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CRYOGENIC ENGINEERING III LOW TEMPERATURE PROPERTIES OF MATERIALS 1
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CRYOGENIC ENGINEERING III

CRYOGENIC ENGINEERING IIILow temperature properties of materials

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Thermal PropertiesThermal Expansion/ContractionSpecific Heat of SolidsThermal Conductivity2

Thermal Expansion/ContractionThe linear coefficient of thermal expansion is the fractional change in length per unit change in temperature while the stress is constant.In general, the coefficient of thermal expansion (t) decreases with the decrease in temperature.Most contraction occurs till 80 K.3

Thermal Expansion/ContractionInternal energy is low at cryogenic temperature.So the atoms vibrations will be less and so intermolecular distance will be low.Hence, the coefficient of thermal expansion (t) increases with the increase in temperature.

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Specific HeatIt is the energy required to change the temperature of a unit mass of substance by 1 C, holding the volume or pressure as constant.Debye treated solid as an infinite elastic continuum.A parabolic frequency distribution was derived for the atoms vibrating in lattice.

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Debye Theory6

Debye Theory7

Debye Theoryspecific heat decreases with the decrease in temperature.The variation is a cubic equation in absolute temperature at very low temperatures.

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Thermal ConductivityThermal conductivity, k, is the property of a material which indicates its ability to conduct heat.In general, k decreases with the decrease in the temperature.However, for pure metals the variation is slightly different from that of impure metals and alloys.

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Conduction in Pure MetalsThe Electron and Phonon motion cause heat conduction.The contribution of electron motion to heat conduction is predominant above LN2 temperature.Conduction depends on the product of electronic specific heat and mean free path.

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Conduction in Pure MetalsThis product being a constant above LN2, the k remains constant above LN2.As the temperature is lowered, phonon contribution increases and k also increases11

Conduction in Pure MetalsIt reaches a high value until the mean free path of the electrons equals to the dimensions of test specimen.

When this condition is reached, the surface exhibits a resistance causing the k to decrease.12

Impure & Alloy Metals13

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Electric PropertiesDecreasing the temperature decreases the vibration energy of the ions. This results in smaller interference with electron motion.Therefore, electrical conductivity of the metallic conductors increases at low temperature.14

SuperconductivityThe state of the SC is governed by Temperature (K), Current Density (A/mm2) and Magnetic Field (Tesla).15

Bardeen-Cooper-Schrieffer TheoryElectron being a negatively charged particle, moves easily through the space between the adjacent rows of positively charged ions.This motion is assisted by the electrostatic force which pulls the electrons inward.In SC state, the electrons interact with each other and form a pair. This interaction is a very low energy process (0.1 eV) called as phonon interaction.16

Bardeen-Cooper-Schrieffer TheoryThe electron pair so formed moves easily and the second electron follows the first electron during the motion. As a result, this electron pair travelling together, encounters less resistance.This electron pair is called as a Cooper Pair.17

High Tc and Low Tc MaterialsSuperconducting materials are distinguished depending upon the critical temperature they exhibit.the materials having transition temperature above 77 K are called as High Tc materials.18

Meisner EffectAt room temperature, if a material is subjected to a magnetic flux, the flux lines of force penetrate through the material.As soon as the material becomes superconducting, it repels the magnetic flux lines.This phenomenon is called as Meisner Effect.19