Fi s o de ansi ions by conduc ion calo ime y: Applica ion o deu e a ed
po assium dihyd ogen phospha e e oelas ic c ys al unde uniaxial
p essu e
M. C. Galla do and J. Jime
´nez
Ins i u o Mix o Ciencia de Ma e iales CSIC-Uni e sidad de Se illa, P.O. Box 1065, Se illa, Spain
M. Ko alewski
Ins i u e o Physics, A. Mickiewicz Uni e si y, Umul owska 85, 61-614 Poznan, Poland
J. del Ce oa)
Ins i u o Mix o Ciencia de Ma e iales CSIC-Uni e sidad de Se illa, P.O. Box 1065, Se illa, Spain
~Recei ed 3 June 1996; accep ed o publica ion 9 Decembe 1996!
The speci ic hea cand he hea powe Wexchanged by a Deu e a ed Po assium Dihyd ogen
Phospha e e oelec ic- e oelas ic c ys al ha e been measu ed simul aneously o bo h dec easing
and inc easing empe a u e a a low cons an a e ~0.06 K/h!be ween 175 and 240 K. The
measu emen s we e ca ied ou unde con olled uniaxial s esses o 0.3 and 4.560.1 ba applied o
ace ~110!.A T
5207.9 K, a i s o de ansi ion is p oduced wi h anomalous speci ic hea
beha io in he in e al whe e he ansi ion hea appea s. This anomalous beha io is explained in
e ms o he empe a u e a ia ion o he hea powe du ing he ansi ion. Du ing cooling, he
ansi ion occu s wi h coexis ence o phases, while du ing hea ing i seems ha me as able s a es a e
eached. Excluding da a a ec ed by he ansi ion hea , he speci ic hea beha io ag ees wi h he
p edic ions o a 2-4-6 Landau po en ial in he ange o 4–15 K below T while loga i hmic beha io
is ob ained in he ange om T o 1 K below T . Da a ob ained unde 0.3 and 4.5 ba uniaxial
s esses exhibi he same beha io . © 1997 Ame ican Ins i u e o Physics.
@S0021-8979~97!05606-5#
INTRODUCTION
The e oelec ic c ys al o po assium dihyd ogen phos-
pha e ~KDP!shows a well es ablished i s o de ansi ion a
empe a u e Tc5123 K as shown by se e al echniques.1
This ansi ion is be ween a e agonal pa aelec ic phase a
high empe a u es, and an o ho hombic e oelec ic-
e oelas ic phase a low empe a u es. The ansi ion is close
o ic i ical poin ~TCP!2and because o his se e al phe-
nomena show unusual c i ical beha io wi h a small la en
hea obse ed. TCP may be easily ob ained a hyd os a ic
p essu e abou 2.4 kba .
When KDP is deu e a ed ~DKDP c ys al!, bo h he an-
si ion en halpy and ansi ion empe a u e inc ease3wi h he
deg ee o deu e a ion. When KDP is 100% deu e a ed, a i s
o de ansi ion occu s a 220 K. The pola iza ion, which is
conside ed he o de pa ame e , he shea s ain uxy and he
bi e ingence Dnxy a e p opo ional o each o he . This
p ope y allows he use o an ex e nal shea s ess
s
xy o an
ex e nal elec ic ield Ez o induce modi ica ions in uxy and
Pz. Consequen ly, a compe i ion4be ween elec os a ic and
elas ic ene gies akes place.
DKDP has been s udied by means o di e en
echniques1such as neu on di ac ion,5x ays,6dielec ic
measu emen s,7e c. The speci ic hea has been measu ed by
se e al au ho s.8–11 The speci ic hea shows a e y high peak
a ansi ion empe a u e T , and in some cases,8,9 a double
maximum has been obse ed. This e ec has no been
clea ly explained.
On he o he hand, we mus poin ou ha :
~i!I is necessa y o know when wo phases coexis o
disc imina e da a a ec ed by he ansi ion en halpy,
and
~ii!due o he e oelec ic- e oelas ic cha ac e o
DKDP, he e ec o uniaxial p essu e and/o he elec-
ic ield should be known.
In his a icle he speci ic hea and he hea powe ex-
changed by a DKDP c ys al du ing he ansi ion we e mea-
su ed simul aneously, unde con olled uniaxial p essu e.
The measu emen s we e made in a conduc ion calo ime e
while cooling o hea ing he sample a a e y low cons an
a e ~0.06 K/h!.
THE EXPERIMENTAL APPROACH
The expe imen al sys em has p e iously been desc ibed
in de ail in an ea lie wo k.12 The senso is o med by wo
luxme e s ~
1and
2!, wo pla inum esis ance hea e s ~R1
and R2!, a calo ime e block ~hea sink, H!and a de ice (B)
o apply an uniaxial p essu e o he sample (S). The a ange-
men o hese elemen s is shown in Fig. 1.
Each luxme e is made o 50 ch omel–cons an an he -
mocouples connec ed in se ies and placed in pa allel lines.
They a e igid enough o be used o apply uniaxial s ess o
he c ys al. The sample is p essed be ween he wo luxme-
e s ~Fig. 1!. One o hem ~
2!is ixed o he calo ime e
block (H) while he o he one ~
1!is p essed by bellows (B)
connec ed h ough a capilla y (C) o an ou e p essu e bo le
o N2. An a ay o al es allows us o con ol he p essu e in
a!Elec onic mail: [email p o ec ed]
2584 J. Appl. Phys. 81 (6), 15 Ma ch 1997 0021-8979/97/81(6)/2584/6/$10.00 © 1997 Ame ican Ins i u e o Physics
he bellows. Ex eme p ecau ions we e aken o achie e sym-
me y in he de ice wi h espec o plane x50~shown by
e ical dashed line in Fig. 1!. The block and wo adia ion
shields su ounding i a e placed in o a he me ic ou e case
whe e a high acuum can be p oduced ~1027To !.
The assembly, su ounded by a coiled ube, is placed in
a Dewa illed wi h alcohol. The empe a u e o he alcohol
ba h is con olled by a low o liquid N2 h ough he coil. The
block empe a u e is measu ed wi h a pla inum he mome e
Leads & No h up ~mod. 8164 B!and a Tinsley esis ance
b idge ~mod. Ambassado ! o 60.01 K. The em p oduced
by he luxme e s is measu ed by a Kei hley 181 nano ol -
me e . All o he de ices a e con olled by an HP-75000 da a
acquisi ion sys em and a HP-Vec a compu e .
Deu e a ed KDP single c ys als we e g own by he
Holden slow-cooling me hod.13 Ve y good op ical quali y
c ys als we e ob ained. The deg ee o deu e a ion was es i-
ma ed o be 82% using he ela ion be ween Tcand he deu-
e a ion con en gi en by B ezina.3The di ec ion pe pendicu-
la o ~110! ace was o ien ed h ough he mo phology o he
c ys al and he sample in he o m o a cylinde ~3.02 mm
hick and 10.5 mm in diame e !was p epa ed. The base o
he cylinde coincides wi h ~110! ace which allows applica-
ion o uniaxial p essu e
s
xy o he sample.
The speci ic hea o he sample is measu ed using he
ollowing p ocedu e: we s a om he s eady s a e ob ained
when he same powe W0is dissipa ed in bo h hea e s ~R1
and R2!. Because he e is a high acuum in he calo ime e
~1027To !and he maximum empe a u e di e ence be-
ween sample and block is always less han 0.06 K, we as-
sume he e is no la e al hea loss. Thus, W0c osses h ough
he luxme e p oducing a cons an em V0. A he ini ial
ime he powe is cu o and he em V( ) is in eg a ed up o
he ime 1when he new he mal equilib ium wi h he block
is eached. Le V1be he cons an alue o he inal em .
I has been shown14 ha he he mal capaci y o he
sample is ob ained by
C52
b
~A2A0!A5
E
0
1V~ !2V1
V02V1d ,~1!
whe e
b
is he he mal esis ance o he luxme e s and A0is
he alue o Awhen he expe imen is ca ied ou wi hou a
sample. A0and
b
a e de e mined by calib a ion.
I he measu emen s a e ca ied ou unde quasis a ic
condi ions by changing he empe a u e o he blocks a a
e y low cons an a e ~in hese measu emen s
]
T/
]
50.06
K/h!, he em V1is e y small and p ac ically cons an . The
em is p opo ional o he hea lux, which changes he em-
pe a u e o he sample a he same a e as he empe a u e o
he block ~V15
a
W,
a
de e mined by calib a ion!. When
he e is a dissipa i e e ec in he sample o a i s o de
ansi ion is p oduced, V1changes wi h ime and i s alue is
p opo ional espec i ely o he dissipa i e powe o he hea
powe necessa y o p o oke he en halpy change in he an-
si ion. Thus, he a ia ion o V1allows us o de e mine when
he e is coexis ence o phases.
The measu emen s we e ca ied ou o bo h dec easing
and inc easing empe a u e and a wo alues o applied
uniaxial s ess on ace ~110!: 0.3 ba and 4.560.1 ba . The
a ia ion o he sample empe a u e du ing he measu emen
p ocess was es ima ed o be app oxima ely 0.03 K.
RESULTS AND DISCUSSION
In Fig. 2 he speci ic hea cand he hea powe
W5V1/
a
a e ep esen ed e sus empe a u e TBo he calo-
ime e block when cooling and wi h he uniaxial p essu e o
0.3 ba . The da a collec ed in he ange 207.85–208.00 K
co e he phase ansi ion poin . In his ange cshows a
double maximum as ound in p e ious8,9 measu emen s. We
will a emp o explain his beha io la e .
On he o he hand, since he empe a u e di e ence be-
ween he ends o he luxme e s is DT5
b
W, and assuming
ha he block has a uni o m empe a u e TB, he empe a u e
o he sample bounda y TScan be ob ained. In Fig. 3, TBand
TSa e ep esen ed e sus ime. Fa om T , he di e ence
TS2TBis abou 1023K and is cons an . Du ing he ansi-
ion, TSseems o emain cons an ~207.93 K!like a i s
o de ansi ion wi h bo h phases a equilib ium.
FIG. 1. Diag am o he senso : F1and F2, hea luxme e s; R1and R2,
hea e s; S, sample; B, bellows; D luxme e s and bellows con aine ; H, hea
sink; C, capilla y.
FIG. 2. DKDP speci ic hea ~s!and hea powe ~l! s block empe a u e
du ing cooling.
2585J. Appl. Phys., Vol. 81, No. 6, 15 Ma ch 1997 Galla do
e al.
Thus da a ob ained o block empe a u e in he ange
207.85–208.00 K a e a ec ed by he la en hea . Excluding
hese da a he monophase speci ic hea o DKDP is ep e-
sen ed e sus TSin Fig. 4.
To s udy he beha io o he singula pa o he speci ic
hea i is necessa y o de e mine he la ice con ibu ion ~base
line!. We conside ed h ee exp essions used in he
li e a u e15,16 o de e mine he base line: ~1!c05a1bT,~2!
c05a1bT1dT2, and ~3!c05a1b/T, whe e a,b,da e
cons an s. The bes i o ou da a is he second exp ession
~whe e a520.1714, b55.2631023, and d526.72231026!,
which is ep esen ed by he hin line in Fig. 4. I mus be
poin ed ou ha exp essions ~2!and ~3!p ac ically coincide
abo e 190 K, which is he empe a u e ange we will discuss
below.
Figu e 4 shows a ail shape beha io o 10 K abo e T
simila o ha ob ained by Reese.10 This ail is due o luc-
ua ions o he o de pa ame e . The e oelec ic luc ua ions
abo e T we e obse ed by Blei e al.17 and hey co ela ed
his luc ua ion wi h he acous ic mode componen which is
pola ized along he e oelec ic axis. Fo uniaxial e oelec-
ic c ys als, his singula pa o he speci ic hea has a loga-
i hmic di e gence wi h empe a u e. Figu e 5 p esen s,
Dc/T2 s ln[(T2T )/T ]. Linea beha io is ob ained simi-
la o ha ound in KDP15 and Pb3~PO4!.16
Conside a 2-4-6 Landau Po en ial:18
G~T,Q!5A
2~T2Tc!Q21B
4Q41C
6Q6,~2!
whe e A,B,C, and Tc, a e cons an and Qis he o de
pa ame e . Below T he singula pa o he speci ic hea is
exp essed by:
Dc5A2T
2
A
B224AC~T2Tc!.~3!
In Fig. 6 (T/Dc)2is ep esen ed e sus T2T . The
abo e exp ession is sa is ied in he ange o 4-15 K below
T . The de ia ion om classical beha io nea T is a ib-
u ed o he luc ua ions o he o de pa ame e and loga i h-
mic beha io could be expec ed. Reese and May10 a emp ed
o i he singula pa o he speci ic hea o a powe law
di e gence and o a loga i hmic di e gence. Thei da a seem
o show a be e i o a loga i hmic di e gence al hough
hei esul s we e no comple ely conclusi e. In Fig. 7 i is
shown ha Dclinea ly depends on ln(T2T ) in a empe a-
u e ange om T o 1 K below T . These esul s con i m
he loga i hmic di e gence sugges ed by Reese and May.
Da a ob ained on hea ing a e e y simila o hose ob ained
on cooling; ne e heless he e a e some di e ences we will
discuss below.
FIG. 3. Block empe a u e TB, and sample bounda y empe a u e TS s ime
du ing cooling and hea ing. Hea powe e sus ime du ing cooling.
FIG. 4. DKDP speci ic hea s sample empe a u e du ing cooling ~a!and
du ing hea ing ~b!Thin line is bes i by equa ion o ype c05a1bT1dT2.
FIG. 5. Loga i hmic empe a u e dependence o he singula pa o DKDP
speci ic hea abo e T .
2586 J. Appl. Phys., Vol. 81, No. 6, 15 Ma ch 1997 Galla do
e al.
In Fig. 8, he speci ic hea and hea lux exchanged by
he sample a e ep esen ed e sus block empe a u e. The
ansi ion occu s in a smalle empe a u e ange han when
cooling ~0.08 K!. As we would expec he hea powe has he
opposi e sign as when cooling. Du ing he ansi ion he spe-
ci ic hea da a show nega i e alues. This beha io will be
explained la e .
Bo h TBand TSa e also shown in Fig. 3 on hea ing.
Unlike when cooling, TSis no cons an du ing he ansi ion,
bu dec eases o he cons an alue ob ained on cooling.
These esul s sugges ed we should ca y ou a mo e de ailed
s udy o he sample empe a u e e olu ion du ing he ansi-
ion when hea ing and when cooling. This s udy will be dis-
cussed below.
Excluding da a a ec ed by he ansi ion hea , he spe-
ci ic hea ob ained when hea ing is also ep esen ed e sus T
in Fig. 4. As is common in o he e oelec ic ma e ials he
ansi ion is b oade on hea ing han on cooling and he ail
on he pa aelec ic phase sp eads o e a la ge empe a u e
ange ~;30 K!. Da a ob ained du ing hea ing show simila
beha io o hose shown in Figs. 5, 6, and 7.
To ob ain mo e in o ma ion abou he sample empe a-
u e e olu ion du ing he ansi ion, he em V1~expe imen al
ze o!was measu ed e e y 15 s while cooling o hea ing he
sample a he same cons an a e o 0.06 K/h bu wi hou
dissipa ion in hea e s R1and R2. Figu e 9 shows W5
a
V1
e sus block empe a u e o bo h cooling and hea ing. On
cooling, he ansi ion sp eads o e a empe a u e ange
g ea e han on hea ing as we discussed abo e. We can also
deduce ha he kine ics a e di e en : on cooling, di e en
peaks appea which can be conside ed as consecu i e pa ial
changes o phases o ea angemen o domain s uc u es.
These peaks p ac ically do no appea when hea ing. This
beha io ag ees wi h ha epo ed by Bo na el and Cach.4
They measu ed he dielec ic cons an and simul aneously
obse ed he e oelec ic domain s uc u e o DKDP du ing
he ansi ion. On cooling om he pa aelec ic phase he
domain s uc u e exhibi s ea angemen o he domain com-
plexes and modi ica ion o he domain wid h wi h dec easing
empe a u e. On he con a y, du ing hea ing he domain
s uc u e, which has been s abilized a low empe a u es,
does no change i s con igu a ion.
Figu e 10 shows he e olu ion o he sample bounda y
empe a u e when cooling ~a!and when hea ing ~b!.Aswas
sugges ed abo e, when cooling TSseems o s ay cons an
FIG. 6. Tempe a u e dependence o he singula pa o DKDP speci ic hea
below T acco ding o Landau heo y.
FIG. 7. De ia ion om classical beha io : loga i hmic empe a u e depen-
dence o singula pa o DKDP speci ic hea e y close o T .
FIG. 8. DKDP speci ic hea ~s!and hea powe ~l! s block empe a u e
du ing hea ing.
2587J. Appl. Phys., Vol. 81, No. 6, 15 Ma ch 1997 Galla do
e al.
du ing he ansi ion. F om his da a, oge he wi h he be-
ha io shown in Fig. 9 we can deduce ha his ansi ion
~cooling!is p oduced wi h equilib ium be ween pa a and
e oelec ic phases.
On he con a y, as shown in Fig. 3, when hea ing a
dec ease o he empe a u e in he su oundings o he
sample is p oduced. We mus poin ou ha he minimum
alue o TSin he ansi ion egion ~207.96 K!p ac ically
coincides wi h he cons an empe a u e o he ansi ion
~207.93 K!when cooling. These da a sugges ha he sample
passes h ough me as able s a es and a a empe a u e highe
ha he ansi ion empe a u e, a sudden phase ansi ion oc-
cu s. Thus, he la en hea p oduces a empe a u e dec ease a
he sample bounda y which is de ec ed by he luxme e s.
F om he abo e we can deduce a e y small he mal hys e -
esis which ag ees wi h he beha io ob ained by Bo na el
and Cach.4
On he o he hand, in eg a ion o he hea powe ep e-
sen ed in Fig. 9 allows us o calcula e he la en hea o his
DKDP c ys al. The es ima ed alues a e 2.32 J/g and 2.20 J/g
o cooling and hea ing, espec i ely. These alues a e lowe
han he alue o 2.99 J/g ob ained by Reese.10 The di e -
ence can be a ibu ed o he ac ha he sample s udied in
his a icle has a lowe deg ee o deu e a ion han he sample
s udied by Reese whose ansi ion empe a u e is highe han
ou s ~220 and 208 K, espec i ely!. I we assume a linea
ela ion be ween la en hea and deu e a ion deg ee, he
abo e di e ence allows us o es ima e ha ou sample is
77% deu e a ed; his alue ag ees well wi h ha ob ained
~82%! om he B ezina ela ion be ween ansi ion empe a-
u e and deg ee o deu e a ion.
All o hese measu emen s we e also ca ied ou wi h an
applied cons an s ess o
s
54.560.1 ba on ace ~110!.We
ob ained he same beha io desc ibed abo e ~
s
50.3 ba !,
e en he same ansi ion empe a u e. A 1% displacemen o
da a was ound, bu his di e ence is simila o he e o
a ibu ed o his ype o measu emen . This can be expec ed
because S asyuk e al.19 p edic ha only uniaxial p essu e
se e al o de s o magni ude highe han applied du ing hese
measu emen s can ha e a signi ican in luence on he speci ic
hea o DKDP.
We mus poin ou ha uniaxial p essu e simila o ha
applied in his s udy p oduces signi ican e ec s on he spe-
ci ic hea o S TiO3 e oelas ic c ys al.20 Ne e heless he
coincidence o da a ob ained unde 0.3 and 4.560.1 ba
uniaxial p essu e can be conside ed as p oo o he ep oduc-
ibili y o ou measu emen s.
Now we will discuss he beha io o he speci ic hea
da a in he ansi ion egion. I has been shown ha when
cooling a double maximum appea s ~ o bo h 0.3 and 4.5
60.1 ba !and when hea ing, nega i e alues we e ob ained
in bo h cases. These could be a ibu ed o he ac ha he
change o he base line V1p oduces g ea e o s in he de-
e mina ion o he in eg al A in Eq. ~1!, hus p oducing non-
sense da a. Ne e heless, we mus poin ou ha he a ia ion
o V1wi h ime is aken in o accoun in Eq. ~1!and he
me hod wo ks p ope ly when V1linea ly changes wi h ime.
The ime dependence o V1does no jus i y such big anoma-
lies in he speci ic hea da a. Thus, we hink he e mus be
ano he explana ion o he abo e anomalous beha io o he
da a.
In a p e ious pape , he speci ic hea o a iglycine sul-
pha e doped wi h L-alanine ~LATGS! e oelec ic c ys al
was measu ed unde an al e na ing elec ic ield.21 Because
o he dec ease o bias and coe ci e ields nea he ansi ion
empe a u e T , he sample ca ies ou comple e o mino
hys e esis loops. Thus, in a empe a u e ange nea T , which
depends on he ampli ude and equency o he applied ield,
he sample dissipa es a hea powe which depends on he
empe a u e. In ha s udy o an ampli ude o 95 V/cm and a
equency o 1 KHz he empe a u e ange whe e powe was
dissipa ed was 10 K. This powe Wwas measu ed simul a-
neously wi h he ‘‘speci ic hea ’’ o a s eady s a e ~c*!. This
FIG. 9. Hea lux s block empe a u e ~a!when cooling and ~b!when
hea ing.
FIG. 10. Block empe a u e TB~ hin line!and bounda y sample empe a u e
TS~poin s! s ime when cooling and when hea ing.
2588 J. Appl. Phys., Vol. 81, No. 6, 15 Ma ch 1997 Galla do
e al.

‘‘s eady s a e speci ic hea ’’ c*is he ela ion be ween he
hea exchanged by he sample be ween wo s eady s a es and
he co esponding a ia ion o he empe a u e a he sample
su ace. The hea exchanged by he sample as a consequence
o he s eady dissipa ion powe is no aken in o accoun . c*
shows he ollowing beha io : a dec ease in he ange whe e
]
W/
]
Tis nega i e and a la ge inc ease in he egion whe e
]
W/
]
Tis posi i e.
To explain his e ec he di e en ial hea conduc ion
equa ion o a solid wi h uni o m hea powe p oduc ion de-
penden on he empe a u e, was s udied. I was shown ha
he speci ic hea , c*, o his dissipa i e medium is he equi-
lib ium speci ic hea , c,~wi hou dissipa ion!plus a e m
p opo ional o he de i a i e o he dissipa i e powe wi h
espec o he empe a u e. This s a emen was co obo a ed
by expe imen al da a.
In o he wo ds, in a dissipa i e medium he e is an in-
e nal empe a u e dis ibu ion which depends on he dissipa-
ion powe W. Du ing he measu emen p ocess o he spe-
ci ic hea , he empe a u e o he sample changes.22 I W
depends on he empe a u e, he in e nal empe a u e dis i-
bu ion also changes. This change implies a supplemen a y
e m which mus be added o he equilib ium speci ic hea . I
was shown22 ha his supplemen a y e m is p opo ional o
]
W/
]
T.
A quali a i e compa ison be ween he beha io o
DKDP and LATGS unde dissipa i e condi ions can be pe -
o med i we assume, in he i s app oxima ion, ha on qua-
sis a ic cooling o hea ing he la en hea e ec can be con-
side ed as an in e nal powe sou ce o powe sink,
espec i ely.
Al hough we do no ha e enough speci ic hea da a
~Figs. 2 and 8!, when cooling i seems ha he minimum
be ween he wo peaks appea s a a empe a u e whe e he
slope o Wis nega i e ~nega i e con ibu ion o he a ia ion
o he in e nal empe a u e dis ibu ion!while he second big
maximum co esponds o he empe a u e whe e his slope is
posi i e ~posi i e con ibu ion!.
On hea ing we ob ained simila beha io : a la ge de-
c ease in he egion whe e
]
W/
]
Tis nega i e, and an in-
c ease when
]
W/
]
Tis posi i e. When hea ing, he phase
ansi ion occu s h ough me as able s a es wi hou equilib-
ium be ween phases. Thus we mus expec a sudden change
o en halpy a hese empe a u es ~a sha p hea powe sink!.
Consequen ly, he nega i e con ibu ion is so la ge ha spe-
ci ic hea da a each nega i e alue.
Acco ding o he abo e, we can explain he anomalous
speci ic hea da a, ob ained du ing he ansi ion, in e ms o
he change o empe a u e dis ibu ion inside he c ys al p o-
duced by he la en hea .
We mus conclude ha when measu ing speci ic hea
nea a i s o de ansi ion i is necessa y o ake in o accoun
he in luence o he la en hea on he measu emen p ocess.
I is con enien o measu e, simul aneously wi h he speci ic
hea , o he quan i ies which indica e clea ly when he ansi-
ion is p oduced. Thus, he echnique o conduc ion calo im-
e y seems o be app op ia e o his kind o s udy since i is
capable o simul aneously measu ing he speci ic hea and
he hea lux exchanged by he sample. This in o ma ion al-
lows us o exclude da a a ec ed by he ansi ion hea .
ACKNOWLEDGMENT
This wo k was suppo ed by p ojec PB91-601 o he
DGICYT o Spain.
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