Application of compressional cooling to the study of nuclear ordering in solid helium three
Johnson, Richard Torsten
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https://hdl.handle.net/2142/25810
Description
Title
Application of compressional cooling to the study of nuclear ordering in solid helium three
Author(s)
Johnson, Richard Torsten
Issue Date
1969
Doctoral Committee Chair(s)
Wheatley, J.C.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
compressional cooling
nuclear ordering
solid helium-3
Language
en
Abstract
"A powerful cooling technique for He3
has been used to observe
ordering of the nuclear spins in solid He3
He3
atoms in the solid are
localized at lattice sites. Interactions between neighboring atoms, due to
zero point motion, are relatively small until temperatures in the low
I
millidegree Kelvin range are reached. Liquid He
3
is a Fermi liquid.
Due to the Pauli exclusion principle, the nuclear spins in the liquid begin
ordering at much higher temperatures. This difference in ordering temperatures
leads to an interesting region between about 0.5 mOK and
0.32°K in which the solid has a higher entropy than the liquid. In this
temperature range, isentropic conversion of liquid to solid He 3 will produce
cooling. Starting at temperatures above 20 m oK, cooling to below
3 mOK has been obtained. At the lower end of this temperature range,
appreciable ordering of the nuclear spins in the solid has been observed.
A flexible walled cell has been developed for compressing a two
phase, liquid-solid, mixture of He
3
at temperatures below the minimum
in the melting curve. The cell was precooled to about 20 mOK using a continuous
dilution refrigerator. Compression was accomplished using liquid
He as a pressurizing fluid. Along the melting curve, the pressure and
temperature were measured using, respectively, a beryllium copper
capacitor and a cerium magnesium nitrate (CIv.IN) powder thermometer.
The solid entropy has been determined using the Clapeyron equation
for a first order phase transition;
[equation]
where S ,V and S ,V are the molar entropy and volume of solid and
s s 1· 1.
liquid He3
on the melting curve, respectively. The use of this equation
involved a calculation of S based on the 27.0 atm heat capacity measure- "" .
ments of Abel, Anderson, Black, and Wheatley. Also, the values of
V"" - Vs measured by Scribner, Panczyk, and Adams were used. The
. * C:MN thermometer calibration, ,assuming the magnetic temperature T
equal to the Kelvin temperature T, was self consistently done so the
nneasured and calculated values of dP /dT agreed in the 20 to 38 mO K
tennperature range. In this tennperature range, S is still essentially
s
R In 2, the entropy of a connpletely disordered system of spin ~ particles.
However, at lower tennperatures appreciable nuclear ordering was
observed. For exannple, at T * = 3.4 nnoK the measurennents gave
S = 0.58 R = 0.83 R In 2. Using the effective spin Hamiltonian
s
[equation]
where the sunn is only over nearest neighbors, with the high tennperature
expansion for the free energy of a bec Heisenberg antiferronnagnet given
by Baker, Gilbert, Eve, and Rushbrooke, the low temperature data
suggest J /k = -( 1.7 +/- 0.3) mOK. This value is in reasonable agreement
with values of J deduced from higher temperature measurements."
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