Defect Structure and Stability in Uranium and Zirconium Nitrides
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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
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