density-functional theory calculations relevant to hydride

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

3

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

4

NbH (β niobium hydride) bcc Niobium

Infinitely expand structure with periodic boundary conditions

Build a crystal structure

Compare properties of different structures


  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

5

Hydride Phase Formation


Ford D C, Cooley L D and Seidman D N 2013 Supercond. Sci. Technol. 26 095002

6

Interstitial Hydrogen, Oxygen, Nitrogen, and Carbon


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


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?

7



-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

8

Hydrogen Trapping by Oxygen and Nitrogen


9

Hydrogen, Oxygen, and Nitrogen in Niobium Site Vacancies


-1.0

-0.5

0.0

0.5

0 1 2 3 4

Vaca

ncy

Abs

orpt

ion

Ener

gy (

eV)

unpaired electrons


-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


-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

12

Hydrogen, Oxygen, and Nitrogen in Niobium


  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


Hydrogen in Niobium

14

  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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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


density-functional theory calculations relevant to hydride

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