CERAMICS MATERIALS

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Outline

Thermal Properties

Heat capacity

Thermal expansion

Thermal conductivity

Thermal tempering

Optical Properties

Absorption and

transmission

Scattering and

opacity

3

Thermal Properties of Ceramics

4

Introduction5

Physical properties that determine much of the

usefulness of ceramic materials are those directly

related to temperature changes.

In this instance, related to temperature changes is

the thermal properties of a material

6As a consequence of their brittleness and their low

thermal conductivities, ceramics are prone to

thermal shock, i.e. they will crack when subjected to

large thermal gradient.

Thermal stresses will also develop because of

thermal contraction mismatches in multiphase

materials or anisotropy in a single phase.

Heat capacity7

One of the properties related to thermal properties is heat capacity, which is a measure of the energy required to raise the temperature of a material or the increase in energy content per degree of temperature rise.

Heat capacity is normally measured at constant pressure, cp, but theoretical calculations are frequently reported in terms of the heat capacity at constant volume, cv.

8 Thermodynamically, the related equations are:

=

=

; =

=

;

=20

where Q is the heat exchange, U the internal energy, H the enthalpy, the volume thermal expansion coefficient, the compressibility, and V0 the molar volume.

9 The energy required for raising the temperature of a material from its minimum energy state at the absolute zero goes into:

Vibrational energy by which atom vibrate around their lattice positions with an amplitude and frequency that depend on temperature,

Rotational energy for molecules in gases, liquids, and crystals having rotational degrees of freedom,

10

Raising the energy level of electrons in the structure,

Changing the atomic position (such as forming Schottky or Frenkel defects, disordering phenomena, magnetic orientation, or altering the structure of glasses at the transformation range).

All these changes correspond to an increase in internal energy and are accompanied by an increase in configurational energy.

11

From the classical kinetic theory, the heat requires that each atom has an average kinetic energy of kT and an average potential energy of kT for each degree of freedom, where k is Boltzmanns constant.

Thus, the total energy for an atom with 3 degrees of freedom is 3kT, whereas the energy content per gram atom will be 3NkT where N is Avogadros number.

12 In this case, it can be shown that:

=

= 3 = 24.94 /.mol

= 5.96 cal/g. atomC

13

The main result of heat capacity for ceramics system is that the heat capacity increase from a low value at low temperature to a value near 5.96 cal/g-atomoC at temperatures in the neighborhood of 1000oC for most oxides and carbides.

Further increases in temperature do not strongly affect this value, and it is not much dependent on the crystal structure.

14

The heat energy required to raise the temperature of an insulating firebrick is much lower than that required to raise the temperature of a dense fire brick valuable and useful properties of insulating materials for the manufacture of furnace which must be periodically heated and cooled.

For furnaces that must be rapidly heated or cooled, use radiation shielding such as molybdenum sheet or low density fiber or powder insulation which has a low solid content and thus a low heat capacity per unit volume.

Thermal expansion15

Thermal expansion is the fractional change in

volume or linear dimension per degree of

temperature change.

At any particular temperature, we can define

a coefficient of linear expansion and a

coefficient of volume expansion.

16

The formulas are:

=

; =

=

T; =

V

VTFor limited temperature ranges an average

value is sufficient

17The specific volume of any given crystal

increases with temperature, and the crystal

tends to become more symmetrical.

The general increase in volume with

temperature is mainly determined by the

increased amplitude of atomic vibration about

a mean position.

18

The repulsion between atoms changes more rapidly with atomic separation than does the attraction terms; thus the minimum energy trough is non-symmetrical.

The change in volume due to lattice vibration is closely related to the increase in energy content; thus, changes in the thermal expansion coefficient, = dV/dT, with temperature are parallel to the changes in heat capacity.

19

For cubic crystal, the expansion coefficient along different crystalline axes are equal, and the changes in dimensions with temperature are symmetrical; and thus the linear expansion coefficient is the same in any direction.

For non-isometric crystal, the thermal expansion varies along different crystallographic axes; and may be negative in one direction resulting in very low volume expansion

20This can be used for thermal shock applications

such as aluminum titanate, cordierite, and

various lithium aluminum silicate.

Thermal stresses can also be induced by

differential thermal expansion in multiple

materials or anisotropy in the thermal

expansion coefficient of single phase solid.

Resistance to thermal shock21

The capacity of a material to withstand failure due to the rapid cooling of a brittle body is termed thermal shock resistance.

For a ceramic body that is rapidly cooled, the resistance to thermal shock depends not only on the magnitude of the temperature change, but also on the mechanical and thermal properties of the material.

22

The thermal shock resistance is best for ceramics

that have high fracture strengths f and high

thermal conductivities, as well as low moduli of

elasticity and low coefficients of thermal expansion.

The resistance of many materials to this type of

failure may be approximated by a thermal shock

resistance parameter TSR

23

TSR formula is:

where E is the modulus of elasticity and is

coefficient of thermal expansion, f is fracture

strength, and k is thermal conductivity.

Thermal conductivity24

Thermal conductivity is the amount of heat conducted

through the body per unit temperature gradient.

The basic equation for thermal conductivity is:

=

where dQ is the amount of the heat flowing normal to

the area A in time d

25

The heat flow is proportional to the temperature

gradient, -dT/dx, and the proportionality factor being

a material constant, the thermal conductivity k.

Ceramics have low thermal conductivity compared with

metals.

Heat is transported by the conduction band electrons in

metals as well as atomic vibrations, whereas in ceramics

heat is transported only by atomic vibrations.

Thermal conduction process26

The conduction process for heat energy transfer

under the influence of a temperature gradient

depends on

The energy concentration present per unit volume,

Its velocity movement, and

Its rate of dissipation with the surroundings.

27

In gases, individual atoms or molecules exchange

kinetic energy by collision;

the heat energy present is simply equal to the heat

capacity per unit volume,

the velocity of molecular motion can be calculated

from kinetic theory, and

the rate of energy dissipation depends on the rate

of collision between atoms or molecules.

28

If a temperature gradient in which the concentration

of molecules is N and their average velocity is v, the

average rate at which molecules pass a unit area in

the x direction is equal to

1

3

29

If energy equilibrium is obtained by collisions between molecules and the average distance between collisions, the mean free path is l, molecules moving parallel to the x axis have an energy of

+

where Eo is the mean energy at x = 0, E/x is the energy gradient in the x direction.

30

Combining the previous equations:

=

=

1

3

Since

=

=

The conductivity is given by

=1

3

where c is the heat capacity per unit volume.

Thermal Conductivity, k31

Thermal Protection System32

FRSI, felt reusable surface insulation; AFRSI, advanced flexible

reusable surface insulation; LRSI, low-temperature reusable

surface insulation; HRSI, high-temperature reusable surface

insulation; RCC, reinforced carboncarbon composite.

33

This photograph shows a

white-hot cube of a silica fiber

insulation material, which, only

seconds after having been

removed from a hot furnace,

can be held by its edges with

the bare hands.

34

Initially, the heat transfer from the surface is relatively rapid; however, the thermal conductivity of this material is so small that heat conduction from the interior [maximum temperature approximately 1250C (2300F)] is extremely slow.

This material was developed especially for the tiles that cover the Space Shuttle Orbiters and protect and insulate them during their fiery reentry into the atmosphere.

Thermal tempering35

Because of transparency and chemical inertness of

inorganic glasses, their use in everyday life are

ubiquitous.

However, for many applications, especially where

safety is concerned, as manufactured, glass is

deemed to be too weak and brittle.

36

Fortunately, glass can be significantly strengthening

by a process called thermal tempering, which

introduces a state of compressive residual stress on

the surface.

The thermal process involves heating the glass body

to a temperature above its glass transition

temperature, followed by a two-step quenching

process.

37

During the first quenching stage, initially the surface

layer contracts more rapidly than the interior and

become rigid while the interior is still in a viscous

state.

During the second quenching step, the entire glass

sample is cooled to room temperature.

38

Given that the interior will have cooled at a slower

rate than its exterior, its final specific volume will be

smaller than that of exterior.

By using this techniques, the mean strength of soda-

lime silicate glass can be raised sufficient to permit

its use in large doors and windows or safety lenses.

39

Another reason for using this techniques is that the

release of large amount of stored elastic energy upon

fracture tends to shatter the glass into great many

fragments which are less dangerous than larger shards.

Windshield are made of two sheets of tempered glass

in between which a polymer layer embedded.

The function of latter is to hold the fragments of glass

together in case of fracture and to prevent them from

becoming lethal projectiles.

Optical Properties of Ceramics

40

41

Introduction

Since the beginning of civilization, the allure of materials was mainly because of aesthetic and priced because of their transparency, brilliance, and color.

In today advent of technology, the optical properties of glass and ceramics are even more important, for example in commercial fiber-optic networks to transfer gigabits of information per second.

The basic42

The basic principles of ceramics optical properties are based on the interaction between light or electromagnetic radiation impinging on a solid, which can be transmitted, absorbed, and scattered.

For a total incident flux of photons Io energy conservations requires that Io = IT + IR + IA where IT, IR, and IA represent the transmitted, reflected, and absorbed intensities, respectively.

43

The intensity, I, is the energy flux unit area and has the unit of J/m2.s

Dividing both sides of the previous equation with Io yields

1 = T + R + A

where T, R, and A are the fraction of light transmitted, reflected, and absorbed, respectively.

A material cannot simultaneously be highly absorptive, reflective and transmissive.

44

There are several optical properties of ceramics materials:

Refraction: apparent bending of light rays as they pass from one medium to another. For example, a rod immersed in a fluid will appear bent.

Reflection; not all light that is incident on a surface is refracted, a portion of it can be reflected.

Absorbance and transmittance; the transmittance T through a transparent medium is proportional to the amount of light that is neither reflected nor absorbed.

45

Shininess and inability to transmit visible light indicates high

absorption linear absorption coefficient high reflection (up to R = 1)

and R determine how light interacts with a material

Refractive index n46

velocity of light in vacuum: c = 299,792,458 m/s

velocity of light in any other medium: v (v < c)

refractive index n = c/v

c can be related to 0 and 0

v can be related to and

Due to small susceptibilities of

ceramics

47

Values between 1 and 4

air: 1.003

silicate glasses: 1.5 to 1.9

solid oxide ceramics: 2.7

Dependent on structure-type and packing geometry

glasses and cubic crystals: n is independent of direction

other crystal systems: n larger in closed-packed directions

SiO2: glass = 1.46, tridymite = 1.47, cristobaltite = 1.49,

quartz = 1.55

Reflection and refraction48

n can be expressed with the angles of incidence and refraction

n can be used to describe reflectivity R

n and R vary with wavelength

Absorbance and color49

Non-reflected light can be transmitted or absorbed

Absorption process is a function of energy

(wavelength)

Absorption: fractional change of light intensity

50

Absorption coefficient is a material property and a function of the wavelength

=4

Absorption of photon: excitation of electron from

valence to conduction band. Only if photon energy > band gap hv Eg

Magnitude of band gap determines if the material

does not absorb (transparent)

absorbs certain wavelength (opaque)

51

Absorption of certain

wavelength results in color

Generating color in ceramics:

Addition of transition

elements with incomplete d

band filling V, Cr, Mn, Fe, Co,

Ni

References52

M.W. Barsoum, Fundamental of Ceramics, Institute

of Physics Publishing, Philadelphia, 2003.

W.D. Kingery, H.K. Bowen, D.R. Uhlmann,

Introduction to Ceramics, 2nd ed., John Wiley &

Sons, New York, 1976.

W.D. Callister, Fundamentals of Materials Science and

Engineering, 5th ed. 2001