density-functional theory calculations relevant to hydride
TRANSCRIPT
Density-Functional Theory Calculations Relevant to Hydride Formation and
Prevention SRF - Paris - September 23, 2013
Denise Ford
Argonne National Laboratory (previously affiliated with Fermi National Accelerator Laboratory
and Northwestern University)
Acknowledgments
Dr. Lance Cooley
Prof. David Seidman
Computing resources at Fermilab and Argonne National Laboratory
Funding from Fermilab
2 SRF 2013 Denise Ford September 23, 2013
SRF Cavity Limitations Related to Impurities in Niobium
Quench
Q - disease Q - slope
Ideal
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Impurities can be dissolved in the metal
and cause reduction of Tc and local heating
form precipitates with local magnetic moments or reduced Tc
SRF 2013 Denise Ford September 23, 2013
Density Functional Theory Modeling
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NbH (β niobium hydride) bcc Niobium
Infinitely expand structure with periodic boundary conditions
Build a crystal structure
Compare properties of different structures
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Solve the electronic structure problem for the model systems using DFT in VASP
Assess properties such as binding energy, charge distribution, and niobium lattice strain
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Hydride Phase Formation
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Ford D C, Cooley L D and Seidman D N 2013 Supercond. Sci. Technol. 26 095002
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Interstitial Hydrogen, Oxygen, Nitrogen, and Carbon
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tetrahedral absorption (H)
octahedral absorption (O,N,C)
Nb128H Nb128O Nb128N Nb128C
Charge on interstitial atom (e-) -0.65 -1.35 -1.63 -1.76
Binding energy (eV) -2.41 -7.02 -7.39 -8.48
Lattice strain energy (eV) 0.11 0.83 0.83 0.96
Ford D C, Cooley L D and Seidman D N 2013 Supercond. Sci. Technol. 26 105003
Hydride Phase Prevention by Absorbed Oxygen
Further examination of oxygen showed Interstitial oxygen traps interstitial hydrogen
Oxygen preferentially migrates to niobium site vacancies over hydrogen
Mechanism for the low temperature bake (which mitigates Q-slope) -> Break up hydride phases
-> Detrap hydrogen from niobium lattice defects
-> Block phase nucleation sites with oxygen atoms
-> Trap interstitial hydrogen with interstitial oxygen atoms
Would nitrogen have a similar effect?
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SRF 2013 Denise Ford September 23, 2013
Ford D C, Cooley L D and Seidman D N 2013 Supercond. Sci. Technol. 26 105003
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
2 3 4 5 6 7 8 9X-H Distance (Å)
Bind
ing
Ener
gy (e
V)
X=N
X=O
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Hydrogen Trapping by Oxygen and Nitrogen
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Hydrogen, Oxygen, and Nitrogen in Niobium Site Vacancies
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-1.0
-0.5
0.0
0.5
0 1 2 3 4
Vaca
ncy
Abs
orpt
ion
Ener
gy (
eV)
unpaired electrons
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-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0 1 2 3 4
unpaired electrons
Atomic Radius (A) Charge when Interstitial (e) Vacancy Absorption Energy (eV) Strain Releif by Vacancy Absorption (eV)
Hydrogen, Oxygen, and Nitrogen in Niobium Site Vacancies
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-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
0 1 2 3 4
unpaired electrons
Atomic Radius (A) Charge when Interstitial (e) Vacancy Absorption Energy (eV) Strain Releif by Vacancy Absorption (eV)
Hydrogen, Oxygen, Nitrogen, and Carbon in Niobium Site Vacancies
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Hydrogen, Oxygen, and Nitrogen in Niobium
SRF 2013 Denise Ford September 23, 2013
Vacancy trapping and detrapping energies1,2,3 : N>O>H
Effect on superconducting transition temperature4,5,6
O>N>H
hydride precipitates Tc < 2 K
some nitrides Tc > 10 K
1. Hautojarvi P, et al. 1985 Phys. Rev. B 32 4326–31; 2. Igata N, Miyahara K, Ohno K and Hakomori K 1982 J. Nucl. Mater. 108/109 234–9; 3. Wechsler M S and Murty K L 1989 Metall. Trans. A 20A 2637–49; 4. DeSorbo W 1963 Phys. Rev. 132 107–23; 5. Jisrawi N M, et al. 1998 Phys. Rev. B 58 6585–90; 6. Ohlendorf D and Wicke E 1979 J. Phys. Chem. Solids 40 721–8
Conclusions
Suggested improvements for processing Tailor bake temperature and time to eliminate hydride
precipitates and supply the appropriate amount of oxygen to prevent their reformation
Potentially use nitrogen for milder effect on superconducting transition temperature
Future work Examine the formation of nitride phases in niobium
Examine the effect of various NbxNy, NbxNyHz, NbxOyHz complexes on the superconducting properties of the niobium
Examine the role of dislocations in hydride phase formation/prevention
13 SRF 2013 Denise Ford September 23, 2013
Hydrogen in Niobium
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α, α’ – interstitial hydrogen dispersed in bcc niobium
β, ε – ordered hydrogen interstitials in fco niobium
δ – ordered hydrogen interstitials in fcc niobium – fluorite structure
λ, λc – experimentally unconfirmed phases R.E. Ricker, G.R. Myneni, J. Res. Natl. Inst. Stand.
Technol., 115, 1 (2010).
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SRF 2013 Denise Ford September 23, 2013
Density Functional Theory Modeling
15
Solve the electronic structure problem for the model system
Parameters Vienna Ab Initio Simulation Package (VASP)
Plane wave basis set w/400 eV cutoff
PAW pseudopotentials to describe atomic cores
PBE-GGA exchange-correlation functional
0.25/Å gamma-centered k-point mesh
Bader Method to assign local properties
SRF 2013 Denise Ford September 23, 2013