Phase stability off ZrH1.5 : a DFT study

Phase stability of ZrH

1.5

- a DFT study PärA.T.Olsson

1

,JakobBlomqvist

2

,ChristinaBjerken

3

1

MalmöUniversity,email: Par.Olssonmah.se

2

MalmöUniversity,email: Jakob.Blomqvistmah.se

3

MalmöUniversity,email: Christina.Bjerkenmah.se

Duetoitslowthermalneutron apture rossse tionandgood orrosionresistan e,

zir onium-based alloys are ommonly employed as fuel ladding material in the ore of nu lear power

rea tors. Whileinservi e, thefuel ladding materialis in onta twithwater, whi hpromotes

theoxidationofZr. Thispro essreleasesfreehydrogen,ofwhi haportionentersthealloyand

givesrisetotheformationofbrittlehydrides. This anhaveadetrimentalee tontheintegrity

andthelongevityofthematerial. Amongthezir oniumdihydrides(ZrH

_x

,

1.5 ≤ x ≤ 2

),thefa e enteredtetragonal

ǫ

(c < a)

andthe ubi uorite-type

δ

phasesareknowntoexist. The

δ → ǫ

phasetransitionisknowntodependonthehydrogen on entration,where

ǫ

ispreferredathigh hydrogen on entrationsand

δ

o ursatlower hydrogen ontent. At whi h on entration and underwhat onditionsthetransitiono ursisnotwellestablishedandthereismu hdis repan y

amongtheexperimentalobservations.

Thepurposeofthisworkistoinvestigatethethermalinuen eonthephasestabilityofZrH

1.5

usingquantumme hani aldensityfun tionaltheory(DFT).Thefreeenergyisstudiedfor

dier-enttemperaturesbasedonthequasi-harmoni approximationusingthephonondensityofstates

and theele tron density ofstates. AllDFTsimulations areperformed usingthe

QUANTUM-ESPRESSOpa kage,whi hisaplanewavebasedDFTpa kage. Fortheele tron-ionintera tion

wehave usedultrasoftpseudopotentials oftheVanderbilt type. ForZrapseudopotential that

onsiders4d

2

5s

2

valen eele tronsandthe4s

2

4p

6

semi- orestatesinthevalen ebandwasused

while onlythe 1s

1

ele tron is treated for H. The employed ex hange orrelation fun tional is

that ofPerdew, Burke andErnzerhof (PBE)within theframeworkofthegeneralized gradient

approximation.

Wehave evaluated thedieren e infreeenergy for the

δ

and

ǫ

phases for thetemperature range20-500 Kin Fig. 1. Thetetragonalstru ture hasthelowestfreeenergy forlow

temper-atures. However, if the temperatureis in reased, at 229K the

δ

phasebe omes more stable. Thisimpliesthataphasetransitiono ursatthattemperatureanditexplainswhythe ubi

δ

phaseisobservedexperimentallyatroomtemperature,despitethelowformation energyofthe

tetragonal

ǫ

phase.

100

200

300

400

500

−50

0

50

Free energy

F

δ

−F

ε

[meV/Zr−atom]

T [K]

T = 229.2 K

Figure1: Dieren ein freeenergyfor

δ

( ubi )and

ǫ

(tetragonal,

c < a

)hydrides fordierent temperatures. Thereisaphasetransitionat229Kwherethetetragonalphasetransformsinto

ubi .