DIFFUSION
Many reactions and processes that are important in the treatment of materials rely
on the transfer of mass either within a specific solid (ordinarily on a microscopic
level) or from a liquid, a gas, or another solid phase. This is necessarily
accomplished by diffusion, the phenomenon of material transport by atomic
motion.
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, and
2. The atom must have sufficient energy to break bonds with its neighbor atoms
and then cause some lattice distortion during the displacement.
This energy is vibrational in nature. At a specific temperature some small fraction
of the total number of atoms is capable of diffusive motion, by virtue of the
magnitudes of their vibrational energies.
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 schematically in Fig. 1.
This mechanism is aptly termed vacancy diffusion. Of course, 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.
Both self-diffusion and inter diffusion occur by this mechanism; for the latter, the
impurity atoms must substitute for host atoms.
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INTERSTITIAL DIFFUSION
The second type of diffusion involves atoms that migrate from an interstitial
position to a neighboring one that is empty. This mechanism is found for inter
diffusion 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 interstitials and do not normally diffuse
via this mechanism.
This phenomenon is appropriately termed interstitial diffusion Fig.1b. In most
metal alloys, interstitial diffusion occurs much more rapidly than diffusion by the
vacancy mode, since the interstitial atoms are smaller and thus more mobile.
Furthermore, there are more empty interstitial positions than vacancies; hence, the
probability of interstitial atomic movement is greater than for vacancy diffusion.
Fig.1 Schematic representations of (a) vacancy diffusion and (b) interstitial diffusion
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STEADY-STATE DIFFUSION
Diffusion is a time-dependent process that is, in a macroscopic sense, the quantity
of an element that is transported within another is a function of time.
𝐽𝐽 =
𝑀𝑀
𝐴𝐴𝐴𝐴
J = diffusion flux, 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
of time. The units for J (kg/m2-s or atoms/m2-s).
If the diffusion flux does not change with time, a steady-state condition exists.
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 =
𝛥𝛥𝛥𝛥 𝐶𝐶𝐴𝐴 − 𝐶𝐶𝐵𝐵
=
𝛥𝛥𝛥𝛥 𝑋𝑋𝐴𝐴 − 𝑋𝑋𝐵𝐵
Concentration in terms of mass of diffusing species per unit volume of solid (kg/m3
or g/cm3).
𝑑𝑑𝑑𝑑
𝐽𝐽 = −𝐷𝐷
𝑑𝑑𝑑𝑑
The constant of proportionality D is called the 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. Above equation is sometimes called Fick’s first law.
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.
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Fig.2 (a) Steady-state diffusion across a thin plate. (b) A linear concentration profile
for the diffusion situation in (a).
NONSTEADY-STATE DIFFUSION
Most practical diffusion situations are nonsteady-state ones. That is, the diffusion
flux and the concentration gradient at some particular point in a solid vary with
time, with a net accumulation or depletion of the diffusing species resulting.
𝜕𝜕𝜕𝜕
𝜕𝜕
𝜕𝜕𝜕𝜕
=
�𝐷𝐷 �
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
known as Fick’s second law, is used. If the diffusion coefficient is independent of
composition.
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Fig. 3 Concentration profiles for nonsteady-state diffusion taken at three different
times, t1, t2, and t3.
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DIFFUSION COATINGS
Diffusion coating(s) are element(s) intentionally deposited on the substrate
material for the purpose of producing diffusion saturated layers on the substrate
material, using chemo-physical processes, particularly thermo-and electrochemical reactions.
TERMINOLOGY
Diffusion coatings are also known as ‘pack cementation’, but this term should be
reserved only for one particular method diffusion coating in solid phase in closed
reactors – otherwise, the word ‘cementation’ should be eliminated.
Depending on the diffused element, an ending ‘-izing’ is added to the elements
name, e.g., boron-izing, carbonizing, chromizing etc. Aluminum diffusion coatings
even have two names: aluminizing and calorizing.
PRINCIPLES
1. The mechanism of diffusion coatings generally can be described in the
following ways:
There initially must be higher concentration of the material to be diffused into the
substrate, and then a translocation of the atoms occurs from the region with higher
concentration into the region with lower concentration. Thus, diffusion results in
the equalizing and stabilizing of material concentration.
2. There are three basic stages caused by the thermochemical mobility of the
atoms participating in the diffusion process:
• Formation of active atoms of the material to be diffused into the substrate,
depending on the composition of the diffusion phase;
• Adsorption of active atoms by the substrate material, which depends on the
character of mutual inter-reaction between the components of the diffusion
phase and with the substrate;
• Diffusion of the element(s) atoms into the metal or alloy, which is controlled
by: the substrate of the active atoms to be diffused (e.g., their atom radius)
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and substrate material, and by the activation energy, mutual solubility of
alloying or inter-reacting elements, etc. the active atoms can more easily
diffuse in vacancies, at phase and grain boundaries, and at dislocations and
other defects of the crystalline structure.
The element(s) to be diffused share the following characteristics with the substrate
material: a mutually unlimited or limited solubility forming intermetallic
compounds, and/ or a chemical bond.
In case they do not have the above bonds, the elements to be diffused can form so
called ‘independent structures’ (e.g., active non-metallic elements with small atom
radius, like B, C, or N with non metallic elements having big atom radiuses
forming substitutional solid solutions).
3. The process causes the diffusion coating material to disperse in the direction of
the lower concentration of the substrate. The amount is equal to the difference
between the amount of diffusion coating elements passing into the substrate and
in the reverse direction (substrate elements into the coating). Therefore, the
amount is proportional to the gradient of concentration (or the decrease of
concentration at distance X from a reference interface). This relation is
expressed by Fick’s First Law
𝑑𝑑𝑑𝑑
𝐽𝐽 = −𝐷𝐷
𝑑𝑑𝑥𝑥
In turn, D depends on the frequency (Vo) of atoms jumps from one position to
another, and their atomic diameters (a); therefore
D = a2.Vo
The concentration charge of the diffused element with time (t) is expressed by
Fick’s second law
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
𝜕𝜕
=
�𝐷𝐷 �
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 𝜕𝜕𝑥𝑥
The relationship between the diffusion coefficient (D) and the temperature follows
Arrhenius Law:
𝐷𝐷 = 𝐷𝐷𝑜𝑜 𝑒𝑒 −(𝑄𝑄 ⁄𝑅𝑅𝑅𝑅 )
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Do= a2.Vo= Frequency factor (cm2/sec);
Q= Activation energy (cal/gm atom);
R= Universal gas constant (cal/gm mole);
T= Temperature (K)
Activation energy is the energy required to produce the diffusive motion of one
mole of atoms. A Large activation energy results in a relatively small diffusion
coefficient.
4. In summary, the diffusion coefficient increase (along with factors) when the
following occur:
• Increased diffusion temperature
• Increased vacancies, and other defects in the crystalline structure of the
substrate material, including a less perfect crystalline lattice;
• Decreased atomic radius of the elements to be diffused, and an increase of
its concentration
• Lower diffusion activation
PROCESS DESCRIPTION
The pack cementation, or pack diffusion, process diffuses the coating material into
the substrate, generally to impart oxidation and high temperature corrosion
resistance to the coated part. Most often, the coating material is a powder of
aluminum, chromium cobalt or alloys of these materials.
The parts to be coated are placed in a retort or sled in a mixture of the coating
material and an inert powder, such as aluminum oxide, along with a halide salt.
The retort is then placed in a protective atmosphere (hydrogen or argon) furnace
and brought up to the coating temperature. The salt vaporizes and combines with
the coating to generate the transporting vapor species. The retort is placed in a
furnace and brought to a temperature at which the coating material will react with
the salt to form a metallic halide vapor, which comes in contact with the surface of
the parts to form the coating.
In the aluminizing process, a source of Al reacts with a chemical activator on
heating to form a gaseous compound (e.g., pure Al with NaF to form AlF). This
gas is the transfer medium that carries aluminum to the component surface. The
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gas decomposes at the substrate surface depositing Al and releasing the halogen
activator. The halogen activator returns to the pack and reacts with the Al again.
Thus, the transfer process continues until all of the aluminum in the pack is used or
until the process is stopped by cooling. The coating forms at temperatures ranging
from 700 to 1100oC over a period of several hours.
Features of the Pack Cementation Process
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Metallurgically bonded to the substrate
Batch processing for high production rates
Can be used to coat large or small components
Coats both external and internal surfaces, even deep, small bores
Can be tailored to meet specific requirements
Economical process
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