
Fisher
, E. S.
, Westlake
, D. G.
, and Ockers
, S. T.
, 1975
, “Effects of Hydrogen and Oxygen on the Elastic Moduli of Vanadium, Niobium, and Tantalum Single Crystals
,” Phys. Status Solidi A
, 28
(2
), pp. 591
–602
. 43.
Grena
, R.
, Celino
, M.
, and Tarquini
, P.
, 2011
, “DFT Study of Interstitial Hydrogen in Tantalum Lattice
,” Int. J. Hydrog. Energy
, 36
(21
), pp. 13858
–13865
. 44.
Dai
, S.
, Xiang
, Y.
, and Srolovitz
, D. J.
, 2014
, “Atomistic, Generalized Peierls–Nabarro and Analytical Models for (111) Twist Boundaries in Al, Cu and Ni for All Twist Angles
,” Acta Mater.
, 69
, pp. 162
–174
. 45.
Devincre
, B.
, 1995
, “Three Dimensional Stress Field Expressions for Straight Dislocation Segments
,” Solid State Commun.
, 93
(11
), pp. 875
–878
. 46.
Vitek
, V.
, 1998
, “Atomic Structure of Dislocations in Intermetallics With Close Packed Structures: A Comparative Study
,” Intermetallics.
, 6
(7–8
), pp. 579
–585
. 47.
Joós
, B.
, and Duesbery
, M. S.
, 1997
, “The Peierls Stress of Dislocations: An Analytic Formula
,” Phys. Rev. Lett.
, 78
(2
), pp. 266
–269
. 48.
Joós
, B.
, Ren
, Q.
, and Duesbery
, M. S.
, 1994
, “Peierls-Nabarro Model of Dislocations in Silicon With Generalized Stacking-Fault Restoring Forces
,” Phys. Rev. B
, 50
(9
), pp. 5890
–5898
. 49.
Barnoush
, A.
, and Vehoff
, H.
, 2008
, “In Situ Electrochemical Nanoindentation: A Technique for Local Examination of Hydrogen Embrittlement
,” Corros. Sci.
, 50
(1
), pp. 259
–267
. 50.
Wriedt
, H. A.
, and Oriani
, R. A.
, 1974
, “Effect of Hydrogen on Young’s Modulus of Ta, Nb, and V
,” Scr. Mater.
, 8
(3
), pp. 203
–208
. 51.
Hachet
, G.
, Metsue
, A.
, Oudriss
, A.
, and Feaugas
, X.
, 2018
, “Influence of Hydrogen on the Elastic Properties of Nickel Single Crystal: A Numerical and Experimental Investigation
,” Acta Mater.
, 148
, pp. 280
–288
. 52.
Magerl
, A.
, Berre
, B.
, and Alefeld
, G.
, 1976
, “Changes of the Elastic Constants of V, Nb, and Ta by Hydrogen and Deuterium
,” Phys. Status Solidi. (A)
, 36
(1
), pp. 161
–171
. 53.
Wen
, M.
, Barnoush
, A.
, and Yokogawa
, K.
, 2011
, “Calculation of All Cubic Single-Crystal Elastic Constants From Single Atomistic Simulation: Hydrogen Effect and Elastic Constants of Nickel
,” Comput. Phys. Commun.
, 182
(8
), pp. 1621
–1625
. 54.
Spivak
, L. V.
, and Lunarska
, E. A.
, 2006
, “The Effect of Hydrogen on the Shear Modulus of Polycrystalline Aluminum
,” Tech. Phys. Lett.
, 32
(1
), pp. 55
–57
. 55.
Senkov
, O. N.
, Dubois
, M.
, and Jonas
, J. J.
, 1996
, “Elastic Moduli of Titanium-Hydrogen Alloys in the Temperature Range 20 °C to 1100 °C
,” Metall. Mater. Trans. A.
, 27
(12
), pp. 3963
–3970
. 56.
Senkov
, O. N.
, Chakoumakos
, B. C.
, Jonas
, J. J.
, and Froes
, F. H.
, 2001
, “Effect of Temperature and Hydrogen Concentration on the Lattice Parameter of Beta Titanium
,” Mater. Res. Bull.
, 36
(7–8
), pp. 1431
–1440
. 57.
Wang
, Z.
, Shi
, X.
, Yang
, X.-S.
, Liu
, Z.
, Shi
, S.-Q.
, and Ma
, X.
, 2020
, “The Effects of Hydrogen Distribution on the Elastic Properties and Hydrogen-Induced Hardening and Softening of α-Fe
,” Appl. Sci.
, 10
(24
), p. 8958
. 58.
Barnoush
, A.
, and Vehoff
, H.
, 2010
, “Recent Developments in the Study of Hydrogen Embrittlement: Hydrogen Effect on Dislocation Nucleation
,” Acta Mater.
, 58
(16
), pp. 5274
–5285
. 59.
Psiachos
, D.
, Hammerschmidt
, T.
, and Drautz
, R.
, 2011
, “Ab Initio Study of the Modification of Elastic Properties of α-Iron by Hydrostatic Strain and by Hydrogen Interstitials
,” Acta Mater.
, 59
(11
), pp. 4255
–4263
. 60.
Kresse
, G.
, and Hafner
, J.
, 1994
, “Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal–Amorphous-Semiconductor Transition in Germanium
,” Phys. Rev. B
, 49
(20
), pp. 14251
–14269
. 61.
Kresse
, G.
, and Furthmüller
, J.
, 1996
, “Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis set
,” Comput. Mater. Sci.
, 6
(1
), pp. 15
–50
. 62.
Kresse
, G.
, and Joubert
, D.
, 1999
, “From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method
,” Phys. Rev. B.
, 59
(3
), pp. 1758
–1775
. 63.
Ramachandran
, A.
, Zhuang
, H.
, and Lackner
, K. S.
, 2020
, “Probing the Interactions Between Interstitial Hydrogen Atoms in Niobium Through Density Functional Theory Calculations
,” Mater. Today Commun.
, 25
, p. 101415
. 64.
Pryde
, J. A.
, and Titcomb
, C. G.
, 1969
, “Solution of Hydrogen in Niobium
,” Trans. Faraday Soc.
, 65
, pp. 2758
–2765
. 65.
San-Martin
, A.
, and Manchester
, F. D.
, 1987
, “The H−Ti (Hydrogen-Titanium) System
,” Bull. Alloy Phase Diagr.
, 8
(1
), pp. 30
–42
. 66.
Zuzek
, E.
, Abriata
, J. P.
, San-Martin
, A.
, and Manchester
, F. D.
, 1990
, “The H-Zr (Hydrogen-Zirconium) System
,” Bull. Alloy Phase Diagr.
, 11
(4
), pp. 385
–395
. 67.
Zaw
, A. K.
, Chernov
, I. I.
, Staltsov
, M. S.
, Kalin
, B. A.
, and Efimov
, V. S.
, 2015
, “Hydrogen Retention by Vanadium-Titanium Alloys
,” Inorg. Mater. Appl. Res.
, 6
(2
), pp. 138
–142
. 68.
Yamanaka
, S.
, Miyake
, M.
, and Katsura
, M.
, 1997
, “Study on the Hydrogen Solubility in Zirconium Alloys
,” J. Nucl. Mater.
, 247
, pp. 315
–321
. 69.
Sugimoto
, H.
, and Fukai
, Y.
, 1992
, “Solubility of Hydrogen in Metals Under High Hydrogen Pressures: Thermodynamical Calculations
,” Acta Metall. Mater.
, 40
(9
), pp. 2327
–2336
. 70.
Fukai
, Y.
, and Sugimoto
, H.
, 1983
, “Enhanced Solubility of Hydrogen in Metals Under High Pressure: Thermodynamical Calculation
,” Trans. Jpn. Inst. Met.
, 24
(11
), pp. 733
–740
. 71.
San-Martin
, A.
, and Manchester
, F. D.
, 1992
, “The Al–H (Aluminum-Hydrogen) System
,” J. Phase Equilib.
, 13
(1
), pp. 17
–21
. 72.
Wayman
, M. L.
, and Weatherly
, G. C.
, 1989
, “The H−Ni (Hydrogen-Nickel) System
,” Bull. Alloy Phase Diagr.
, 10
(5
), pp. 569
–580
. 73.
Movchan
, D. N.
, Teus
, S. M.
, Mogilny
, G. S.
, and Gavriljuk
, V. G.
, 2013
, “Hydrogen in Nickel: Hydride or Miscibility Gap?
,” http://dspace.nbuv.gov.ua/xmlui/handle/123456789/104132, Accessed May 16, 2022.74.
Teus
, S. M.
, and Gavriljuk
, V. G.
, 2018
, “Electron Structure and Thermodynamics of Solid Solutions in Ni–H System
,” Mater. Sci. Eng.
, 2
, pp. 101
–109
.75.
Antonov
, V.
, Belash
, I.
, and Ponyatovskii
, E.
, 1977
, “TP Phase Diagrams of the Ni–D and Ni–H Systems at Temperatures to 375 C and Pressures to 20 kbar
,” Dokl. Akad. Nauk SSSR
, 233
(6
), pp. 1114
–1117
.76.
Jiang
, D. E.
, and Carter
, E. A.
, 2004
, “Diffusion of Interstitial Hydrogen Into and Through bcc Fe From First Principles
,” Phys. Rev. B
, 70
(6
), p. 064102
. 77.
Sun
, L.
, Xiao
, W.
, Huang
, S.
, Wang
, J.
, and Wang
, L.
, 2018
, “Improving the Mechanical Processing of Titanium by Hydrogen Doping: A First-Principles Study
,” Int. J. Hydrog. Energy
, 43
(13
), pp. 6756
–6764
. 78.
Weck
, P. F.
, Kim
, E.
, Tikare
, V.
, and Mitchell
, J. A.
, 2015
, “Mechanical Properties of Zirconium Alloys and Zirconium Hydrides Predicted From Density Functional Perturbation Theory
,” Dalton Trans.
, 44
(43
), pp. 18769
–18779
. 79.
Kamm
, G. N.
, and Alers
, G. A.
, 1964
, “Low-Temperature Elastic Moduli of Aluminum
,” J. Appl. Phys.
, 35
(2
), pp. 327
–330
. 80.
Simmons
, G.
, 1965
, Single Crystal Elastic Constants and Calculated Aggregate Properties
, Southern Methodist University
, Dallas, TX
, pp. 36
–151
.81.
Rayne
, J. A.
, and Chandrasekhar
, B. S.
, 1961
, “Elastic Constants of Iron From 4.2 to 300 K
,” Phys. Rev.
, 122
(6
), pp. 1714
–1716
. 82.
Carroll
, K. J.
, 1965
, “Elastic Constants of Niobium From 4.2 deg to 300 degK
,” J. Appl. Phys.
, 36
(11
), pp. 3689
–3690
. 83.
Fisher
, E. S.
, and Renken
, C. J.
, 1964
, “Single-Crystal Elastic Moduli and the hcp—bcc Transformation in Ti, Zr, and Hf
,” Phys. Rev.
, 135
(2A
), pp. A482
–A494
. 84.
Jamal
, M.
, Jalali Asadabadi
, S.
, Ahmad
, I.
, and Rahnamaye Aliabad
, H. A.
, 2014
, “Elastic Constants of Cubic Crystals
,” Comput. Mater. Sci.
, 95
, pp. 592
–599
. 85.
Fellinger
, M. R.
, Hector
, L. G.
, and Trinkle
, D. R.
, 2017
, “Ab Initio Calculations of the Lattice Parameter and Elastic Stiffness Coefficients of bcc Fe With Solutes
,” Comput. Mater. Sci.
, 126
, pp. 503
–513
. 86.
Ikehata
, H.
, Nagasako
, N.
, Furuta
, T.
, Fukumoto
, A.
, Miwa
, K.
, and Saito
, T.
, 2004
, “First-Principles Calculations for Development of Low Elastic Modulus Ti Alloys
,” Phys. Rev. B
, 70
(17
), p. 174113
. 87.
Colonna
, F.
, and Elsässer
, C.
, 2017
, “First Principles DFT Study of Interstitial Hydrogen and Oxygen Atoms in the MAX Phase Ti 2 AlN
,” RSC Adv.
, 7
(60
), pp. 37852
–37857
. 88.
Kartamyshev
, A. I.
, Vo
, D. D.
, and Lipnitskii
, A. G.
, 2016
, “The Interaction Between Light Impurities and Vacancies in Titanium and Aluminum Metals: A DFT Study
,” St. Petersburg Math. J.
, 2
(2
), pp. 96
–102
. 89.
Connétable
, D.
, Wang
, Y.
, and Tanguy
, D.
, 2014
, “Segregation of Hydrogen to Defects in Nickel Using First-Principles Calculations: The Case of Self-Interstitials and Cavities
,” J. Alloys Compd.
, 614
, pp. 211
–220
. 90.
Di Stefano
, D.
, Mrovec
, M.
, and Elsässer
, C.
, 2015
, “First-Principles Investigation of Quantum Mechanical Effects on the Diffusion of Hydrogen in Iron and Nickel
,” Phys. Rev. B.
, 92
(22
), p. 224301
. 91.
Aboud
, S.
, and Wilcox
, J.
, 2010
, “A Density Functional Theory Study of the Charge State of Hydrogen in Metal Hydrides
,” J. Phys. Chem. C.
, 114
(24
), pp. 10978
–10985
. 92.
Poletaev
, D. O.
, Aksyonov
, D. A.
, Vo
, D. D.
, and Lipnitskii
, A. G.
, 2016
, “Hydrogen Solubility in hcp Titanium With the Account of Vacancy Complexes and Hydrides: A DFT Study
,” Comput. Mater. Sci.
, 114
, pp. 199
–208
. 93.
Udagawa
, Y.
, Yamaguchi
, M.
, Abe
, H.
, Sekimura
, N.
, and Fuketa
, T.
, 2010
, “Ab Initio Study on Plane Defects in Zirconium–Hydrogen Solid Solution and Zirconium Hydride
,” Acta Mater.
, 58
(11
), pp. 3927
–3938
. 94.
Mouhat
, F.
, and Coudert
, F.-X.
, 2014
, “Necessary and Sufficient Elastic Stability Conditions in Various Crystal Systems
,” Phys. Rev. B.
, 90
(22
), p. 224104
. 95.
Gadijak
, G.
, Karpushin
, A.
, Korolenko
, I.
, Morokov
, Y.
, Sorokin
, A.
, and Tomasek
, M.
, 1984
, “Adsorption of Hydrogen on Si(111). Comparison of the Generalized Bethe Lattice and Recursion Methods
,” Sov. Phys. Semicond.
, 18
, pp. 638
–641
.96.
Ravindran
, P.
, and Asokamani
, R.
, 1997
, “Correlation Between Electronic Structure, Mechanical Properties and Phase Stability in Intermetallic Compounds
,” Bull. Mater. Sci.
, 20
(4
), pp. 613
–622
. 97.
Becke
, A. D.
, and Edgecombe
, K. E.
, 1990
, “A Simple Measure of Electron Localization in Atomic and Molecular Systems
,” J. Chem. Phys.
, 92
(9
), pp. 5397
–5403
. 98.
Garg
, P.
, Adlakha
, I.
, and Solanki
, K. N.
, 2018
, “Effect of Solutes on Ideal Shear Resistance and Electronic Properties of Magnesium: A First-Principles Study
,” Acta Mater.
, 153
, pp. 327
–335
. 99.
Psiachos
, D.
, Hammerschmidt
, T.
, and Drautz
, R.
, 2011
, “Ab Initio Study of the Modification of Elastic Properties of α-Iron by Hydrostatic Strain and by Hydrogen Interstitials
,” Acta Mater.
, 59
(11
), pp. 4255
–4263
. 100.
Fellinger
, M. R.
, Hector
, L. G.
, and Trinkle
, D. R.
, 2017
, “Ab Initio Calculations of the Lattice Parameter and Elastic Stiffness Coefficients of bcc Fe With Solutes
,” Comput. Mater. Sci.
, 126
, pp. 503
–513
. 101.
Zhang
, Q.
, Tian
, Y.
, Liu
, S.
, Yang
, P.
, and Li
, Y.
, 2020
, “First-Principles Study of the Elastic Properties of Nickel Sulfide Minerals Under High Pressure
,” Minerals
, 10
(9
), p. 737
. 102.
Healy
, D.
, Timms
, N. E.
, and Pearce
, M. A.
, 2020
, “The Variation and Visualisation of Elastic Anisotropy in Rock-Forming Minerals
,” Solid Earth
, 11
(2
), pp. 259
–286
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