Finite temperature in uen e on the elasti properties of zir onium Pär A.T.Olsson
1
,Kwadwo Kese2
,Anna-MariaAlvarezHolston
2
1
Malmö University,email: Par.Olssonmah.se
2
StudsvikNu learCorporation
Be useofitslowthermalneutron apture rossse tion,zir oniumbasedalloysare ommonly
employed asfuel ladding materialsintoday'slight/heavy waterrea tor ores. Insu h
environ-mentsthematerialis onstantly subje ted tothe bombardment of highenergy neutrons, whi h
ollide withprimary kno k-on atoms and ause mi rostru tural damage inthelo alized region.
Thisleads to in reased on entrations ofva an y andself-interstitial lustersand in reased
dis-lo ation density. This auses a hardening of thematerial and an irradiation-indu ed hange in
theelasti properties.
The purpose of this work is to model how these properties vary with the amount
irradia-tion damage. To study howthese ee tsin uen e the material, we resortto lassi al mole ular
dynami s (MD) and quantum me hani al density fun tional theory (DFT). The primary
mod-elling tool of this proje t is MD, however for ben hmarking purposes and to aid the hoi e of
interatomi potential wewill useDFT.
The rstpartofthisproje tandthes opeofthispresentationistoevaluatethetemperature
dependent elasti onstantsfor Zr. Toa hieve this we have ondu ted DFT al ulationswithin
the quasi-harmoni approximation (QHA) at dierent temperatures, where the Helmholtz free
energy is al ulated asa fun tionstrainfrom whi h theelasti onstants anbeextra ted. The
elasti propertiesarethen ttedto the universalrelation byVarshni 1
,whi h isasemi-empiri al
relation that is known to des ribe the elasti properties of solids a urately. In Figure 1 we
have ompared the DFT al ulated results of
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33
with experimental data 2. It is seen that the
temperature in uen e onelasti properties arewell representedbytheDFTmodel.
We have also used MD to evaluate the temperature dependen e of the elasti properties of
Zr. Forthispurposewetestedtwodierentembedded-atommethod(EAM)potentials. TheMD
al ulated elasti onstant were obtained using a quasi-stati approa h where the stress tensor
is measured asa fun tion of strain. It isfound that both potentials approximately apture the
temperature dependent elasti onstants.
Thiswork is nan edbytheKnowledgeFoundation throughgrant no 20130022.
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[GPa]
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DFT
Expt.
Figure 1: Temperature dependen e of
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al ulated using DFT ompared with experimental measurements. The solidlinesrepresent tsto theVarshni relation.1
Y.P.Varshni,Phys. Rev. B,2,3952,(1970).
