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1043-T06-02-E06-02

Defect Structure and Stability in Uranium, Zirconium and Titanium Nitrides © 2008 Materials Research Society R.W. Grimes2, E.A. Kotomin1, N.J. Ashley2, P. Van Uffelen1, Yu. Mastrikov3, Yu. Zhukovskii3 & V.V. Rondinella1 1

Institute for Transuranium Elements, Karlsruhe, Germany

2

Dept. Materials, Imperial College London, UK

3

Institute of Solid State Physics, University of Latvia, Latvia

Contents • Titanium and Zirconium Non-Stoichiometry – – – –

Method Alternate Configurations Lattice Parameter Results Population Analysis

© 2008 Materials Research Society

• Uranium Nitride – – – –

Method Results for Pure Uranium Nitride Lattice Distortion due to Defects Frenkel Defects

• Conclusions

Titanium and Zirconium Nitride Non-Stoichiometry © 2008 Materials Research Society

Methodology - Simulation code • Plane-wave basis set density functional theory (DFT) code • CASTEP 2.1.1(academic version)

© 2008 Materials Research • Perdew-Wang 91 GGA functional

Society

• Ultrasoft pseudopotential representation • 3×3×3 Monkhorst-Pack grid k-point set (approximate k-point separation of 0.04 Å-1)

Simulation technique – configurational averaging • Alternate configurations • Configurational averaging based on energy and temperature

© 2008 Materials Research Society a=

∑ ni [e

− ΔEi kT

(ai .bi .ci ) 3 ] 1

i

∑n e i

i

− ΔEi kT

Ti(1-x)N Non-stoichiometry – Lattice Parameter

© 2008 Materials Research Society

Ti(1-x)N Non-stoichiometry – Nitrogen deficient

© 2008 Materials Research Society

Zr(1-x)N Non-stoichiometry – Lattice Parameter

© 2008 Materials Research Society

Zr(1-x)N Non-stoichiometry – Nitrogen deficient

© 2008 Materials Research Society

ZrN Non-stoichiometry – Population Analysis Vacancy Models Composition

Original Charge (e)

Nearest Neighbour Charge (e)

Second Neighbour Charge (e)

Zr

Zr

N

Zr

N

1.09

-0.79

-

-0.93

N

Zr0.75N

-0.82 0.97 -0.87 © 2008 Materials1.01 Research Society

Zr0.88N Zr0.94N

0.94

-0.84

0.90

-0.87

0.86

-0.86

0.86

-

Zr1.06N

0.63

-0.86

0.86

-0.86

Zr1.14N

0.56

-0.86

0.88

-0.86

Zr1.33N

0.54

-0.86

0.93

-

ZrN

0.86

-0.86

ZrN Non-stoichiometry – Population Analysis Vacancy Models Composition

Original Charge (e)

Nearest Neighbour Charge (e)

Second Neighbour Charge (e)

Zr

Zr

N

Zr

N

1.09

-0.79

-

-0.93

N

Zr0.75N

-0.82 0.97 -0.87 © 2008 Materials1.01 Research Society

Zr0.88N Zr0.94N ZrN Zr1.06N Zr1.14N Zr1.33N

0.86 Nitrogen Deficiency

-0.86

0.94

-0.84

0.90

-0.87

0.86

-0.86

0.86

-

0.63

-0.86

0.86

-0.86

0.56

-0.86

0.88

-0.86

0.54

-0.86

0.93

-

ZrN Non-stoichiometry – Population Analysis Vacancy Models Composition

Original Charge (e)

Nearest Neighbour Charge (e)

Second Neighbour Charge (e)

Zr

Zr

N

Zr

N

1.09

-0.79

-

-0.93

N

Zr0.75N

1.01 -0.82 0.97 -0.87 © 2008 Metal Materials Research Society

Zr0.88N Zr0.94N

Deficiency

0.94

-0.84

0.90

-0.87

0.86

-0.86

0.86

-

Zr1.06N

0.63

-0.86

0.86

-0.86

Zr1.14N

0.56

-0.86

0.88

-0.86

Zr1.33N

0.54

-0.86

0.93

-

ZrN

0