Mg university, KTU univeraity Btech Module 1 (8 hours) Introduction: Historical development- application of cryogenics -present areas involving cryogenic engineering-cryogenics in space technology- cryogenics in biology and medicine￾superconductivity applications. Module 2 (12 hours) Basic thermodynamics applied to liquefaction and refrigeration process – isothermal, adiabatic and Joule Thomson expansion process -efficiency to liquefaction and coefficient of performances- irreversibility and losses. Low temperature properties of engineering materials: mechanical properties – thermal properties -electrical and magnetic properties. Properties of cryogenic fluids- superconductivity and super fluidity - materials of constructions for cryogenic applications. Module 3 (15 hours) Gas liquefaction systems: Production of low temperatures – general liquefaction systems￾liquefaction systems for neon, hydrogen and helium. Module 4 (15hours) Cryogenic refrigeration systems: ideal refrigeration systems- refrigerators using liquids and gases as refrigerants- refrigerators using solids as working media - adiabatic demagnetization method. Module 5 (10 hours) Cryogenic storage and transfer systems: Cryogenic fluid storage vessels- cryogenic fluid transfer systems-cryo pumping. Teaching scheme Credits: 4 3 hours lecture and 1 hour tutorial per week             Text Books 1. Barron R., Cryogenic Systems, Oxford Science Publications 2. Scott R.B., Cryogenic Engineering, Van Nostrand Co. Reference Books 1. Mamata Mukhopadyay., Fundamentals of Cryogenic Engineering, PHI Learning 2. Haseldon G.G., Cryogenic Fundamentals, Academic Press 3. Flynn T.M., Cryogenic Engineering, Marcel Dekker.

1. CRYOGENICS

2. 3
Module I
INTRODUCTION TO CRYOGENIC SYSTEMS
1.1. Introduction
The word cryogenics means, literally, the production of icy cold; however,
the term is used today as a synonym for low temperatures. The point on the
temperature scale at which refrigeration in the ordinary sense of the term ends and
cryogenics begins is not sharply defined. The workers at the National Bureau of
Standards at Boulder, Colorado, have chosen to consider the field of cryogenics as
that involving temperatures below ­150°C (123 K) or ­ 240°F (2200
R). This is a
logical dividing line, because the normal boiling points of the so­called permanent
gases, such as helium, hydrogen, neon, nitrogen, oxygen, and air, lie below ­ 150°C,
while the Freon refrigerants, hydrogen sulfide, ammonia, and other conventional
refrigerants all boil at temperatures above ­150°C. The position and range of the field
of cryogenics are illustrated on a logarithmic thermometer scale in Fig. 1.1.
In the field of cryogenic engineering, one is concerned with developing and
improving low­temperature techniques, processes, and equipment. As contrasted to
low­temperature physics, cryogenic engineering primarily involves the practical
utilization of low­temperature phenomena, rather than basic research, although the
dividing line between the two fields is not always clear­cut. The engineer should be
familiar with physical phenomena in order to know How to utilize them effectively;
the physicist should be familiar with engineering principles in order to design
experiments and apparatus.
A system may be defined as a collection of components united by definite
interactions or interdependencies to perform a definite function. Examples of
common engineering systems include the automobile, a petroleum refinery, and an
electric generating power plant. In many cases the distinction between a system and a
component depends upon one's point of view. For example, consider the
transportation system of a country. An automobile is a system also; however, it
would be only one part or subsystem of the entire transportation system. Going even
further, one could speak of the power system, braking system, steering system, etc.,

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of the automobile. In general, we shall use the term cryogenic system to refer to an
interacting group of components involving low temperatures. Air liquefaction plants,
helium refrigerators, and storage vessels with the associated controls are some
examples of cryogenic systems.
Fig. 1.1. The cryogenic temperature range.
1.2. Historical background
In 1726 Jonathan Swift wrote in Gulliver's account of his trip to the
mythical Academy of Lagado:
He (the universal artist) told us he had been thirty years employing his
thoughts for the improvement of human life. He had two large rooms full of
wonderful curiosities, and fifty men at work. Some were condensing air into a dry
tangible substance, by extracting the nitre, and letting the aqueous or fluid particles
percolate.

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At the time Gulliver's Travels was written, air was considered to be a
"permanent gas." Thus Swift envisioned the liquefaction of air some 150 years
before the feat was actually accomplished.
In the 1840s, in an attempt­ to relieve the suffering of malaria patients, Dr.
John Gorrie, a Florida physician, developed an expansion engine for the production
of ice. Although Dr. Gorrie’s engine was used only to cool air for air conditioning of
sickrooms and was not part of a cryogenic system, most large­scale air liquefaction
systems today use the same principle of expanding air through a work­producing
device, such as an expansion engine or expansion turbine, in order to extract energy
from the air so that the air can be liquefied.
It was not until the end of 1877 that a so­called permanent gas was first
liquefied. In this year Louis Paul Cailletet, a French mining engineer, produced a fog
of liquid­oxygen droplets by precooling a container filled with oxygen gas at
approximately 300 atm and allowing the gas to expand suddenly by opening a valve
on the apparatus. About the same time Raoul Pictet, a Swiss physicist, succeeded in
producing liquid oxygen by a cascade process.
In the early 1880s one of the first low­temperature physics laboratories, the
Cracow University Laboratory in Poland, was established by Szygmunt von
Wroblewski and K. Olszewski. They obtained liquid oxygen "boiling quietly in a test
tube" in sufficient quantity to study properties in April 1883. A few days later, they
also liquefied nitrogen. Having succeeded in obtaining oxygen and nitrogen as true
liquids (not just a fog of liquid droplets), Wroblewski and Olszewski, now working
separately at Cracow, attempted to liquefy hydrogen by Cailletet's expansion
technique. By first cooling hydrogen in a capillary tube to liquid­oxygen
temperatures and expanding suddenly from 100 atm to I atm, Wroblewski obtained a
fog of liquid­hydrogen droplets in 1884, but he was not able to obtain hydrogen in
the completely liquid form.
The Polish scientists at the Cracow University Laboratory were primarily
interested in determining the physical properties of liquefied gases. The ever­present
problem of heat transfer from ambient plagued these early investigators because the

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cryogenic fluids could be retained only for a short time before the liquids boiled
away. To improve this situation, an ingenious experimental technique was developed
at Cracow. The experimental test tube containing a cryogenic fluid was surrounded
by a series of concentric tubes, closed at one end. The cold vapor arising from the
liquid flowed through the annular spaces between the tubes and intercepted some of
the heat traveling toward the cold test tube. This concept of vapor shielding is used
today in conjunction with high­performance insulations for the long­term storage of
liquid helium in bulk quantities.
A giant step forward in preserving cryogenic liquids was made in 1892
when James Dewar, a chemistry professor at the Royal Institution in London,
developed the vacuum­jacketed vessel for cryogenic­fluid storage. Dewar found that
using a double­walled glass vessel having the inner surfaces silvered (similar to
present­day thermos bottles) resulted in a reduction of the evaporation rate of the
stored fluid by a factor of 30 over that of an uninsulated container. This simple
container played a significant role in the liquefaction of hydrogen and helium in bulk
quantities. In May 1898 Dewar produced 20 cm) of liquid hydrogen boiling quietly
in a vacuum­insulated tube, instead of a mist.
In 1895 two significant events in cryogenic technology occurred. Carl von
Linde, who had established the Linde Eismaschinen AG in 1879, was granted a basic
patent on air liquefaction in Germany. Although Linde was not the first to liquefy air,
he was one of the first to recognize the industrial implications of gas liquefaction and
to put these ideas into practice. Today the Linde Company is one of the leaders in
cryogenic engineering.
After more than 10 years of low­temperature study, Heike Kamerlingh
Onnes established the Physical Laboratory at the University of Lei den in Holland in
1895. Onnes' first liquefaction of helium in 1908 was a tribute both to his
experimental skill and to his careful planning. He had only 360 liters of gaseous
helium obtained by heating monazite sand from India. More than 60 cm3
of liquid
helium was produced by Onnes in his first attempt. Onnes was able to attain a
temperature of 1.04 K in an unsuccessful attempt to solidify helium by lowering the
pressure above a container of liquid helium in 1910.

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The physicists at the Leiden laboratory were interested in investigating the
properties of materials at low temperatures and in checking natural principles known
to be valid at ambient temperatures, at cryogenic temperatures. It was in 1911, while
he was checking the various theories of electrical resistance of solids at liquid­helium
temperatures, that Onnes discovered that the electrical resistance of the mercury wire
on which he was experimenting suddenly decreased to zero. This event marked the
first observation of the phenomenon of superconductivity­the basis for many novel
devices used today.
In 1902 Georges Claude, a French engineer, developed a practical system
for air liquefaction in which a large portion of the cooling effect of the system was
obtained through the use of an expansion engine. Claude's first engines were
reciprocating engines using leather seals (actually, the engines were simply modified
steam engines). During the same year, Claude established l'Air Liquide to develop
and produce his systems.
Although cryogenic engineering is considered a relatively new field in the
U.S., it must be remembered that the use of liquefied gases in U.S. industry began in
the early 1900s. Linde installed the first air­liquefaction plant in the United States in
1907, and the first American­made air­liquefaction plant was completed in 1912. The
first commercial argon­production was put into operation in 1916 by the Linde
company in Cleveland, Ohio. In 1917 three experimental plants were built by the
Bureau of Mines, with the cooperation of the Linde Company, Air Reduction
Company, and the Jefferies­Norton Corporation, to extract helium from natural gas
of Clay County,' Texas. The helium was intended for use in airships for World War I.
Commercial production of neon began in the United States in 1922, although Claude
had produced neon in quantity in France since 1907.
On 16 March 1926, Dr. Robert H. Goddard conducted the world's first
successful flight of a rocket powered by liquid­oxygen­gasoline propellant on a farm
near Auhurn, Massachusetts. This first flight lasted only 2½ seconds, and the rocket
reached a maximum speed of only 22 m/s (50 mph). Dr. Goddard continued his work
during the 1930s and by 1941 he had brought his cryogenic rockets to a fairly high

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degree of perfection. In fact, many of the devices used in Dr. Goddard's rocket
systems were used later in the German V­2 weapons system.
During that same year (1926), William Francis Giauque and Peter Debye
independently suggested the adiabatic demagnetization method for obtaining
ultralow temperatures (less than 0.1 K). It was not until 1933 that Giauque and
MacDougall at Berkeley and De Haas, Wiersma, and Kramers at Leiden made use of
the technique to reach temperatures from 0.3 K (Giauque and MacDougall) to 0.09 K
(De Haas et al.).
As early as 1898 Sir James Dewar made measurements on heat transfer
through evacuated powders. In 1910 Smoluchowski demonstrated the significant
improvement in insulating quality that could be achieved by using evacuated
powders in comparison with unevacuated insulations. In 1937 evacuated­powder
insulations were first used in the United States in bulk storage of cryogenic liquids.
Two years later, the first vacuum powder­insulated railway tank car was built for the
transport of liquid oxygen.
The world became aware of some of the military implications of cryogenic
technology in 1942 when the German V ­2 weapon system was successfully test­
fired at Peenemunde under the direction of Dr. Walter Dornberger. The V­2 weapon
system was the first large, practical liquid propellant rocket. This vehicle was
powered by liquid oxygen and a mixture of 75 percent ethyl alcohol and 25 percent
water.
Around 1947 Dr. Samuel C. Collins of the department of mechanical
engineering at Massachusetts Institute of Technology developed an efficient liquid­
helium laboratory facility. This event marked the beginning of the period in which
liquid­helium temperatures became feasible and fairly economical. The Collins
helium cryostat, marketed by Arthur D. Little, Inc., was a complete system for the
safe, economical liquefaction of helium and could be used also to maintain
temperatures at any level between ambient temperature and approximately 2 K.
The first buildings for the National Bureau of Standards Cryogenic
Engineering Laboratory were completed in 1952. This laboratory was established to

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provide engineering data on materials of construction, to produce large quantities of
liquid hydrogen for the Atomic Energy Commission, and to develop improved
processes and equipment for the fast growing cryogenic field. Annual conferences in
cryogenic engineering have been sponsored by the National Bureau of Standards
(sometimes sponsored jointly with various universities) from 1954 (with the
exception of 1955) to 1973. At the 1972 conference at Georgia Tech in Atlanta, the
Conference Board voted to change to a biennial schedule alternating with the
Applied Superconductivity Conference. This schedule has been followed with
meetings in Kingston, Ontario in 1975, Boulder in 1977, Madison, Wisconsin in
1979, San Diego, California in 1981, and Colorado Springs in 1983.
Early in 1956 work with liquid hydrogen was greatly accelerated when Pratt
and Whitney Aircraft was awarded a contract to develop a liquid hydrogen­fueled
rocket engine for the United States space program. The following year the Atlas
ICBM was successfully test­fired. The Atlas was powered by a liquid­oxygen­RP­l
propellant combination and had a sea level thrust of I. 7 MN (380,000 Ibf). At the
Cape Kennedy Space Center on 27 October 1961, the first flight test of the Saturn
launch vehicle was conducted. The Saturn V was the first space vehicle to use the
liquid hydrogen­liquid­oxygen propellant combination.
In 1966, Hall, Ford, and Thompson at Manchester, and Neganov, Borisov,
and Liburg at Moscow independently succeeded in achieving continuous
refrigeration below 0.1 K using a He3
­He4
dilution refrigerator. This new
refrigeration technique had been proposed in 1951 by H. London. The dilution
refrigerator had certain advantages over the magnetic refrigerator, which relied on
the adiabatic demagnetization principle to achieve temperatures in the 0.01 K to 0.10
K range. Thus considerable research effort has been devoted to the study and
improvement of the dilution refrigerator. .
In 1969 a 3250­hp, 20D­rpm superconducting motor (Fawley motor) was
constructed by the International Research and Development Co., Ltd., in England. In
1972 IRD installed a superconducting motor in a ship to drive the electrical
propulsion system.

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This chronology of cryogenic technology is summarized in Table 1.1.
We see that cryogenics has grown from an interesting curiosity in the times
of Linde and Claude to a diversified, vital field of engineering.
1.3. Present areas involving cryogenic engineering
Present­day applications of cryogenic technology are widely varied, both in
scope and in magnitude. Some of the areas involving cryogenic engineering include:
1. Rocket propulsion systems. All the large United States launch vehicles use
liquid oxygen as the oxidizer. The Space Shuttle propulsion system uses both
cryogenic fluids, liquid oxygen, and liquid hydrogen.
2. Studies in high­energy physics. The hydrogen bubble chamber uses liquid
hydrogen in the detection and study of high­energy particles produced in large
particle accelerators.
3. Electronics. Sensitive microwave amplifiers, called masers, are cooled to
liquid­nitrogen or liquid­helium· temperatures so that thermal vibrations of the
atoms of the amplifier element do not seriously interfere with absorption and
emission of microwave energy. CryogenicaIly cooled masers have been used in
missile detectors, in radio astronomy to listen to faraway galaxies, and in space
communication systems.
Table 1.1. Chronology of cryogenic technology
Year Event
1877 Cailletet and Pictet liquefied oxygen (Pictet 1892).
1879 Linde founded the Linde Eismaschinen AG.
1883 Wroblewski and Olszewski completely liquefied nitrogen and oxygen at the
Cracow University Laboratory (Olszewski 1895).
1884 Wroblewski produced a mist of liquid hydrogen.
1892 Dewar developed a vacuum­insulated vessel for cryogenic­fluid storage
(Dewar 1927).
1895 Onnes established the Leiden Laboratory. Linde was granted a basic patent on
air liquefaction in Germany.
1898 Dewar produced liquid hydrogen in bulk at the Royal Institute of London.

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1902 Claude established l'Air Liquide and developed an air­liquefaction system
using an expansion engine.
1907 Linde installed the first air­liquefaction plant in America. Claude produced
neon as a by­product of an air plant.
1908 Onnes liquefied helium (Onnes 1908).
1910 Linde developed the double­column air­separation system.
1911 Onnes discovered superconductivity (Onnes 1913).
1912 First American­made air­liquefaction plant completed.
1916 First commercial production of argon in the United States.
1917 First natural­gas liquefaction plant to produce helium.
1922 First commercial production of neon in the United States.
1926 Goddard test­fired the first cryogenically propelled rocket. Cooling by
adiabatic demagnetization independently suggested by Giauque and Debye.
1933 Magnetic cooling used to attain temperatures below I K.
1934 Kapitza designed and built the first expansion engine for helium. Evacuated­
powder insulation first used on a commercial scale in cryogenic­fluid storage
vessels.
1939 First vacuum­insulated railway tank car built for transport of liquid oxygen.
1942 The V­2 weapon system was test­fired (Dornberger 1954). The Collins
cryostat developed.
1948 First 140 ton/day oxygen system built in America.
1949 First 300 ton/day on­site oxygen plant for chemical industry completed.
1952 National Bureau of Standards Cryogenic Engineering Laboratory established
(Brickwedde 1960).
1957 LOX­RP­I propelled Atlas ICBM test­fired. Fundamental theory (BCS
theory) of superconductivity presented.
1958 High­efficiency multilayer cryogenic insulation developed (Black 1960).
1959 Large NASA liquid­hydrogen plant at Torrance, California, completed.
1960 Large­scale liquid­hydrogen plant completed at West Palm Beach, Rorida.
1961 Saturn launch vehicle test­fired.
1963 60 ton/day liquid­hydrogen plant completed by Linde Co. at Sacramento,
California.
1964 Two liquid­methane tanker ships designed by Conch Methane Services. Ltd.,
entered service.

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1966 Dilution refrigerator using HeJ­He' mixtures developed (Hall 1966; Neganov
1966).
1969 3250­hp de superconducting motor constructed (Appleton 1971).
1970 Liquid oxygen plants with capacities between 60,000 mJ/h and 70,000 mJ/h
developed.
1975 Record high superconducting transition temperature (23 K) achieved.
Tiny superconducting electronic elements, called SQUIDs (superconducting
quantum interference devices) have been used as extremely sensitive digital
magnetometers and voltmeters. These devices are based on a superconducting
phenomenon, called the Josephson effect, which involves quantum mechanical
tunneling of electrons from one superconductor to another through an insulating
barrier.
In addition to SQUIDs, other electronic devices that utilize superconductivity
in their operation include superconducting amplifiers, rectifiers, transformers, and
magnets. Superconducting magnets have been used to produce the high magnetic
fields required in MHD systems, linear accelerators, and tokamaks. Superconducting
magnets have been used to levitate high­speed trains at speeds up to 500 km/h.
4. Mechanical design. By utilizing the Meissner effect associated with
superconductivity, practically zero­friction bearings have been constructed that
use a magnetic field as the lubricant instead of oil or air. Superconducting
motors have been constructed with practically zero electrical losses for such
applications as ship propulsion systems. Superconducting gyroscopes with
extremely small drift have been developed.
5. Space simulation and high­vacuum technology. To produce a vacuum that
approaches that of outer space (from 10­12
torr to 10­14
torr), one of the more
effective methods involves low temperatures. Cryopumping or freezing out the
residual gases, is used to provide the ultrahigh vacuum required in space
simulation chambers and in test chambers for space propulsion systems. The
cold of free space is simulated by cooling a shroud within the environmental
chamber by means of liquid nitrogen. Dense gaseous helium at less than 20 K

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or liquid helium is used to cool the cryopanels that freeze out the residual
gases.
6. Biological and medical applications. The use of cryogenics in biology, or
cryobiology, has aroused much interest. Liquid­nitrogen­cooled containers are
used to preserve whole blood, tissue, bone marrow, and animal semen for long
periods of time. Cryogenic surgery (cryosurgery) has been used for the
treatment of Parkinson's disease, eye surgery, and treatment of various lesions.
This surgical procedure has many advantages over conventional surgery in
several applications.
7. Food processing. Freezing as a means of preserving food was used as far back
as 1840. Today frozen foods are prepared by placing cartons on a conveyor belt
and moving the belt through a liquid­nitrogen bath or gaseous­nitrogen­cooled
tunnel. Initial contact with liquid nitrogen freezes all exposed surfaces and
seals in flavor and aroma. The cryogenic process requires about 7 minutes
compared with 30 to 48 minutes required by conventional methods. Liquid
nitrogen has also been used as the refrigerant in frozen­food transport trucks
and railway cars.
8. Manufacturing processes. Oxygen is used to perform several important
functions in the steel manufacturing process. Cryogenic systems are used in
making ammonia. Pressure vessels have been formed by placing a preformed
cylinder in a die cooled to liquid­nitrogen temperatures. High­pressure nitrogen
gas is admitted into the vessel until the container stretches about 15 percent,
and the vessel is removed from the die and allowed to warm to room
temperature. Through the use of this method, the yield strength of the material
has been increased 400 to 500 percent.
9. Recycling of materials. One of the more difficult items to recycle is the
automobile or truck tire. By freezing the tire in liquid nitrogen, tire rubber is
made brittle and can be crushed into small particles. The tire cord and metal
components in the original tire can be separated easily from the rubber, and the

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rubber particles can be used again for other items. At present the cryogenic
technique is the only effective one to recover the rubber from steel radial tires.
These are a few of the areas involving cryogenic engineering­a field in
which new developments are continually being made.

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MODULE II
LOW­TEMPERATURE PROPERTIES OF
ENGINEERING MATERIALS
Familiarity with the properties and behavior of materials used in any system
is essential to the design engineer. At first thought, one might suppose that by
observing the variation of material properties at room temperature he could
extrapolate this information down through the relatively small temperature range
involved in cryogenics (some 300°C) with fair confidence. In some cases, such as for
the elastic constants, this may be done with acceptable accuracy. On the other hand,
there are several significant effects that appear only at very low temperatures. Some
examples of these effects include the vanishing of specific heats, superconductivity,
and ductile­brittle transitions in carbon steel. None of these phenomena can be
inferred from property measurements made at near­ambient temperatures.
In this chapter, we shall investigate the physical properties of some
engineering materials commonly used in cryogenic engineering. The primary
purpose of the chapter is to examine the effect of variation of temperature on
material properties in the cryogenic temperature range and to become familiar with
the properties and behavior of materials at low temperatures.
MECHANICAL PROPERTIES
2.1. Ultimate and yield strength
For many materials, there is a definite value of stress at which the strain of
the material in a simple tensile test begins to increase quite rapidly with increase in
stress. This value of stress is defined as the yield strength Sy of the material. For
other materials that do not exhibit a sharp change in the slope of the stress­strain
curve, the yield strength is defined as the stress required to permanently deform the
material in a simple tensile test by 0.2 percent (sometimes 0.1 percent is used). The
ultimate strength Su of a material is defined as the maximum nominal stress attained
during a simple tensile test. The temperature variation of the ultimate and yield
strengths of several engineering materials is shown in Figs. 2.1 and 2.2.

15. 16
Fig.2.1. Ultimate strength for several engineering materials: (I) 2024­T4 aluminum;
(2) beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020
carbon steel; (7) 9 percent Ni steel; (8) Teflon; (9) Invar­36 (Durham et al. 1962).
Many engineering materials are alloys, in which alloying materials with
atoms of different size from those of the basic material are added to the basic
material; for example, carbon is added to iron to produce carbon steel. If the
alloying­element atoms are smaller than the atoms of the basic material, the smaller
atoms tend to migrate to regions around dislocations in the metal. The presence of
the smaller atoms around the dislocation tends to "pin" the dislocation in place or
make dislocation motion more difficult (Wigley 1971). The yielding process in
alloys takes place when a stress large enough to pull many dislocations away from
their "atmosphere" of alloying atoms is applied. Plastic deformation or yielding
occurs because of the gross motion of these dislocations through the material.
As the temperature is lowered, the atoms of the material vibrate less
vigorously. Because of the decreased thermal agitation of the atoms, a larger applied
stress is required to tear dislocations from their atmosphere of alloying atoms. From

16. 17
this line of reasoning, we should expect that the yield strength for alloys would
increase as the temperature is decreased. This has been found to be true for most
engineering materials.
Fig. 2.2. Yield strength for several engineering materials: (1) 2024­ T4 aluminum:
(2) beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020
carbon steel; (7) 9 percent Ni steel; (8) Teflon; (9) Invar­36 (Durham et al. 1962).
2.2. Fatigue strength
There are several ways to express the resistance of a material to stresses that
vary with time, but the most common method is a simple reversed bending test The
stress required for failure after a given number of cycles is called the fatigue strength
Sf. Some materials, such as carbon steels and aluminum­magnesium alloys, have the
property that the fatigue failure will not occur if the stress is maintained below a
certain value, called the endurance limit Se, no matter how many cycles have elapsed.

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The temperature variation of the fatigue strength at 106
cycles for several materials is
shown in Fig. 2.3.
Because of the time involved to complete a test, fatigue data at cryogenic
temperatures are not as extensive as ultimate­strength and yield strength data;
however, for the materials that have been tested, it has been found that the fatigue
strength increases as the temperature is decreased.
Fig. 2.3. Fatigue strength at 1()6 cycles: (I) 2024­ T4 aluminum; (2) beryllium
copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020 carbon steel
(Durham et al. 1962).
Fatigue failure generally occurs in three stages for the case of more than
about 10) cycles: microcrack initiation, slow crack growth until a critical crack size
is achieved, and the final rapid failure either by ductile rupture or by cleavage.
Microcrack initiation usually occurs at the surface of the specimen as a result of
inhomogeneous shear deformation or at small flaws near the surface. The growth of
the microcracks occurs as the material fails at the high­stress region around the tip of

18. 19
the crack. As the temperature of a material is decreased, a larger stress is required to
extend the crack; therefore, we should expect to observe that the fatigue strength
increases as the temperature is decreased.
For aluminum alloys, it has been found (De Money and Wolfer 1961) that
the ratio of fatigue strength to ultimate strength remains fairly constant as the
temperature is lowered. This fact may be used in estimating the fatigue strength for
nonferrous materials at cryogenic temperatures if no fatigue data are available at the
low temperatures.
2.3. Impact strength
The Charpy and the Izod impact tests give a measure of the resistance of a
material to impact loading. These tests indicate the energy absorbed by the material
when it is fractured by a suddenly applied force. Charpy impact strength of several
materials is shown in Fig. 2.4.
Fig. 2.4. Charpy impact strength at low temperatures: (I) 2024·T4 aluminum; (2)
beryl· lium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) CI020
carbon steel; (7) 9 percent Ni steel (Durham et al. 1962).

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A ductile­brittle transition occurs in some materials, such as carbon steel, at
temperatures ranging from room temperature down to 78 K, which results in a
severely reduced impact strength at low temperatures. The impact behavior of a
metal is largely determined by its lattice structure. The face­centered­cubic (FCC)
lattice has more slip planes available for plastic deformation than does the body­
centered­cubic (BCC) lattice. In addition, interstitial impurity atoms interact only
with edge dislocations to retard slipping in the FCC structure; whereas, both edge
and screw dislocations can become pinned in the BCC structure. The metals with a
FCC lattice or hexagonal lattice tend to fail by plastic deformation in the impact test
(thereby absorbing a relatively large amount of energy before breaking) and retain
their resistance to impact as the temperature is lowered. The metals with a BCC
lattice tend to reach a temperature at which it is more energetically favorable to
fracture by cleaving (thereby absorbing a relatively small amount of energy). Thus
these materials become brittle at low temperatures.
Most plastics and rubber materials become brittle upon cooling below a
transition temperature also. Two notable exceptions are Teflon and Kel­F.
2.4. Hardness and ductility
The ductility of materials is usually indicated by the percentage elongation
to failure or the reduction in cross­sectional area of a specimen in a simple tensile
test. The accepted dividing line between a brittle material and 'a ductile one is 5
percent elongation or a strain of 0.05 cm/cm at failure. Materials that elongate more
than this value before failure are called ductile; those with less than 5 percent
elongation are called brittle. The ductility of several materials as a function of
temperature is shown in Fig. 2.5.
For materials that do not exhibit a ductile­to­brittle transition at low
temperatures, the ductility usually increases somewhat as the temperature is lowered.
For the carbon steels, which do have a low­temperature transition, the elongation at
failure drops from 25 to 30 percent for the softer steels down to 2 or 3 percent during
the transition. Obviously, these materials should not be used at low temperatures in
any applications in which ductility is important.

20. 21
Hardness of metals is measured by the indention made in the surface of the
material by a standard indenter. Common hardness tests include (1) Brinell (ball
indenter), (2) Vickers (diamond pyramid indenter), and (3, Rockwell (ball or
diamond indenter with various loads). In general, the hardness of metals as measured
by any of these means is directly proportional to the ultimate strength of the material;
therefore, the hardness increases as the temperature is decreased. This proportionality
is to be expected because a penetration test is essentially a miniature tensile test.
Fig. 2.5. Percent elongation for various materials: (I) 2024­T4 aluminum; (2)
beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) C1020
carbon steel; (7) 9 percent Ni steel (Durham et al. 1962).
2.5. Elastic moduli
There are three commonly used elastic moduli: (1) Young's modulus E. the
rate of change of tensile stress with respect to strain at constant temperature in the
elastic region; (2) shear modulus G. the rate of change of shear stress with respect to
shear strain at constant temperature in the elastic region; and (3) bulk modulus B, the
rate of change of pressure (corresponding to a uniform three­dimensional stress) with
respect to volumetric strain (change in volume per unit volume) at constant
temperature. If the material is isotropic (many polycrystalline materials can be

21. 22
considered isotropic for engineering purposes), these three moduli are related
through Poisson's ratio v, the ratio of strain in one direction due to a stress applied
perpendicular to that direction to the strain parallel to the applied stress:
E
B
3(1 2)

  (2.1)
E
G
2(1 )

  (2.2)
Fig. 2.6. Young's modulus at low temperatures: (I) 2024­ T 4 aluminum; (2)
beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel; (6) ClO20
carbon steel; (7) 9 percent Ni steel (Durham et al. 1962).
The variation of Young's modulus with temperature for several materials is
given in Fig. 2.6.
As the temperature is decreased, interatomic and intermolecular forces tend
to increase because of the decrease in the disturbing influence of atomic and
molecular vibrations. Because elastic reaction is due to the action of these
intermolecular and interatomic forces, one would expect the elastic moduli to

22. 23
increase as the temperature is decreased. In addition, it has been found
experimentally that Poisson's ratio for isotropic materials do not change appreciably
with change in temperature in the cryogenic range; therefore, all three of the
previously mentioned elastic moduli vary in the same manner with temperature.
THERMAL PROPERTIES
2.6. Thermal conductivity
The thermal conductivity kt of a material is defined as the heat­transfer rate
per unit area divided by the temperature gradient causing the heat transfer. The
variation of thermal conductivity of several solids is shown in Fig. 2.7. Values of the
thermal conductivity of cryogenic liquids and gases are given in Appendixes B
through E.
Fig. 2.7. Thermal conductivity of materials at low temperatures: (ll 2024­T4
aluminum: (3) beryllium copper; (3) K Monel; (4) titanium; (5) 304 stainless steel;
(6) C1020 carbon steel; (7) pure copper; (8) Teflon (Stewart and Johnson 1961).

23. 24
To understand the variation of thermal conductivity at low temperatures,
one must be aware of the different mechanisms for transport of energy through
materials. There are three basic mechanisms responsible for conduction of heat
through materials: (l) electron motion, as in metallic conductors; (2) lattice
vibrational energy transport, or phonon motion, as in all solids; and (3) molecular
motion, as in organic solids and gases. In liquids, the primary mechanism for
conduction heat transfer is the transfer of molecular vibrational energy; whereas in
gases, heat is conducted primarily by transfer of translational energy (for monatomic
gases) and translational and rotational energy (for diatomic gases).
U sing principles of kinetic theory of gases (Eucken 1913), we may obtain a
theoretical expression relating the thermal conductivity to other properties of the
material:
tk 1 8(9 5) C    
where = specific heat ratio
= density of material
Cv = specific heat at constant volume
v = average particle velocity
A = mean free path of particles, or average distance a particle travels before
it is deflected
For all gases the thermal conductivity decreases as the temperature is
lowered. Because the product of density and mean free path for a gas is practically
constant, and the specific heat is not a strong function of temperature, the thermal
conductivity of a gas should vary with temperature in the same manner as the mean
molecular speed u, as indicated by eqn. (2.3). From kinetic theory of gases (Present
1958), the mean molecular speed is given by
1 2
c8g RT 
    

24. 25
where gc is the conversion factor in Newton's law (gc = 1 kg­m/N­s2
in the SI system
of units; gc = 32.174 Ibm­ft/lbrsec2
in the British system of units), R is the specific gas
constant for the particular gas (R = Ru/M, where Ru is the universal gas constant,
8.31434 J/mol­K or 1545 ft­lbf/lbmole­o
R, and M is the molecular weight of the gas),
and T is the absolute temperature of the gas. A decrease in temperature results in a
decrease in the mean molecular speed and, consequently, a decrease in the gas
thermal conductivity.
All cryogenic liquids except hydrogen and helium have thermal
conductivities that increase as the temperature is decreased. Liquid hydrogen and
helium behave in a manner opposite to that of other liquids in the cryogenic
temperature range.
For heat conduction in solids, the thermal conductivity is related to other
properties by an expression similar to that for gases,
1
t 3k C   (2.5)
Energy is transported in metals by both electronic motion and phonon
motion; however, in most pure electric conductors, the electronic contribution to
energy transport is by far the larger for temperatures above liquid­nitrogen
temperatures. The electronic specific heat is directly proportional to absolute
temperature (see Sec. 2.7), and the electron mean free path in this temperature range
is inversely proportional to absolute temperature. Because the density and mean
electron speed are only weak functions of temperature, the thermal conductivity of
electric conductors above liquid­nitrogen temperatures is almost constant with
temperature, as would be predicted by eqn. (2.5). As the absolute temperature is
lowered below liquid­nitrogen temperatures, the phonon contribution to the energy
transport becomes significant. In this temperature range, the thermal conductivity
becomes approximately proportional to T­2
for pure metals. The thermal conductivity
increases to a very high maximum as the temperature is lowered, until the mean free
path of the energy carriers becomes on the order of the dimensions of the material
sample. When this condition is reached, the boundary of the material begins to
introduce a resistance to the motion of the carriers, and the carrier mean free path

25. 26
becomes constant (approximately equal to the material thickness). Because the
specific heat decreases to zero as the absolute temperature approaches zero, from
eqn. (2.5) we see that the thermal conductivity would also decrease with a decrease
in temperature in this very low temperature region.
In disordered alloys and impure metals, the electronic contribution and tire.
phonon contribution to energy transport are of the same order of magnitude. There is
an additional scattering of the energy carriers due to the presence of impurity atoms
in impure metals. This scattering effect is directly proportional to absolute
temperature. Dislocations in the material provide a scattering that is proportional to
T2
, and grain boundaries introduce a scattering that is proportional to T3
at
temperatures much lower than the Debye temperature. All these effects combine to
cause the thermal conductivity of allays and impure metals to decrease as the
temperature is decreased, and the high maximum in thermal conductivity is
eliminated in alloys.
2.7. Specific heats of solids
The specific heat of a substance is defined as the energy required to change
the temperature of the substance by one degree while the pressure is held constant
(c ) or while the volume is held constant (cv). For solids and liquids at ordinary
pressures, the difference between the two specific heats is small, while there is
considerable difference for gases. The variation of the specific heats with
temperature gives an indication of the way in which energy is being distributed
among the various modes of energy of the substance on a microscopic level.
Specific heat is a physical property that can be predicted fairly accurately by
mathematical models through statistical mechanics and quantum theory. For solids
the Debye model gives a satisfactory representation of the variation of the specific
heat with temperature. In this model, Debye assumed that the solid could be treated
as a continuous medium, except that the number of vibrational waves representing
internal energy must be limited to the total number of vibrational degrees of freedom
of the atoms making up the medium­that is, three times the total number of atoms.
The expression for the specific heat of a monatomic crystalline solid as obtained
through the Debye theory is

26. 27
D/T
3 4 x
3 x 20
D DD
9RT x e dx T T
C 3R D
(e 1)


   
     
      

(2.6) where
8D is called the Debye characteristic temperature and is a property of the material,
and D(T/ D) is called the Debye function. A plot of the specific heat as given by eqn.
(2.6) is shown in Fig. 2.8, and the Debye specific­heat function is tabulated in Table
2.1. Values of D for several substances are given in Table 2.2.
Fig. 2.8. The Debye specific heat function.

27. 28
Table 2.1. Debye specific heat function
T/ D Cv/R T/ D Cv/R T/ D Cv/R
0.08
0.09
0.10
0.12
0.14
0.16
0.18
0.20
0.25
0.30
0.35
0.40
0.1191
0.1682
0.2275
0.3733
0.5464
0.7334
0.9228
1.1059
1.5092
1.8231
2.0597
2.2376
0.45
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
2.3725
2.4762
2.6214
2.7149
2.7781
2.8227
2.8552
2.8796
2.8984
2.9131
2.9248
2.9344
1.60
1.70
1.80
1.90
2.00
2.20
2.40
2.60
2.80
3.00
4.00
5.00
2.9422
2.9487
2.9542
2.9589
2.9628
2.9692
2.9741
2.9779
2.9810
2.9834
2.9844
2.9900
The theoretical expression for the Debye temperature is given by
1
3
a
D
h 3N
k 4 V
  
   
  (2.7)
where h = Planck’s constant
va = speed of sound in the solid
k = Boltzmann’s constant
N/V = number of atoms per unit volume for the solid.
2.8 Specific Heat of Liquids and Gases
In general, the specific heat Cv of cryogenic liquids decreases in the same
way that the specific heat of crystalline solids decreases as the temperature is
lowered. At low pressures the specific heat cp decreases with a decrease in
temperature also. At high pressures in the neighborhood of the critical point, humps
in the specific­heat curve are observed for all cryogenic fluids (and in fact for all
fluids). From thermodynamic reasoning we know that the difference in specific heats
for a pure substance is given by

28. 29
P
P
p
C C T
T T


    
     
     (2.10)
In the vicinity of the critical point, the coefficient of thermal expansion
P
1
T
 
   
  
becomes quite large; therefore, one would expect large increases of the specific heat
cp in the vicinity of the critical point also.
The specific heat of liquid helium behaves in a peculiar way­it shows a high,
sharp peak in the neighborhood of 2.17 K (3.91o
R). The behavior of liquid helium is
so different from that of other liquids that we shall devote a separate section to a
discussion of its properties.
Gases at pressures low compared with their critical pressure approach the
ideal­gas state, for which the specific heat Cu is independent of pressure. According
to the classical equipartition theorem, the specific heat of a material is given by
Cv = ½Rf (2.11)
where f is the number of degrees of freedom of a molecule making up the material.
For monatomic gases, the only significant mode of energy is translational kinetic
energy of the molecules, which involves three degrees of freedom. From eqn. (2.11)
the specific heat Cv for such monatomic gases as neon and argon in the ideal­gas state
is Cv = 3
/2R. In diatomic gases, other modes are possible. For example, if we consider
a "rigid­dumbbell" model of a diatomic molecule such as nitrogen (i.e., we neglect
vibration of the molecule), there are three translational degrees of freedom plus two
rotational degrees of freedom. We consider only two rotational degrees of freedom
because the moment of inertia of the molecule about an axis through the centers of
the two atoms making up the molecule is negligibly small compared with the
momel1t of inertia about an axis perpendicular to the interatomic axis. From eqn.
(2.11) the specific heat Cv for the rigid­dumbbell model of an ideal diatomic gas
would be Cv = 5
/2R. This is true for most diatomic gases at ambient temperatures, at
which the gases obey classical statistics. Because the molecules in a diatomic gas are
not truly rigid dumbbells, we should also expect to have vibrational modes present,

29. 30
in which the two molecules vibrate around an equilibrium position within the
molecule under the influence of the interatomic forces holding the molecule together.
In this case, two more degrees of freedom due to the vibrational mode would be
present, so the specific heat for a vibrating­dumbbell molecule would be Cv = ~R
according to the classical theory.
In the actual case, the rotational and vibrational modes are quantized, so
they are not excited if the temperature is low enough. The variation of the specific
heat of diatomic hydrogen gas with temperature is illustrated in Fig. 2.9. At very low
temperatures, only the translational modes are excited, so the specific heat Cv takes
on the value 3
/2R, the same as that of a monatomic gas. To determine whether the
rotational modes will be excited, one must compare the temperature of the gas with a
characteristic rotation temperature r, defined by
2
r 2
h
8 Ik
 
 (2.12)
where h = Planck's constant
I = moment of inertia of the molecule about an axis perpendicular to the
interatomic axis
k = Boltzmann's constant
If the temperature is less than about 1
/3 r the rotational mode is not appreciably
excited; if the temperature is greater than about 3 r, the rotational mode is practically
completely excited. Most diatomic gases become liquids at temperatures higher than
3 r; however, H2, D2, and HD are exceptions to this statement. Because of the small
moment of inertia of the hydrogen molecule, the characteristic rotation temperature
is quite a bit above the liquefaction temperature for hydrogen ( r = 85.4 K or
153.7o
R for hydrogen, so 3 , = 256.2 K or 461.1o
R). The specific heat Cv of
hydrogen gas rises from 3
/2R at temperatures below about 30 K (54°R) to 5
/2R at
temperatures above 255 K (459°R).

30. 31
The vibrational modes for a diatomic gas are also quantized and become
excited at temperatures on the order of a characteristic vibration temperature v
defined by
h
k

 
f
(2.13)
Fig. 2.9. Variation of the specific heat c, for hydrogen gas.
where fv is the vibrational frequency of the molecule. The characteristic vibration
temperature for gases is much higher than cryogenic temperatures, so the vibrational
mode is not excited for gases at cryogenic temperatures ( v = 6100 K or 1O,980o
R
for hydrogen gas).
The change in the specific heat of hydrogen between 30 K and 255 K is
important for hydrogen liquefiers and hydrogen­cooled helium liquefiers because it
affects the effectiveness of the heat exchangers, as we shall see in Chap. 3.
At pressures higher than near ambient, the specific heats of gases vary in a
more complicated manner with temperature and pressure. A complete coverage of
this effect is beyond the scope of our present discussion.
2.9. Coefficient of thermal expansion
The volumetric coefficient of thermal expansion is defined as the
fractional change in volume per unit change in temperature while the pressure on the

31. 32
material remains constant. The linear coefficient of thermal expansion t is defined
as the fractional change in length (or any linear dimension) per unit change in
temperature while the stress on the material remains constant. For isotropic materials,
= 3 t. The temperature variation of the linear coefficient of thermal expansion
for several materials is shown in Fig. 2.10.
The temperature variation of the coefficient of thermal expansion may be
explained through a consideration of the intermolecular forces of a material. The
intermolecular potential­energy curve, as shown in Fig. 2.11, is not symmetrical.
Therefore, as the molecule acquires more energy (or as its temperature is increased),
its mean position relative to its neighbors becomes larger; that is, the material
expands. The rate at which the mean spacing of the atoms increases with temperature
increases as the energy or temperature of the material increases; thus, the coefficient
of thermal expansion increases as temperature is increased.
Fig. 2.10. Linear coefficient of thermal expansion for several materials at low
temperature: (I) 2024­T4 aluminum; (2) beryllium copper; (3) K Monel; (4) titanium;
(5) 304 stainless steel; (6) C1020 carbon steel (NBS Monograph 29, Thermal
Expansion of Solids at Low Temperatures).

32. 33
Since both the specific heat and the coefficient of thermal expansion are
associated with intermolecular energy, one might expect to find a relationship
between the two properties. For crystalline solids, the Gruneisen relation expresses
this interdependence:
GC
B
 
 
(2.14)
where is the density of the material, B is the bulk modulus, and G is the
Gruneisen constant, which is independent of temperature as a first approximation.
Values of the Gruneisen constant for some materials are presented in Table 2.4.
Table 2.4. Values of the Gruneisen constant for selected solids
Material G
Aluminum 2.17
Copper 1.96
Gold 2.40
Iron 1.60
Lead 2.73
Nickel 1.88
Platinum 2.54
Silver 2.40
Tantalum 1.75
Tungsten 1.62
We have seen previously that the bulk modulus B is not strongly dependent
upon temperature for solids (it increases somewhat as the temperature is decreased);
therefore, the coefficient of thermal expansion for solids should vary with
temperature in the same way that the Debye specific heat varies with temperature.
This general variation has been found true experimentally. At very low temperatures
(T < D/12), the coefficient of thermal expansion is proportional to T3
•
ELECTRIC AND MAGNETIC PROPERTIES
2.10. Electrical conductivity
The electrical conductivity k, of a material is defined as the electric current
per unit cross­sectional area divided by the voltage gradient in the direction of
current flow. The electrical resistivity re is the reciprocal of the electrical

33. 34
conductivity. The variation with temperature of the electrical resistivity of several
materials is shown in Fig. 2.12.
Fig.2.11. Variation of the intermolecular potential energy for a pair of molecules. At
absolute zero, the molecular spacing would be r0.
When an external electric field is applied to an electric conductor, free
electrons in the conductor are forced to move in the direction of the applied field.
This motion is opposed by the positive ions of the metal lattice and impurity atoms
present in the material. Decreasing the temperature of the conductor decreases the
vibrational energy of the ions, which in turn results in a smaller interference with
electron motion. Therefore, the electrical conductivity increases as the temperature is
lowered for metallic conductors.
One of the first theories of electric resistance was developed by Drude
(Kittel 1956), who treated the free electrons as an "electron gas." He obtained the
following expression for the electrical conductivity:

34. 35
2
e
e
(N / V)e
k
m


 (2.15)
where N/V = number of free electrons per unit volume
e = charge of an electron
= electron mean free path
me = mass of an electron
 = average speed of an electron
Equation (2.15) gives the correct order of magnitude for the electrical
conductivity of a metal such as silver at room temperature if we assume that N/V is
on the order of the number of valence electrons per unit volume, is on the order of
the interatomic spacing, and the mean electron kinetic energy is given by
2
3
e 2½m kT  , according to classical theory. In order to obtain the correct
temperature dependence for the electrical conductivity from eqn. (2.15), however, we
must assume that the electron mean free path is inversely proportional to T ½
because
the electrical conductivity is approximately inversely proportional to absolute
temperature.
An application of quantum mechanics and band theory to the problem of
prediction of the electrical conductivity does not result in an equation different from
eqn. (2.15); however, it does allow us to predict the correct relationships for the
electron velocity and mean free path. According to the quantum­mechanical picture,
the velocity appearing in eqn. (2.15) is the average velocity of the electrons near the
so­called Fermi surface of the metal. For ordinary temperatures this velocity is
practically constant:
1
3n
F
e e
h 3 N
2 m 2 m
 
         (2.16)

35. 36
Fig. 2.12. Electrical resistivity ratio for several materials at low temperatures:
(1)copper; (2) silver; (3) iron; (4) aluminum (Stewart and Johnson 1961).
2.11. Superconductivity
One of the properties of certain materials that appears only at very low
temperatures is superconductivity ­ the simultaneous disappearance of all electric
resistance and the appearance of perfect diamagnetism. In the absence of a magnetic
field, many elements, alloys, and compounds become superconducting at a fairly
well­defined temperature, called the transition temperature in zero field T0.
Superconductivity can be destroyed by increasing the magnetic field around the
material to a large enough value. The magnetic field strength required to destroy
superconductivity is called the critical field HC. For Type I superconductors, there is
a single value of the critical field at which the transition from superconducting to
normal behavior is abrupt. For Type II superconductors (so­called "hard"
superconductors), there is a lower critical field HC1, at which the transition begins,

36. 37
and an upper critical field HC2 at which the transition is complete. Table 2.5 lists the
critical field at absolute zero H0 and the transition temperature for several materials.
Note that some alloys are superconductors even though the pure elements making up
the alloys are not superconductors.
For Type I specimens in the shape of a long cylinder or wire placed parallel
10 the applied magnetic field, the critical field is well defined at every temperature
and is a function of temperature. The critical field may be related approximately to
the absolute temperature by
2
C 0 0H H [1 (T / T ) ]  (2.24)
Although the parabolic relationship is not exactly true, it is adequate for
many purposes.
The phenomenon of superconductivity was discovered by Kamerlingh
Onnes in 1911 while investigating the electric resistance of mercury wire. After its
discovery, this new state of matter became the object of investigation by several
theoretical and experimental physicists to determine the properties of
superconductors and to try to explain the basic mechanism of the phenomenon. The
early attempts to develop a thermodynamic theory were unsuccessful because it was
assumed that any magnetic field present within the material in the normal state
remained frozen­in when the substance became superconducting.
Gorter (1933) applied the principles of reversible thermodynamics to the
superconducting phenomenon and obtained results that were in excellent agreement
with experimental measurements. This caused quite a bit of discussion because many
investigators thought that the transition was not thermodynamically reversible. In the
same year, this matter was cleared up somewhat by an experiment by Meissner and
Ochsenfeld (1933). They cooled a monocrystal of tin in a magnetic field until it
became superconducting and found that the magnetic field was expelled from within
the material when the sample became superconducting, as shown in Fig. 2.13. The
results of the Meissner­Ochsenfeld experiment indicated that the magnetic flux
density within a bulk superconducting material (Type I) was always zero, no matter
what value of magnetic flux density existed within the material before the transition.

37. 38
Superconductivity was shown to be a case not only of zero electric resistance but
also of perfect magnetic insulation. The Meissner effect as the expulsion of the
magnetic field when a material becomes superconducting is called, forms the basis
for the frictionless bearing and superconducting motor.
Fig. 2.13. The Meissner effect. When a material is normal, the magnetic flux lines
can penetrate the material. When the material becomes superconducting, the
magnetic field is expelled from thin the material.
Shortly after the discovery of the Meissner effect, two "phenomenological
theories" of superconductivity were proposed. Gorter and Casimir (1934) proposed a
two­fluid model, in which two types of electrons took part in the electric current­the
normal or "uncondensed" ones and the superconducting or "condensed" ones. This
model was used to predict thermodynamic properties of superconductors with good
success. Fritz and Heinz London (1935) proposed an electromagnetic theory that, in
conjunction with the classical Maxwell equations of electromagnetism, predicted
many of the electric and magnetic properties of superconductors. The results of the
calculations made by the Londons showed that the magnetic field actually did
penetrate the surface of a superconductor for a very small distance (on the order of
0.1 m) called the penetration depth. The results also predicted that extremely thin
superconductors should have much higher critical fields than thick ones. Kropschot
and Arp (1961) suggested that this property of thin superconducting films could be
used in high­field, thin­film superconducting magnets.
Both the theory of the Londons and the theory of Gorter­Casimir predicted
many of the properties of superconductors, but the theories did not explain the "why"

38. 39
of the phenomenon. It was not until 1950 that an acceptable fundamental theory of
superconductivity was suggested. Frolich (1950) and Bardeen (1950) independently
proposed a mechanism involving the interaction of electrons in the superconductor.
Their ideas were developed into the BCS theory in 1957 by Bardeen, Cooper, and
Schrietfer (1957). They applied the quantum theory to pairs of electrons produced by
a special electron­lattice interaction. This process may be visualized as one in which
the first electron moving through the lattice causes a slight displacement of the ions,
which results in a positive screening charge slightly greater than the charge of the
electron. The second electron is then attracted toward the net positive charge region.
A correlation exists between all the pairs of electrons in the superconductor, and a
finite amount of energy is required to break up the pair, corresponding to the so­
called energy gap for the superconductor. As the temperature is increased above the
threshold value, enough energy is available to uncouple the electron pair, and the
material becomes normal.
Ginzburg and Landau (1950) developed a phenomenological theory that
explained the difference between the Type I and Type II superconductors in terms of
a parameter k, which was related to the surface energy of the material. Those
materials for which k is less than 1/ 2 have a positive surface energy and are Type
I superconductors. On the other hand, those materials for which k is greater than
1/ 2 have a negative surface energy and are Type II superconductors. This theory
of superconductivity is now known as the GLAG theory after the four Russian
contributors: Ginzburg, Landau, Abrikosov, and Gor’kov. Based on the concepts of
the theory, relationships between the parameter K and the upper and lower critical
fields were established.
C
C1
H (0.081 ln k)
H
k 2

(2.26)
and
C2 CH 2 kH
From a practical standpoint, eqn. (2.27) indicates that materials with a large
value of K will have a high value of the upper critical field HC2.

39. 40
For materials which have a relative permeability of approximately unity, the
magnetic induction and the magnetization M are related by
= 0(H+M) (2.28)
For Type I superconductors, the magnetic induction is zero, and H = –M.
At. The behavior of Type II superconductors is similar, for fields less than the lower
critical field HC1. For higher magnetic fields, the field begins to penetrate the
material, and the behavior of the material is shown in Fig. 2.14.
There are several properties that change either abruptly or gradually when a
material makes the transition from the normal to the superconducting state. Some of
these properties include:
1. Specific heat. The specific heat increases abruptly when a material becomes
superconducting.
2. Thermoelectric effects. All the thermoelectric effects (Peltier, Thomson,
and Seebeck effects) vanish when a material becomes superconducting. A
superconducting thermocouple would not work at all.
3. Thermal conductivity. In the presence of a magnetic field, the thermal
conductivity of a pure metal decreases abruptly when the metal becomes
superconducting, although for some alloys (for example, Pb­Bi in a limited
range of compositions) the opposite is true. In the absence of a magnetic
field, there is no discontinuous change in the thermal conductivity, but the
slope change is sharp on the conductivity­temperature curve.
4. Electric resistance. For Type I superconductors the decrease of resistance
to zero is quite abrupt; however, for Type II superconductors the change is
sometimes spread over a temperature range as large as 1 K.
5. Magnetic permeability. The magnetic permeability suddenly decreases to
zero for Type I superconductors (the Meissner effect); however, for Type II
superconductors the Meissner effect is incomplete for magnetic fields
greater than the lower critical field.

40. 41
Fig. 2.14. Variation of the magnetization with applied magnetic field intensity for
Type I and Type II superconductors.
Over the years considerable experimental effort has been expended in the
study of superconducting alloys and compounds in order to develop materials that
would remain superconducting at high values of magnetic field and at temperatures
nearer to liquid­hydrogen temperature (about 20 K). The materials most used for
superconducting magnets have been either the body­centered­cubic alloys of niobium
and titanium or the cubic beta­tungsten­type (Al5) compounds, such as Nb3Sn.
The body­centered­cubic alloys have been used in construction of magnets
with field strengths up to 10 tesla, while the niobium­titanium alloys can reach 12
tesla. In order to achieve thermal and magnetic stability, the niobium­titanium wires
used in superconducting magnets are usually clad with high­conductivity copper.
Although the compound niobium­tin has superconducting properties somewhat
superior to niobium­titanium, Nb3Sn is extremely brittle, and special fabrication
methods are required for its use.
PROPERTIES OF CRYOGENIC FLUIDS
2.12. Fluids other than hydrogen and helium
A summary of some of the thermodynamic and transport properties of fluids
commonly used in cryogenic engineering is shown in Table 2.6. Further data on fluid
properties are contained in the appendix.

41. 42
Liquid nitrogen is a dear, colorless fluid that resembles water in appearance.
At standard atmospheric pressure (101.3 kPa) liquid nitrogen beils at 77.36 K
(139.3°R) and freezes at 63.2 K (113.8°R). Saturated liquid nitrogen at 1 atm has a
density of 807 kg/m3
(50.4 lbm/ft3
) in comparison with water at 15.6o
C (60°F), which
has a density of 999 kg/m3
(62.3 lbm/ft). One of the significant differences between
the properties of liquid nitrogen and water (apart from the difference in normal
boiling points) is that the heat of vaporization of nitrogen is more than an order of
magnitude smaller than that of water. At the normal boiling point, liquid nitrogen has
a heat of vaporization of 199.3 kJ/kg (85.7 Btu/lbm), while water has a heat of
vaporization of 2257 kJ/kg (970.3 Btu/lbm).
Nitrogen with an atomic number of 14 has two stable isotopes with mass
numbers 14 and 15. The relative abundance of these two isotopes is 10,000:38. They
are relatively difficult to separate.
Because nitrogen is the major constituent of air (n.08 percent by volume or
75.45 percent by weight), it is produced commercially by distillation of liquid air.
Liquid oxygen has a characteristic blue color caused by the presence of the
polymer or long­chain molecule O4. At 1 atm pressure liquid oxygen boils at 90.18 K
(162.3°R) and freezes at 54.4 K (98.00
R). Saturated liquid oxygen at 1 atm is more
dense than water at 15o
C (liquid­oxygen density = 1141 kg/m3
= 71.2 lbm/ft3
). Oxygen
is slightly magnetic (paramagnetic) in contrast to the other cryogenic fluids, which
are nonmagnetic. By measuring the magnetic susceptibility, small amounts of
oxygen may be detected in mixtures of other gases. Because of its chemical activity,
oxygen presents a safety problem in handling. Serious explosions have resulted from
the combination of oxygen and hydrocarbon lubricants.
Oxygen with an atomic number of 16 has three stable isotopes of mass
numbers 16, 17, and 18. The relative abundance of these three isotopes is
10,000:4:20.
Oxygen is manufactured in large quantities by distillation of liquid air
because it is the second most abundant substance in air (20.95 percent by volume or
23.2 percent by weight).

42. 43
Liquid argon is a clear, colorless fluid with properties similar to those of
liquid nitrogen. It is inert and nontoxic. At 1 atm pressure liquid argon boils at 87.3
K (157.1o
R) and freezes at 83.8 K (150.8°R). Saturated liquid argon at 1 atm is more
dense than oxygen, as one would expect, because argon has a larger molecular
weight than oxygen (argon density = 1394 kg/m3
= 87.0 Ibm/ft3
for saturated liquid at
1 atm). The difference between the normal boiling point and the freezing point for
argon is only 3.5 K (6.3°R).
Argon has three stable isotopes of mass numbers 36, 38, and 40 that occur in
a relative abundance in the atmosphere in the ratios 338:63:100,000.
Argon is present in atmospheric air in a concentration of 0.934 percent by
volume or 1.25 percent by weight. Because the boiling point of argon lies between
that of liquid oxygen and that of liquid nitrogen (slightly closer to that of liquid
oxygen), a crude grade of argon (90 to 95 percent pure) can be obtained by adding a
small auxiliary argon­recovery column in an air­separation plant.
Neon is another gas that can be produced as a by­product of an air
separation plant. Liquid neon is a clear, colorless liquid that boils at 1 atm at 27.09 K
(48.8°R) and freezes at 24.54 K (44.3°R). The boiling point of neon is somewhat
above that of liquid hydrogen. But the fact that neon is inert, has a larger heat of
vaporization per unit volume, and has a higher density makes it an attractive
refrigerant when compared with hydrogen.
Neon (atomic weight = 20.183) has three stable isotopes of mass numbers
20, 21, and 22 that occur in a relative abundance in atmospheric air in the ratios
10,000:28:971.
Liquid fluorine is a light yellow liquid having a normal boiling point of
85.24 K (153.4°R). At 53.5 K (96.4°R) and 101.3 kPa, liquid fluorine freezes as a
yellow solid, but upon subcooling to 45.6 K (82°R) it transforms to a white solid.
Liquid fluorine is one of the most dense cryogenic liquids (density at normal boiling
point = 1507 kg/m3
= 94.1 Ibm/ft3
).
Fluorine is characterized chemically by its extreme reactivity, as indicated
by the emf of its electrochemical half cell (E = –2.85 volts). Fluorine will react with

43. 44
almost all inorganic substances. If fluorine comes in contact with hydrocarbons, it
will react hypergolically with a high heat of reaction, which is sometimes sufficiently
high that the metal container for the fluorine is ignited. Such metals as low­carbon
stainless steel and Monel, which are used in fluorine systems, develop a protective
surface film when brought in contact with fluorine gas. This surface film prevents the
propagation of the fluorine­metal reaction into the bulk metal.
Fluorine is highly toxic. The fatal concentration range for animals is 200
ppm­hr (Cassutt et al. 1960). That is, for an exposure time of I hour, 200 ppm of
fluorine is fatal; for an exposure time of 15 minutes, 800 ppm is fatal; and for an
exposure time of 4 hours, 50 ppm is fatal. The maximum allowable concentration for
human exposure is usually considered to be approximately 1 ppm­hr. The presence
of fluorine in air may be detected by its sharp, pungent odor for concentrations as
low as I to 3 ppm. Because of its high toxicity, liquid fluorine is not utilized on a
large scale.
Methane is the principal component of natural gas. It is a clear, colorless
liquid that boils at 1 atm at 111.7 K (201.1o
R) and freezes at 88.7 K (159.7°R).
Liquid methane has a density approximately one­half of that for liquid nitrogen
(methane. density = 424.1 kg/m3
= 26.5 lbm/ft3
). Methane forms explosive mixtures
with air in concentrations ranging from 5.8 to 13.3 percent by volume. Liquid
methane has been shipped in large quantities by tanker vessels. The Methane Pioneer
made her maiden voyage on January 28, 1959 with 5000 m3
of LNG (liquid natural
gas). Since that time, several vessels have been commissioned for LNG transport.
2.13. Hydrogen
Liquid hydrogen has a normal boiling point of 20.3 K (36.5o
R) and a density
at the normal boiling point of only 70.79 kg/m3
(4.42 Lbm/ft3
). The density of liquid
hydrogen is about one­fourteenth that of water; thus, liquid hydrogen is one of the
lightest of all liquids. Liquid hydrogen is an odorless, colorless liquid that alone will
not support combustion. In combination with oxygen or air, however, hydrogen is
quite flammable. Experimental work (Cassutt et al. 1960) has shown that hydrogen­
air mixtures are explosive in an unconfined space in the range from 18 to 59 percent
hydrogen by volume.

44. 45
Natural hydrogen is a mixture of two isotopes: ordinary hydrogen (atomic
mass = 1) and deuterium (atomic mass = 2). Hydrogen gas is diatomic and is made
up of molecules of H2 and HD (hydrogen deuteride) in the ratio of 3200:1. A third
unstable isotope of hydrogen exists, called tritium; however, it is quite rare in nature
because it is radioactive with a short half life.
One of the properties of hydrogen that sets it apart from other substances is
that it can exist in two different molecular forms: ortho­hydrogen and para­
hydrogen. The mixture of these two forms at high temperatures is called normal
hydrogen which is a mixture of 75 percent orthohydrogen and 25 percent para­
hydrogen by volume. The equilibrium (catalyzed) mixture of o­H2 and p­H2 at any
given temperature is called equilibrium­hydrogen (e­H2). The equilibrium
concentration of p­H2 in e­H2 as a function of temperature is given in Table 2.7. At
the normal boiling point of hydrogen (20.3 K or 36.5o
R), equilibrium hydrogen has a
composition of 0.20 percent o­H2 and 99.80 percent p­H2. One could say that it is
practically all para­hydrogen .
The distinction between the two forms of hydrogen is the relative spin of the
particles that make up the hydrogen molecule. The hydrogen molecule consists of
two protons and two electrons. The two protons possess spin, which gives rise to
angular momentum of the nucleus, as indicated in Fig. 2.15. When the nuclear spins
are in the same direction, the angular momentum vectors for the two protons are in
the same direction. This form of hydrogen is called ortho­hydrogen. When the
nuclear spins are in opposite directions, the angular­momentum vectors point in
opposite directions. This form of hydrogen is called para­hydrogen.
Table 2.7. Equilibrium concentration of para­hydrogen in equilibrium­hydrogen
Temperature
(K)
Mole fraction
Para­Hydrogen
20.27 0.9980
30 0.9702
40 0.8873
50 0.7796
60 0.6681
70 0.5588
80 0.4988
90 0.4403

45. 46
100 0.3947
120 0.3296
140 0.2980
160 0.2796
180 0.2676
200 0.2597
250 0.2526
300 0.2507
Deuterium can also exist in both ortho and para forms. The nucleus of the
deuterium atom consists of one proton and one neutron, so that the high­temperature
composition (composition of normal deuterium) is two­thirds ortho­deuterium and
one­third para­deuterium. In the case of deuterium, p­D2 converts to o­D2 as the
temperature is decreased, in contrast to hydrogen, in which o­H2 converts to p­H2
upon decrease of temperature. The hydrogen deuteride molecule does not have the
symmetry that hydrogen and deuterium possess; therefore, HD exists in only one
form.
As one can see from Table 2.7, if hydrogen gas at room temperature is
cooled to the normal boiling point of hydrogen, the o­H2 concentration decreases
from 75 to 0.2 percent; that is, there is a conversion of o­H2 to p­H2 as the
temperature is decreased. This changeover is not instantaneous but takes place over a
definite period of time because the change is made through energy exchanges by
molecular magnetic interactions. During the transition, the original o­H2 molecules
drop to a lower molecular­energy level. Thus the changeover involves the release of
a quantity of energy called the heat of conversion. The heat of conversion is related
to the change of momentum of the hydrogen nucleus when it changes direction of
spin. This energy released in the exothermic reaction is greater than the heat of
vaporization of liquid hydrogen, as one can see from the tabulated values of the heat
of conversion and heat of vaporization shown in Appendix D.2.

46. 47
Fig. 2.15. Ortho­hydrogen and para­hydrogen.
When hydrogen is liquefied, the liquid has practically the room­temperature
composition unless some means is used to speed up the conversion process. If the
unconverted normal hydrogen is placed in a storage vessel, the heat of conversion
will be released within the container, and the boil­off of the stored liquid will be
considerably larger than one would determine from the ordinary heat in leak through
the vessel insulation. Note that the heat of conversion at the normal boiling point of
hydrogen is 703.3 kJ/kg (302.4 Btu/lbm) and the latent heat of vaporization is 443 kJ
/kg (190.5 Btu/lbm). The conversion process evolves enough energy to boil away
approximately 1 percent of the stored liquid per hour, so the reaction would
eventually result in much of the stored liquid being boiled away. For this reason, a
catalyst is used to speed up the conversion so that the energy may be removed during
the liquefaction process before the liquid is placed in the storage vessel.
In the absence of a catalyst, the ortho­para transformation is a second order
reaction (Scott et al. 1934); that is, the rate of change of the o­H2 mole fraction is
given by
20
2 0
dx
C x
dt
 
(2.29)
where C2 is the reaction­rate constant, 0.0114 hr–1
for hydrogen at the normal boiling
point, and x0 = 1 – xp is the mole fraction of o­H2 present at any time t. If eqn. (2.29)
is integrated from the initial time when the a­H2 composition is that in normal
hydrogen (0.750), the mole fraction of o­H2 at any time is given by
o
2
0.75
x
1 0.75C t

 (2.30)

47. 48
for liquid hydrogen at the normal boiling point. In the presence of a catalyst that is
well mixed with the hydrogen, the reaction approaches a first order reaction for the
gas phase (Chapin et al. 1960), for which
20
1 0
dx
C x
dt
 
(2.31)
where C1 is the reaction­rate constant, which depends upon the catalyst used, the
temperature, and the pressure of the gas. If the catalyst is added to the liquid phase,
the reaction is a zero­order one (Cunningham et al. 1960), for which
0
0
dx
C
dt
 
(2.32)
where C0 is the reaction­rate constant for the zero­order reaction, which also depends
upon the catalyst, the fluid temperature, and the pressure.
Fig. 2.16. Specific heat c. for p­H2• n­H2• and o­H2 (by permission from Fowler and
Guggenheim 1949).

48. 49
These two forms of hydrogen have different specific heats because of the
different weighting of the energy levels of the two forms, as indicated in Fig. 2.16.
Because of this difference in specific heats, other thermal and transport properties are
also affected. For example, para­hydrogen gas has a higher thermal conductivity than
ortho­hydrogen gas because of the higher specific heat of p­H2.
2.14. Helium 4
Helium has two stable isotopes: He4
, the most common one, and He3
.
Ordinary helium gas contains about 1.3 × 10–4
percent He3
, so when we speak of
helium or liquid helium, we shall be referring to He4
, unless otherwise stated. Liquid
He4
has a normal boiling point of 4.214 K (7.58°R) and a density at the normal
boiling point of 124.8 kg/m3
(7.79 lbm/ft3
), or about one­eighth that of water. Liquid
helium has no freezing point at a pressure of 101.3 kPa (1 atm). In fact, liquid helium
does not freeze under its own vapor pressure even if the temperature is reduced to
absolute zero. At absolute zero, liquid helium 4 must be compressed to a pressure of
2529.8 kPa (24.97 atm or 366.9 psia) before it will freeze, as indicated in Fig. 2.17.
Liquid He4
is odorless and colorless and has an index of refraction near that of
gaseous He4
(nr = 1.02 for liquid He4
). The heat of vaporization of liquid He4
at the
normal boiling point is 20.90 kJ/kg (8.98 Btu/lbm), which is only 1
/110 that of water.
Although helium is classified as a rare gas, and it is one of the most difficult
gases to liquefy, its unusual properties have excited so much interest that helium has
been the object of more experimental and theoretical research than any of the other
cryogenic fluids.

49. 50
Fig. 2.17. Phase diagram for helium 4.
We notice from Fig. 2.17 that the phase diagram of He4
differs in form from
that of any other substance. As mentioned previously, liquid He4
does not freeze
under its own vapor pressure; therefore, there is no triple point for the solid­liquid­
vapor region of helium as there is for other substances. There are two different liquid
phases: Liquid helium I, the normal liquid; and liquid helium II, the superliquid. The
phase transition curve separating the two liquid phases is called the lambda line, and
the point at which the lambda line intersects the vapor­pressure curve is called the
lambda point, which occurs at a temperature of 2.171 K (3.9lo
R) and a pressure of
5.073 kPa (0.050 atm or 0.736 psia).
In Fig. 2.18, we see that the specific heat of liquid helium varies with
temperature in an unusual manner for liquids. At the lambda point, the liquid specific
heat increases to a large value as the temperature is decreased through this point.
With a little imagination, one could say that the form of the specific­heat curve looks
somewhat like the small Greek letter lambda; hence, the name lambda point. It was
first believed that the transition form helium I to helium II was a second­order
transition; however, later work has shown that the transition is more complicated.

50. 51
Because the specific heat of liquid helium has such a different behavior
from that of other liquids, we should expect that the other thermal and transport
properties could also differ in behavior. Strangely enough, the thermal conductivity
of helium I decreases with a decrease in temperature, which is similar to the behavior
of the thermal conductivity of a gas.
Heat transfer in the other form, helium II, is even more spectacular. When a
container of liquid helium I is pumped upon to reduce the pressure above the liquid,
the fluid boils vigorously (depending upon the rate of pumping) as the pressure of the
liquid decreases. During the pumping operation, the temperature of the liquid
decreases as the pressure is decreased and liquid is boiled away. When the
temperature reaches the lambda point and the fluid becomes liquid helium II, all
ebullition suddenly stops. The liquid becomes clear and quiet, although it is
vaporizing quite rapidly at the surface. The thermal conductivity of liquid helium II
is so large that vapor bubbles do not have time to form within the body of the fluid
before the heat is quickly conducted to the surface of the liquid. Liquid helium I has
a thermal conductivity of approximately 24 mW/m­K (0.014 Btu/hr­ft­o
F) at 3.3 K
(6°R), whereas liquid helium II can have an apparent thermal conductivity as large as
85 kW/m­K (49,000 Btu/hr­ft­°F) – much higher than that of pure copper at room
temperature! There is some question about defining a thermal conductivity for liquid
helium II because the thermal conductivity defined in the ordinary manner depends
not only on temperature, but also on the temperature gradient and the size of the
container (Keesom et al. 1940). The reason for this behavior will illustrate the nature
of this unique liquid.
One of the unusual properties of liquid helium II is that it exhibits
superliquidity; under certain conditions, it acts as if it had zero viscosity. In
explaining the behavior of1iquid helium II, it has been proposed (Landau 1941) that
the liquid be imagined to be made up of two different fluids: the ordinary fluid and
the superfluid, which possess zero entropy and can move past other fluids and solid
boundaries with zero friction. Using this model, liquid helium II has a composition of
normal and superfluid that varies with temperature, as shown in Table 2.8. At

51. 52
absolute zero, the liquid composition is 100 percent superfluid; at the lambda point,
the liquid composition is 100 percent normal fluid.
Fig. 2.18. Specific heat of saturated liquid helium 4.
The addition of heat to liquid helium II raises the local temperature of the
liquid around the point where heat is being added, which raises the concentration of
normal molecules and lowers the concentration of superfluid ones. The superfluid
then moves to equalize the superfluid concentration throughout the body of the
liquid. Because the superfluid is frictionless, it can move rapidly; therefore, we see
that the high apparent thermal conductivity of helium II is really due to a fast
convection process rather than simply to conduction.
This type of transfer mechanism also explains the so­called "fountain effect"
that is observed in liquid helium II (Allen and Jones 1938; Keller 1969). When heat
is added to the powder in the apparatus shown in Fig. 2.19, the increase in
temperature tends to raise the concentration of normal fluid, and the superfluid
rushes in to equalize the concentration. Normal fluid, because of its viscosity, cannot
leave through the small openings between the fine powder particles very rapidly. The
amount of helium quickly builds up within the tube as a result of this inflow of