The Eet of Grain-Domain-Size on
Levitation Fore of Melt Growth Proessing
YBCO Bulk Superondutors
W. M. Yang 1;3
, L.Zhou 2
, Y. Feng 2
,P.X. Zhang 2
,C.P. Zhang 2
,
Z.M.Yu 2
,X.D.Tang 2
1:
Departmentofphysis,ShaanxiNormalUniversity, Xi'an,Shaanxi, 710062,China
2
NorthwestInstituteforNonferrousMetalResearh,
P.O.Box51,Xi'an,Shaanxi,710016, China
3
LASUP-Laboratorio deAplia~oesdeSuperondutores,
Depto. de Eletrotenia, Esolade Engenharia,UFRJIlhadoFund~ao,
Cx.P. 68515,21945-970, Riode Janeiro, RJ,Brasil
Reeivedon28February,2002
Eetsofgrain-domain-size(GDS)onlevitationforehavebeendiretlyinvestigatedandidentied
inwell-texturedYBCObulks. A single-grain-domain YBCObulk(=30mm)was preparedbya
topseededmeltgrowthproess,thendividedintotwo,threeandfourgrain-domaintoaquirethe
levitationforesofsampleswithdierentGDS.Itisfoundthatthelevitationforeofthesamples
monotonouslydereaseswiththedereasingoftheaverageGDS(orwiththeinreasingofthetotal
lengthgrain-boundariesofthesample). Themaximumlevitationforeforthesingle-grain-domain
sampleisabout1.68,2.05and2.4timeshigherthanthatofthesampleswithtwo,three,andfour
grain-domains. It is onluded that the levitation fore of a single-grain-domain YBCO bulk is
higherthan that of samples with multi-grain-domains. It is also found that the levitation fore
isproportionaltotheaveragegrain-domainradius,butinverseproportionaltothetotal lengthof
grain-boundariesofthesample, asimplephysial modelhasbeenprovidedandwellinterpretthe
experimentresults.
I Introdution
High levitation foreof single-domainYBCO bulk
su-perondutorshasmadeitpossibleforvarious
applia-tions, suh as non-ontated superonduting bearing
[1,2℄, ywheel[3-8℄,magneti levitationtransport
sys-tems [9,10℄and motors [11,12℄. It isbelieved that the
energylossof superonduting magnetiywheelisas
little as 0.1% per hour, only one tenth of that with
onventional bearings. The ommerialization of this
tehnique will not only redue the energy losses, but
alsomaketheeletriityonsumptionmoreeonomial
andreasonabletomeetourdemands.
Thelevitationforebetweenasuperondutorand
amagnetisloselyrelatedwiththeritialurrent
den-sityJandtheradiusRoftheinduedshieldingurrent
loops(ISCL)inasuperondutor. HigherJandlarger
Rareveryimportanttoahievehigherlevitationfore
[13℄. Nowsingle-domain YBCO bulksuperondutors
anbe fabriated in manylabs [14-21℄,soarelatively
larger R of ISCLan beahievedwhile a magnet
ap-isgenerallyaboutseveralentimetersindiameters,and
limitedto10mforhighqualityYBCObulkuptonow,
beauseof thegrains miss-orientation duringthe melt
growthproess.
The levitation fore is also related with many
pa-rameters, suh as thikness of the sample [22℄,
grain-orientation[15,26-28℄,temperature,magnetield
dis-tributions [23-25℄, and the gap between
superondu-tor/magnet[29℄et. Reently,aneletromaglev
exper-imentperformedonasingle-domainYBCObulk(=
30mm)andamultiple bulkomprisedsmallerdisks(
=10mm) [30℄. It is found that the levitation fore of
asinglelargerYBCOdisksissuperiortoassembliesof
smallerdisks,theexperimentsweredonewithdierent
samplesand espeially the geometri shape of the
as-sembledsmallerdissouldnotwellmaththevolume
shapeof the=30mmsingle-domain YBCO sample.
Butthe physial mehanismsgoverningthe levitation
fore assoiated with the grain-domain-size (GDS) or
ISCL are not learly. We annot see any report
wasdiretlydonebyusingasingle-grain-domainYBCO
bulksuperondutors.Identiationoftherelationship
between the levitation fore and GDS of YBCO bulk
isnotonlyinterested tofundamental studies,but also
veryimportantforpratial.
In this paper, a single-domain YBCO bulk
(=0mm) wasfabriatedanddividedinto two,three,
andfour grain-domains. Thelevitation fore
measure-ments were done on the YBCO samples with a
sin-gle, two, three, and four grain-domainsto investigate
thephysialmehanismsofGDSonthelevitationfore
ofwell-texturedYBCO superondutors,and asimple
physial model has been dedued and well explained
theexperimentaldata.
II Experiments
Samples preparation. X-ray Pure YBa
2 Cu
3 O
y , 4N
purity Y
2 O
3
and PtO
2
powders were weighed and
mixed in the weight ration of 90.5:8.5:1. The
well-mixed powder was uniaxially pressed into
pel-lets of =35mm15mm in a steel mould. The
Nd
1+x Ba
2 x Cu
3 O
y
singlerystalswerepreparedinair
[32℄ and used asseeds in this study. Thepellets with
seedwereputintoafurnaewithatemperature
gradi-ent1-4 o
C/min vertialdiretion. The sampleswere
heated up to 1040-1060 o
C at a rate of 120 o
C/h, and
heldfor2-6hoursforhomogenousmelting. Afterthat,
the samples were ooled to about 1020 o
C at a rate
of 10-30 o
C/h, and further ooled to 940-960 o
C at a
rateofabout1 o
C/h,thenthesampleswere ooledto
room temperature at a rate of 120 o
C/h. Finally the
as-grown samples were annealed at 400-550 o
C for a
week inowingO
2 .
Thetypialphotograph of a single-domain YBCO
bulk (=30mm) is shown in Fig. 1. The
grain-orientation of the sample was investigated by XRD,
optial, SEMand -sanexaminations. All results
in-diate that theYBCO sampleis asingle-domainwith
-axisnormaltoitstopsurfae(resultsnotshownhere).
The sample was rstlydivided into two grain-domain
after levitation fore measurement, and then divided
into three and four grain-domains by a line-saw, so
that we an make four well-textured YBCO samples,
eahof them hasthe samesize (=30mm)and
grain-orientations,butonlywithdierentGDS.Thesamples
with a single, two, three and four grain-domains are
named asa, b, and d respetively, as shematially
shown in Fig. 2. Thevolume and shapeof four
sam-ples are onsidered as the same beause the diameter
1cm
Figure1.Optialphotographofsingle-domainYBCObulk
superondutor.
b
a
c
d
Figure2. ShematidiagramoftheongurationofYBCO
bulksampleswithdierentgrain-domains. a)
Single-grain-domain; b) two grain-domain; ) Three grain-domain; d)
Fourgrain-domain.
Thelevitationforesweremeasuredinahomemade
devie[24,25℄.Amagnetof30mmindiameterwasused
forallthelevitationforemeasurements. Themagneti
eldisabout0.5Tattheenterofthetopsurfae. At
the beginning of eah measurement, the sample was
symmetriallyxedontheaxiallineofthemagnetand
kept50-60mmbelowthemagnet. Afterthesamplewas
ompletelyooledtoliquidnitrogentemperature(zero
eld ooling),then the magnetwasmoved towardsto
andawayfromthesamplebyaontrolledmotor. Thus
the levitation fore as a funtion of distane between
themagnetandthesampleanbeobtained. The
max-imumlevitationforewasmeasuredatagapof0.1mm
III Results and disussion
Thelevitationfore valuesweremeasuredinzeroeld
ooledstateat77Kforthesamplesa,b,andd,shown
in Fig.3. As weansee fromthis gure,thelevitation
foresaremuhdierentforthesampleswithdierent
GDS.Themaximumlevitationforeis67.5Nobtained
inthesingle-grain-domainsamplea,andtheminimum
oneis28.15Nobtainedinthesampledwithfour
grain-domains. Theurveoflevitationforesisshiftingtothe
leftsideandtheslopoftheurvesisgradually
dereas-ing withthe inreasingofgrain-domainnumbersfrom
onetofourorrespondingtotheurvesa,b,anddin
Fig.3. These mean that the levitationfore dereases
withtheinreasinggrain-domainnumbers(orwiththe
dereasingofgrain size),whiletheshape,size and
vol-ume oftheYBCO bulksarethesame.
-1
0
1
2
3
4
5
6
7
0
20
40
60
80
Magnet:
φφφφ
30mm, B=0.5T
YBCO Sample Shape:
a
b
c
d
L
e
v
itati
o
n
f
o
rc
e
(N
)
Distance (cm)
Figure3.Thelevitationforesversesdistaneat77Kforthe
meltgrownYBCObulksamplewithdierentgrain-domain
size.
In order to make learly the relationship between
the levitation fore and the GDS, the maximum
lev-itation fores of the four samples were olleted and
drawnasafuntionoftheorrespondingaverage
grain-domain radius R, as shown in Fig. 4. As we ansee
fromFig. 4,thelevitationforemonotonouslyinreases
from28.15Nto67.5NwhiletheRinreasesfrom0.75m
to 1.5m, theinreasingfatorisaround2.4. The
ex-perimental showed that the levitation fore is nearly
proportional to the average radius of grain size, this
resultsisinagreementwithreferene[13℄. Butthe
lev-itationforewillnotgotozerowhileRisextrapolated
0.6
0.8
1.0
1.2
1.4
1.6
0
10
20
30
40
50
60
70
L
e
v
ita
ti
o
n
fo
rc
e
(N)
Average grain radius R (cm)
Figure4.Maximumlevitationforeversustheaveragegrain
radius of samples with dierent grain-domainnumbersat
liquidnitrogentemperature.
10
12
14
16
18
20
22
0
10
20
30
40
50
60
70
Experimental data
Calculated results
L
e
v
ita
ti
o
n
fo
rc
e
(N
)
ρρρρ
total
(cm)
0.4
0.6
0.8
1.0
30
40
50
60
70
Le
v
ita
ti
o
n
fo
rc
e
(N
)
ρρρρ
min
/
ρρρρ
total
Figure 5. The maximum levitation fore versus the total
grain-boundarylengthtotalofsampleswithdierent
grain-domainnumbersatliquidnitrogentemperature.
Thegrainboundaryofthesampleinreases
gradu-allywiththeinreasingofgrain-domainnumbersafter
eahutting,theboundariesformedbyuttingwill
en-tirely stop the indued shielding urrent to ross the
narrowuttinggap,andleadto somenewandsmaller
induedshielding urrentloop(ISCL) (omparedwith
that before eah utting), and nally result in a
re-dutionin levitation fore. The total length of
grain-domain boundaries inreasesfrom sample ato d with
inreasingofthegrain-domainnumbers. Letusassume
total
representthetotallengthofgrain-domain
bound-ariesofYBCOsample,then
total =R
s ,2R
s +4R
s ,
2R
s +6R
s
and 2R s+8R
s
forsamplesa,b, andd
respetively, where R
s
is the radiusof sample a. Fig.
5showsthe maximum levitation fore of the samples
with dierent
total
. As we an see from Fig.5, the
levitationforedereasesquiklywiththeinreasingof
total
. Theuxpinningforeisverystrongforthe
well-textured YBCO samples under 0.5 T at 77 K, so the
layeralongthegrain-domain-boundariesofthesample.
Here the indued urrent an be regarded as only a
onstantsurfaeurrent,sothetotallengthofISCLis
equalto the
total
. Basedonthis,
total
isrelatedwith
thelevitationforeoforrespondingYBCOsamples.
Thelevitationfore Fisproportionaltotheradius
ofISCL [13℄. Howabouttherelationshipbetweenthe
levitationforeand
total
? Consideringasetofsamples
withdierentGDS.LetA denotethetopsurfaearea
of asingle-grain-domainsuperonduting sample, and
thenthesamplewas
n= R
2
r 2
n
(1)
divided into several equivalent smaller grain-domains
(n=1, 2, 3..., represent the numbers of smaller
grain-domains). R and r
n
denote the radius of the
single-domain sampleand the sampleswith n smaller
grain-domain respetively. Then A=nA
n
, where A
n isthe
top surfaeareaof the smallergrain-domains. Sothe
nanbedesribedas:
Thenthetotalgrain-boundarylengthofthesample
withnsmallergrain-domainsanbewrittenas:
total
=n2r
n
(2)
Substitute equation (1) to (2), the average
grain-domainradiusofthesamplewithmultiple
r
n =
min
total
R (3)
grain-domainsanbeformulatedas:
Where
min
is the grain-boundary length (or
perimeter) of the single-grain-domainsample without
any utting.
min
= 2R =
total
, orresponding to
n=1:
AordingtoRef[13℄,thelevitationforeis
propor-tional to the radius r
n
of thegrain-domains, thus the
levitation foreof samplewith n grain-domainanbe
desribedas:
F
n =
min
total F
1
(4)
Where F
1
is the maximum levitation fore of the
single-domain sample orresponding to
total =
min .
This meansthatthelevitation foreis inverse
propor-tionalto
total .
In this experiment,
min
=2R
s ,
total =2R
s +
L;F
1
=67:5N, and R
s
=15mm. L, the lengthof
in-troduedgrainboundariesbyutting,isof0;4R
s ,6R
s
and8R
s
forthesampleswithsingle,two,threeandfour
grain-domainsrespetively. Then, inthis experiments,
thelevitationforeanbeformulatedas:
F
L =
2R
s
2R
s +L
F
1
(5)
Thelevitationfore of thesample withdierentL
in Fig.5. As weansee from Fig.5, the alulated
re-sult is in good agreementwith theexperimental data.
The insert in Fig.5 shows that the experimental data
forms astraight line between the levitation fore and
min =
total
. This onformsthat thelevitation fore is
reallyinverseproportionaltothetotalgrain-boundary
lengthofthesuperondutingsample.
IV Conlusion
A single-grain-domainYBCOsample(=30mm)has
beenpreparedbyatopseededmeltgrowthproessand
separated into two, three and four grain-domains
af-tereahlevitationforemeasurements. Themaximum
levitation fore of the single-domain sample is about
1.68, 2.05 and 2.4 times higher thanthat of the
sam-ples with two, three, and four grain-domains
respe-tively. It is foundthat thelevitation foreof a
single-domain YBCO bulk is muh higher than that of the
same sized samples with smaller gain-domains. The
levitationforeisinverseproportiontothetotallength
ofgrain-boundariesofthesample,and asimple
physi-al model hasbeensuggestedand wellinterpreted the
experimentresults.
This work is supported by the Ministry of
Si-eneand Tehnologyof China(NKBRSF-G19990646),
Projet\973".
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