diffusion properties of selected table of contents i. introduction ii. background diffusion...
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T.C. MARMARA UNIVERSITY
FACULTY OF ENGINEERING METALLURGICAL AND MATERIALS ENGINEERING
DIFFUSION PROPERTIES OF SELECTED MATERIALS
(Metallurgical and Materials Engineering)
Prof.Dr. Ersan KALAFATOLU
TABLE OF CONTENTS
II. BACKGROUND Diffusion Mechanisms
Non-steady state Diffusion
Diffusion in gases
Diffusion in Liquids
Diffusion in solids
Diffusion Coefficient Measurements
V. DISCUSSION OF RESULTS
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.
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.
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.
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
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
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)
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
In the present treatment, the concentration profile is assumed to be linear, as depicted
in Figure 2.b, and
Concentration gradient = xC =
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
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
conditions of nonsteady-state, use of Equation 3 is no longer convenient; instead, the
partial differential equation;
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
Solutions to this expression are possible when physically meaningful boundary
conditions are specified. Comprehensive c