adiabatic demag

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Adiabatic demagnetization

INTRODUCTION

Dictionary

PPhhoottoonn CCoooolliinngg b byy AAddiiaa b baattiicc DDeemmaaggnneettiizzaattiioonn means the process of cooling photons in an

atom by the method called adiabatic demagnetization.

According to third law of thermodynamics cooling of a material is possible only till absolute

o. i.e. 0 Kelvin. This temperature is reached by freezing the movement of molecules of a

substance.

Encyclopedia

Adiabatic Demagnetization Refrigerators (ADRs) have been used as reliable tools for cooling

to temperatures below 100 mK for over 60 years [1]. In the 1970s, however, ADRs took a

back seat in the typical low temperature laboratory environment to the dilution refrigerator,

which offers higher cooling power (although at the expense of additional complication). The

last several years have witnessed the development of two-stage ADRs which, when combined

with a low-temperature mechanical cryocooler, will achieve temperatures below 100 mK

without cryogens. In an ADR, a paramagnetic material is suspended in a magnetic field,

typically provided by a superconducting magnet. The refrigerant is thermally isolated from

higher temperature stages of the cryostat and thermally connected

to the parts that are to be cooled. Many suitable paramagnetic materials are salts of hydration,

and the salt is housed in a hermetically sealed container (the ³salt pill´) to prevent

dehydration in the cryostat¶s vacuum.

The temperature of a substance is determined by the average velocity of its molecules: the

faster they move, the warmer the substance. At absolute zero molecules have minimal kineticenergy (or zero-point energy) and heat energy cannot be extracted from them. The molecules

are not motionless, however, due to the uncertainty principle of quantum mechanics, which

entails that the atoms cannot have both a fixed position and zero momentum at the same time;

instead, the molecules of a substance at absolute zero are always "wiggling" in some manner.

Absolute zero is zero Kelvin, equal to -273.15 degrees Celsius and -459.67 degrees



Fahrenheit. The coldest known place in the universe is the Boomerang Nebula, where the

temperature is -272° Celsius. Scientists at Massachusetts Institute of Technology have gone

much lower than that by using laser traps and other techniques to cool rubidium to 2 × 10-9

Kelvin."

LAWS OF THERMODYNAMICS

ZEROTH LAW:

The zeroth law states that if two systems are in thermal equilibrium with a third system, they

are also in thermal equilibrium with each other.

FIRST LAW:

The first law of thermodynamics is an expression of the principle of conservation of

energy.

The law expresses that energy can be transformed, i.e. changed from one form to another, but

cannot be created nor destroyed. It is usually formulated by stating that the change in the

internal energy of a system is equal to the amount of heat supplied to the system, minus the

amount of work performed by the system on its surroundings.

A closed system is one where no material is transferred across the system boundaries. Only

heat and work are transferred to the system as shown in the picture above.

As work is done on a real gas, the temperature and pressure increase and some heat will be

transferred out of the system.

As a real gas expands, it does work on the surroundings and the temperature and pressure

decrease. Heat is transferred to the system.



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We balance t e changes in the internal energy of the gas with the amount of heat transferred

to/from the gas and work done by/on thegas. This energy balance is called the f irst law for a

closed system. It is wr itten

differential form dU = dQ - dW

integrated form (1)

SEC LAW:

Second law has been explained by two scientists called Kel in plank andR udolf Clausius

Both have explained single concept in different way.

Kelvin plank : It is impossible to devise an engine which, working in a cycle, shall produce no

effect other than the extraction of heat from a reservoir and the performance of an equal

amount of work

Rudolf Clausi us: No process is possible whose sole result is the transfer of heat from a body

of lower temperature to a body of higher temperature

This is an example of refr igeration cycle



According to this law if the temperature of system to be cooled has to come down to 0k work

supplied will be infinity.

ENTROPY

In classical thermodynamics, the entropy of a system is the ratio of heat content to

temperature (equation 1),

And the change in entropy represents the amount of energy input to the system which does

not participate in mechanical work done by the system (equations 2, 3)

S = Q/T----------------------------------------------------------------------------------------------------- 1

In equation 1, S is the entropy, Q is the heat content of the system, and T is the temperature

of the system. At this time, the idea of a gas is made up of tiny molecules and temperature

representing their average kinetic energy, had not yet appeared. Carnot & Clausius thought of

heat as a kind of fluid, a conserved quantity that moved from one system to the other. It was

Thomson who seems to have been the first to explicity recognize that this could not be the

case, because it was inconsistent with the manner in which mechanical work could be

converted into heat.

The temperature of the system is an explicit part of this classical definition of entropy, and a

system can only have "a" temperature (as opposed to several simultaneous temperatures) if it

is in thermodynamic equilibrium. So, entropy in classical thermodynamics is defined only for

systems which are in thermodynamic equilibrium.

As long as the temperature is t constant, it's a simple enough exercise to differentiate equation

1, and arrive at equation 2.

S = Q/T------------------------------------------------------------------------------------------------ 2



Here the symbol " " is a representation of a finite increment, so that S indicates a "change"

or "increment" in S, as in S = S1 - S2, where S1 and S2 are the entropies of two different

equilibrium states, and likewise Q. If Q is positive, then so is S, so if the internal heat

energy goes up, while the temperature remains fixed, then the entropy S goes up. And, if the

internal heat energy Q goes down ( Q is a negative number), then the entropy will go down

too.

Clausius and the others, especially Carnot, were much interested in the ability to convert

mechanical work into heat energy, and vice versa. This idea can lead us to an alternate form

for equation 2, that will be useful later on. Suppose you pump energy, U, into a system,

Part of the energy goes into the internal heat content, Q, making Q a positive quantity, but

not all of it. Some of that energy could easily be expressed as an amount of mechanical work

done by the system ( W, such as a hot gas pushing against a piston in a car engine). So thatQ = U - W, where U is the energy input to the system, and W is the part of that

energy that goes into doing work. The difference between them is the amount of energy that

does not participate in the work, and goes into the heat reservoir as Q. So a simple

substitution allows equation 2 to be re-written as equation 3.

S = ( U - W)/T---------------------------------------------------------------------------------------3

This alternate form of the equation works for heat taken out of a system ( U is negative) or

work done on a system ( W is negative), just as well. So it gives the better idea of the

classical relation between work, energy and entropy.

THIRD LAW OF THERMODYNAMICS

Third law states that ³It is im£ ossibl ¤ f or any materi al b y any process t o cool below absolute

zero´

This postulate related to but independent of the second law is that it is impossible to cool a

body to absolute zero by any finite process. Although one can approach absolute zero as

closely as one desires, one cannot actually reach this limit. The third law of thermodynamics,

formulated by Walter Nernst and also known as the Nernst heat theorem, states that if one

could reach absolute zero, all bodies would have the same entropy. In other words, a body at



absolute zero could exist in only one possible state, which would possess a definite energy,

called the zero-point energy. This state is defined as having zero entropy.

so to cool any material to zero Kelvin or near zero Kelvin we require to stop the motion of

the molecules of an atom. As this is not possible it is impossible to cool any material to zeroKelvin. Still scientists have reached temperature as low as 50 micro Kelvin, Which is almost

considered as zero Kelvin

GENERAL COOLING METHODS

� Freezing to 00 c (vapor compression or absorption)

� Dilution refrigeration

� Adiabatic demagnetization refrigeration.

VAPOR COMPRESSION REFRIGERATION

A simple vapor compression refrigeration system consists of the following equipments¶)

Compressor ii) Condenser iii) Expansion valve iv) Evaporator The schematic diagram of the

arrangement is as shown in Fig.6.5. The low temperature, low pressure vapor at state B is

compressed by a compressor to high temperature and pressure vapor at state C. This vapor is

condensed into high pressure vapor at state D in the condenser and then passes through the

expansion valve. Here, the vapor is throttled down to a low pressure liquid and passed on to

an evaporator, where it absorbs heat from the surroundings from the circulating fluid (being

refrigerated) and vaporizes into low pressure vapor at state B. The cycle then repeats.The

exchange of energy is as follows:



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a) Compressor requires work, w. The work is supplied to the system from the surroundings.

b) Dur ing condensation, heat Q1 the equivalent of latent heat of condensationetc, is lost from the refr igerator.

c) Dur ing evaporation, heat Q2 equivalent to latent heat of vapor i ation is

absorbed by the refr igerant.

d) There is no exchange of heat dur ing throttling process through the expansion

valve as this process occurs at constant enthal py.

SIMPLE VAPOR COMPR ESSION CYCLE:



Figure shows a simple vapor compression refrigeration cycle on T-s diagram for

different compression processes. The cycle works between temperatures T1 and T2

representing the condenser and evaporator temperatures respectively. The various process of

the cycle A-B-C-D (A-B¶-C¶-D and A-B´-C´-D) are as given below:

Indian Institute of Technology Madras

i) Process B-C (B¶-C¶ or B´-C´): Isentropic compression of the vapor from state B to C. If

vapor state is saturated (B), or superheated (B´), the compression is called dry compression.

If initial state is wet (B¶), the compression is called wet compression as represented by B¶-C¶.

ii) Process C-D (C¶-D or C´-D): Heat rejection in condenser at constant pressure. S

iii) Process D-A: An irreversible adiabatic expansion of vapor through the expansion value.

The pressure and temperature of the liquid are reduced. The process is accompanied by

partial evaporation of some liquid. The process is shown by dotted line.

iv) Process A-B (A-B¶ or A-B´) : Heat absorption in evaporator at constant pressure. The

final state depends on the quantity of heat absorbed and same may be wet (B¶) dry (B) or

superheated (B´).

DILUTION REFRIGERATION (DR)



A dilution refrigerator (DR) is the most common pre cooling stage for sub-milekelvin

demagnetization experiments. The usefulness of the DR comes from its ability to provide

cooling at 0.02-0.04 K for long periods of time while the heat of magnetization is being

rejected by the demagnetization stage. In order to make these advantages of the DR available

to researchers who need the microgravity of space for their experiments.

The liquid helium of the DR can be controlled by the use of capillary forces in sintered metal

sponges. It is found, however, that the small pores needed to control large heights of liquid on

the ground are too small to allow sufficient liquid flow for effective cooling.

First a shallow single-cycle version of the refrigerator that does not require large

heights of liquid to be supported by capillary forces is built. The liquid chambers are next to

each other and are filled with sinter with relatively open pores; these pores will allow much

freer flow of the helium. The gravity independence of this design will be tested by tilting the

system so that one chamber is slightly above or below the other and by inverting both

chambers. The operation of the refrigerator should be unaffected by tilts of 5-10 degrees or

by the inversion of the chambers.

TYPE OF REFRIGERATOR NEEDED

To carry out research at low temperatures it is necessary to have a refrigerator that 1) cools to

the required temperature, 2) is reliable and, 3) if possible, operates continuously for the

duration of the experiment, whether that is hours or days. On the ground the need for

temperatures below 0.3 K is almost universally met by the He-3-He-4 dilution refrigerator. Its

usefulness arises from the fact that it operates continuously, it can provide a substantial

cooling power at temperatures from around 1.0 K down to 0.010 K and below and it can run

uninterrupted for as long as several months.

There are many very interesting physics experiments that need the unique microgravity

Environment of space but which also need lower temperatures than are currently available. In



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Order to investigate phenomena that occur at very low temperatures, particularly in super

fluid He-3, the capability for extending research to temperatures of 0.001 K in space needs to

be developed. On the ground, temperatures to 0.001 K and below are reached with adiabatic

Demagnetization systems that are pre cooled with helium dilution refrigerators. Similar

Temperatures can be achieved in space if the dilution refrigerator can be adapted to work in

Microgravity.

WORKING:

Figure shows how dilution a refrigerator operates. The lowest temperatures occur in the

mixing chamber where there is a phase boundary between liquid He-3 and liquid He-4.

Cooling is produced when He-3 crosses this boundary into the He-4. From the mixing

chamber this dilute He-3 flows through the He-4 to a higher temperature chamber where it is

fractionally distilled from the He-4. The resulting He-3 gas is collected by the charcoal pump.

The cooling cycle ends when all the He-3 is in the charcoal pump. Because the refrigerator

uses adsorption onto charcoal for its pumping, all operations can be controlled by heaters and,

as a consequence, there are no moving parts in the refrigerator.



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NUCLEAR DEMAGNETIZATION

This method is one of the oldest and in principle simples methods of reaching the

temperatures below 1K. It has been proposed in 1926 by Debye and Giauque, long before the

dilution refrigerator has been invented. Compared to the dilution refrigerator it allows

reaching substantially lower temperatures, in micro Kelvin scale. The main operating

principle is based on the entropy conservation in the closed system.

WORKING PRINCIPLE

y Adiabatic magnetization: A magnetocaloric substance is placed in an insulated

environment. The increasing external magnetic field (+H) causes the magnetic dipoles

of the atoms to align, thereby decreasing the material's magnetic entropy and heat

capacity. Since overall energy is not lost (yet) and therefore total entropy is not

reduced (according to thermodynamic laws), the net result is that the item heats up (T

+ Tad).



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The basic operating principle of an adiabatic demagnetization refrigerator (ADR) is the use of

a strong magnetic field to control the entropy of a sample of material, often called the

"refrigerant". Magnetic field constrains the orientation of magnetic dipoles in the refrigerant.

The stronger the magnetic field, the more aligned the dipoles are, and this corresponds to

lower entropy and heat capacity because the material has (effectively) lost some of its internal

degrees of freedom. If the refrigerant is kept at a constant temperature through thermal

contact with a heat sink (usually liquid helium) while the magnetic field is switched on, the

refrigerant must lose some energy because it is equilibrated with the heat sink. When the

magnetic field is subsequently switched off, the heat capacity of the refrigerant rises again

because the degrees of freedom associated with orientation of the dipoles are once again

liberated, pulling their share of equipartitioned energy from the motion of the molecules,

thereby lowering the overall temperature of a system with decreased energy. Since the system

is now insulated when the magnetic field is switched off, the process is adiabatic, i. ̈

., the

system can no longer exchange energy with its surroundings (the heat sink), and its

temperature decreases below its initial value, that of the heat sink.

The operation of a standard ADR proceeds roughly as follows. First, a strong magnetic field

is applied to the refrigerant, forcing its various magnetic dipoles to align and putting these

degrees of freedom of the refrigerant into a state of lowered entropy. The heat sink then

absorbs the heat released by the refrigerant due to its loss of entropy. Thermal contact with

the heat sink is then broken so that the system is insulated, and the magnetic field is switched

off, increasing the heat capacity of the refrigerant, thus decreasing its temperature below the

temperature of the helium heat sink. In practice, the magnetic field is decreased slowly in

order to provide continuous cooling and keep the sample at an approximately constant low

temperature. Once the field falls to zero or to some low limiting value determined by the

properties of the refrigerant, the cooling power of the ADR vanishes, and heat leaks will

cause the refrigerant to warm up.

CONSTRUCTIONFerric ammonium alum (FAA) has a spin ion density of 1.17 3 1024 kg-1, Its magnetic

properties, combined with its high solubility in water, make FAA a practical working

substance and nearly ideal paramagnetic material for 100 mK operation from a pumped LHe

bath. Table 1 summarizes some of the relevant physical properties of FAA.



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Table 1

Some physical proper ties of AA

Chemical symbol e(NH4)2(SO4)212H2O

20°C solubility 1.2 g/cc

35°C solubility 4.0 g/cc

Crystal density 1.35 g/cc

Unfor tunately, AA has a few proper ties which complicate its use. AA is corrosive to

copper-based alloys. This effect is not subtle. It is found that gold plating the inner walls of a

brass tube was not enough to prevent the salt from eating throughthe 500 mm tube wall

within a few days. Consequently, no copper alloys used in the SPH can be allowed to come

into contact with the AA. Attempts were also made to grow AA pills in MACOR (a glass-

ceramic made by Corning) and Plexiglass housings. In both cases the housings cracked



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electricity one can save lot of space, energy and cost of maintenance.

3. The another application is called Josephson junction, this is able to measure very

weak magnetic patterns, those produce in brains, heart and lungs etc. hence it is used

in ecg, scanning etc.



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REFERENCES

y TIFR

Talk by Mr. Naren (2010)

y History of thermodynamics

By Ingo Muller

y NPTEL-IITM

Video lectures by Prof. S.K Som

y Basic and applied thermodynamics

P.K.Nag

Tata Mc Grawhill Publication

y Construction techniques for adiabatic demagnetization refrigerators

using ferric ammonium alum

by: Grant W. Wilson, Peter T. Timbie Uni

it

f C

i !

y Wikipedia

y Ask .com

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