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John R Hull

L E Delong

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DEPINNING OF FLUX LINES AND AC LOSSES IN MAGNET- .
SUPERCONDUCTOR LEVITATION SYSTEM *
“A. N. Terentiev, John R. Hull,# and L. E. DeLong
Dept. of Physics and Astronomy, University of Kentucky
Lexington, KY 40506 USA
#Energy Technology Division, Argonne National Laboratory
9700 South Cass Avenue, Argonne, IL 60439 USA
i&y=3Ejp&@
J41U1g 2&7~fi Thesubmitted manuscript has been authored by asontrector of the U.S. Government under contract No. W-31-
109-ENG-3S. Accordingly, the U.S. Government retaina a
~ aq’)~
nonexsfusive,royelty-fraakm.sa to pubfish or reproduce the
published form of this contribution,or allow others to do so,
for U.S. Governmentpwposes.
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/wL”/t~/~p_ /~&@ ,
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M2S-HTSC-VI Conf., Houston, TX (Feb. 2000).
*Work partially supported by the U.S. Department of Energy, Energy Efficiency and
Renewable Energy, as part of a program to develop electric power technology, under
Contract W-31-109-Eng-38.
DISCLAIMER
This report was prepared as an account of work sponsored
by an agency of the United States Government. Neither the
United States Government nor any agency thereof, nor any
of their employees, make any warranty, express or implied,
or assumes any legal liability or responsibility for the
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its use would not infringe privately owned rights. Reference
herein to any specific commercial product, process, or
service by trade name, trademark, manufacturer, or
otherwise does not necessarily constitute or imply its
endorsement, recommendation, or favoring by the United
States Government or any agency thereof. The ‘views and
opinions of authors expressed herein do not necessarily
state or reflect those of the United States Government or
any agency thereof.
.
DISCLAIMER
Portions of this document may be illegible
in electronic image products. Images are
produced from the best available original
document.
, —...———— —— --7————- -
2
““collected at room temperature from water-filled controlled-pore glasses (CPG) with radius of 15,
24.and 32A contained in an aluminum sample cell Backgrounds were initially collected from the dry
glass samples. The glass was then immersed into water, allowed to fill, and subsequently weighed.
The samples were approximately cylindrical in shape with an average radius of approximately 3 mm.
Table I gives the amount of absorbed water in each case along with the empty sample mass.
Table I - Samples size and amount of absorbed water.
Pore radhs Empty glass (g) H,O (g) % of absorbed H,O
15A 3.14 0.53 14
“ -“---%lA— —2+8 &62— - 21 —---- -- ----- — _ __________ ___
32A 0.53 0.24 31
The detector efilciencies were normalized to a vanadium scan. Fig. 1 shows the spectrum for a
water d~oplet_o~24 ~ radius and momentum transfers...o~&.+anda_2.35.35~-l. The solid fits to the+.daw_..--..
include an elastic contribution (dashed curve) from the sample cell and glass, and a broadened
contribution from the mobile water in the sample. It was necessary to allow the elastic intensity to
vary as a fitting parameter. It varied in strength from approximately 0.5 of the empty cell signal at
low _Qto -~e .rneasured_n@gs~y at hi~h Q. We attrib~te..the attenuation of this signal to multiple -
scattering and self-shielding effects upon the addition of water to the samples.
-3
.-”
Ei
-1 0 1 2
co(meV)
Figure 1- QENS spectrum for water contained in a
porous glass of 24 ~ radius and momentum
transfers of 0.80 and 2.35 ~-* as indicated. The
heavy solid line is the full fit to the data and
includes a constant background term, an elastic
term (dashed curve) from the sample cell and
glass, and a broadened term (light solid line) from
the mobile water.
I / / / / I
o 1 2 3
(0 (meV)
Figure 2 – QENS spectra of tbe 24A sample. Solid
curves are fits to the data using the model described
in Eqs. 1-4 with the addition of an elastic term used
to describe the scattering from the glass and the
aluminum sample can.
3. QUASI-ELASTIC NEUTRON SCATTERING OF WATER IN CONFINED SPACES:
METHOD OF ANALYSIS
The simplest analytical model to describe the diffusion of the water molecules assumes
decoupled translational and rotational motions [7]. The decoupling is necessary in order to have a
tractable model, suitable for fitting to the data as given below.
. ..=.., . ...— ......... , .. a. ., . ,- ., .,,. .. !..,..,* ..,, . .}.,- ... —— .. ..
. 3
Sm(Q,co) = ECU2>Q2 ‘3T(Q>co)C3R(Q,CLI) (1)
where u is the energy transfer, <uz> the Debye-Wailer factor, T(Q, u) denotes the contribution from
the translational motion of the molecule and R(Q, a) the contribution for the low-frequency rotational
motion. The particles are assumed to diffuse uniformly on a sphere of radius a, with a rotational time
constant G. For a random rotational motion R(Q, et) is given by [8]:
1(1+l)Dr
R(Q,co) = j~(Qa)~(Qa) +~l~fzz + V jf(Q4
(l(l+l)Dr)2 +C02
(2)
..—.— _.. --- _ .— —.——.—— —.-— ..-. —...
where a is taken as the O-H distance in a water molecule (0.98 ~), D~ is the rotational difision
constant and jl are the spherical Bessel functions. The rotational diffusion is characterized by a
Y
relaxation time Zr = ~~ .
r
T(Q,co)=~
r(Q)
~ r2(Q)+co2
(3)
L..—— ...— — .—— ----—..—..--—- --
~Q) is given by the unbounded medium expression for typical jump diffusion as:
DtQ2
r (Q)=
L2
and Dt =—
l+DtQ2ro 6r0
(4)
where G is the average residence time between jumps and Dtis the translational diffusion constant,
4. RESULTS AND DISCUSSION
The experimented results have been analyzed by two procedures. In the first, the translational
Lorentzian was constrained to the behavior dictated by Eq. 4. In addition, it was found neceskiry to
constrain the value of the rotational diffusion constant, Dp Previous work observed very little change
at room temperature in D,for water in porous glass [4]. Consequently, the value of D,was held fixed
at that observed for a bulk water sample at 30.OK.The quality of the resulting fit is illustrated in Fig. 2
(as noted above it was necessary to allow the intensity of the elastic term to vary). The values of the
fitting parameters are recorded in Table II along with the results obtained for bulk water.
The line-width T(Q) was then allowed to vary @dependently at each Q-value, again with r,
fixed at the observed value for bulk water. Fig. 3 shows ~Q) obtained for each sample as a function
of momentum transfer with fixed G. The solid lines were calculated using the fitted values of Dtand
q given in Table II. The excellent agreement illustrates the applicability of the random jump
diffusion model to the translational motion for the confined water.
Table II – Parameters extracted from fits to the QENS spectra using the model described in Eqs. 1-4. The value of
the rotational difiksion constant was held freed at that observed for the bulk water sample. The value of L is
detenn.ined from the fitted parameters using Eq. 4.
Pore radius L (ii) %(10-12see) D,(lo-s cm2/seC) ?(10-12see) <u3m
15A 3.39 &0.18 6.4 & ().4 3.(3* ().3 1.07 (freed) 0.36 &0.1
24A 2.47 * 0.07 4.4 * ().1 2.3 A o.1 1.07 (fixed) 0.17 &0.02
32A 1.60 A 0.05 1.67 A 0.07 2.6 &().1 1.07 (f~ed)’ 0.24 * 0.02
Bulk water 1.53 &0.06 1.6&().l 2.49 &0.07 1.07 A 0.08 0.56 * 0.01
In this paper we have described the diffusion of water molecules in a porous hydrophilic
borosilicate glass in terms of a simple model. The Q dependence of the narrow quasi-elastic line
width can be described by a jump diffusion model, consistent with previous observations of water
.... ... . . . . . ...- ..1.-. . . ——L-., .,. ,, .. .
-—-— –.
4
0 diffusion in porous media. It is clear from Table II that while the residence time for jump diffusion
(n) shows a slowing down with decreming pore radius the values upon confinement, the values of D,
are very similar to that of bulk water. The most significant result of this study is illustrated in Fig. 4.
The mean residence time shows a marked dependence on the pore radius, what is consistent with
previous measurements of water in porous media. It is also consistent with a previous study of water
diffusion in the interior of reverse micelles and on biopolymers [9]. As in these studies, we attribute
this behavior to deviations in structure from the ideal hydrogen-bonded network. New QE neutron
scattering studies are being planned as a function of temperature to understand the behavior of water
in CPG at supercooled temperatures. In particular, it will be interesting to note if any zoning of water
occurs in this system with -preferen&Lfimzb~~w~~motioti~oleculesclosestto-tie~ure----
surface.
“cl0.30 . ‘32AtiXiK—24Antius■0.25A 15Andius
~ 0.20. ●
?#- o.l~ ..–.
r--
0.10-
●
0.05. ——— ——— ___ ,__
0,00
0123456 7 15 20 25 30
Q’ (A-2) Pore Radius (~)
.... .—.x.——
—.
Figure 3- The hwhm of the translational Lorentzian Figure 4- Dependence,of th6 mean residence
~Q) of Eq. (3) = a function of Q’.The solid lines time, G, on the pore radius. The dashed line is
are determined using the jump diffusion model with the value obser&d for bulk water.
the values given in Table II.
Acknowledgments
Work benefited from the use of IPNS at ANL., funded by the U.S. DOE contract No. W-31-109-Eng-
38. KWH wishes to thank the support of the U.S. DOE under contract No. DE-AC05-960R22464.
References
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D.D., Tulk C.A., Svensson E.C. and Loong C.K., Phys. Rev. Letters 83 (1999) 258A Di Cola D.,
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. .. ,., . . .....- — .— .—


DEPINNING OF FLUX LINES AND AC LOSSES IN MAGNET- . SUPERCONDUCTOR LEVITATION SYSTEM *

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DEPINNING OF FLUX LINES AND AC LOSSES IN MAGNET- . SUPERCONDUCTOR LEVITATION SYSTEM *

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