diffusion properties of selected table of contents i. introduction ii. background diffusion...

T.C. MARMARA UNIVERSITY

FACULTY OF ENGINEERING METALLURGICAL AND MATERIALS ENGINEERING

DEPARTMENT

DIFFUSION PROPERTIES OF SELECTED MATERIALS

Mnevver BAYAZITLI

(Metallurgical and Materials Engineering)

SENIOR PROJECT

ADVISOR

Prof.Dr. Ersan KALAFATOLU

STANBUL 2005

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TABLE OF CONTENTS

I. INTRODUCTION

II. BACKGROUND Diffusion Mechanisms

Steady-state Diffusion

Non-steady state Diffusion

Diffusion in gases

Diffusion in Liquids

Diffusion in solids

Diffusion Coefficient Measurements

III. PROCEDURE

IV. RESULTS

V. DISCUSSION OF RESULTS

VI. CONCLUSION

VII. REFERENCES

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I.INTRODUCTION

The fragrance of flowers in a corner of a room drifts even to far distances.

When one droplet of ink is dripped into a cup of water, the ink soon spreads, even

without stirring, and quickly becomes invisible. These facts show that even if there is

no macroscopic flow in a gas or a liquid, molecular movement can take place, and

different entities can mix with each other.

It can be seen that examples of diffusion in everyday life are to much; the

diffusion of sugar in a cup of tea, the vaporization of water in a teakettle, cloud

formation, clothes drying, etc.

Engineers are concerned with diffusion when studying lots of subjects; such

as: gas absorption, seperation, crystallization and extraction, production and heat

treatment of metals, drying, cutting and welding metals, mass transfer in waste

treatment.

Many reactions and processes which are mentioned above, rely on the transfer

of mass either within a specific solid or from a liquid, a gas, or another solid phase.

This is accomplished by diffusion. The purpose of this project is to study the

properties of diffusion process, to observe the diffusion mechanisms and the diffusion

in gases, liquids and solids, to find the diffusion coefficient of selected materials by

doing experiments and using the formulas of diffusion.

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II. BACKGROUND

DIFFUSION MECHANISMS

From an atomic perspective, diffusion is just the stepwise migration of atoms

from lattice site to lattice site. In fact, the atoms in solid materials are in constant

motion, rapidly changing positions. For an atom to make such a move, two

conditions must be met:

1. There must be an empty adjacent site.

2. The atom must have sufficient energy to break bonds with its neighbor

atoms and then cause some lattice distortion during the displacement (1).

This energy is vibrational in nature. At a specific temperature some small

fraction of the total number of atoms is capable of difusive motion, by virtue of the

magnitudes of their vibrational energies. This fraction increases with rising

temperature. Several different models for this atomic motion have been proposed; of

these posibilities, two dominates for metallic diffusion.

Vacancy Diffusion

One mechanism involves the interchange of an atom from a normal lattice

position to an adjacent vacant lattice site or vacancy, as represented in Figure 1. This

process necessitates the presence of vacancies, and the extent to which vacancy

diffusion can occur is a function of the number of these defects that are present;

significant concentrations of vacancies may exist in metals at elevated temperatures.

Since diffusing atoms and vacancies exchange positions, the diffusion of atoms in one

direction corresponds to the motion of vacancies in the opposite direction. Both self-

diffusion and interdiffusion occur by this mechanism.

Instertitial Diffusion

The second type of diffusion involves atoms that migrate from an instertitial

position to a neighboring one that is empty. This mechanism is found for

interdiffusion of impurities such as hydrogen, carbon, nitrogen, and oxygen, which

have atoms that are small enough to fit into the interstitial positions. Host or

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substitutional impurity atoms rarely form instertitials and do not normally diffuse via

this mechanism. This phenomenon is appropriately termed instertitial diffusion,

shown in Figure 1.

Figure 1 schematic representation of vacancy and instertitial diffusion.

In most metal alloys, instertitial diffusion occurs much more rapidly than

diffusion by the vacancy mode, since the instertitial atoms are smaller, and thus more

mobile. Furthermore, there are emptier instertitial positions than vacancies; hence,

the probability of instertitial atomic movement is greater than for vacancy diffusion.

STEADY-STATE DIFFUSION

Diffusion is a time-dependent process that is, in macroscopic sense, the

quantity of an element that is transprted within another is a function of time. Often it

is necessary to know how fast diffusion occurs, or the rate of mass transfer. This rate

is frequently expresses as a diffusion flux (J), defined as the mass (or equivalently, the

number of atoms) M diffusing through and perpendicular to a unit cross-sectional area

of solid per unit time. In mathematical form, this may be represented as;

J = tA

M.

(Equation 1.a)

Where A denotes the area across which diffusion is occuring and t is elapsed diffusion

time. In differential form, this expression becomes;

J = dt

dMA1 (Equation 1.b)

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The units for J are kilograms or atoms per meter squared per second (kg/m2-s or

atoms/m2-s).

If the diffusion flux does not change with time, a steady-state condition exists.

One common example of steady-state diffusion is the diffusion of atoms of a gas

through a plate of metal for which the concentrations (or pressures) of the diffusing

species on both surfaces of the plate are held constant. This is represented

schematically in Figure 2.a.

When concentration C is plotted versus position (or distance) within the solid

x, the resulting curve is termed the concentration profile; the slope at a particular

point on this curve is the concentration gradient:

Concentration gradient = dxdC (Equation 2.a)

Thin metal plane

PA>PB

and constant Gas at pressure PB

Gas at pressure PA Direction of diffusion of gaseous species Area, A Figure 2.a Steady-state difusion across a thin plane Concentration of diffusing Species (C) CA CB Position (x) xA xB Figure 2.b A linear concentration profile for the diffusion situation

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In the present treatment, the concentration profile is assumed to be linear, as depicted

in Figure 2.b, and

Concentration gradient = xC =

BA

BA

xxCC

(Equation 2.b)

For diffusion problems, it is sometimes convenient to express concentration in terms

of mass of diffusing species per unit volume of solid (kg/m3 or g/cm3).

The mathematics of steady-state diffusion in a single (x) direction is

relatively simple, in that the flux is proportional to the concentration gradient through

the expression;

J = dxdCD (Equation 3)

The constant of proportionality D is called diffusion coefficient, which is expressed

in square meters per second. The negative sign in this expression indicates that the

direction of diffusion is down the concentration gradient, from a high to a low

concentration. Equation 3 is sometimes called Ficks first law.

Sometimes the term driving force is used in the contex of what compels a

reaction to occur. For diffusion reactions, several such forces are possible; when

diffusion is according to Eguation 3, the concentration gradient is the driving force.

One practical example of steady-state diffusion is found in the purification

of hydrogen gas. One side of a thin sheet of palladium metal is exposed to the impure

gas composed of hydrogen and other gaseous species such as nitrogen, oxygen, and

water vapor. The hydrogen selectively diffuses through the sheet to the opposite side,

which is maintained at a constant and lower hydrogen pressure.

NONSTEADY-STATE DIFFUSION

Most practical diffusion situations are nonsteady-state. That is diffusion

flux and the concentration gradient at some particular point in a solid varies with time,

with a net accumulation or depletion of the diffusing species resulting. Under

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conditions of nonsteady-state, use of Equation 3 is no longer convenient; instead, the

partial differential equation;

tC =

xCD

x. (Equation 4.1)

Known as Ficks second law, is used. If the diffusion coefficient is independent of

composition, Equation 4.1 simplifies to;

tC = 2

2

xCD

(Equation 4.2)

Solutions to this expression are possible when physically meaningful boundary

conditions are specified. Comprehensive c