Elastic Modulus of the (GaAs) m (AlAs) n Superlattices
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ELASTIC MODULUS OF T14E (GaA.s)m(AlA.s)n SUPERLATTICES VADIH YU. HIROVITSKII T.nst..itit.e Grosu•]
for Power nng.inee.r.inS,Academy
St..r. 5, K.ish.inev 2770P8,
Moldova,
o:f Sciences
of 1oldova,
(USSR)
ABSTRACT The ul].tratiin
(GaAs) m(AlAs)n superlat.t.ices ( SL ) grown are formally considered as a resuilt. of ordering-type
along [001]
an initial hypothbet.ical mMixed crystal (G A._ A )As w.ith x = m/(m+n).From this point, of vjiew changes of elst.ic modl)us tonsor (EMT) induced by ordering can be calulasted nearly In a spirit, of pbenomenological Landaui thbeory of second-order phase t.rns.lt..ions. Tt. is shown that. a change of E1WT component. . 66is completeoly determined by symmetry properties of t.wo t.ranslat.ional ( Dzyaloshlnsli) invariant.s of m+n power in phase transition from
the expansion of SL thermodynamic potential In a power series In order parameter components. The changes of t.be ot.her P-MT component.s depend on the second power of order paramet.er. . The express~ions are fouind oiut. t.o connect. ( SL -
,MT of a defini t.e ordered
pbase
family wJ.it.h m+n = 3 ) w.it..h that. of the .nitial one.
INTRODUCTION
As well known, t.e
ayers
art..i fIic.ial
of two di fferent.
stru-ctures cons.ist.ing of alteprna-
sem.i conductors possess un.i que
p~hysical properties and more and more. .int.ensively are used in devices. Tn this connection there l.s a. problem to choose ,, p.'•'uj,, th.e only strnucture l.n a. large number of them th.a.t crysta.l.lophysir.l. constants . Tn other word~s i.t its
ha.s req.i.ed. necesnary to
know the dependence of physicatl. properties of layerred. str.uctu7res on its ntrurti.al. p.-arameters such a.s directi.on and. va.l.u.e of sperperi.od. composi.ti.on, etc.Th.e pproa.ch. to solve thits problem (how
to
alcl, ate
ultrathin ST.)
is
e.ffecti ve proposed. in
crystal. lophysi.cra.l
this p.ape•.
constants
of
Tt i.s ba.sed. on the
fa.ct that th.ST. can be con.sid.er•ed. a.. a. si.ngl.e crysta.l. derived, from some ini.ti.a.l crysta...,ine str.x.ct•re by Tm.l.ti.pl.yinng i.t.s pri.mi.tive
cel.We are st~arti~ng -From an idapure A.allW c ompouind. wi~th. the space group Td and w.it.h A atom .in a-position and R at.om In c-pos it.•on. Then. a completely disordered sol.td sol ut.i on Mat. Res. Soc. Symp. Proc. Vol. 291. @1993 Materials Research Society
316
( Ax( 1.) A.tx(2))
R
in
the framework- of virt.ui.,l
crysta.l. concept
cbaract.erized by homogeneous probabl I it.y p = xe for any su1biattice point, of t.be puirpe crys.tal to be occupled by atom.
aA(1)
Obvjious.ly, the space. grooup and Wyckoff positions syst.e.m
this fictitious
(virt•ual)
crystal
coincides wit.,h those
i.s
of
of pure
A LAIPV. Suich a "mixed crystal" we shall call. init..ial crystalline structure (.TCS).A complication of ST. primitive cell is cauised by the loss of some TCS space symmetry Piement.s duie to a periodical arrangement. of two kinds of A at.oms over the system of one-fold a-positions translat.ionally equ.ivalent. in IC$..Tn othber words, SL can be
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