Resolving phase stability in the Ti-O binary with first-principles statistical mechanics methods
Abstract
The Ti-O system consists of a multitude of stable and metastable oxides that are used in wide ranging applications. In this work we investigate phase stability in the Ti-O binary from first principles. We perform a systematic search for ground state structures as a function of oxygen concentration by considering oxygen-vacancy and/or titanium-vacancy orderings over four parent crystal structures: (i) hcp Ti, (ii) ω-Ti, (iii) rocksalt, and (iv) hcp oxygen containing interstitial titanium. We explore phase stability at finite temperature using cluster expansion Hamiltonians and Monte Carlo simulations. The calculations predict a high oxygen solubility in hcp Ti and the stability of suboxide phases that undergo order-disorder transitions upon heating. Vacancy ordered rocksalt phases are also predicted at low temperature that disorder to form an extended solid solution at high temperatures. Predicted stable and metastable phase diagrams are qualitatively consistent with experimental observations, however, important discrepancies are revealed between first-principles density functional theory predictions of phase stability and the current understanding of phase stability in this system.
- Authors:
-
- Univ. of California, Santa Barbara, CA (United States). Dept. of Materials
- Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Materials Science and Engineering
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1544302
- Alternate Identifier(s):
- OSTI ID: 1430563
- Grant/Contract Number:
- AC02-05CH11231; DMR1436154
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Materials
- Additional Journal Information:
- Journal Volume: 2; Journal Issue: 3; Journal ID: ISSN 2475-9953
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Gunda, N. S. Harsha, Puchala, Brian, and Van der Ven, Anton. Resolving phase stability in the Ti-O binary with first-principles statistical mechanics methods. United States: N. p., 2018.
Web. doi:10.1103/physrevmaterials.2.033604.
Gunda, N. S. Harsha, Puchala, Brian, & Van der Ven, Anton. Resolving phase stability in the Ti-O binary with first-principles statistical mechanics methods. United States. https://doi.org/10.1103/physrevmaterials.2.033604
Gunda, N. S. Harsha, Puchala, Brian, and Van der Ven, Anton. Fri .
"Resolving phase stability in the Ti-O binary with first-principles statistical mechanics methods". United States. https://doi.org/10.1103/physrevmaterials.2.033604. https://www.osti.gov/servlets/purl/1544302.
@article{osti_1544302,
title = {Resolving phase stability in the Ti-O binary with first-principles statistical mechanics methods},
author = {Gunda, N. S. Harsha and Puchala, Brian and Van der Ven, Anton},
abstractNote = {The Ti-O system consists of a multitude of stable and metastable oxides that are used in wide ranging applications. In this work we investigate phase stability in the Ti-O binary from first principles. We perform a systematic search for ground state structures as a function of oxygen concentration by considering oxygen-vacancy and/or titanium-vacancy orderings over four parent crystal structures: (i) hcp Ti, (ii) ω-Ti, (iii) rocksalt, and (iv) hcp oxygen containing interstitial titanium. We explore phase stability at finite temperature using cluster expansion Hamiltonians and Monte Carlo simulations. The calculations predict a high oxygen solubility in hcp Ti and the stability of suboxide phases that undergo order-disorder transitions upon heating. Vacancy ordered rocksalt phases are also predicted at low temperature that disorder to form an extended solid solution at high temperatures. Predicted stable and metastable phase diagrams are qualitatively consistent with experimental observations, however, important discrepancies are revealed between first-principles density functional theory predictions of phase stability and the current understanding of phase stability in this system.},
doi = {10.1103/physrevmaterials.2.033604},
journal = {Physical Review Materials},
number = 3,
volume = 2,
place = {United States},
year = {Fri Mar 30 00:00:00 EDT 2018},
month = {Fri Mar 30 00:00:00 EDT 2018}
}
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Works referenced in this record:
Kinetics of Anatase Electrodes: The Role of Ordering, Anisotropy, and Shape Memory Effects
journal, July 2012
- Belak, Anna A.; Wang, Yizhou; Van der Ven, Anton
- Chemistry of Materials, Vol. 24, Issue 15
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
Properties and Promises of Nanosized Insertion Materials for Li-Ion Batteries
journal, February 2012
- Wagemaker, Marnix; Mulder, Fokko M.
- Accounts of Chemical Research, Vol. 46, Issue 5
Investigation of the optical property and photocatalytic activity of mixed phase nanocrystalline titania
journal, September 2013
- Paul, Susmita; Choudhury, Amarjyoti
- Applied Nanoscience, Vol. 4, Issue 7
Thermal stabilization of the hcp phase in titanium
journal, March 2004
- Rudin, Sven P.; Jones, M. D.; Albers, R. C.
- Physical Review B, Vol. 69, Issue 9
Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress
journal, April 2013
- Monserrat, Bartomeu; Drummond, N. D.; Needs, R. J.
- Physical Review B, Vol. 87, Issue 14
Interstitial Order-Disorder Transformation in the Ti-O Solid Solution. I. Ordered Arrangement of Oxygen
journal, July 1969
- Yamaguchi, Sadae
- Journal of the Physical Society of Japan, Vol. 27, Issue 1
Size Effects in the Li 4+ x Ti 5 O 12 Spinel
journal, December 2009
- Borghols, W. J. H.; Wagemaker, M.; Lafont, U.
- Journal of the American Chemical Society, Vol. 131, Issue 49
Projector augmented-wave method
journal, December 1994
- Blöchl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979
A DFT-D study of structural and energetic properties of TiO 2 modifications
journal, October 2012
- Moellmann, Jonas; Ehrlich, Stephan; Tonner, Ralf
- Journal of Physics: Condensed Matter, Vol. 24, Issue 42
Magnetic and Crystal Structure of Titanium Sesquioxide
journal, June 1963
- Abrahams, S. C.
- Physical Review, Vol. 130, Issue 6
Screened hybrid density functionals applied to solids
journal, April 2006
- Paier, J.; Marsman, M.; Hummer, K.
- The Journal of Chemical Physics, Vol. 124, Issue 15
Crystal Structure of the ZrO Phase at Zirconium/Zirconium Oxide Interfaces: Crystal Structure of the ZrO Phase …
journal, June 2014
- Nicholls, Rebecca J.; Ni, Na; Lozano-Perez, Sergio
- Advanced Engineering Materials, Vol. 17, Issue 2
ɛ-TiO, a Novel Stable Polymorph of Titanium Monoxide
journal, December 2015
- Amano, Shinsaku; Bogdanovski, Dimitri; Yamane, Hisanori
- Angewandte Chemie International Edition, Vol. 55, Issue 5
Superior Electrode Performance of Nanostructured Mesoporous TiO2 (Anatase) through Efficient Hierarchical Mixed Conducting Networks
journal, August 2007
- Guo, Y.-G.; Hu, Y.-S.; Sigle, W.
- Advanced Materials, Vol. 19, Issue 16, p. 2087-2091
From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999
- Kresse, G.; Joubert, D.
- Physical Review B, Vol. 59, Issue 3, p. 1758-1775
The O−Ti (Oxygen-Titanium) system
journal, April 1987
- Murray, J. L.; Wriedt, H. A.
- Journal of Phase Equilibria, Vol. 8, Issue 2
Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
journal, January 1998
- Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.
- Physical Review B, Vol. 57, Issue 3, p. 1505-1509
Effective cluster interactions from cluster-variation formalism. I
journal, September 1991
- Asta, M.; Wolverton, C.; de Fontaine, D.
- Physical Review B, Vol. 44, Issue 10
Titanium dioxide@titanium nitride nanowires on carbon cloth with remarkable rate capability for flexible lithium-ion batteries
journal, December 2014
- Balogun, Muhammad-Sadeeq; Li, Cheng; Zeng, Yinxiang
- Journal of Power Sources, Vol. 272
Large Impact of Particle Size on Insertion Reactions. A Case for Anatase Li x TiO 2
journal, April 2007
- Wagemaker, Marnix; Borghols, Wouter J. H.; Mulder, Fokko M.
- Journal of the American Chemical Society, Vol. 129, Issue 14
Generalized cluster description of multicomponent systems
journal, November 1984
- Sanchez, J. M.; Ducastelle, F.; Gratias, D.
- Physica A: Statistical Mechanics and its Applications, Vol. 128, Issue 1-2
Automating first-principles phase diagram calculations
journal, August 2002
- Walle, A.; Ceder, G.
- Journal of Phase Equilibria, Vol. 23, Issue 4
Twinborn TiO 2 –TiN heterostructures enabling smooth trapping–diffusion–conversion of polysulfides towards ultralong life lithium–sulfur batteries
journal, January 2017
- Zhou, Tianhong; Lv, Wei; Li, Jia
- Energy & Environmental Science, Vol. 10, Issue 7
Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic properties and phase diagrams
journal, July 2002
- Walle, A. van de; Asta, M.
- Modelling and Simulation in Materials Science and Engineering, Vol. 10, Issue 5
corrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS, , and NiO
journal, January 2016
- Patrick, Christopher E.; Thygesen, Kristian S.
- Physical Review B, Vol. 93, Issue 3
Electrical and Magnetic Properties of TiO and VO
journal, April 1972
- Banus, M. D.; Reed, T. B.; Strauss, A. J.
- Physical Review B, Vol. 5, Issue 8
Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile
journal, August 2015
- Lan, Tian; Li, C. W.; Hellman, O.
- Physical Review B, Vol. 92, Issue 5
Ab initiomolecular dynamics for liquid metals
journal, January 1993
- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 47, Issue 1, p. 558-561
High-temperature stability of δ′-ZrO
journal, December 2015
- Chen, Min-Hua; Puchala, Brian; Van der Ven, Anton
- Calphad, Vol. 51
Trap-State Distributions and Carrier Transport in Pure and Mixed-Phase TiO 2 : Influence of Contacting Solvent and Interphasial Electron Transfer
journal, August 2008
- Knorr, Fritz J.; Mercado, Candy C.; McHale, Jeanne L.
- The Journal of Physical Chemistry C, Vol. 112, Issue 33
Crystal structures of Ti under high pressure: Theory
journal, April 2003
- Kutepov, A. L.; Kutepova, S. G.
- Physical Review B, Vol. 67, Issue 13
The B−Ti (Boron-Titanium) system
journal, December 1986
- Murray, J. L.; Liao, P. K.; Spear, K. E.
- Bulletin of Alloy Phase Diagrams, Vol. 7, Issue 6
Thermodynamic properties of titanium from ab initio calculations
journal, January 2015
- Argaman, Uri; Eidelstein, Eitan; Levy, Ohad
- Materials Research Express, Vol. 2, Issue 1
Elastic properties and stress-temperature phase diagrams of high-temperature phases with low-temperature lattice instabilities
journal, December 2014
- Thomas, John C.; Van der Ven, Anton
- Physical Review B, Vol. 90, Issue 22
Reinvestigation of the Phase Diagram for the System Titanium-Oxygen
journal, April 1966
- Wahlbeck, Phillip G.; Gilles, Paul W.
- Journal of the American Ceramic Society, Vol. 49, Issue 4
Thermodynamics of the Zr-O system from first-principles calculations
journal, September 2013
- Puchala, B.; Van der Ven, A.
- Physical Review B, Vol. 88, Issue 9
Direct gaseous nitridation of the Ti–6Al–4V alloy by nitrogen
journal, January 2000
- Ponticaud, Carine; Guillou, Annie; Lefort, Pierre
- Physical Chemistry Chemical Physics, Vol. 2, Issue 8
High Lithium Electroactivity of Nanometer-Sized Rutile TiO2
journal, June 2006
- Hu, Y.-S.; Kienle, L.; Guo, Y.-G.
- Advanced Materials, Vol. 18, Issue 11, p. 1421-1426
Strongly Constrained and Appropriately Normed Semilocal Density Functional
journal, July 2015
- Sun, Jianwei; Ruzsinszky, Adrienn; Perdew, John P.
- Physical Review Letters, Vol. 115, Issue 3
The anatase phase of nanotopography titania plays an important role on osteoblast cell morphology and proliferation
journal, July 2008
- He, Jie; Zhou, Wei; Zhou, Xiaojian
- Journal of Materials Science: Materials in Medicine, Vol. 19, Issue 11
Studies on the lower oxides of titanium∗
journal, January 1958
- Pearson, A. David
- Journal of Physics and Chemistry of Solids, Vol. 5, Issue 4
Evolutionary approach for determining first-principles hamiltonians
journal, April 2005
- Hart, Gus L. W.; Blum, Volker; Walorski, Michael J.
- Nature Materials, Vol. 4, Issue 5
Compressive sensing as a paradigm for building physics models
journal, January 2013
- Nelson, Lance J.; Hart, Gus L. W.; Zhou, Fei
- Physical Review B, Vol. 87, Issue 3
Direct Diffusion through Interpenetrating Networks: Oxygen in Titanium
journal, July 2011
- Wu, Henry H.; Trinkle, Dallas R.
- Physical Review Letters, Vol. 107, Issue 4
Formation of Anatase and TiO from Ti Thin Film after Anodic Treatment and Thermal Annealing
journal, January 2011
- Chung, Yu-Lin; Gan, Der-Shin; Ou, Keng-Liang
- Journal of The Electrochemical Society, Vol. 158, Issue 10
Linking the electronic structure of solids to their thermodynamic and kinetic properties
journal, March 2010
- Van der Ven, A.; Thomas, J. C.; Xu, Qingchuan
- Mathematics and Computers in Simulation, Vol. 80, Issue 7
Structural dependence of apatite formation on titania gels in a simulated body fluid
journal, December 2002
- Uchida, Masaki; Kim, Hyun-Min; Kokubo, Tadashi
- Journal of Biomedical Materials Research, Vol. 64A, Issue 1
Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
journal, February 1997
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 78, Issue 7
Computation of alloy phase diagrams at low temperatures
journal, January 1998
- Kohan, A. F.; Tepesch, P. D.; Ceder, G.
- Computational Materials Science, Vol. 9, Issue 3-4
The Crystal Structure of So-Called delta-Titanium Oxide and Its Structural Relation to the omega-Phases of Some Binary Alloy Systems of Titanium.
journal, January 1959
- Andersson, Sten; Einarsson, Pall; Magnéli, Arne
- Acta Chemica Scandinavica, Vol. 13
Interstitial Order-Disorder Transformation in the Ti-O Solid Solution. IV. A Neutron Diffraction Study
journal, April 1970
- Yamaguchi, Sadae; Hiraga, Kenzi; Hirabayashi, Makoto
- Journal of the Physical Society of Japan, Vol. 28, Issue 4
A Lightweight TiO 2 /Graphene Interlayer, Applied as a Highly Effective Polysulfide Absorbent for Fast, Long-Life Lithium-Sulfur Batteries
journal, March 2015
- Xiao, Zhubing; Yang, Zhi; Wang, Lu
- Advanced Materials, Vol. 27, Issue 18
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996
- Kresse, G.; Furthmüller, J.
- Computational Materials Science, Vol. 6, Issue 1, p. 15-50
Oxygen and nitrogen interstitial ordering in hcp Ti, Zr, and Hf: An ab initio study
journal, October 2010
- Ruban, A. V.; Baykov, V. I.; Johansson, B.
- Physical Review B, Vol. 82, Issue 13
DFT+ U calculations of crystal lattice, electronic structure, and phase stability under pressure of TiO 2 polymorphs
journal, August 2011
- Arroyo-de Dompablo, M. E.; Morales-García, A.; Taravillo, M.
- The Journal of Chemical Physics, Vol. 135, Issue 5
Cluster Approach to Order-Disorder Transformations in Alloys
book, January 1994
- Fontaine, D. De
- Solid State Physics, p. 33-176
Phase stability and nondilute Li diffusion in spinel
journal, March 2010
- Bhattacharya, Jishnu; Van der Ven, Anton
- Physical Review B, Vol. 81, Issue 10
Investigating the Energetic Ordering of Stable and Metastable TiO 2 Polymorphs Using DFT+ U and Hybrid Functionals
journal, August 2015
- Curnan, Matthew T.; Kitchin, John R.
- The Journal of Physical Chemistry C, Vol. 119, Issue 36
First principles phase diagram calculations for the octahedral-interstitial system αTiOX, 0≤X≤1/2
journal, December 2012
- Burton, Benjamin Paul; van de Walle, Axel
- Calphad, Vol. 39
First-principles calculations of the phase stability of
journal, June 2002
- Muscat, Joseph; Swamy, Varghese; Harrison, Nicholas M.
- Physical Review B, Vol. 65, Issue 22
High-Energy, High-Rate, Lithium-Sulfur Batteries: Synergetic Effect of Hollow TiO 2 -Webbed Carbon Nanotubes and a Dual Functional Carbon-Paper Interlayer
journal, October 2015
- Hwang, Jang-Yeon; Kim, Hee Min; Lee, Sang-Kyu
- Advanced Energy Materials, Vol. 6, Issue 1
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996
- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186
Review of the anatase to rutile phase transformation
journal, December 2010
- Hanaor, Dorian A. H.; Sorrell, Charles C.
- Journal of Materials Science, Vol. 46, Issue 4
C-Ti (Carbon-Titanium)
journal, January 1998
- Okamoto, H.
- Journal of Phase Equilibria and Diffusion, Vol. 19, Issue 1
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium
journal, May 1994
- Kresse, G.; Hafner, J.
- Physical Review B, Vol. 49, Issue 20, p. 14251-14269
Cooperative Magnetic Transitions in the Titanium‐Oxygen System: A New Approach
journal, March 1970
- Mulay, L. N.; Danley, W. J.
- Journal of Applied Physics, Vol. 41, Issue 3
Anatase formation on titanium by two-step thermal oxidation
journal, December 2010
- Okazumi, Takuro; Ueda, Kyosuke; Tajima, Kazuki
- Journal of Materials Science, Vol. 46, Issue 9
First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides
journal, July 2013
- Wojdeł, Jacek C.; Hermet, Patrick; Ljungberg, Mathias P.
- Journal of Physics: Condensed Matter, Vol. 25, Issue 30
Interstitial Superlattice of Ti 6 O and Its Transformation
journal, October 1966
- Yamaguchi, Sadae; Koiwa, Masahiro; Hirabayashi, Makoto
- Journal of the Physical Society of Japan, Vol. 21, Issue 10
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008
- Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I.
- Physical Review Letters, Vol. 100, Issue 13
Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992
- Perdew, John P.; Chevary, J. A.; Vosko, S. H.
- Physical Review B, Vol. 46, Issue 11
Density functional theory analysis of the structural and electronic properties of TiO2 rutile and anatase polytypes: Performances of different exchange-correlation functionals
journal, April 2007
- Labat, Frédéric; Baranek, Philippe; Domain, Christophe
- The Journal of Chemical Physics, Vol. 126, Issue 15
Study of the TiO to Anatase Transformation by Thermal Oxidation of Ti Film in Air
journal, March 2011
- Kao, Chung-Ho; Yeh, Sung-Wei; Huang, Hsing-Lu
- The Journal of Physical Chemistry C, Vol. 115, Issue 13
Growth of titanium oxide crystals of controlled stoichiometry and order
journal, May 1972
- Roy, Rustum; White, William B.
- Journal of Crystal Growth, Vol. 13-14
O-Ti (Oxygen-Titanium)
journal, July 2011
- Okamoto, H.
- Journal of Phase Equilibria and Diffusion, Vol. 32, Issue 5
Matplotlib: A 2D Graphics Environment
journal, January 2007
- Hunter, John D.
- Computing in Science & Engineering, Vol. 9, Issue 3
Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981
- Perdew, J. P.; Zunger, Alex
- Physical Review B, Vol. 23, Issue 10, p. 5048-5079
Choice of U for DFT+ U Calculations for Titanium Oxides
journal, March 2011
- Hu, Zhenpeng; Metiu, Horia
- The Journal of Physical Chemistry C, Vol. 115, Issue 13
C−Ti (Carbon-Titanium)
journal, June 2006
- Okamoto, H.
- Journal of Phase Equilibria and Diffusion, Vol. 27, Issue 3
Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles
journal, December 2013
- Thomas, John C.; Ven, Anton Van der
- Physical Review B, Vol. 88, Issue 21
The ordered structure of TiO
journal, August 1967
- Watanabé, D.; Castles, J. R.; Jostsons, A.
- Acta Crystallographica, Vol. 23, Issue 2
First-principles investigation of migration barriers and point defect complexes in B2–NiAl
journal, May 2009
- Xu, Qingchuan; Van der Ven, Anton
- Intermetallics, Vol. 17, Issue 5
Thermodynamics of Lithium in TiO 2 (B) from First Principles
journal, April 2012
- Dalton, Andrew S.; Belak, Anna A.; Van der Ven, Anton
- Chemistry of Materials, Vol. 24, Issue 9
Phase Analysis Studies on the Titanium-Oxygen System.
journal, January 1957
- Andersson, Sten; Collén, Bengt; Kuylenstierna, Ulf
- Acta Chemica Scandinavica, Vol. 11
Cluster expansion and the configurational theory of alloys
journal, June 2010
- Sanchez, J. M.
- Physical Review B, Vol. 81, Issue 22
Interstitial Order-Disorder Transformation in the Ti-O Solid Solution. II. A Calorimetric Study
journal, October 1969
- Koiwa, Masahiro; Hirabayashi, Makoto
- Journal of the Physical Society of Japan, Vol. 27, Issue 4
Magnetic Susceptibility Measurements of Rutile and the Magnéli Phases of the Ti-O System
journal, February 1967
- Keys, L. K.; Mulay, L. N.
- Physical Review, Vol. 154, Issue 2
Enthalpy of the Anatase-Rutile Transformation
journal, November 1967
- Navrotsky, A.; Kleppa, O. J.
- Journal of the American Ceramic Society, Vol. 50, Issue 11
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journal, May 2019
- Ångqvist, Mattias; Muñoz, William A.; Rahm, J. Magnus
- Advanced Theory and Simulations, Vol. 2, Issue 7
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journal, January 2019
- Rushchanskii, Konstantin Z.; Blügel, Stefan; Ležaić, Marjana
- Faraday Discussions, Vol. 213
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journal, August 2018
- Gunda, N. S. Harsha; Van der Ven, Anton
- Physical Review Materials, Vol. 2, Issue 8
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text, January 2019
- Ångqvist, Mattias; Muñoz, William A.; Rahm, J. Magnus
- arXiv