Document

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k
Phase diagram 01.ZrV 2
,<'
. A. S.8alankin
F.n~inr:~rmg.Physi:sl!ls:itul~.
,Sut:mlttc:d Junc: 'j5~ ¡QS2¡
F:;
Moscou'
~'
T,..:d. Tda !Lcn::.¡::a'::. 24. 3':75-3':77 I:-Iovc:mbtr I~S2¡
p;.xC$ !;amb.:rs: 81.3(')!<:. 64.7C.Kb
~.~><:_:-l:~ ..~l'\H:,l!r~ \"paC":!groUp'O¡¡ot Z'rV. is :m..,
::Ab!~ in'rr;e.iia"'!!r ?tt"!r Ús !di;":¡':.iO~f;1 Depending on
:i!<;1
S:.lt<:oí the :n..;esngate<l.s&I:1ple, this.loss oí stabilit!-;
oí the hr~h-temperatur,e ppase can bE::maniíeSted by: 1)'
a Stru-=r.:ral tl"ans,ition accompanied"by partíal 'dielec~
'::rizátior.~ oí" the electror. energy spectrum3,4in which case
the 10w.-temperatUre pbase can be rbombobedra!$ or ortho:nombrc"; 2) an electronic .transition whicb dbes not alter
.:t:oecrystal lattice syminetrj,$.:; 3)consecutivEI occurrence
of the electronic and structural transitions.$
Expansioh oí the tbermodYD&mic pOtential oí ZrV: in
~."-rros oC.he whole rational Oasis o: invariantS is (to wi:h";¡terms oi the íou.rtbpoweroí
me :Jrder parapleter)
'=4,1,.,. ~./~-bl/...:..C,I.~d,~"~d.j,V..:.. A,I...:..=,/.l
-:,J:,.,Ei,I,Ji..:..!I,I,I...:..JI,t'I,.
-~
(1)
"";¡ere
where ~ is th~
Ir.,
"="'*-"
PF
"
"
"
.!!.
01 th(?
,-,T ) ,
1
-1:,
.
tbe exiStencE
2) cubic
=O;
w~th~ .. O; 3) rbom~hedral t xy = tX%= &y%(space grou
D~) witb !I.. O; 4. 5) orthorhombic
(Dl) ~ith ~ ",:,0and l\ "'.. O;
.
with.!l..
O; 7) triclinic"&xy"
=
&xY' t x% &yz
6) monocltnic
t xy"
=O
&XZ =,c.yz
&xz" &y%wi:b ~..
O,
Phases 1-5 had been observ~tt experU:1~nta1ly,3-1 A
complE:te phase diagram of Zr~2 corresponding to the
thermodyna!f1ic potentla,! of Ee¡. .(~) is ~ setof LntersectU"6
hypersurfaces in a nine-dimer-sional space oí the coefficientS Dio di.an~ ai (i. = 1, 2hand bt. CI. andAs, The
majo featlÍres ofthe pha.se transitions in ZrVz can be described'by considerlrtg a phase diagran1 using the coordiDateSal - d: =1¡~Cw as sbown :11Fig. l. Tbe re!atloDth~ ot!ler
pan::,e~t::r::;
('3,.') be ¡:ied~ced (raro
<l,
t
J,=.:.:;
/
,,~}are C'omponentS oí the strain censor; ~ is theenergy
.1E'lectrtc~) gap. Tbe coefficients a i. b¡, CI, di, and
'. car. be expressed in terms oí componen!s oí the ten~':l'8repres~nting secocd-, th:rd-. and íocrth-ordez: elas'."~.Jnoduli In tbe usual wa).!.
e,
al:d m6men~n:.
.
I¡~,;,~,~~<;..
1.=<.,'61-". !'='~,":"C~I""'C;" .
I.,~,~..
,1
..~
. - ( O .' (
..,.,-..,-c;,/,.<,,-,..-c...J..,...'
'~I-C;.. <,,-<..1.
~"J"""7'~"')'
energ::
The ,;hermodynamic
pou~n;'lal (l)admitS
of seven di1ferent phases:
1) cubic-wi:b-,¡l
,¡hipS be:weell
t '~'\"i
C~r'~;:.::.r.t; ¡:F
~;:r~:.;jr. ;:::e:a~':,c::
~i":ctrl,m-
and PF are.!he;Ferm\
J
3
8J
(2)
/
/ :H""; ¡ ,"...
1.
-'
.! J/ ! ' ¡,1
J
/1
/I/;' -.:
.
"
¡'c.,
FtG. 1. ;>~:ISc:~:a!!ram ol Zr"z {or
9l >0, G: :>?,.~ > 0,,5, > O.
/ t)1zz
f¡
1/1
11
.
,'lrll¡
~~11
S')v Phys, Soltd State 24111 l. November 19820038,5654/82/1
1 1977.02
$03.90
@ 1983 Americlr. Institute 01 Physics
1977
r
I
~tlong the path nI (Refs. 3 and 41, The COt1\'erSe trans',
írom the pbase 3 to tlIe cubic pbase 2 can occur aJO!!':
pat!l IV if the compound does not go over to the s."",
~,
...,.f("ductitlg state before,
'-
i~
¡
::-
i
..- 6f-
:j'V:!\
/1
F!G. 2, Tempc:atU~ de;>endenceof
the !)lIlkmt'dulus B o( ZrVzr~ccrded
in the rango:af phase r1'3nsitians(the
ccnt:nuc1Iscu~e is c:alcu:arec the.
oreti.:ally).
~~: ~jC ~J'; ::O:,-r<
Tbe thermodyn:lmiC potential o.í Eq. (1) al!ows us .
describe the ano!l1alles oí the physical prop'3rties cct:\;'
ring at the phase tr:ln~ition,F1gure
2,givesth!:i teJn~:'
rure dcpendence oí the~bulk móaulusoi ZrV2 in the ;~g
oí the pbase transition íthermod)'11<1.:ni7,path ti). The t"
surements were madI>..
in the saDle way as in J;t'"-f.2. 1
contluuous curv,"- ls :;he :.heoreticai dependence, whici::.
agrees well with the experimental resulta UXii:ltS)
,
~e conditlOn d matching oí :l:e calcu!ated diagrar.: :o the
:xperimental rp..suitS. ¡On!)" the part oí the dragra:n deí.."ledby C44:: O is sho;vn in Fig. l.) The Une oí fit'St¡raer tra.nsitiollS betWeeD tbe pbases 1 aad 3;is a parabola
vbicb splits atthetI'iple
point TI intO.a line.of4second)rder transitions between phases 1 and 2 and a Une, oí
irst:-order transitions betweenpbases
2 aad 3,anc! the
ast Une transforms me tricritical
polnt !vi; 10 a line oí
¡na.se tra.as itlons between phases 2 and 3.
Tbe ther~odyna.mic path along which tbe high-t~m'"
¡eratuÍ'e pbase~ 1oí ZrV\2 loses its stá.bility is a functiOn
)f Stoicbiometry. degree oí disorder"J 3.Ildpresence oí im¡urities (pariicularÍ)' of hyo.rogen), Tbe patb 1-.1 repre¡entS aepbase tia."lsitidn írom 1 tO 2 p!:,od1J.Cinga.,dielecric gap.$.¡ 'Along the path II- h. the 10ss 'oí s tabll itY oí
he pbase 1 occurs as 'a result ór'consecuti..;e electrQnic
LIIdstrucrural tra.nsitions.~.1 A doubJe pbase transitipn
:n accordance \Vith the termi!1ology oí R eL 9) occurS
1;~.?~;)9~~~~i;~~~~ ~;:~.~~=:::~~:
~~~..~~~=;:,T~::. L~~;r:~r.l. ~. :~
zA, S. S~Ia:tk:r:,¡O"S, B..:.no",-;;, ::" \'. S1<or~'.'.
?:S'!'!":O
Z.'-,7~<~. ::1,14510981) [Sov. Tedl. ?h\:s. Lett, 2, ;;21 (¡SS1);.
JV. M. Pan. l. E. Bulakh. A. L...Kasatkin,a:\d.";. D. Shc'J~ne:lko,?is'~,
Zh. Eksp.Te.or. riz.!2.- 629 09';5) [JET? Len,ll, S94~1j7S)J.
~'. V, Nemoshka.lenko,V. Ya. Nagomr!. ~!, 7.J<o.1gut.M. .A.,Minc!!::"
A. D. Shevcbenlco,ano l. E. Bulakh. Metailófizika ~, 29 (1981).
s.¡, A, Finkel' and E¡ A. p.Jshka~,", Zh. E:ksp.Teor. riz,.:!!. 842 Cl98ij}
(SoY.Phvs.1m 51, 42~ (1980)1.
cQ. Rapp: 1. 10V:l_. aod T. Claeson, ¡lh,'s. Lett. "'12, 159 (1974).
-!.€. v, Galos!11n;s,
v, N. Kozhanov, 5. V. Verkhovlkl!, M. A. Boro:di~l,
E. p. ~manov, T. S. Shu!,?ina,and K. ~. Mikhale,', Fi::.Met, Metallo
, 52. 12060981).
,
,;;¡ p. Sakh.,enko and V. ~!. Talano,'. riz, T,'crj. Tela n,eni!'.frad) ::,
2435 (1Yi9):~. 785 (1!:180)[So\'; Ph~'s.$olió State 11. 1~Ol (19~9):l:.
458 0980)].
9D. G. Sannikov. Pis'ma Z~. E1<sp.Teor, F,:. :n, 3420:.>301fjETPLen,
l!, 312 (iesO)l: ¡,¡.
'.
Tr3.lls1ated by A. Tybulewicz
1~d
S0V, ?r.ys.
SÓ"d Stalc
24(111.
Nov"mber
1982
0038.5554!82/11
1978.02
$03.90
,;J 198)
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¡"stito_te 01 Phy~;':S