Sorne requirernents for a theory to explain probable roorn

REVISTA MEXICANA DE FíSICA 45 SUPLEMENTO
JUNIO 1999
1. 118-121
Sorne requirernents for a theory to explain probable roorn-ternperature
superconductivity and unusual rnagnetic properties of narrow channels in
oxidised atactic polypropylene
D.M. Eagles*
Instituto de Investigaciones en Materiales, U"h'ersidad Nacional Autónoma de México
Apartado postal 70-360, 045/0 México, D.F., Mexico
e-mail: [email protected]
Recibido el27 de febrero de 1998; aceptado cl2 de abril de 1998
Mea:-;urements of electrieal conductivity. Ihermal conduetivity nnd magnelic propertics of narrow channels through oxidiscd films of atnclic
polypropylcnc rcported in Ihe lnsl ten yenrs are rcvicwcd. and rensons nre given why il is thought thal c1nims of room-temperature supercondllctivity in su eh channcls in Ihis material are valid. Five requirements for ~mythcory which can explain allthe experimental results are
listed. and a diseussion is given of how one candidate theory may satisfy these requirements.
Kl'YlI'ord.\': Room-temperature
superconductivity;
diamagnetism: met<lmagnelism; ataclic polypropylene
Se revisan lns mediciones de conductivitidad eléclrica, conduclividad térmica y de las propiedades magnéticas de cnnales nngostos n través
de peliclllns oxidadas de polipropileno ntáctico. reportados en los últimos diez años. y :-;edan argumentos de porqué In afirmnción de que
dichns canales presentan supercondllctividad n temperatura ambiente es válida. Se lisIan cinco requisitos para cualquier leorín que quiera
explicar todos los resullados experimentnles y se dn una discusión de una tcoría que puede satisfacer eslos requisitos.
Descriptores: Superconductividad
rAes:
a temperatura ambiente; diamagnctislllo: mctalllagnctismo:
polipropilcno atáctico
73.6I.Ph; 74.25.H,,; 74.70.Kn
1. Summary of experimental results
(h) A prohahle
1.1. Electrical measurements and thermal conductivity
Thcrc have heen c1aims in lhe litcraturc of room-tcmpcralurc
supcn:onductivily
in narrow channels through films ol" oxi.
llpper limil 01' channel
from atlcmpts lo see conduction
rOl"closely spaccd conlacls [4].
(e) A separation
of conducting
film 01' 0.3 ¡"TI thickncss
diumelers
01' 2 ¡"TI
in Ihc planes
af films
channels
of7-8¡lnl
in one
[2].
discd atactic polypropylcnc sincc 1988 [1]. anJ three papcrs
rcaffirming this claim appcarcd in 1989, lwo fmm lhe Instilute nI' Synlhclic Polymcric Materials in Moscow {2, 3] amI
olle from Ihe folTe Institute in what was lhen Lcningrad [4].
Thc l1Ims werc usually oxidiscd hy hcating in air al
IDOoe l'ollowed hy irradialion wilh ulLraviolel light, hui some
rcsults
on lilms oxidised
hy lcaving
for several
pcrformcd
with In prcssure
contacts
and a
eu
hase
c¡cetroJe. \Vhen lhe In conlacls wcrc pUl in various positions
jt was founu that thcrc were insulating,
poorly conducting,
and relatively highly conducting
points. The llrst indication
of possible supcrconductivity
was that the resistan ce 01' Ihe
poinls wilh goou conJuclívíty
JiJ not depend on the film
Ihickness, rOl"films 01' tlp to 100 ¡1tn thickness, ami was approximately equal to Ihat of lhe contact directty in louch with
Ihe hase electrode [1-3J.
Some other interesting results of electrical mcasurcmenls
reponed in the 1989 papers were:
(a) Changcs
perature
pies [3).
(c) A slow dccline in the nUlllber oI" condllc.:ting channels
over a pcrinl\ of so me days when magnclic liclds of
aholll (J. I T \Vere applied parallel lo film surfuces [2].
ycars in air
al room tcmpcraturc wcre also disclIsscd [1,3]. Work was
lllostly
(d) An incrcase nI' conductivity
by a factor aF abaut 250
rOl" quite small applied pressures
(:::::::
70 g.cm-2)
{4J.
of R by nine ordcrs of magnilude by tcmcycling ncm room temperature
in same sam-
(1) Experimcnts
wilh 0.5 A currents
wilh In contacts
and
2-3 A \vilh eu contacls whcre Ihe contacts mcltcd pcrIllitlcd dcdllctions that Ihe high-condllctivity
state persisled up lo ahove 429 K (lhe mclting point nf In) and
also, fmm the cxperilllcnt with Cu contacts. that Ihcre
was no heat evollllion in lhe polymer for current densities j > 3 x lO(; Acm-2 [3].
The strongest indications Ihal channcls Ihrough lilms of
oxidiscd alaclic polypropylene
are supercandllcting
al room
lemperalure came frolll Ihree propcrties reponed in 1990 and
1991 [5-71. These are:
l. Thcir electrícal conductivily
at room tempcraturc
is at
least two and prohahly more Ihan lIve orders of magnitude grealcr Ihan that ofCu [5, G].
SOME REQUIREMENTS
2. The highly eondueting
state is deslroyed
in pulsed
Illcasurements
aboye a critica! current, ami this clcs!ruelion
is nol by lhermal
effeel'
[6].
clcctronic contribution to lhe therin lhe channcls, implying a violation
nI' lhe Wict.lcmann~Franz
law by scvcrnl ordcrs 01' magnilude [7J.
3. Thcrc is a ncgligiblc
mal conduclivily
A lowcr I¡mil on Ihe channel electrical conductivity
a al
room lcmpcraturc
is obtaincd in two ways, dircctly from a
four.prohc mcasurcmcnt
by lhe Joffe lnstitulc group [5j and
indircctly from lhe lack ofthcrmal decomposition
in rcpcJtcd
pulscd-currcnt
IllCaSUrClllcnts
by lhe Moscow group [6], in
comhination with mC<lsurcmcnls uf low thermal conduclivity of channcJs [7]. Thc indircct mcthod givcs conductivitics
over five ordcrs of magnitlldc grcaler than that of eu, whilc
Ihe direct melhod givcs a lower limit for a 01' lllore than two
orders nI" magnitllde grcater than that of eu ir channcl diamelers are assumcu to have Iheir eSlimated upper Iimit of
2//111 14, G], 01' 01' nearly flve orders af magniluJe greatcr Ihan
that af eu ir an eSlimatc 01' Ihe channcl diamcter of O.l/lm is
maJe by identiflying the contact rcsislancc with a spreading
resis(ance associaleo with lhe cantacl metal [5}. The violation
of the Wicdemann-Franz
law indicales that the channcls are
superconliucling,
ralher than having ultra-high normal conductivity.
Two other prnpcrties
4. The crilical
conducting
700 K.
5. The crilical
of the channcls
lemperature
currenl
estimalcd
ror destruction
or sllpcrconducling
stale
uensilY jc ,....,5
119
FOR A THEORY TO EXPLAIN PROBABLE ROOM-TEMPERATURE.
X
crileria
occurrcd
ovcr a fcw hundred
hours viewing
time for
ficlds in lhe range 01' 80 to 400 Oc, bUI nonc for zera fteld
or for f1clds grealer than 800 Oc. AH five evenls gave torces
pushing Ihe samples 10wanJs lower fields, corresponding
lo
diamagnetisl1l.
1I is prohahle
(ha! holh properties
2 ami 3 are associated
wilh whal happcns when conducting channels join up at their
ends lo I'orm closed loops. This was ftrst suggested by lhe
Moseo\V group for properly 3 in 1993 [IOJ.
2. Why conducting channels exist
Grigorov el al. [11, 12] argue Ihat conducling channnels are
likely lo exist in any elaslol11er (material with very low elastic
constanls) which contains a surtkient concenlration
01' rotatable electrical dipolar groups. In an elaSlomer an extra chargc
can orient allllipoles
wilhin sOllle radius Ro given by
=
Ro
(cD /rrvC,oc)'.
,
( I)
Herc D and vare
the dipole moment and volume 01' the
group, G is the shear l110dulllS ol" the material, and fCX) is lhe
high-frcquency
dielectric constan!. Assuming D ;::::::
3 Dehye,
v ;::::::
0.1 nm\ ('00
2.2, ano Ihal G lies in Ihe range 4100 MPa, \Ve lind Ro
(3"= 2) nlll.
=
=
In such an elastomer
timate:
material
(:1) It is energetically
favourable
Grigorov
el
al. lll,
12] es-
in [61 are:
01' lhe highly
satisfies
Te >
109 Acm-:.!,
(h) Ir the stalic dielectric
1.2. l\Iagnetic properties
for some atoms (o ionise,
wilh ions ami eleclrons hoth surrounded
aligned dipoles, provided that there are
dipoles in any rcgion of radius Ro. An
its surrounding rcgion of aligned Jipoles
type nI" polaron,
constanl
by regions of
three or mOfe
cleclron plus
is an unuslIal
is more lhan a few limes
it is energetically
favourahle for polarons lo join
up in pairs, and then in long slrings called "supcrpolarons'., Currenl carriers can move up anu down lhe
slrings rairly freely.
f(X),
\Ve now come lo magnclic properlies. There are threc anomalous magnelic properties thal nced explaining:
1, \Vhm is callcu
"anomalous
ferromugnelism"
by the
Moscow group, hut which should perhaps he calleó
mctamagnelism,
with a Iransilion field in the range 01'
0.1 lo 0.2 T, scen in \VeJl oxidised films [8].
2. Large diamagnelism
al low applied fields in aboul
10% 01' films stlldied [3]. The diamagnelic
susceplibilily at 10\V fields
(l/lI)
JI
is approximately
proportional
The estimaled diamelcr 01"Ihe superpolaron
strings is of
the order 01' a nanoJ11clcr, hut diame(ers (JI' conducting channeis have been infcrred fmm experil11ents [4-6] lo be in the
range 0.1 lo 2 Illll, ami so il has to he poslulatcd
Ihal the
strings or fIIamcnts combine
con<!ucting channels.
in quite large numbers
lo form
lo
19J
3. Occasional
spontaneous
forces tending to push smllpies towards lower lields in inhomogeneous
magnetic
liclds [10).
3. Sorne reqllirements for a theory to explail1
hoth sllperconductivity and magnetic properties of channels
lo
Study nf lhe thirJ property
rcquircs
a criterion
ror
whether a sponlaneous
rorce is signifkant cnollgh lo he worlh
counling, Three crilcria were c/losen, ha sed on strength, duration amI rale nI" grO\vth, Five cvenls salisfying the required
Assllllling a pairing thcory, we neeu large pair binding
encrgics, al Icasl 0.1 eV ror ronm-Icmperaturc
supercont!uctivi(y, or at least 0.2 cV ror sllperconductivity
al
700 K, supposing (hat pair hinuing energies nccd to be
al leasl about 4/cll T('.
Re\', Me.\". F{s. 45 SI (1999) 11R-121
tu..!. EACiLES
I2n
2. \\'e /leed cilhcr small pair cffcctive masscs, at Icast in
lhe dircction along Ihe channcls, or un un usual pair
di.\pcrsillll rclation [131. Olhcrwisc {he Bosc-Einstl'in
(ollticnsatioll tcmpcraturc Tu uf bosons will ¡¡mil 1~
10 rairly small \'alucs.
\Ve llave maJe cakulations 01' TlJ for non.jntcracling
hosons ror lhe case 01'quadratic dispcrsion relatians chafactcriscd hy dilTcrcnll1lasscs .\[/, and i\lT parallel and perpendicular 10 liIamenl tlircclions in <.In array 01' flIarncnts ll..J 1.11
lhe tralls\'crsc cUI-off cncrgy 1FT associated wilh lhe millillllllll tilamcnt separatíon is smallcr than kHTn. we lInd
fmm l1ulllcrica\ rcsults rOl"thrcc cases with diffcring ratios
(kIlT/I/I\"'rJ
thal, for a suflicicnlly largc numbcr 01' lila.
IllClltS.
(2)
whcrc (' is lhc linear ('arrier conccntration in a filament, anu
separalion. If, e.g., e ~ 107 cm-I and
1/'/ ;:;: '2 1111l,
then. to obtJ.in Tu
700 K we need an average mass 01' aholll 1..11I1¡. Sincc lransversc masses are prohahl)' laid)' large, small longitudinal basan massC's \\'ould he
nccdcd inlhis Iypc of model.
¡Ir is Ihe filament
=
3. In order lo cxplain \ C( (1/ H) in samples "howing
lliamagnctism, which implies magnelic mamenls indcpenden( of 11. we prohahly nced large circulaling suIK'I'l'Urrents lo arise \vhencvcrchanncl
cnds join to fOfln
¡¡ closed loop.
4. \Ve Ill'ed to explain why the direction af such curren(s
is sllch ;1" lo give magnelic momcnts in lhe directioll
('ppo<.,ite lo l!lal of Ihe applied licld, in both susceptihility ami spolllancolls-force
mcasurements.
5. \Ve nccd (o cxplain Illelamagnetic transitions
llClic liclds in Ihe mnge of 0.1 lo 0.2 T.
for mag-
.l, I'ossihlc lhcories
-l.I, Iligh-drift-n~locity molle!
Tlli"nwdl'l \\'as inlrodllced in 1994 [15.16], anu is hased on
:tn old idea nI Parlllcnlcr 11 jll~at enhancements 01'electron~
clcclron allfaL'lions can occur at drift vclocilies close lo Ihe
\"l'loL'Íly \lf "iollnd 01' 10 a phase velocity of whatevcr excita~
tion is Illedialing the anraclion. Consequcnces of the mooel
j"or m;\gllelic propertics are oiscusscd in [18]. A disclIssion of
h(1\\ ll1i" Illodel (!t:;¡ls wilh Ihe lI\'c poinls mcnlionco in Ihe
prC\'illlb "L',,:Iion is gi\'ell hdnw.
l. Pail" hinding encrgies Illay he large hccause 01 (he
cnhanced inlel'at:liOIlS al srecial drin vclocitics melllinlled
,lhove. For Fcrllli ellergies slllall compared wilh the el1crgy 1/:...-' 01"\'ihale\'cr Illcdi:J1t::sthe pairing, this cnhancclTlcnl
hecolllcs inlinite rOl' qllasi onc-dimensional
systellls in lhe
/?('I'.M"x.
¡:[~.-l5SI
simplest pcrturhalioll approach to e1ectron elcclron
attraclions It5. lGl. 11wa" suggestco in [16] Ihat plaslTlons of enL'rg:'
1.S eV migllt llledialC the attraction. For so me dis.
cllssion of whal may l1;¡ppen heyond pcrturhalion theory sec
pnin! 2 helo\\'.
2. EITecti\'c masses nf pairs. in\'crscly proportional 10 the
cur\':Ilure of the energy. E, \>crsus ccnter-of-mass wa\'e vector 1\" for pairs, L'olllJ he small ir E wcre lo go through a sharp
lllininUllll at'some llplilllUJIl 1\'. Preliminar)' calculatians for
hipo1arons in one-dimension using a \'ariational melhod appropriale ror intermediate cOllpli ng strenglhs ano the assumrlion Ihal hare electrol1s have a constant effectivc muss do not
SllPPOr! Ihe idea 01' a second minimum in E al l\ i- O. Ha\\'e\'L'r. after inL'iusinn or a conjeclured approximale methoJ nf
Irealing ellecls uf b:lIld encrgics for hare clcctrons rroportional lo [1 - ("os (J,'(/)]. where a is Ihe lattkc constanl ano
k is :In eleClron wave number, il scems that. 1'01'some coup1ing conslants, the hipolaron encrgy can go down lo a cusp.
like rninimum ror 1\' equal lo its maximum possible value,
I\"ll
= 2;;/11. Thlls Ihere mi.lY he an unusual oispersion rclation. rfllm lhe Illllllcrieal caklllations we have done up 'o
now, il arrears that Iherc will he an aprroximatcly
linear dependencc nI"cllergy on \\':I\"e \"CClOrITIcasured fmm A"ni near
I\'/ll'
hecoming sllhlinear rurther a\\'ay. [1' clcclrie currcnts
fmm pairs with particular wavc \'cclors are proportional 10
dE /d /\'. thell. for a 1inL'ar dispcrsion relation. lherc would he
tWll lypes 01' pairs wilh clJual and orpositc largc vclocities.
althollgh the sl;¡lc at Ihe ClISPwill presumably consist 01' a superposition 01' stales \\'ilh ('qual alllJ opposite \"elocilies. \Villl
no l'xlernal perturhalioll, a condel1satc wilh states at (he cusp
with tcro nel velocity Illay he e.\pccled. However, the ocgcnerae)' 01"Ihe (wo ~lales fmm which Ihe zOl1c-cdge cu"p slalc
is cOlllposcLl will hl' hroKCll hy an c\ternal pcrturhalion sllch
as ,1Il i.lpplied currcnl 1'01'<l quasi onc-dimensional
f¡lament
wilh end COIlIlL'Clioll". or a magnctic lielJ rOl' a li1ament in
Ihl' r01"1llof a closl'd loop. Then. sincc cXL'hange inter:.u.:tions
Illakc a superposition 01"IWOcondensates from nearly degen~
t:rate slates cnergelically unfavourahlc [19], we expcct Ihat a
,Iale willl a high CLlITcntdensily in OJll' 01' Ihe 1\\"0 directions
will be prcfcrred. Evell rol' a linear dispcrsion for a single
quasi-onc dimensional lIlamcnt, \Ve necd lo in\"okc inh::raction hetwcen 1¡lamenls within a channel in order to ohtain a
finitc eondL'llsalion Icmperalure.
3. LlI'gc circulating cUlTenls can occur in <:loscd loops.
since high drift n:locilies ( a fe\\' limes 107 CI11.S-1) were
prcfcrrcd in Ihe original mooel [16]. and, for appropriate
sln:nglhs of e!ccIHlll-\lnson eoupling ano energics 01" the
ho:-,oll" \\'hich induL'e pairing. dri!'t \'clacities can he nf this
OIoer loo in Ihe hipolaron Ihcory wilh a cusp-like minilllulll
in lhe pair encrg:y al lhe tone edgc.
4. ¡\ pos"ihle expbnation as 10 why lhe initial direc(ion 01'
lhe cirnJ!aling currents lllay he such as lo opposc the applil:d
licld is as rollows. To c10sc a loop, 011average lhe material of
the loop has ((l 1110\'L'l110re IOwards Ihan away from the cenlcr, ~lIld(lile GIII lhlls illvo"'c Lcnz's 1aw as applicd 10 moving
wire sq!l1lellls lo ,11()\',' lhal lhc indllced e.m.r. for Ihis l11otion
4
(j\)'N) tlx-t21
SOME I{EQUIREr-.lENTS FUR A THEORY TO EXI'LAIN PROBABLE ROOi\1-TEMPERATURE
is such as to cause
which produces
currents
\\'ith a direction
a licld opposite
01' circulation
to the applied
\\'hichcvcr
explanation
is invoked for the inilial curren!
dircctioll, it is expe<.:led that, in tlue course, (he loop as a
\,,'hole Illal' rotate so Ihat its momenl beco mes parallcl to the
011
a timc scalc which \ViII decreasc
as Ihe applieJ
tic Id
illLTeases. A reversal fmm diamagnctisrn
lo paramagnelisll1
was reponed in [L 101 in a 1600 Oe field 011 a limescale 01'
lhe onler 01' a minute.
5. iV1clamagneLism in the moJel is associated
wilh a tranlo a fcrromagnetic
array 01'
sition from an i.lnliferromagnetic
121
5. Conclusions
licld.
An altcrnative
possihle explanation
more dependent Oll
details of Ihe high-drift-velocitl'
moJel was givcll in [18].
llcld,
..
elelllelltary
long-thin current loops. To explain a transition
liL'ld 01' c.g. 0.12 T, \Ve need ahout 30 fIlall1ents per current
loop [181.
There is experimcntal evidence ror superconductivity
and unusual ll1agnetic properties in narrow channels through films
of oxidised atactic po.lypropylene.
Although
not discussed
here, there is also evidence
that some of the same unusual propcrties
are present
in fIIms 01' polydimeth1'lsilox-
ane [20,211. Only one candidate theory to explain aJl types
ordata has heen puhlished in any detail [15, lG, 181, and this
theory nccds more work ror ils justification
heyond perturhation thcory.
More groups should try to reproduce and extentl the Russian experimental
work. SOIllC suggested worthwhilc experiments are listed in [18].
Acknowledgcmcnts
4.2. l\lodcl with l'x(.'han~e-inclllced triplet pairing
I shollld Iike to Ihank L.N. Grigorov
There is very liule puhlishcJ on this moJel 1'et, which \Vas
mClltiollcd in [12J, and so it is difficult (o asscss ils plausihilily al prcscnt.
dence ami discllssions, D. Likhatchev ror a verhal translation
01' a long Russian papel', I.G. Kaplan rol' sOllle commcnts on
a draft 01' Lhe manuscript, M. de Llano rol' a preprint. ami O.
Navarro rOl' a Spanish version 01' the title and ahslrac!.
Addrc:-,s fwm Arri 1 199X: 56, Portland
don N 15 ..J.SX. England.
1. L.i'\. llrigorov
LOJl-
lO.
L.N. Grigorov.
"nu TCl'hnological
Infol'ma-
anu L.N. Gríg(lf()v.
Vyosoko-
I'i."",,,
3. N.S. EnikoloPY"Il. LN. Grigorov. "Ild S.G. Smiroov".
Zh. I:'kSJ1. TcOl: Fi~. 49 (19R9) 3261JETP
Len 49 (1989) J71].
ct a/., DoU. Akad, Nauk. 5S5R J09
fi03 [SOl'. Phys. DoUad)' 3-1 (1989) 101fi].
11.
D.N. Rognchcv,
J5 (1993)
S()ct/ill. IJ
f)cflo.\'Í/ed Aniell' No. 238/
and S.G. Smirnova,
(AlI-Union
InstilUlc rol' Scicnlific
(ion, 2J .\Ian:h 19HX), V X8,
2. S.G. Smirnovn,
E.1. Shklyarovn,
//lo/. Soctli/l. 1/ .\ 1 (19X9) fi6?
Rond, To((cnharn,
L.N. Grigorov,
1921
for extensive
anu A.Y. Kracv,
r PO/)'I1Il'r
Makm/llof.
5cicllCl'
corrcspon-
Vy.wkol1lol.
.'5 (1993) 1625 J.
ChCIIl., Macl'OlIIol. 5."1/1/', 37 (1990)
159: L.N. Grigorov, Pis '/l/a 7h. Tdh. Fiz. 17(5) (1991) 45. (501'.
T,,('h. /'ltr.\'. 1.('((. 17 (1991) 36S).
12.
L.N. Grigoro\'. Y.t\-1. Anurccv, anu S.G. Smirnovn.
C1I(,1II.,Macromo!. .\~\'/Jlp..n (1990) 177.
Makmlllol.
13. M. Casas ('/ a/., COl/{/. ¡\fall. T//('oril's IJ 13 (\ 998J
1..J..D.i\-l Eaglcs./'1IY.l'ica
C. JOI (1998) 165.
,1. Vi\1. Arkhangorouskil
( 1()X9)
IS. D.M. Eagks. in: Pmc. COI,f Ph\'s.
SIIP('I'[,Olldlll.tOJ'S,
;.1.
\'.1\-1. Arl\hangorodskil.
A.N, lonov,
Y.M, Tuchkcvich,
Shlimal\, Pi.\ '1/1(/ Zh. J::ksl'. Teor. Fiz. 51 (1990)
SI (I'NO) 671.
n.
(l. \'. Dcrnichcva
228 [J/JI'
j.
('( a/., Pis
S.G. Smirnova,
Z/¡.
211. Eksp.
Ll'1/.
and S.G. Smirnova,
399 [5I1percOIu/lfctil'll\',
5\'(,I'k1l-
O.V [)cmichcva,
anu L.N. Grigorov,
l'i,\"lI/a
(1988) 212 [JETI' Lel/. 48 (t 988) 2311.
O. L.N. Grigmov, ami D.N. Rogachcv,
230 (1993) fi2S.
Alv/n.
Cr)'st. Liql/id Cryst.
e 225
(1994)
Phys. Rn:
Parmcnlcr.
116
222; 280 (1997)
(1959) D90;
0.,\1. E:lglcs . .I. 511/)crcO/u/. 11 (1998)
19. P. [\;o/icrcs.
/'/¡ys.
n,l'. TcOl: n,. 48
R.I!.
AJo/cclI/armu/Oxide
335.
140 (1'-)65)
1\ 1952.
TC01: Fiz. 51 (1990)
18.
O.Y. Demichcva,
4 (1991)
345J.
1G. D.M. Eaglcs. PltysiC(I
17.
C//('III.
7 (1994) 679.
S/ljwrcolUl.
ami I.S.
56 [J/:TP
Lell. SI (1990) 2581.
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.s.
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C;lmbridgc.
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A 38 (1996) 1321 J.
el a/., Vysoko/l1o/. 50('di/l. A .'8 (1996)
SciCIICl' A 38 (1996)
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