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

Download DIFFUSION PROPERTIES OF SELECTED TABLE OF CONTENTS I. INTRODUCTION II. BACKGROUND Diffusion Mechanisms Steady-state Diffusion Non-steady state Diffusion Diffusion in gases Diffusion

Post on 10-Mar-2018




5 download

Embed Size (px)






    Mnevver BAYAZITLI

    (Metallurgical and Materials Engineering)



    Prof.Dr. Ersan KALAFATOLU

    STANBUL 2005

  • 2



    II. BACKGROUND Diffusion Mechanisms

    Steady-state Diffusion

    Non-steady state Diffusion

    Diffusion in gases

    Diffusion in Liquids

    Diffusion in solids

    Diffusion Coefficient Measurements






  • 3


    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


    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.

  • 4



    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

  • 5

    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.


    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


    (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)

  • 6

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


    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


    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

  • 7

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

    in Figure 2.b, and

    Concentration gradient = xC =




    (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.


    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

  • 8

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

    partial differential equation;

    tC =


    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



    (Equation 4.2)

    Solutions to this expression are possible when physically meaningful boundary

    conditions are specified. Comprehensive c


View more >