1. Thermal Properties of Materials
Department of Physics
K L University

2. Brief Introduction
“Thermal property” is meant the response of a material to the application of heat.
As a solid absorbs energy in the form of heat, its temperature rises and its dimensions increase. The energy may be transported to cooler regions of the specimen if temperature gradients exist, and ultimately, the specimen may melt.
Thermal Properties:
Heat capacity
Atomic vibrations, phonons
Temperature dependence
Contribution of electrons
2. Thermal expansion
Connection to anharmonicity of interatomic potential
Linear and volume coefficients of thermal expansion
Thermal conductivity
Heat transport by phonons and electrons

3. Atomic Vibrations
The atoms and ions that are bonded together with considerable inter atomic forces, are not motionless.
Due to the consistent vibrating movements, they are permanently deviating from their equilibrium position.
Atomic vibrations are in the form of lattice waves or phonons.

4. Heat Capacity
Heat capacity is a property that is indicative of a material’s ability to absorb heat from the external surroundings.
It is defined as the amount of energy required to produce a unit temperature rise.
Mathematically, it is expressed as:
Where dQ is the energy required to produce a temperature change equal to dT.
Heat capacity has units as J/mol-K or Cal/mol-K.

5. Specific Heat
For comparison of different materials, heat capacity has been rationalized.
Specific heat is heat capacity per unit mass. It has units as J/kg-K or Cal/kg-K.
With increase of heat energy, dimensional changes may occur. Hence, two heat capacities are usually defined.
Heat is absorbed through different mechanisms:
1. Lattice vibrations and
2. Eelectronic contribution.

6. Classical Theory of specific heat
(Dulong- Petit Law)
Assumptions:
Vibrating atoms can be considered as linear harmonic oscillators
All the atoms are vibrating with the same frequency
The constant value of the heat capacity of many simple solids is sometimes called Dulong – Petit law
In 1819 Dulong and Petit found experimentally that for many solids at room temperature,
cv ≈ 3R = 25 J - K-1mol-1
Merits & De-Merits:
This law of Dulong and Petit (1819) is approximately obeyed by most solids at high T ( > 300 K).
But by the middle of the 19th century it was clear that CV  0 as T  0 for solids.

7. Quantum Theory of specific heat
(Einstein’s Theory)
Planck (1900): vibrating oscillators (atoms) in a solid have quantized energies
[later QM showed is actually correct]
Einstein (1907): model a solid as a collection of 3N independent 1-D oscillators, all with constant , and use Planck’s equation for energy levels
Merits & De-Merits:
This law also valid at high temperatures.
At low temperatures specific heat varies exponentially.

8. Debye’s Theory of specific heat
According to this theory a solid is considered as an ensemble of independent quantum harmonic oscillators vibrating at a frequency ν.
Debye advanced the theory by treating the quantum oscillators as collective modes in the solid (phonons) and showed that
Heat capacity has a weak temperature dependence at high temperatures (above Debye temperature θD) but decreases down to zero as T approaches 0K.

9. At low temperatures, vibrational heat contribution of heat capacity varies with temperature as follows:
The above relation is not valid above a specific temperature known as Debye temperature. The saturation value is approximately equal to 3R.

11. The electron contribution to cv is proportional to temperature,
cvel = γT
and becomes significant (for metals only) at very low temperatures
(remember that contribution of phonons cv ~ AT3 at T → 0K).

12. Characteristics of Specific Heat
Characteristics of an object with low specific heat:
Fast heated up: have a faster temperature increase
Fast cooled down: have a faster temperature decrease
Sensitive to temperature changes
Ex: Aluminium, copper etc
Characteristics of an object with high specific heat:
Heats up and cools down at a slower rate
Requires more heat to rise its temperature by a specific amount
Can absorb a great amount of heat
Ex: plastic, water, concrete etc

13. Applications of Specific Heat
1. Substances having a small specific heat capacity can be quickly heated up, it also experience a big change in temperature even though only small amount of heat is supplied. 2. Substances having a small specific heat capacity, are very useful as material in cooking instruments such as frying pans, pots, kettles and so on, because, they can be quickly heated up even when small amount oh heat is supplied.
Substances that have a high specific heat capacity is suitable as a material for constructing kettle handlers, insulators and oven covers, because, a high amount of heat will cause only a small change in temperature aka the material won't get hot too fast!

14. 4. Sensitive thermometers also must be made from materials with small specific heat capacity so that it can detect  and show a change of temperature rapidly and accurately.
5. Heat storage instruments are very useful and they are usually made of substances with a high specific heat capacity.
6. Water as a cooling agent acts excellent as a cooling agent in engines. Water is also used in houses in cold climate countries because as it is heated up (boiled) it tends to retain heat and warm the house due to its high specific heat capacity.

15. Thermal Expansion
Increase in temperature may cause dimensional changes.
Linear coefficient of thermal expansion (α) defined as the change in the dimensions of the material per unit length.
T0 and Tf are the initial and final temperatures (in K)
l0 and lf are the initial and final dimensions of the material and ε is the strain.
α has units as (°C)-1.
α values: for metals 5-25x10-6 , for ceramics x10-6 ,for polymers x10-6

16. Where Δv and vo are the volume change and the original volume.
A volume coefficient of thermal expansion, αv (=3α) is used to describe the volume change with temperature.
Where Δv and vo are the volume change and the original volume.
An instrument known as dilatometer is used to measure the thermal expansion coefficient.
At microscopic level, because of asymmetric nature of the potential energy trough, than increase in vibrational amplitude. changes in dimensions with temperature are due to change in inter-atomic distance, rather than increase in vibrational amplitude

18. If a very deep energy trough caused by strong atomic bonding is characteristic of the material, the atoms separate to a lesser and the material has low linear coefficient of thermal expansion.
This relationship also suggests that materials having a high melting temperature – also due to strong atomic bonds – have low thermal expansion coefficients.

19. Thermal Expansion in Metals, Ceramics and Polymers
Material
αl (/oC)
Metals Al
23.6 Cu
17.0 Au
14.2 Fe
11.8
Ceramics
Alumina
7.6
Magnesia
13.5
Soda-lime glass
9.0
Polymers
Polythene
Nylon
144
Thermal Expansion in Polymers > Metals > Ceramics

20. Thermal Expansion

22. Applications of Thermal Expansion
Fixing of Iron Rim to a Wooden Wheel
Gap in Railway Tracks
Opening a Tightly Fixed Lid of a Bottle 
Thermometers

23. Thermal Conductivity Thermal conductivity:
Thermal conductivity is ability of a material to transport heat energy through it from high temperature region to low temperature region.
The heat energy, Q, transported across a plane of area A in presence of a temperature gradient ΔT/Δl is given by
where k is the thermal conductivity of the material.
It has units as W/m.K.
It is a microstructure sensitive property.
Its value range
o for metals
o for ceramics 2-50
o for polymers order of 0.3

24. Mechanisms - Thermal conductivity
Heat is transported in two ways – electronic contribution, vibrational (phonon) contribution.
In metals, electronic contribution is very high. Thus metals have higher thermal conductivities. It is same as electrical conduction. Both conductivities are related through Wiedemann-Franz law:
where L – Lorentz constant (5.5x10-9 cal.ohm/sec.K2)
As different contributions to conduction vary with temperature, the above relation is valid to a limited extension for many metals.

25. Thermal Conductivity in Metals, Ceramics and Polymers
Material k
Metals Al
247 Cu
398 Au
315 Fe 80
Ceramics
Alumina 39
Magnesia
37.7
Soda-lime glass
1.7
Polymers
Polythene
0.46
Nylon
0.24
Thermal conductivity in Metals > Ceramics > Polymers

26. THE IRON–IRON CARBIDE (Fe–Fe3C) PHASE DIAGRAM

27. Heat Treatment Methods

28. Definition of heat treatment
Heat treatment is an operation or combination of operations involving
Heating at a specific rate,
Soaking at a temperature for a period of time and
Cooling at some specified rate.
The aim is to obtain a desired microstructure to achieve certain predetermined properties (physical, mechanical, magnetic or electrical).

29. Objectives of heat treatment
To increase strength, harness and wear resistance
(bulk hardening, surface hardening)
To increase ductility and softness
(tempering, recrystallization annealing)
To increase toughness
(tempering, recrystallization annealing)
To obtain fine grain size
(recrystallization annealing, full annealing, normalising)
To remove internal stresses induced by differential deformation by cold working, non-uniform cooling from high temperature during casting and welding
(stress relief annealing)

30. To improve machineability
(full annealing and normalising)
To improve cutting properties of tool steels
(hardening and tempering)
To improve surface properties
(surface hardening, corrosion resistance-stabilising treatment and high temperature resistance-precipitation hardening, surface treatment)
To improve electrical properties
(recrystallization, tempering, age hardening)
To improve magnetic properties
(hardening, phase transformation)

31. Heat treatment processes
Hardening
Tempering
Annealing
Nitriding

32. Hardening
A material is normally hardened by heating the metal to the required temperature and then cooling it rapidly by plunging the hot metal into a quenching medium, such as oil, water, or brine.
Properties:
Brittleness
Hardness
Strength

33. Hardening

34. Hardening

35. Tempering Properties: Ductility Softness Toughness
Tempering consists of heating the metal to a specified temperature and then permitting the metal to cool. The rate of cooling usually has no effect on the metal structure during tempering. Therefore, the metal is usually permitted to cool in still air.
Properties:
Ductility
Softness
Toughness

36. Annealing
Metal is annealed by heating it to a prescribed temperature, holding it at that temperature for the required time, and then cooling it back to room temperature.
The rate at which metal is cooled from the annealing temperature varies greatly.
Properties:
Ductility
Softness

37. Nitriding
It is the introduction of the nitrogen in to the surface of certain type of steels by heating it and holding it at a suitable temperature in contact with particularly dissociate (distance) ammonia or other suitable media.
Properties:
Surface hardening