Table Of ContentNORTHWESTERN UNIVERSITY
LOW TEMPERATURE THERMAL CONDUCTIVITY OF TITANIUM
A DISSERTATION
SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree
DOCTOR OF PHILOSOPHY
FIELD OF PHYSICS
By
Carl Jennings Rigney
EVANSTON, ILLINOIS
January, 195>1
ProQuest Number: 10101889
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TABLE OF CONTENTS
I. INTRODUCTION
Types of studies made of thermal conductivities Page 1
The problem 3
II. EXPERIMENT
Description of apparatus h
Instruments 8
Table of Apparatus 9
Principles of the measurements 10
Chemical analysis of specimens 12
Method of determining temperature differences 111.
Sample calculations 17
Results ' 21
III. EXPERIMENTAL ERRORS
Thermocouple errors 2U
Radiation losses 25
Calibration errors 26
Expected error 28
IV. DISCUSSION OF RESULTS
Comparison with other results 29
Correlation with theory 30
Conclusions 31
V. APPENDIX
A. Empirical equations representing thermal conductivity 33
B. Bibliography 35
C* Acknowledgements 36
D. Vita 37
623119
1
I. INTRODUCTION
This investigation of the thermal conductivity of Titanium at
.ow temperatures is of consequence chiefly for its practical value
with regard to the potential use of that metal, now that i t is avail
able in commercial quantities, in instances where a strong, light,
:orrosion-resistant material can be used to advantage in the construc
tion of low temperature apparatus* Generally, comparison with theory
is difficult because of the extreme sensitivity of thermal conductiv
ity to impurity content; and few detailed correlations exist, except
those due to Wilson.
In metals, both the crystal lattice and the conduction electrons
transport heat* The conducting electrons are scattered by the thermal
vibrations of the atoms in the crystal lattice and by the imperfections
in the lattice itse lf. These imperfections also decrease the lattice
conduction. Recently, experimenters have used magnetic fields in
efforts to diminish the electronic conduction enough to extrapolate
and find the lattice conduction alone, but the accuracy of the extra
polation is questioned on theoretical *2 The effect of lattice
grounds
imperfections is studied by measuring, at a fixed temperature, the
conductivities of samples of a metal with a range of impurity contents*
Most of the common metals have been investigated by Griineisen and
Goens,3 and the results of their study are embodied in an empirical
Mffilson, A.H.7 Semi-Conductors and Metals, (Cambridge University
Press, 1939) $ PP 102-111.
^Sondheimer, E.H., and Wilson, A. H., Proc. Roy. Soc. A, 190$ h35,
(19U7).
3Gruneisen, E., and Goens, E., Z. Physik, UU, 6l5, (1927).
2
(relation. They found that the thermal conductivity of a metal at a
fixed temperature is a linear function of its residual electrical
resistivity, i. e., the resistance of the impure metal at zero degrees
felvin. An extrapolation to zero residual resistance, corresponding to
the case of a perfect lattice, gives the ’'ideal1* thermal conductivity,
which is the combination of the electronic and the lattice conductiv
ities for a pure crystal -with a perfect lattice. This "ideal" con
ductivity depends only on thermal vibrations and is therefore depend
ent on temperature alone.
The temperature dependence and the behavior of the Wiedemann—
rranz ratio have been the most widely studied features of heat
jonduction by metals; but impurities strongly affect the results,
ispecially at low temperatures, so coefficients which are genuinely
jharacteristic of the pure metals have been sought. Progress has
>een made through the development of two empirical relations: that
lue to Gruneisen and Goens, and Bidwell's discovery of a relation
jetween thermal conductivity, density, and specific heat in the solid
state and the thermal conductivity of the metal in the liquid state.
' ’heoretical equations given by Wilson have the same form as these two
ampirical expressions.2 Details of the correlation are given in
, appendix A •
Wilson also developed a method to carry out theoretical cal
culations for the temperature dependence of thermal conductivity in
-Bidwell, C. C., Phys. Rev., 32, 311, (1928); 33, 2U9, (1929)5
58, 561, (195577
■Wilson, A. H., Semi-Conductors and Metals, (Cambridge University
Press, 1939), pp 103-109.
3
■i
the case of monovalent metals* Using this method with assumed values
for the number of conduction electrons per atom, Makinson was able to
give explicit^, results for copper and bismuth in terms of the residual
2
resistiv ities as parameters indicating impurity content. Makinson*s
results are in excellent agreement with experimental data, considering
the approximations used. No explicit theoretical calculations have
been made for metals other than those which can be treated as monoval
ent. Thus recent investigations of thermal conductivities have been
predominately experimental.
An extensive survey of the literature indicates that the thermal
conductivity of titanium and its temperature dependence have not been
investigated below zero degrees Centigrade, although measurements on
electrical resistiv ity and the thermoelectric effects have been car
ried down to liquid air temperatures *3 Measurements of the thermal
conductivity above room temperature have been carried out.^
It is the purpose of this investigation to augment the body of
scientific knowledge with regard to the physical properties of metals
by measuring the thermal conductivity of commercial titanium at cer
tain temperatures from the liquid hydrogen range to the melting point
of ice. In light of the foregoing paragraphs, the correlation between
theory and experiment in this field requires measurements on highly
purified m aterials and a careful control of im purities. This problem
is proposed for study in the near future.
1Wilson, A. H.» Eroc« Camb. Phil. Soc„, 3£, 371, (1937).
^Makinson, R. E. B., FToc. Camb. Phil. Soc., 3k > U7U, (1938).
3Greiner, E. S., and E llis, W. C., Trans. A.I ♦ M.E♦ , 180, 6$7, (19U9) *
^Mimeographed tables from the National Lead Co., stating results from
the Battelle Memorial Institute.
a
II. EXPERIMENTAL APPARATUS AND PROCEDURE
Since the measurements of primary interest were to be made some
200°C below room temperature, the apparatus incorporated features de
signed to minimize the exchange of heat between the surroundings and
the specimen under investigation* A Dewar flask sixty centimeters
deep was used as a container for the refrigerant liquid; and immer
sion of the titanium sample to a depth of fifty centimeters was af
forded by fixing the sample into the base of a copper cylinder, which
was supported by a long, vertical connecting tube of monel metal.
The monel tube led the thermocouple wires and the heater leads down
into the copper cylinder. A MZM -bend in the tube prevented the
thermal radiation of the room from reaching the specimen* With the
help of copper mesh which was stuffed into the bend, thermal contact
between the lead wires and the tube was established. Conduction of
heat from the room by the lead wires was practically eliminated,
since this bend was immersed to a depth of some thirty-five centi
meters. To minimize conduction by the air, the system was evacu
ated to a pressure below 0*01 microns. A copper spool, supported
by the titanium specimen itse lf, was wound with U00 centimeters of
A.W.G. number 32 gauge manganin wire to provide the heat input.
Copper-constantan thermocouples, in thermal contact with the titan
ium iro'd through thin copper rings, were used to determine the temp
erature gradient along the specimen. Radiation losses were deter
mined by a substitution method. The connections between instruments
and equipment used in the measurements are shown in Figure 1.
5
FIGURE 1
BLOCK DlAG&AM OF APPARATUS
Galvanometer
Rubicon Type B
Dry Cells Potentiometer Bpply Standard Oell
Cenoo
Hyvao
Selector Switch Pump
lead
Storage Batteries
Ice-Water Bath
Oil
Bheostat
Diffusion
Thermo coup le_-.
Pump
Leads
Voltmeter — McLSOD liquid Air
GAUGE Trap
Milliammeter Liquid Air
Trap
Heater Leads
Glass Tubing PIBANI
GAUGE
^ _ _Mone1^ Metal_
connecting tube A$u>
METERS
DEWAR FLASK
Copper Cylinder
containing specimen
6
In the following discussion, reference w ill be made to Figure 2,
which gives details of the copper cylinder and monel metal connecting
tube.
To afford ease in exchanging samples, the base of the cylinder A
was soldered to the cylinder proper B with a low melting point alloy.
The titanium rod C was pressed into the copper base A at room tem
perature, and the greater coefficient of thermal expansion of copper
assured good thermal contact at low temperatures. Copper rings D of
one millimeter thickness, to which thermocouples were attached with
soft solder, were pressed on the titanium rod. to afford good thermal
contact between the thermocouples and the titanium, which cannot be
soldered in a ir. The rings also fixed the positions for measurement
of the temperature gradient.
The thermocouple wires and the heater leads were introduced
into the vertical monel tube E by the top assembly F. The assembly
consisted of a fla t, annular piece of brass G, which was soldered to
the top end of tube E, and a fla t circular piece H, which was screwed
to piece G but separated from its surface by rubber gaskets. The
wires entered between the rubber surfaces. All the wire segments
which were in contact with the rubber had been soaked in a beeswax-
rosin mixture. The top assembly was given a heavy coat of the wax
so that the heads of the screws were completely covered, resulting
in a vacuum-tight seal.
On entering the copper cylinder the wires were held away from
the sample and against the copper walls by a second metal cylinder J
so that the wires entered the space in which the specimen stood from
