Recovery, Recrystallization, and Grain-Growth

Abstract

This is a brief review of the important phenomena of recovery, recrystallization as well as grain-growth. The three mentioned phenomena are the mechanisms by which metals and alloys fix the structural damage introduced by the mechanical deformation and, as a consequence, in the physical and mechanical properties. These rehabilitation mechanisms are thermally activated. For this process, the materials have to be heated and any such heat-treatment is meant to reduce deformation-induced break is termed annealing. Other or different heat-treatments lead to recovery and recrystallization. It is rather strange that, though these phenomena are extremely important in metallurgical science and engineering, not so much work has been done as that in corrosion and shape memory technologies. An attempt has been made here to summarize all important aspects of these phenomena for the benefits of students of metallurgy, chemistry and solid state physics.

Full text

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Recovery, Recrystallization, and Grain-Growth
1Iqra Zubair Awan* and 2Abdul Qadeer Khan
1Institute Charles Gerhard, Ecole Nationale Superieure de Chimie,
34040 - Montpellier, France.
2Fellow and Ex-President, Pakistan Academy of Sciences, Islamabad, Pakistan.
iqrazubair@gmail.com*
(Received on 14th November 2018, accepted in revised form 1st January 2019)
Summary: This is a brief review of the important phenomena of recovery, recrystallization as well
as grain-growth. The three mentioned phenomena are the mechanisms by which metals and alloys
fix the structural damage introduced by the mechanical deformation and, as a consequence, in the
physical and mechanical properties. These rehabilitation mechanisms are thermally activated. For
this process, the materials have to be heated and any such heat-treatment is meant to reduce
deformation-induced break is termed annealing. Other or different heat-treatments lead to recovery
and recrystallization. It is rather strange that, though these phenomena are extremely important in
metallurgical science and engineering, not so much work has been done as that in corrosion and
shape memory technologies. An attempt has been made here to summarize all important aspects of
these phenomena for the benefits of students of metallurgy, chemistry and solid state physics.
Keywords: Deformation, Heat Treatment, Annealing, Recovery, Recrystallization, Grain-growth, Stresses
Grain Boundaries, Dislocations.
Introduction
The dynamic phenomenon of recovery,
recrystallization and grain-growth play a very
important role in Physical Metallurgy, Chemistry of
the Solid State and Solid State Physics. Hence this
review for the benefit of students and teachers of the
above-mentioned disciplines. Humphreys and
Hatherly (referred to later) have stated that:
“Recrystallization is related to annealing phenomena
which happen during thermomechanical processing
of materials has accepted as being mutually of
technological importance and scientific interest. The
phenomena include most widely studied in metals
and there be a vast literature spanning over about 150
years. Metallurgical research in this field is mainly
determined by the necessities of industry, mainly for
metal forming processes for better products.”
Dierk Raabe [1] of Max-Planck Institute
fuer Eisenforschung, Düsseldorf, Germany has
written an excellent article in his book, Physical
Metallurgy, Fifth Edition, 2291-2397 (2014) on
Recovery and Recrystallization: phenomenon,
Physics, Models, and Simulation. He has mentioned
the earliest investigators who had worked on
deformation of metals and related phenomena. The
works of Kalirher [2], Sorby [3] 1886 and 1887,
Stead [4] 1898, Rosenhain [5] 1914, Ewing and
Rosenhain [6] 1899a and 1899b, Alterhum [7] 1922,
Carpenter and Elam [8] 1920, Czochoralski [9] 1927,
Burgers and Louwerse [10] 1931 and Burgers [11]
1941. Surprisingly, the excellent work of Erich
Schmidt and Walter Boas [12] 1935/1950 has not
been mentioned.
Terminologies
“The mechanism in which metals and alloys
repair the structural damage caused by deformation,
and incidentally through the resulting changes in the
physical as well as mechanical properties and the fix
mechanisms which are induced by thermal treatment,
are term as annealing, recovery, recrystallization and
grain growth. We will define these terminologies one
by one. These structural changes take place in
annealing after cold deformation during hot working.
Since all these structural changes require diffusion,
they depend on thermal activation to cause
rearrangement of dislocations and grain limitations
[13, 14].
Annealing
“The term annealing is a very general term
used in heat treatments of metals and alloys. It
includes any cycle of heating and cooling of metallic
materials, irrespective of temperatures, rates and
terms involved in the cycle. Depending upon the
material being treated and the object of treatment,
annealing operations may involve any of a very broad
range of heating rates, soaking temperatures and
soaking times and cooling rates. These methods can
be used for stress-relieving, recrystallization and
grain growth.
*To whom all correspondence should be addressed.
GENERAL AND PHYSICAL

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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During annealing, the material is heated to a
temperature not far below the critical seized for a
adequate period of time to achieve the desired
changes meant for the heat treatment, and then cooled
to room temperature on a desired time. The purpose
of annealing is to eliminate partially or completely
the strain hardening produced by earlier mechanical
forming operations, so that it can be put into service
in a relatively soft, ductile condition. It must be
realized that annealing involves recrystallization in
which a combination of cold working and subsequent
heating causes new stress-free crystals in a matrix
which is itself stress free. A full anneal treatment is a
process intended to reduce the metal treated to its
softness possible condition. The term, “annealing” is
generally used, without qualifications or further
description, as full anneal. The full anneal is widely
used on steels to remove the effects of cold working,
eliminate residual stress and improve the
machinability of medium and high carbon grades.
“Cold work is supposed to be a plastically
deformation of metal by temperature that are low
relative to its melting point. A rough rule-of-thumb is
to assume that if esthetics deformation carried out on
temperature lesser to its one-half M.P it corresponds
to cold functioning Mainly the energy depleted in
cold work appears in the form of heat but a fixed
fraction is stored in the metals as strain energy related
with a variety of lattice defects, dislocations,
vacancies, formed by the deformation. The total
energy stored depends on the deformation process
and several other variables such as composition of
the metal, the speed and temperature of deformation.
The data from the work of Gordon [15], shows that
the stored energy increases with increasing
temperature, however on a decreasing rate, the
fraction of total energy stored decreases with
increasing deformation. The latter effect is shown in
Fig. 1 “[15]. The quantity of stored energy can be
significantly increased by increasing the magnitude
of deformation, lowering the deformation
temperature and through alloying an uncontaminated
metal.”[13]. “We know that cold working increases
greatly the quantity of dislocations in a metal. A soft
annealed metal be able to have dislocation densities
of 106-108 per cm square, and heavily cold worked
metal up to 1012. These dislocations represent crystal
defects with associated lattice strains; - increase the
dislocation density increases the strain energy of the
metal “[13].
Fig. 1: (a) Stored energy of cold work and fraction
of the total work of deformation remaining
as stored energy for high purity copper
plotted as functions of tensile elongation
(From Data of Gordan, P., Trans.AIME, 203
1043 [1955]). [14].
Fig. 1: (b) Anisothermal anneal curve. Electrolytic
copper. (from Clarabrough, H. M.,
Hargreaves, M. E., and West, G. W., Proc.
Roy. Soc. Lomdon, 232 A, 552 [1995]). [14]
Fig. 1: (c) Isothermal anneal curve. High purity
copper. (From Gordon, P., Trans AIME ,
203 1043 [1955].) [14].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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“Retained energy is caused by point defect
in cold work. A screw dislocation can cut another
screw dislocation and generate a close-packed line of
vacancies and interstitials similar to it glides with the
point defect produced depending on the relative
Burgers vectors of the intersecting dislocations
Because strain energy related to vacancy is smaller
than with related to interstitial atom the vacancies are
formed in larger number than interstitial atoms.
Cold work metal may soften due to liberated
energy of deformed metal is grater than that of
annealed metal that is equal to stored strain energy
Therefore distorted metal on heating speedily return
to soften state.
The measurement of stored energy in a
sample has been described nicely by Clarebrough
et.al [16] and reproduced by Reed-Hill [14]. They
have used anisothermal and isothermal annealing
methods to do it. Fig. 2 and 3 show the experimental
results. Both the anisothermal and isothermal curves.
(Figs. 2, 3) illustrate maxima corresponding to the
huge energy releases. Metallographic examination of
these samples show the growth of a totally new set of
strain-free crystals which grow at the rate of the
novel roughly distorted crystals. This method is
termed as recrystallization and is due to
rearrangement of the atoms into crystals by a lower
free energy [13-16].
Fig. 2: Anisothermal- anneal curve for cold worked
nickel. At the top of the Fig curves are also
drawn to show the effect of annealing
temperature on the hardness and incremental
resisitivity of the metal. (From the work of
Clarebrough, H.M. Hargreaves, M. E. West,
G.W., Proc. Roy. Soc., London, 232A 252
[1955] ) [14].
Fig. 3: Recovery of the yields strength of a zinc
single crystal at room temperature (After
Schmid, E., and Boas, W., Kristallplastizitat,
Julius Springer, Berlin{1935}
“According to Reed-Hill [14], the major
energy release of the curves (Figs. 2 and 3),
correspond to recrystallization but both the curves
show that energy is released before recrystallization.
The dashed lines systematically, on both curves,
delineate the recrystallization portion of the energy
release. The areas below each solid curve that lie to
the left and over the dashed lines correspond to an
energy release not related to recrystallization. In the
anisothermal anneal curve, this release of strain
energy starts at temperatures well below those at
which crystallization starts. Similarly, in the
isothermal anneal curve, it initiate at the beginning of
annealing cycle also it is almost complete before
recrystallization starts. The fraction of the annealing
cycle that occurs before recrystallization is called
recovery. Reaction that takes place in recovery stages
are significantly maintin progress of recrystalization
in those areas which are still not converted into
crystals.” [14].
“We have so far cursoraly discussed
annealing, recovery, recrystallization and grain
growth. But before discussing these phenomena in
detail, it is important to define the third state of
annealing, viz., and grain growth. When
recrystalization is completed during annealing, grain
growth occurs. In grain growth, certain of the
recrystallized grains continue to grow up in size,
however only at the expense of new crystals, which
should disappear. The important aspects of these
phenomena are now discussed.
We understand that “annealing, recovery,
recrystallization and grain growth are microstructural

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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changes that happen during heating (annealing) later
than cold plastic deformation or during hot working.
These 3 mechanisms are sometimes referred like
restoration processes as they resolve the
microstructural configuration to a lower energy
level” [17]. In addition to the fine works by Reed-
Hill [14] and Wu Hsun /Makins/ Semiatin [17], 3
other excellent works by Mittemeijer [18] and
Humptereys, F.J., M. Hatherly [19] and Raabe [1] are
a must for Physical Metallurgy/Solid State Chemistry
students and teachers. The following discussion is
based on the works of the above mentioned authors.
Recovery
In cold work changes takes place in both
physical and mechanical properties. Plastic
deformation increases strength, hardness and
electrical resistance but it decrease ductility.” [14].
“The initial change in structure and properties that
occur upon annealing a cold-worked metal is
considered the beginning of recovery. As recovery
progress, the following structural changes occur in
sequence. [17].
1. The disappearance (annealing out) of point
defects, vacancies and their clusters.
2. The eradication and reorganization of
dislocations.
3. Polygonization (Sub-grain formation and Sub-
grain growth).
4. The arrangement of recrystallization nuclei
energetically capable of more growth.” [17]
“These structural changes do not engage
high angle boundary migration. Consequently, during
this stage of annealing, the quality of the deformed
metal essentially does not change.” [17]
“In the recovery phase of annealing, the
physical and mechanical properties tend to recovery
their original values. That the variety of physical and
mechanical properties does not recover their values at
the same speed indicates complicated nature of the
recovery method. Fig. 4 shows another anisothermal
curve corresponding to the energy released on
heating cold work polycrystalline nickel. Point C
defines the region of recrystallization. Plotted on the
same diagram are curves showing change in electrical
resistivity and hardness as a function of temperature.
It is visible that the resistivity is completely
recovered before the start of recrystallization. But,
the most important change is in the hardness
simultaneously with recrystallization of the matrix.
[17]
Fig. 4: Recovery of the yield strength of zinc single
crystal at two different temperatures. (From
the data of Drouard, R., Washburn, J., and
parker, E.R., Trans. AIME, 197 1226
{1953}.) [14]
Recovery in Single crystals
“According to Reed-Hill [14], the density of
the cold worked state is directly related to the
complexity of the deformation that produces it. The
lattice distortions are simpler in a single crystal
distorted by simple glide than in a particular crystal
deformed by many glide (simultaneous slip on
numerous system), and lattice distortions might be
still more dense in a polycrystalline metal. If a single
crystal is deformed by simple glide (slip on a single
plane) in a manner that does not bend the lattice, it is
quite possible to completely recuperate its hardness
not including recrystallization of the specimen.
Actually it is impossible to recrystallize a single
crystal deformed simply by easy glide, even if it is
heated to temperatures as high as the melting point.
Fig. 5 shows schematically a stress-strain curve used
for a zinc single crystal strained in tension at room
temperature when it deforms by basal (plane) slip.
Basal plane is a plane perpendicular to the principal
axis in monoclinic, rombohedral, tetragonal and
trigonal/hexagonal crystal systems. It is parallel to
the lateral or horizontal axis in crystals. A difficulty
arises for crystals having hexagonal symmetry in that
some crystallographic correspondent directions will
not have the same position of indices. This is
circumvented in utilizing a four-axis, or Miller-
Bravais, coordinate system. The three a1, a2 and a3
axes are all enclosed within a single plane (called the
basal plane) and are at 120o angles to one another.
The z axis is perpendicular to this basal plane.

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 5: Schematic Laue patterns showing how
polygonization breaks up asterated X-ray
reflections into a series of discrete spots.
The diagram on the left corresponds to
reflections from a bent single crystal, that on
right corresponds to the same crystal after an
anneal that has polygonized the crystal. [14].
“We have already mentioned that in cold
work changes happen both in properties of metal.
While plastically deformed material is studies by X-
ray diffraction techniques, the X-ray reflections turn
into characteristic of the cold worked state. Laue
patterns of deformed single crystals show
pronounced asterism corresponding to lattice
curvatures. In the same way, Debye-Scherrer
photographs of deformed polycrystalline metal
exhibit diffraction lines that are not pointed, but
broadened, in agreement with the complicated
environment of the residual stresses and deformations
that continue in undesirable crystalline metal
following cold working. [14]. before we discuss
recovery phenomenon we would again state that
“plastic deformation is achieved principally by
passage of dislocations through the lattice. In the
early stages of deformation, the dislocations are
relatively long, straight, but few. With increasing
deformation more dislocations from other slip
systems are generated, causing interactions among
the various dislocations. These dislocations and
clusters of short loops tend to tangle and to align
themselves roughly to broaden boundaries. Fig. 6A
and 6B, demonstrate the above-mentioned processes.
Differently annealing after plastic
deformation completely restores the original state,
Mittemeijer [18] has explained that only a fractional
restoration of the material properties as sooner than
the plastic deformation is realized. During the
rearrangement/partial eradication of the dislocations
in the method of recovery, the grain margins in the
material do not progress; the recovery procedure
occurs more or less homogenously during the matter,
in flagrant contrast with recrystallizaton,
characterized through the sweeping of the high-angle
grain margins throughout the deformed matrix. This
procedure, thus, takes place clearly heterogeneously.
It is to be understood that recovery is induced, later
than the plastic deformation (by cold work), via
annealing at a suitable, elevated temperature,
definitely lower half of the melting temperature in
Kelvin. However, if the deformation occurs at high
temperatures, as in hot rolling, recovery processes
already run while the material is still being deformed.
One then speaks of active recovery.
Fig. 6: Schematic representation of the hexagonal
ice lh until illustrating the a1, a2, a3 and axes
and the basal, prism and pyramidal planes.
Dislocation annihilation and rearrangement
Mittemeijer [18] explains that, “The heavy
force for the moving of the dislocations leading to
different pattern and/or to a fractional annihilation of
dislocations in a reduction of the strain energy
included in the strain fields of a dislocations. This
decrease of the stored energy in the substance
actually decreases the motivating force for the
(largely) following recrystallization (recovery and
recrystallization may overlie.” [18]
“The total destruction of dislocations can
occur through many different mechanisms.
Dislocation can transfer through glide beside a single
slip plane, by cross-slip and by climb. Obviously
(edge) dislocations of conflicting sign on the similar
slip plane can turn into annihilated via gliding to
contract, Figs. 7 and 8 [18]. If these two metal
dislocations of conflicting sign are of boundary type
and on two different glide planes, their feasible
annihilation requires a mixture of climbs with glide
processes, Fig. 8. That means that dislocations
annihilation occurs only at high temperatures. Two
initial dislocations on two dissimilar glide planes, if
screw type, are annihilated via cross-slip [18].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 7: Annihilation of two (edge) dislocations of
opposite sign by glide [18].
Fig. 8: Annihilation of two edge dislocations of
opposite sign by climbs and glides [18].
“It must be appreciated that energy stored in
a metal by plastic deformation makes it
thermodynamically unstable. Self-diffusion provides
a mechanism for the restoration of atoms in deformed
region to low energy positions and to enable the
metal to approach toward the truly stable condition of
minimum free energy. Since diffusion involves the
independent activation and migration of individual
atoms, it can, and in this case does, occur without
producing detectable changes in the grain size of the
metal or in its visible microstructure – except,
perhaps, for a progressive reduction in the intensity
of the deformation bands revealed by etching. It does,
however, accomplish a progressive elimination of
local crystallographic distortion, and so of both
macroscopic and microscopic residual stress, a
reduction in hardness and strength, and slow
restoration of the metal to its original properties, viz.,
plasticity, electrical resistivity, magnetic
permeability, corrosion, resistance, etc. These
changes in the structural sensitive properties of the
metal, and the diffusion process by which they occur,
and jointly referred to as recovery of the cold-worked
metal. It must be noted that like all diffusion process,
recovery occurs at a rate that is restricted largely via
the temperature of the metal and its initial state of
internal energy. The temperature dependence of the
recovery rate in the plastically cold-worked metal,
and the same amount of recovery may occur in one
minute at, say 380 ºC that must require 100 years at
room temperature.
“One of the most remarkable aspects of the
recovery process is that the changes in properties it
produces are not always concurrent. For example, in
cold-rolled steel, the first detectable result of
recovery is the relief of macroscopic and microscopic
residual stresses, which is often essentially complete
before these are detectable changes in its hardness,
strength or plasticity properties. This makes possible
the commercial heat treatment called a low-
temperature stress-relieving anneal, intended to
reduce the level of residual stress, improve corrosion
resistance, and increase magnetic permeability etc.,
without appreciably reducing the strength and
hardness of a cold-worked metal. So that the extent to
which recovery has progressed may be accurately
controlled. The light anneal is usually accomplished
by prolonged heating at a relatively low
temperature.” [21]. It is usually followed by slow
cooling of the material to avoid development of a
new generation of residual stresses by non-uniform
thermal contraction during cooling.
Coming back to the explanation of
dislocation, annihilation and rearrangement by
Mittemeijer [18]. Dislocation may also glide beside a
slip plane and upon colliding with a grain boundary
be incorporated into the grain-boundary structure.
Thus the dislocation as an isolated defect could lose
its individuality by local atomic shuffles in the grain
border, in association through the loss of atomic
energy and in this sense annihilation of the
dislocation has occurred as well. The release of strain
energy can also be realized by rearrangement of the
dislocations within a single grain of the matter. If the
numbers of dislocations of conflicting sign are
unequal, complete dislocation annihilation via any of
the first two processes mentioned above is not
possible. The presence of imbalanced numbers of
dislocations of single slip plane: a bent grain outcome
by an excess of edge dislocations of the similar type.
Upon annealing, these edge dislocations can strive
for measures in ‘walls’ and thus form low-angle tilt
limits, Fig. 9. This arrangement takes place by climbs
and short range glide, Fig. 10.

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 9: (a) Dislocation model of a low angle grain
boundary. (b) The geometrical relationship
between ϋ, the angle of tilt, and d, the
spacing between the dislocations [14].
Fig. 10: (a) Bending of a single grain experiencing
glide along a single slip plane: a curved
grain results by an excess of edge
dislocations of the same type. (b) upon
annealing, these edge dislocations can strive
for arrangements in walls, by climb and
short-range glide and thus form low angle
tilt boundaries polygonization of a bended
grain by rearrangement of edge dislocations.
[18].
Polygonization and subgrains
“A particularly simple form of structural
recovery is observed while a crystal is bent in such a
way that only one glide system operates, and is then
annealed. The crystal breaks up into a fig of strain-
free, small, subgrains, every preserving the local
orientation of the original bent crystal, and separated
by plane sub-boundaries which are normal to the
glide vector of the active glide plane. This procedure
or phenomenon is termed polygonization, as a
smoothly curved lattice vector in the crystal turns
into fraction of a polygon. For full description, see
Hibbard and Dunn [21]. In polygonized metals, the
sub-boundaries can be revealed by etching. They are
able to be seen in the form of thick rows of pits, Fig.
11. You have to understand polygonization procedure
in conditions of the dislocation distribution. When a
crystal undergoes plane gliding, it is followed by
possible for all dislocations, both positive and
negative, to pass right through the crystal and out at
the surface. In bend-gliding, a numeral of excess
dislocations of one sign must stay in the crystal to
contain the plastic (permanent deformation of the
material without break by the temporary application
of force) curvature. This strain implies the presence
of a lot of extra lattice planes by the outer surface,
which terminates at border dislocations inside the
crystals. When the bent crystal is annealed, these
dislocations reorganize themselves in walls or tilt
margins normal to the Burgers vector, since in this
position they largely relieve each other’s elastic strain
fields. Fig. 12A shows the structure of a tilt boundary
in additional detail. Afterward stages of
polygonization happen by progressive merging of
pairs of nearby boundaries; the driving force for this
comes from the progressive decrease of the boundary
energy per dislocation in the boundary, as the
disorientation angle Ɵ increases. The rate of this
process, sketched in Fig. 12B, is also restricted by
dislocation climb, since the dislocations in the two
merged boundaries will not be uniformly spaced
unless some dislocations scale”. [13].
Fig. 11: Bent, annealed and etched single crystal of
aluminium, showing sub-boundaries. X70
(After Cahn {1949}.) [13]

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 12: (a) structure of a tilt boundary. The two
subgrains are mutually titled through an
angle Ɵ. [13]
Fig. 12: (b) Tilt boundaries meeting at a “triple
point”. The tilt axis relating the orientations
of the two subgrains is normal to the plane
of the Fig.
According to Mittemeijer [18] rays that the
process of polygonization is exposed in X-ray
diffraction outline by the replacement of powerfully
broadened reflection, observed after the plastic
deformation, by a sequence of neighbouring separate
spots, observed upon succeeding annealing. In simple
words, when a bent crystal is annealed, the bent
crystal breaks up into a numeral of closely related
small ideal crystal segments. This process is also
termed polygonization [22].
Dislocation movements in polygonization
According to Reed-Hill [14], “An edge
dislocation is able of moving either by slip on its slip
plane or by climb in a way perpendicular to its slip
plane. Both are essential for polygonization, as
shown in Fig. 13, where the indicated vertical
progress of all dislocation represents a climb, through
the horizontal progress a slip. Polygonization results
decrease of strain energy. We may also state that the
strain field of dislocations grouped resting on slip
planes produces an effective force that makes them
shift into sub-boundaries. This force exists at every
temperature, except at low temperatures edge
dislocation cannot climb. However, because the
dislocation climbs depends on the progress of
vacancies (an activated procedure through energy
temperature), the speed of polygonization increases
speedily by temperature. However, increasing the
temperature also aids the polygonization process in
another manner, for the movement of dislocations by
slip also becomes easier at elevated temperatures.
This fact is detectable by the fall of the critical
resolved shear stress for slip with rising temperature.
The elevated the temperature, the further complete is
the polygonization process. When every of the
dislocations include dissociated themselves from the
slip planes as well as have aligned themselves in low-
angle boundaries wherever two or more sub-
boundaries join to form a single boundary. The angle
of rotation of the sub-grains across the boundary has
to grow in this process. The coalescence of sub-
boundaries results from the fact that the strain energy
linked with a combined boundary is below that
associated by two separated boundaries. The progress
of sub-boundaries that occur in coalescence is simple
to understand, for the boundaries are arrays of edge
dislocations which, in turn, are entirely capable of
movement either through climb or glide by high
annealing temperature. By time or temperature the
rate of coalescence decreases so as to the
polygonization process reaches a new or less stable
state with widely spaced, about parallel, sub-
boundaries. The process is complicated actually that
slip occurs on a numeral of interconnecting slip
planes and lattice curvatures are complex bend and
vary with position in the crystal. The effect of such a
complex deformation on the polygonization
procedure is shown in Fig. 14 [21] which reveals a
sub-structure resulting from deforming a only crystal
in a tiny rolling mill after being annealed at 1100 ºC.

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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The boundaries in Fig.14 are sub-boundaries and are
not grain boundaries. No crystallization has taken
place in this highly polygonalized single crystal.
Such sub-structures are usually formed in cold
worked polycrystalline metals that have been
annealed at temperatures high enough to cause
polygonization, but not high enough, or long enough
to cause recrystallization. [14].
Fig. 13: Both climb and slips are involved in the
arrangements of edge dislocations. [14]
Fig. 14: Complex polygonized structure in a silicon-
iron crystal that was deformed 8 percent by
clod rolling before it was annealed 1hr at
1100⁰C. (Hibbard, W.R., Jr., and Dunn)
Recovery phenomenon at high and low temperatures
“Polygonization is rather a complicated
process which cannot be easily expressed in terms of
a simple rate equation similar to that used to describe
the recovery process after easy glide. Because
polygonization involves dislocation climb, relatively
high temperatures are required for rapid
polygonization. In distorted polycrystalline metals
high-temperature recovery is measured to be
basically a matter of polygonization and eradication
of dislocations. [14].
“At lower temperature other processes are of
greater importance. At these temperatures, recovery
process is considered as mainly a matter of reducing
the amount of point defects to their equilibrium rate.
The most important defect is a vacancy which may
contain a finite mobility even at moderately low
temperatures.
Dynamic recovery
“High temperature effects the progress of
dislocations into subgrains this process can actually
start at high temperature so that metal undergo
dynamic recovery. The tendency for dislocations to
form cell/sub-structure is quite strong in pure metals
and it can occur at very low temperatures”. [14]. at
more elevated temperatures, the cause of dynamic
recovery naturally becomes stronger, as the mobility
of the dislocations increases by increasing
temperature. The product is that the cells/sub-grains
tends to form at small strains, the cell walls become
narrower/ thinner and much more sharply definite
and the cell size become bigger. Dynamic recovery
is, therefore, is frequently a strong factor in the
deformation of metals below hot working conditions.
[14]
“Dynamic recovery has a strong result on
the shape of the stress-strain curve. This is because
the movement of dislocations from their slip planes
into walls lowers the average strain energy associated
with the dislocations. The result of this is to make it
less complicated to nucleate the additional
dislocations that are needed to more strain the metal.
Dynamic recovery thus tends to lower the valuable
rate of work-hardening.” [14]
“It must be appreciated that the function of
dynamic recovery is not the similar in every metals.
Dynamic recovery occurs most strongly in metals of
high stacking-fault energies as well is not readily
observed in metals of extremely low stacking-fault
energy. This happens in alloys like brass. The
dislocation structure resulting as of cold work in
these latter resources often shows the dislocations
still aligned beside their slip planes”. [14]
“The correspondence between the ability of
a metal to undergo dynamic recovery and the
magnitude of its stacking-fault energy suggests that
the primary mechanism concerned in dynamic
recovery is thermally activated cross-slip. It is
important to note the basic underlying difference

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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between dynamic recovery and static recovery, such
as occurs inside annealing after cold work. In static
recovery, the movement of the dislocations into the
cell walls occurs as a result of the interaction stresses
among the dislocations themselves. In dynamic
recovery, the functional stress causing the
deformation is added to the stresses acting among the
dislocations. As a result dynamic recovery effects
might be observed at very low temperatures, and at
these temperatures the applied stresses are able to be
very large.” [14].
Raabe [1] and Mittemeijer [18] have also,
more or less, given the same explanation and
description of recovery and dynamic recovery.
Kinetics of recovery
Not much literature is available on the
kinetics of recovery. Mittemeijer [18] and Raabe [1]
have discussed briefly the kinetics of recovery.
Hibbad and Dunn [21] have also discussed it
comprehensively in a paper published in 1957. Li
[23] has given a comprehensive review of recovery in
regard to both microstructure and properties. But
Mittemeijer’s explanation, though brief, is good
enough to comprehend the kinetics of recovery.
“According to him, the recovery procedure occurs
more or less homogenously through the material, and
the theory of heterogeneous transformation has no
direct importance for recovery. For homogenous
reaction, the possibility for the transformation to
occur is the same for all locations in the virginal
scheme explained by Mittemeijer [18], Humphreys
and Hatherly [19] and Li [24]. Accordingly, the
transformation speed decreases monotonically from t
= 0 onwards. The direction for the degree of
transformation has been excellently explained by
Mittemeijer [18 – Pages 429-431]. According to him,
the recipes intended for the determination of the
effective, in general activation energy of the
homogeneously happening recovery is the similar for
heterogeneous transformations.” According to him,
recovery be capable of a complex process where a
variety of sub-processes can contribute
simultaneously (viz., the unraveling of the effects of
nucleation growth) with impingement modes on the
overall kinetics of mixed transformations. Also sub-
processes may occur repeatedly, prohibiting a direct
application.” [18]. Balluffi et al [25] have thoroughly
discussed the rate of recovery of a given defect which
is annealing out thermally activated motion which is
often expected to follow a rate equation of the form
-dn/dt = f (n,q1, q2 --- qn) exp {-E/KT} (1)
where n = the total average fault concentration, t =
the time, T = the temperature, K = the Boltzmann
Constant, and E = the activation energy. The q’s
represent the properties of the solid leading to defect
annihilation (e.g., the spatial distribution of sinks).
The kinetics is generally measured by measuring a
microscopic physical property p. If p = p(n),
independent of t, T, and the q’s, and if the q’s are
temperature independent,
-dp/dt = F (p, q1, q2 ----qn) Exp {-E/KT} (2)
Equation (2) can be integrated in the form
- =
(3)
According to eq. (3), p is then a function
only of the temperature-compensated time Ɵ, i.e.,
p = p (Ɵ) (4)
According to Balluffi et al. [25] there are at
least 3 methods for determining the important quality
E from these equations using isothermal or isochronal
annealing data.
Method I. The times required to reach a
given value of p during isothermal annealing are
measured at different temperatures. Hence
Ɵ1 = t1 Exp {-E/KT1} = Ɵ2 = t2 exp {-E/KT2} (5)
Method II. The isothermal annealing
temperature is suddenly changed and the
corresponding change in annealing rate is
determined. In this case, the defect state is presumed
to be the same at the two temperatures and
accordingly,
=exp (6)
Method III. If both the isothermal and
isochronal annealing date are available for initially
identical specimens, the relation
ln∆t1 = Const – E/KTi (7)
Can be used, where ∆t1 is the increase of
isothermal annealing time necessary to produce the
same property change increase as is observed in the i-

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
11
th isothermal annealing pulse at Ti. These methods
can only be used when it can be shown that equation
(4) and many situations can be visualized in which
this relation would not be obeyed. According to
Balluffi et al. [25] much more information can be
obtained by investigating the annealing spectrum
over a range of temperature by measuring during
heating at a constant rate α = T/t Under such
condition, the integration of eq. (3) becomes more
difficult. As an illustration of the behavior to be
expected, eq. (2) may be readily integrated with it
and takes the simple form.
-dp/dt = K0py exp {-E/KT} (8)
where K0 is a constant, and r is an integer.
When r = 1 (first order kinetics, the result is
lnp/po -K0 (E/αK) (Kt/E)2 exp {-E/KT} (9)
A typical annealing spectrum obtained at a
constant heating rate, as in Fig. 15, from which it is
visible that the annealing occurs over a restricted
temperature range centered at Ta where the rate is a
maximum. It is convenient to plot dp/dt Vs T, as in
Fig 15, yielding an annealing peak at T = Ta. Further
analysis shows that Ta should occur at about:
Ta (10)
and that the peak width at half maximum, ∆T is given
by
2.5 (11)
It is seen that the peak is broadened and
occurs at a higher temperature as α increases. Higher
order kinetics can be analyzed within a similar way
yielding comparable results. [25].
In such cases it is found that the peak
position, Ta, depends upon the initial concentration
of defects and that the peak width, ∆T, increases
rather with the order. [25]
Fig. 15: (a) schematic diagram of annealing of a
physical property p as a function of
temperature during heating at a constant
rate. (b) Annealing rate peak as a function of
temperature during heating at a constant
rate. The diagram is for first order kinetics.
Here Ta is the temperature of the maximum
annealing rate, and E is the activation
energy. [26].
Influence of recovery on recrystallization
R.A. Vandermeer and Paul Gordon [26]
have discussed the influence of recovery on
recrystallization. According to them, the growth of a
recrystallized grain into a stained matrix is forced by
the difference in the stored energy of deformation
that is present on the two sides of the migrating grain
boundary. If the stored energy amount per unit
volume of unrecrystallized material is continuously
reduced during the course of recrystallization through
competing recovery phenomena, after that the
immediate rate of growth (boundary migration)
should also decrease. That this is, in fact, the
explanation for the observed decrease in growth rates
with time was shown by making isothermal
calorimetric measurements of the discharge of stored
energy through annealing. [26]. The authors have
pointed out that, from the calometric measurements it
was found out that the processes of recovery and
recrystallizaton overlapped in aluminium-bases
alloys and that they competed by each other for the
available stored energy of cold work. The retardation
of recrystallization in simultaneous recovery is

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probably a common phenomenon. Leslie et al [27]
had observed that the rate of growth of recrystallized
grains in iron and iron-manganese alloys decreased
by time during recrystallization. They suggested that
the probable reason for this decrease was a lowering
of the residual strain energy per unit volume of the
distorted metal because of recovery happening
simultaneously with recrystallization. They presented
softening curves based on hardness capacity showing
that much recovery was taking place.
The control of recovery on recrystallization
is, however, certainly more pronounced in some
metals than in others. The manner in which the
retardation of recrystallization by simultaneous
recovery is influenced by impurities is not well
established. This occurrence may be rationalized by
the hypothesis that the addition of impurities or trace
elements decreases the recrystallization rate more
rapidly than the recovery rate [26].
Metarecovery and orthorecovery
Vandermeer and Gordon [26] have
mentioned the work of Cherian et al [28] who
observed 2 different recovery processes in
polycrystalline, commercially pure aluminium before
strained 9.2% in tension at room temperature. Once a
recovery treatment at low temperatures, less than 100
oC,and these investigators found an important
lowering of the initial flow stress upon re-straining.
After an additional strain of regarding 4%, the flow
stress was restored to essentially that value which
would have been obtained if the specimen had not
been specified recovery anneal. This Cherian et al.
[28] called “Meta recovery”. At higher recovery
temperatures, 150 oC – 200 oC, they observed not
only met recovery but also an enduring decrease in
the flow stress of the improved material relative to
that of unrecovered material at the similar total strain
for all strains. This they called “Ortho recovery”. The
kinetics of meta- and ortho recovery observed by
Cherian et al. [28] were reported to be distinctly
different, and the indications were that ortho recovery
occurred more slowly than metarecovery. They found
activitation energy for ortho recovery of
33,000col/mole.
According to Perryman [29], metallographic
and X-ray observation on the underside of
polycrystalline specimens of aluminium distorted at
room temperature rose reliable with the idea that
there were two stages of recovery. Perryman [29]
observed that recovery at temperatures as low as
room temperature formed much more different sub-
structures than were present directly after
deformation. Perryman [29] found that recovery at
high temperatures, approaching recrystallization
temperatures formed structural changes much similar
to those observed at the lower temperatures:
According to Vandermeer and Gordon [26],
that the retarding affects of isothermal
recrystallization was associated by a decrease in the
linear speed of growth of the recrystallized grains as
a function of annealing time.
(a) Calometric measurements of the progress of
stored energy showed that recovery and
recrystallization overlie to a large amount in the
aluminium alloys. the motivating force for
recrystallization was constantly reduced in
recovery.
(b) Increasing impurity / trace element content were
found to favour recovery over recrystallization.
(c) It was recommended that the two recovery
stages corresponded to (a) the decrease in
dislocation density inside sub-grains and the
rearrangement of the dislocations located in the
sub-grains boundaries into more stable
configurations, and (b) gradual growth of those
sub-grains that subtended small misorientation
angles respecting their neighbours.
(d) That the calometric measurements on Al +
0.0068 at % Cu had revealed two different
stages in the energy release in recovery
annealing. That was in agreement with the
earlier investigations on recovery in aluminium.
(e) Gay et al. [30] were led to conclude as of their
X-ray microbeam studies that recovery was
associated with a rearrangement of dislocations
in the sub-grain boundary regions as well as with
the possible progress of dislocations from the
sub-grain inside to the boundaries.
Recovery of various properties
Recovery of mechanical properties
Cahn [13] has discussed in some detail the
recovery of mechanical, physical, electrical,
electromagnetic properties and of microstructures.
He has shown that nickel, brass, copper,
every metal through low stacking-fault energy,
showed no drop in hardness in stress release or
recovery, and so little climb as well as rearrangement
of dislocations can occur, particularly in brass and
copper. As the flow stress and hardness are a purpose
of the concentration and disposition of dislocations,
this immutability of dislocation structure proceeding
to recrystallization implies that the mechanical
properties as well remain fixed. minor dislocation

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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movements have been postulated to explanation for
significant stored energy release through recovery in
some metals such as silver, but such rearrangement
ought to be sufficiently slight to disappear the yield
stress unchanged. In other metals, such as aluminium
as well as α-iron being the most significant,
dislocations can climb simply and equally these
soften during a recovery anneal. Under favorable
conditions, the total work-hardening may be
recovered with no intervention of recrystallization.
[13]. Cahn [13] has further mentioned that works of
various investigators. The general rule, according to
him, is: the better the deformation, the lesser is the
fraction, R, of the work-hardening that be able to be
recovered via a standard recovery anneal.
“Crystals of hexagonal metals, Zn, Cd are
exceptions, once exceptions. These can recover
totally even later than huge strains by simple glide.
Fig. 16 and 17 show the softening isothermals for
polycrystalline iron pre-strained in tension. One can
observe that the rate of softening is highest at the
beginning as well as steadily diminishes. Perryman
[29] has decreased the kinetics of recovery in their
dependence on pre-strain, pre-straining temperature
and annealing temperature. Fig 18 (a) exhibits partial
recovery of polycrystalline pre-strained 30% and
annealed at 225 oC [13]. And Fig 18 (b) shows
aluminium pre-strained 0, 30, or 40%, in tension and
recovered at room temperature etc.
Fig. 16: Changes in hardness, release in energy, and
change in electrical resistivity upon
isothermal heating of a copper rod
(Clarebrought et al., 1955.) [1]
Fig. 17: Recovery kinetics of deformed iron
expressed in change in the relative flow
stress (Leslie et al. 1963) [1].
“Mechanical properties of distorted metals
or alloys for instance flow stress, hardness and
ductility normally recover monotonically towards the
standard characteristic of the fully annealed state with
the exception of brass, Cu-Al solid solutions and
further similar alloys that are subject to slight anneal-
hardening when annealed at temperatures excessively
low to cause recrystallization, Fig. 19. A relationship
of the form α = Kt -1/2 has been found between the
cell diameter t and the yield stress α in aluminium,
Fig 20. This relationship is similar to the Hall-Petch
equation which defines the yield stress of
polycrystalline steels as a function of grain diameter.
Fig. 18: (a) Fractional recovery of polycrystalline
alluminium prestrained 30% and annealed at
225⁰C (after Thornton and Cahn{1961}.)
[13].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 18: (b) Aluminium prestrained 0%, 30%, or 40% in tension and recovered at room temperature under
simultaneous imposed fatigue cycles over a 3% range of strain. Δεa. The stress range required to
maintain this strange range adjusts itself automatically as the materials softens or hardens. (After
coffins and Travernelli {1965}.) [13]
Fig. 19: Aluminium alloy deformed in tension and
recovery annealed (a) at 100⁰C
(metarecovery), and (b) at 150⁰C
(orthorecovery). (After Cherian et al.
{1949}). [13].
Fig. 20: Correlation between cell size and flow stress
in aluminium. (After Ball {1957}.) [13].
Recovery of electrical properties
“Plastic deformation faintly increases the
electrical resistivity. Lot of work has been done to the
stages in which the electrical resistivity proceeds to
its entirely annealed value. Fig 21 shows
approximately the six stages into which the process is
usually divided. For detailed discussion please
consult Cahn [13], Baluffi et al. [25] and
Clarebrough et al. [16].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 21: The stages in the annealing out of imperferctions produced in copper by various methods. (After
Koehler et al. {1957}.) [13].
Electromagnetic properties
According to Raabe [1], plastic deformation
slightly increases resistivity, just as Cahn [13] has
mentioned. For more details, please consult Beek and
Hu [31], Haassner [32] Humphreys and Hatherly
[19], Doherty et al. [33], Doherty [34].
Recovery of textures
“The mechanical properties of metals mostly
depend on their microstructure as well as texture
(preferred orientations) which are consequence of
equally composition and thermo-mechanical
treatment to which they are exposed. As
recrystallizaton is characterized by the formation as
well as motion of new high-angle grain boundaries,
recovery conserve the existing grain structure with
the original deformation texture that was formed
during cold working. For detailed discussion, please
consult Raabe [1]. The recovery process affects
simply in-grain dislocation as well as cell
substructure and it can lead to the inheritance of the
new cold-working texture of the heat-treated
material”. [1].
Recovery of stored internal energy
“When a part of metal is plastically
distorted, a definite quantity of external work has to
be expended in the procedure. A small part of this
work is retained as stored energy, in addition to
annealing the metal is progressively released in the
form of heat. Cahn [13] has discussed it in detail and
has referred to other investigations. Fig. 22, form
Clarebrough et al. [16] exhibits some interesting
results. For detailed treatment see Cahn [13].
Recovery of other physical properties
“A number of other physical properties are
modified / changed by plastic deformation and then
recover towards their original values during heat
treatment. From the kinetics and magnitude of this
recovery, deductions can be drawn about the
migration and interaction of defects. Cahn [13] has
briefly discussed this phenomenon and has referred to
a few works on this topic. For detailed information
and references, please consult Cahn [13].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 22: Power differential, representing released energy, during the uniform heating of plastically twisted
pure copper rod. Recovery of resistivity and hardness are also shown. (After Clarebrought et al.
{1955}.) [13].
Fig. 23: Various stages in the recovery of a plastically deformed material. [19]

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Humphreys and Hatherly [19] have
mentioned recovery kinetics of many other complex
structures.
Measurements of recovery kinetics
Humphreys and Hatherly [19] have
discussed this process in detail. In simple terms, they
have said that: “Recovery is a comparatively
homogeneous process in conditions of both space as
well as time. Once viewed on a scale which is larger
than the cell or sub-grain size, most areas of a sample
are changing in a comparable way. Recovery
progresses regularly with time and there is no readily
individual beginning or ending of the process.”
“Experimentally, recovery is often considered by
changes within a single parameter, such as hardness,
yield stress, resistivity or heat evolution. If the
change on or after the annealed condition is XR, then
the kinetics of recovery are determined from
experiment. It is frequently complicated to obtain a
fundamental insight into recovery from such
analyses, initially because the association of the
parameter XR to the microstructure is generally very
complex and secondly because recovery may involve
a number of concurrent or consecutive atomistic
mechanisms (Fig. 23) each with its own kinetics.
Empirical kinetic relationships
Experimental results have been analyzed in
conditions of numerous different empirical relations
among XR and t. The two most usually reported
isothermal relationships, which we will refer to as
types 1 and 2, are as follows:
Type 1 kinetics
= - (1)
which, on integration gives
XR = c2 – c1 ln t (2)
where c1 and c2 are constants
Apparently, this form of relatrionship cannot
be valid during the early stages of recovery (t → 0)
when XR → X0 or at the end of recovery (t → ∞)
when XR → 0.
Type 2 kinetics
= -c1 (3)
Which, on integration gives?
- = (m-1)c1t (4)
For m > 1, and
ln(XR) - ln(X0) = c1t (5)
For m = 1
The relationship between the amount of
recovery and temperature was found over a wide
range of conditions to be:
R = c1lnt -
Recrystallization
We have just discussed recovery. “Recovery
and recrystallization are two mainly different
phenomena. Recovery and recrystallization were
identified as important phenomena for more than 100
years and they are well-documented in the
metallurgical solid state chemistry and solid state
physics literature. “The process of recrystallization of
plastically deformed metals and alloys is of
fundamental significance in the processing of
metallic alloys in support of two reasons. The first is
to soften and restore the ductility of the material
hardened by low temperature deformation (less than
50% of the absolute melting temperature). The
second is to organize the grain structure of the last
product [33]. This subject has been nicely reviewed
by Humphreys and Hatherly [19] and Haessner [32].
Doherty et al. [33] have mentioned that within all
structural transformations, there are two alternate
types of transformation as initially recognized by
Gibbs. In the first of these, Gibbs I, typically called
nucleation and growth – the conversion is wide in the
magnitude of the structural change but is, initially,
spatially restricted with a sharp boundary between the
old and the new structures. The second type of
transformation, Gibbs II, frequently described as
continuous or homogeneous, the transformation is
initially small in the magnitude of the structural
change, but it occurs throughout the parent structure.
One annealing plastically deformed materials, both
dislocation recovery, that takes place before as well
as during recrystallization and too normal grain
growth are Gibbs II transformation which occur
uniformly during the sample while recrystallization
also abnormal grain growth are Gibbs I
transformations.” [34].
It must be noted that all investigations,
reports start with the basic facts that: “When a cold-

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worked metal is held at a high enough temperature
for a long enough time, and without interference by
other physical changes in it, the process of recovery
becomes at last complete. But, usually, however, a
temperature high enough to accomplish it within a
useful short period of time is also high enough so that
a second and quite different process called
recrystallization occurs, to eliminate distortional
energy from the material before it can be dissipated
by the slower process of recovery. Recrystallization
is the appearance, within a mechanically-worked
metal/alloy of a new generation of crystals, identified
with the old crystals in composition and crystal
structure, but differing from them is being entirely
free of stored energy, residual stress and strain-
hardening produced by earlier plastic deformation.
Usually, the new crystals also differ from those they
replace in size, shape and orientation. Like recovery,
recrystallization is a result of the spontaneous effort
of a distorted crystal structure to reduce its free
energy by dissipating as heat the distortional energy
stored in it during previous deformation. Unlike
recovery, recrystallization involves the two important
and well-known processes of nucleation of new
crystals within the solid metal, and growth of these
new crystals to an observable size. [21]. Smith [35],
Hu and Makin [17], Doherty et al. [33], Reed-Hill
[14], Mittemeijer [18], Cahn [13], Raabe [1], Lee and
Han [36], Humphreys and Hatherly [19] etc. etc. have
all used more or less similar explanations of the
phenomenon of recrystallization, i.e. when a metal is
plastically defrost at low temperature relative to its
melting point, it is supposed to be cold worked. The
majority of energy spent in cold working turns into
heat but a definite fraction is stored in the material as
strain energy, residual stress, stored energy etc. That
cold working (or even hot working under certain
conditions) increases greatly the number of
dislocations. Plastic deformation also creates point
defects, vacancies and interstitials which retain
energy. And that the higher temperature, the shorter
the time needed for recovery and recrystallization.
And that the motivating force for recrystallization
comes from the stored energy of cold work. In those
cases in which polygonization is fundamentally
complete earlier than the start of recrystallization, the
stored energy can be assumed to be limited to the
dislocations in polygon walls. The removal of the
sub-boundaries is an essential part of the
recrystallization process.” [14]. and that the
recrystallization process occurs after heavy plastic
deformation and heating at elevated temperature.
Recrystallization removed the dislocations and
dislocation-free grains are formed within the
deformed or recovered structure and release of stored
energy.” [19]. Both Cahn [13] and Raabe [1] have
discussed and differentiated between primary
recrystallization and secondary recrystallization.
Whereas both Cahn [13] and Raabe [1] have
discussed recrystallization and factors that retard or
increase recrystallization, extensively, Mittemeijer
[18] has paid more attention on the phenomenon of
grain-nucleation and grain-growth.
We will briefly discuss the (1) Primary
Recrystallization and related processes, and (2)
Secondary Recrystallization. We will discuss the two
kinds of recrystallization one by one and their related
processes.
Primary Recrystallization
As mentioned earlier, Cahn [13] and Raabe
[1] have discussed Primary Recrystallization
phenomenon in some details. Cahn [13] has quoted
six laws, due to Burke and Turnbull [37] which play
important roles in primary recrystallization:
(a) A minimum deformation is needed to begin
recrystallization.
(b) The lesser the deformation, the higher is the
temperature required to initiate recrystallization.
(c) Increasing the annealing time decreases the
temperature necessary for recrystallization.
(d) The final grain mass depends upon the degree of
deformation and to a smaller degree upon the
annealing temperature, in general being smaller
the greater the degree of deformation and the
lower the annealing temperature.
(e) The larger the original grain size, the larger the
amount of deformation necessary to give
comparable recrystallization temperature and
time.
(f) The quantity of deformation required to give
equivalent – deformational hardening increases
with rising temperature of working as well as, by
implication, for a given degree of deformation a
higher working temperature entails a coarser
recrystallized grain size and a higher
recrystallization temperature.
(g) And to these six laws, Cahn [13] added the 7th
law.
(h) Fresh grains do not grow up into deformed grains
equal or a little different orientation.
(i) An eight law, not strictly concerned with primary
recrystallization:
(j) Constant heating after primary recrystallization is
complete, causes the grain size to increase.
All these laws and theories have been
adequately discussed by Cahn [13] on page 1149.
According to him, the difference is grain size of a

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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recrystallized metal as a purpose of pre-strain as well
as temperature is apt to be rather complex. This
information is sometimes gathered, represented
within a single view diagram, a recrystallization
diagram. Fig. 24 shows such a diagram for
electrolytically refine iron published in 1941 by
Burgers [11]. Later more complex and refined
diagrams were published by the Russian scientists.
“A recrystallization diagram is at best an
approximate: for example, where new grains nucleate
at the boundaries of the distorted grains [26] and
[38], the final grain size must obviously depend on
the grain size before plastic deformation.
Fig. 24: Recrystallization diagram of electrically
refined iron (Burgers, 1941) [13].
“It must also be remembered that resources
with low stacking-fault energy can store a high
fraction of the internal elastic strains due to the
limited cross-slip as well as climb capabilities of the
dislocations during recovery (and recrystallization)
and metals that have a higher stacking-fault energy,
e.g. Al, Fe, can considerably decrease the
deformation energy hence as well the remaining
motivating force for primary recrystallization through
the preceding recovery period.” [1]
“According to Raabe [1], main static
recrystallization proceeds by the formation as well as
motion of new high-angle grain boundaries. In
recrystallization, no new deformation is imposed.
The procedure follows Johnson-Mehl-Avrami-
Kolgomorov (JMAK) sigmoidal kinetics and
typically leads to a refinement the microstructure
(KJMA). Grain structures resulting as of primary
static recrystallization characteristically consist of
equiaxed crystals. The motivating force is provided
in the stored deformation energy, i.e. primarily by the
long-range elastic stresses associated with the
dislocation and subgrain structure that was formed
during plastic deformation. The motivating force can
hence be approximated as being proportional to the
stored dislocation density, the shear modulus, the
magnitude of the Burgers Vector. The mechanical
properties (hardness, yield strength) decay at first
slowly during the incipient recovery (incubation or
nucleation stage) and then very rapidly, i.e.
sigmoidally, when the newly produced grains remove
up the deformation microstructures. Final
impingement of the rising crystals leads to ending of
transformation. The ending of primary
recrystallization is accompanied by a competitive
grain growth” [1].
Kinetics of Primary Recrystallization
Cahn [13] has extensively discussed the
kinetics of primary recrystallization covering some
kinetic experiments, the overlapping of recovery and
recrystallization, the retarding surface of recovery on
retardation, annealing textures, nucleation of primary
grains (we will discuss grain-nucleation and grain-
growth later on), cell growth, enlargement of primary
grains with the role of impurities/ trace elements on
grain refinement/ growth (see Khan 39), special
orientations, vacancies in grain boundaries, primary
recrystallization of two-phase alloys etc etc.
Mittemeijer [18] has discussed the kinetics of
recrystallization as a whole. “According to him the
majority of the kinetic analyses performed of
recrystallization adopt an approach similar to that for
heterogeneous phase transformation kinetics.
“Nucleation”, growth and impingement are illustrious
as three commonly overlapping mechanisms. This
framework can lead to the classical Johnson-Mehl-
Avrami equation (also discussed above by Raabe),
describing the degree of transformation (fraction

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
20
recrystallized) as a task of time at constant
temperature. To emphasize the limited validity of the
standard JMA equation, the basic assumptions made
in its derivation are, isothermal conversion, either
unpolluted site saturation at t = 0 or pure continuous
nucleation, high driving force in order that
Arrhenius-type temperature reliance for the
nucleation and growth are certain, and randomly
dispersed nuclei which produce isotropically”.
Mittemeijer [18] has pointed out the limitations of
JMA analysis and advised not to blindly apply it.
Secondary Recrystallization
This topic has been discussed both by Raabe
[1] and Cahn [13]. First let us see what Raabe [1] has
written about it.
“He says that secondary recrystallization refer
to a particular grain-growth phenomenon where a very
small quantity of grains grow to a dimension that
exceeds the standard grain size by means of one order of
magnitude or else more in terms of the grain diameter.
However, secondary recrystallization is a somewhat
confusing term. When shed into a more appropriate
expression, it is occasionally also referred to as
discontinuous grain coarsening or else discontinuous
grain growth. It does not explain the sweeping of the
deformed microstructure such as encountered in primary
static recrystallization but as an alternative it refers to
the extensive growth of a few large grains in an
otherwise recrystallized grain structure. It has, thus, only
a phonological resemblance to primary static
recrystallization become some text describes the process
in terms of a nucleation stage where a number of the
grains grow first widely in the incipient stage of
secondary recrystallization (pseudo nucleation) and a
subsequent “growth” stage where these enormous
crystals sweep the other regularly sized crystals. This
latter growth stage does not need a definite additional
driving force but the simple fact that some grains are
much better than others as topologically sufficient that
the local curve provides wide further growth of these
candidates. In physics terms, secondary recrystallization
is a grain growth method where a small quantity of
grains grows widely and can assume a size that is more
than 100 times larger than that of the average size of the
grains that surround them. The reason for this behavior
can be restricted back-driving forces, inhomogeneous
microstructures, and in homogeneities in the grain-
boundary properties in terms of energy and mobility. A
typical example is the discontinuous grain growth of
enormous Goss-oriented grains in Fe-3wt% Si soft
magnetic steels”. [1].
According to Cahn [13] “When the primary
recrystallization is complete, the grain structure is not so
far stable. The main motivating force, linked with the
retained energy of deformation, is spent, but the material
still contains grain boundaries which have fixed
interfacial energy. This situation is at best metastable,
and ideal thermodynamic stability is only attained when
the sample has been converted into a monocrystal.
“When the annealing of an firstly distorted
sample is continued long beyond the stage when
primary recrystallization is complete, the even tone of
grain growth may be broken up by the unexpected
extremely rapid growth of some grains only, to
dimensions which may be of the arrange of centimeters,
while the rest of the grain stay small and are finally all
swallowed by the huge grains. This is termed as
secondary recrystallization. Cahn [13] has explained 7
general characteristics, the main being that: (1) the
secondary structure, when complete, occasionally has a
prominent texture. Such a texture constantly differs
from the previous primary texture, and (2) A well-
defined minimum temperature must be exceeded for
secondary recrystallization. The largest grains are
normally produced just above this temperature; at higher
annealing temperatures smaller secondary grains
product, and (3) The motivating force of secondary
recrystallization, and the large grains are well launched,
normally arises from grain boundary energy (just as
does normal grain growth); under special circumstances,
the surface energy of the grains can contribute. Fig. 25
exemplifies several of these regularities. assume a
primary structure contain a grain of approximately twice
the average diameter and that the interfacial energy of
the boundaries separating this grain from its smaller
neighbors (γs) is the similar as the energy of the
boundaries among these neighbors themselves (γp), then
the sides of the large grain have to be convex here as
shown in Fig 26, Cahn [39] if the triple grain junctions
are to be in equilibrium. The configuration, which is
clearly recognizable in Fig 27, Cahn [38] is obviously
instable, since the curved boundaries will become
straight and in the process will distress the equilibrium
at the triple points, which therefore migrate outwards.
The large the grain growth, the more sharply will its
bounding faces turn into curved and the process is thus
self-sustaining. At a convinced size a grain has reached
“breakaway point”, and, after that grows rapidly, getting
the stage of the grain at the top of Fig 27. There is no
mystery, then, about the continuation of secondary
growth once it has happening; only the initial stages are
hard to understand. Cahn [13] has further discussed
qualitative and quantitative analyses of the growth of
grains and has quoted the work of May and Turnbull
[40].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 25: Grain size (long scale) as a function of temperature for pure and MnS-doped 3% silicon-iron, cold-
rolled at 50% to 0.5mm thickness, annealed 1 hour. The drop in curve S is due to an increase in the
number of secondary grain at higher temperatures, until above 1100⁰C all grains grow equally to a
size limited by the sheet thickness. (After May and Turnbull {1958}.) [13].
Cahn [13] has mentioned 3 processes that
might permit a primary grain to grow the breakaway
(see Cahn, p.1189). On the basis of these three
processes, Cahn concluded that it was clear that the
nature of the disperse phase is vital in calculating
secondary crystallization; if there is a extremely
sharp primary texture with a little rogue grains, a
appropriately dispersed second phase is very
important for secondary recrystallization. If the
dispersion drag is insufficient, a large amount normal
grain growth occurs; if it is too huge, the secondary
grains cannot grow at all. Thus in Fig. 26 the primary
grain size of the pure alloy increases more quickly
than that of the alloy (Fe + 3% Si) doped with Mgs
dispersion; the latter under goes secondary
recrystallization, the former does not.” [13]. Calvet
and Renon [41]. Cahn [13] has also discussed in
point surface-controlled secondary recrystallization
and has quoted the works of Detert [42] and Walter
and Dunn [43] and may other investigators. It is
beyond the scope of this evaluation to go into details
about it.

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Fig. 26: Schematic diagram showing effect of the
number of sides of grain on the curvature of
grain boundaries. Six sided grains are in two
dimensional equilibrium; smaller grain
disappear, larger grains grow. (After Coble
and Burke {1963}.) [13]
Fig. 27: Incipient recrystallization in zinc sheet. X
100 [13]
“Cahn [13] has further discussed the
relationship between secondary recrystallization and
sintering and has pointed out the relationship between
pores and particles, the disappearance of pores due to
diffusion of vacancies to the nearby grain boundary
[44]. If, however, secondary recrystallization takes
place, after that all the pores in a secondary grain
have been crossed only once by an affecting
boundary, and moreover one that is moving rapidly.
For effective sintering, then, secondary
recrystallization has to be prevented”.
Kinetics of Secondary Recrystallization
We have already discussed primary and
secondary crystallizations and also the kinetics of
primary recrystallization. We have earlier explained
[13] that when the annealing of an initially deformed
sample is long beyond the range when primary
recrystallization is complete, the even tone of grain
growth may be interrupted by the unexpected very
quick growth of some grains only to abnormal
growth. These large grains eventually swallow the
small grains. This is known as secondary
recrystallization. The drawing force of secondary
recrystallization normally arises from grain boundary
energy below special circumstances; the surface
energy of the grains can contribute [13]. For
secondary recrystallization to occur, it is necessary
that normal growth is initiated or hindered. The
kinetics of the secondary recrystallization usually
follows a proportional growth with the time, Fig. 28.
It is in accordance with the Avranic equation [45]
R = G (t – t0)
where t0 is the nucleation time, G is the growth rate
dR/dt. Initially, the nuclei of the defect-free crystals
form, called the nucleation period, followed by their
growth at a constant rate until all the smaller
deformed crystals have been consumed.
Fig. 28: Variation of recrystallized volume fraction
with time [17].
It is usually accepted that any helpful model
have to not only account for the initial state of the
material but also the continually altering relationship
among the growing grains, the deformed matrix and
any second phase or other microstructural factors.
The situation is further complicated in dynamic

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
23
systems where deformation and recrystallization
happen simultaneously. Accordingly, it has generally
proven not possible to produce a precise predictive
model for industrial processes without resorting to
wide experiential testing. But in it are many
difficulties as it may require industrial equipment that
has not yet actually been manufactured. It is to be
appreciated that most of the investigations have
concluded that the kinetics of primary
recrystallization and secondary recrystallization are
to some extent similar. “The smaller the grain size of
primary recrystallized specimen just before the onset
of secondary recrystallization, the longer for the
evolution of secondary recrystallization. The time for
the evolution of secondary recrystallization gets good
agreement with the calculated time on the assumption
that the coarse grain, which could decrease the
driving force for secondary recrystallized grains to
evolve, in the primary recrystallized specimen could
control the kinetics of secondary recrystallization.
The kinetics of secondary recrystallization is
considered to be controlled mainly by the grain size
distribution of the primary recrystallized specimen.
[46]. Fig. 29 [47] illustrates the kinetics of secondary
recrystallization for cube texture formation in Fe +
3% Si alloy during isothermal annealing at 1050 oC.
The characteristics of this curve for secondary
recrystallization are quite similar to those for primary
recrystallization.
Fig. 29: Kinetics of secondary recrystallization for
cube texture formation in Fe-3Si during
isothermal annealing at 1050⁰C (1920⁰F).
The characteristics of this curve for
secondary recrystallization are quite similar
to those for primary recrystallization. [17].
Annealing and Recrystallization Textures
“When a price of metal is deformed by
several directional process, for instance wire drawing
or rolling, the basic grains obtain a preferred
orientation or texture; the grains estimated, usually
with a good deal of scatter, to an ideal orientation. In
an intense case the whole sample might turn into a
pseudo-single crystal. Occasionally several ideal
orientations co-exist, in order that the total scatter is
greater. The actual orientation distribution of grains
is termed a deformation texture. When such a
material is recrystallized it again acquired a texture,
which may be identical to the preceding deformation
texture but further frequently is quite different – this
is an annealing texture. X-ray diffraction data
obtained as of the sample is used to plot pole figs to
illustrate the annealing/ recrystallization texture.”
[13]. for detailed description phase see Cahn [13],
and Raabe [1].
Deformation Textures
“According to Humphreys and Hatherly
[19], a lot of mechanical and physical properties of
crystals are anisotropic, and consequently the
properties of a polycrystalline combined will depend
on whether the individual grains or subgrains, which
include the sample, are erratically oriented or be
likely to have some in crystallographic orientations of
the crystallites inside a polycrystalline aggregate is
known as the texture of the material. The orientation
that takes place during deformation is not random.
They are a consequence of the actuality that
deformation occurs on the majority favorably
oriented slip or twinning systems and it follows that
the distorted metal acquires a preferred orientation or
texture. If the metal is then recrystallized, nucleation
occurs preferentially in regions of exacting
orientation. The capability of the nucleus to grow
may as well be inferred by the orientations of next
regions in the microstructure. Together these
features, nucleation and growth, make sure that a
texture also develops in the recrystallization material.
Such textures are called recrystallization textures to
differentiate them from the interrelated but rather
different deformation textures from which they
expand”. Reference [19] contains much information
on illustration of textures, deformation textures in
FCC metals, pure metal textures, alloy textures,
deformation textures in BCC metals, and deformation
textures in HCP metals rolling textures, and factors
which influence texture development”.

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24
Formation of Annealing Twins
According to Cahn [13], a normally observed
characteristic of recrystallized structures in certain fcc
metals (Cu, Pb alloys; austenitic steels etc) in the
existence of copious parallel-sided annealing double
lamellae, as shown sketched in Fig. 30. These lamellae
are always boundary by {111} planes or coherent
boundaries --- instantaneously subsequent to primary
recrystallization there are a small number of lamellae
per grain, but their quantity increases through the
progress of grain growth. (For explanation see ref. 13).
Fig31 [19] shows the original annealing twins in
annealed 70:30 brass. Some coherent (CT) and
incoherent (IT) twin boundaries are noticeable.
Humphreys and Hatherly [19] have also explained the
mechanism of twin formation, viz. (1) by growth
faulting (2) by boundary dissociation (3) during
recovery (4) during recrystallization and (5) during grain
growth.
Fig. 30: (a) Annealing twin lamellae in a face- centered
cubic metal grain. (b) Stages in the
development of at twin during grain growth.
[13]
Driving Forces of Recrystallization and Grain Growth
Phenomena
Raabe [1] says that from a thermodynamic
point of view, the majority of recrystallization and
grain-growth phenomena can be properly characterized
as non-equilibrium transformation. In each type of
process, a motivating force acts on a grain-boundary
section. The free-enthalpy alteration of the system is
then linked with the discharge of stored energy per
volume that former swept by the morning grain
boundary.
“In standard, two types of motivating forces
can be distinguished. This first one is a stored volume
energy that acts uniformly in every portion of the
affected grain that is being swept by a moving grain
boundary. During such cases, the stored energy can
frequently be simplified and written in scalar form. A
most important (though simplified) example is the
distinction in the stored dislocation density across a
moving border. It must be emphasized though that for
some experiments, i.e. in the case of differences in
elastic or magnetic energy, the tensorial character of
these mechanisms must be in use into consideration.
The second class of motivating forces is of a
configurational, i.e. a topological character. This means
that the driving force and the discharge in the stored
system energy depend on the accurate local arrangement
of the defects that are removed or else rearranged
through a moving grain boundary. A characteristic
example is constant grain growth, i.e. competitive grain
coarsening, where the motivating force depends on the
local curvature and energy of the grain boundary but not
on the size of the entire grain. Similarly, in continuous
grain growth, the local grain boundary portion that
moves in the direction of its center of curvature in order
to decrease its total length does not “know” the size of
the grain that it encompasses. This means that in this
case only the local capillary driving force matters. It is
conversely not a constant force that acts uniformly in
each volume portion of the similar crystal but it differs
all over in the crystal and polycrystal depending on the
local grain boundary configuration in terms of the
curvature and grain-boundary intersection lines and
points.” For detailed quantitative analysis, please consult
Raabe [1].
Sub-grain Rotation during Recrystallization
James C. M. Li [49] has mentioned the chance
of sub-grain rotation during recrystallization. He has
analyzed thermodynamically and kinetically the option
of the rotation of a sub-grain with respect to its
neighbours as a usual process in recrystallization. He
found that it was dynamically possible if the of rotation
favored the removal of low-angle boundaries more than
that of high-angle boundaries, the removal of twist and
asymmetric boundaries above the tilt and symmetric
boundaries, and the elimination of the large-area
boundaries over that of the small-area boundaries. As
the rotation direction had two degrees of freedom, there
existed a rotation among the two degrees of freedom
such that directions whose two degrees of freedom
satisfied such a rotation provided no driving force for
rotation. Further directions would supply free energy to
rotate within once sense or else opposite. Kinetically
one of the next two processes inside one boundary
might be rate controlling: the cooperative movement of
the dislocations in the boundary, as well as the
cooperative diffusion of vacancies in the lattice. The
rotation of a sub-grain favored the removal of one of the
boundaries which contributed the major fraction of
motivating force as well the largest portion of resistance.
This caused the sub-grain to combine with the new sub-
grain separated by that boundary. The probable time
required for individual coalescence compared favorably
with the experimental rate of sub-grain growth in
aluminium. Figs 32-34 illustrate this phenomenon.
Many investigators have confirmed this observation.

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 31: Annealing twins in annealed 70:30 brass. Some coherent (CT) and in coherent (IT) twin boundaries
are marked. [19]
Fig. 32: Coalescence of two subgrains by rotation of one of them.
a. The original subgrain structure before coalescence.
b. One subgrain is under rotation.
c. The subgrain structure just after coalescence.
d. The final subgrain structure after some subboundary migration. [49]

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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Fig. 33: Cooperative diffusion of vacancies in sub-grain rotation. [49]
Fig. 34: The rate of rotation of the angle tilt boundary. [49].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
27
Dynamic Recrystallization
“The term dynamic recrystallization refers
to all recrystallization phenomena that happen
through the plastic deformation. See for references
[1]. “Dynamic recrystallization is often experimental
during hot deformation of prepared alloy. It appears
to be quite comparable to the process which occurs in
metals and is to be predictable in materials where
recovery is slow and there is maintenance of huge
amounts of stored energy. For grain boundary
passage and dynamic recrystallization evidence,
please refer to [19]. The physical mechanisms
responsible for dynamic are comparable in a lot of
aspects to those controlling static (primary)
recrystallization. Single crystal studies have exposed
that twining plays a significant role in dynamic
recrystallization, yet in polycrystalline materials
twining can play an important role in the propagation
of dynamic recrystallization, mainly in low stacking
fault energy alloys. Doherty et al. [33] have
discussed texture development during dynamic
recrystallization, post-dynamic recrystallization,
effect of solute elements on precipitation and on
dynamic recrystallization, geometric dynamic
recrystallization. Dynamic recrystallization is
thermally activated as well as its progress obeys the
Avrami equation.
An extensive, detailed review article on
dynamic recrystallization titled, “A Review on
Dynamic Phenomena in Metallic Materials by Huang
and Loge” [48] was accepted for publication in
Materials Design on 3 September, 2016 (ref. PH –
S0264 – 1275 (16) 31175-3, DOI:10.1016/j.madjes,
2016.09.012, Ref JMADE 2262 as a PDF file). Its
introduction and summary are reproduced here for
students, researchers, teachers for further
consultation.
Introduction
Mainly the metallic parts during their
processing cycle, subjected to hot deformation,
through which dynamic recrystallization (DRX)
frequently takes place. The final microstructure and
mechanical properties of the alloys are mostly
determined by the recrystallization and linked
annealing phenomena, and the research on
recrystallization can date back to 150 year ago [1].
The rapid progress of the DRX theory from 1960s
was summarized by McQueen in 2004 [2]. Several
important factors can have a major effect on DRX;
these contain the stacking fault energy (SFE), the
thermo-mechanical processing (TMP) conditions, the
initial grain size, chemistry and microchemistry of
the material in terms of solute level and second phase
particles etc., which is also the reason why a vast
quantity of related works can be found in literature.
During hot deformation, discontinuous
dynamic recrystallization (DDRX) is often observed
for low SFE materials, where nucleation of new
strain-fee grains occurs and these grains grow at the
rate of regions occupied of dislocations. Cell or
subgrain structures by low angle grain boundaries
(LAGBs) are formed through deformation for
materials with high SFE due to the proficient
dynamic recovery, they gradually progress into high
angle grain boundaries (HAGBs) at larger
deformations, a process which is known as
continuous dynamic recrystallization (CDRX) [1].
Besides DDRX and CDRX, another comparatively
new theory of geometric dynamic recrystallization
(GDRX) was also experimental on deforming
aluminium to big strains at elevated temperatures. In
this case, the deformed grains turn into extended with
local serrations but stay distinguishable through
deformation to large strains unless their thickness is
below 1-2 subgrain size, at which time the developed
serrations become pinched off and equiaxed grains
with HAGBs are formed. Substantial grain
refinement is thus obtained during the grain
elongation as well as thinning. Numerical models are
developed for these three types of DRX, most of
them are focused on DDRX [3], with sparse models
on CDRX [4] and mostly unexploited GDRX models
[5].
It should be prominent that there is no strict
separating line among these three types of behaviors.
For example, CDRX was observed through rolling of
fine-grained 304, austenitic stainless steel which is of
low SFE [6], DDRX was reported for high SFE high
purity Al [7], CDRX and DDRX can even co-exist
during hot working of Mg-3Al-1Zn [8] or duplex
stainless steel [9]. When designing new alloys, the
adding together of alloying elements to the base
material may adjust it’s SFE [10] and thus changes
the recrystallization mode. Even designed for the
same material, altering the TMP conditions [11] or
initial grain size [12] can also direct to the transition
from DDRX to CDRX. Meanwhile, CDRX and
GDRX can as well operate along with, e.g., in
Zircaloy-4 [14]. Due to the increasing requirements
on the formability of the metallic parts, products
which were before formed at room temperature,
where DRX is in general irrelevant, are currently
often processed at warm or else hot temperatures [14,
15]. It is not simple to identify which type of the
three DRX processes is in use at certain TMP
conditions since they share some similarities and can
take place concurrently and/or transitionally. There is

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
28
really a hot debate between researchers within the
recrystallization field on whether CDRX or GDRX
should be responsible for the grain modification of
aluminium [16], the center issue is whether the
HAGBs experiential after big deformation are altered
from LAGBs, microshear/ deformation bands, or
original HAGBs.
The recrystallization phenomenon in
common was reviewed in 1997 by the top experts in
this area [17], since then the EBSD technique, which
can offer invaluable information on the development
of the crystallographic orientations and facilities the
understanding of different DRX processes, has been
widely spread. CDRX and DDRX were recently
reviewed in an outstanding and extensive review
paper [18], however, GDRX was not covered and the
related DRX numerical models were only in brief
described. The evaluation of the three types of DRX
processes was only infrequently mentioned in a few
articles [19-21]. This short review paper covers
seminal basic works as well as very recent
contributions to all the three DRX processes. It
differs from the above mentioned review papers since
it updates key aspects on DRX from affecting factors,
characterization methods to mechanisms and
mathematical models.
The main objective of this paper is to offer a
short review of the different types of DRX observed
through hot deformation for different types of
metallic alloys, i.e., DDRX, CDRX and GDRX. The
review offered is proposed to equip the beginners in
metallurgy with a brief insight into the DRX
phenomenon. For more details on this topic, the
interested readers are referred to the classic textbook
on recrystallization [1] and the two outstanding but
longer review papers [17, 18]. In Section 2, the
terminologies used in this field are initially
summarized, together with the key factors
influencing the DRX processes, as well as the
corresponding characterization methods. The
transitions among the various types of DRX
processes are only briefly discussed due to deficiency
of literature data. From Section 3 to 5, more details
on the three types of DRX are given, including their
mechanisms and related numerical models. Finally,
in Section 6, further studies inside the DRX field are
recommended.
Dynamic recrystallization
Terminology
In recrystallization processes there are
different phenomenological categories, a lot of them
are interrelated and the borderlines among them are
often nuclear. It is favorable to recall all these
processes, even though a number of them will not be
covered in this evaluation work. In addition, there are
also some terminologies in recrystallization field
which are worth mentioning before going into the
details of DRX.
Defects like dislocations with interfaces
increase in deformation which makes the material
thermodynamically unstable. When deforming metal
at eminent temperatures, thermally activated
processes ten to remove these defects in order to
decrease the free energy of the system. The
microstructure and also the properties can be
moderately restored to their original values before
deformation by recovery during annihilation as well
as rearrangement of dislocations. Recovery usually
brings relatively homogeneous microstructural
changes and it generally does not involve the
migration of HAGBs among the deformed grains
[17]. Analogous recovery processes may take place
in annealing or else throughout deformation, which
are known as static recovery (SRV) and dynamic
recovery (DRV), respectively.
The “development of a new grain structure
in a distorted material by the formation and migration
of HAGBs determined by the stored energy”
introduced by plastic deformation is termed as
recrystallization [17]. Recrystallization may take
place heterogeneously with apparent nucleation and
growth stages, and in this case it is described as a
discontinuous process. Differently, it can as well take
place homogeneously such that the microstructures
change progressively with no clear nucleation and
growth stage, exhibiting a continuous character.
Static recrystallization (SRX) refers to the
recrystallization process through annealing while that
occurred in deformation at elevated temperatures is
called dynamic recrystallization (DRX). During the
initial stages of annealing, fine dislocation-free
crystallites are produced by SRV, these nuclei grow
and use the strain hardened matrix, determined by the
stored energy associated with the dislocations and/or
sub-boundaries. This process is the most studied and
widely used recrystallization process, which can be
classified as discontinuous static recrystallization
(DSRX). SRX can also take place consistently
without apparent nucleation and growth stage, a good
illustration is when Al alloys with particle-stabilized
subgrain structure are annealed at elevated
temperatures. Fine particles precipitate out along
grain/subgrain boundaries, gradual subgrain growth
takes place during subsequent annealing due to the
coarsening of dispersoids (reduced pinning force) and

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29
LAGBs misorientations increase progressively until
they are transformed into HAGBs. In this way, a new
microstructure develops homogeneously throughout
the distorted matrix, and is thus labeled as continuous
static recrystallization (CSRX) or extended recovery.
Back to DRX, the definitions of these three
types of DRX processes is given in the introduction
section, i.e., discontinuous dynamic recrystallization
(DDRX), continuous dynamic recrystallization (CDRX)
and geometric dynamic recrystallization (GDRX). It
will not be reiterated here, but more information will be
given for each DRX process in later sections. It is
important that, if the straining is stopped after the critical
strain for DDRX although the annealing temperature
does not drop adequately fast, the recrystallization
nuclei formed in the material will produce with no
incubation time into the matrix with higher stored
energy. This phenomenon is known as metadynamic
recrystallization (MDRX) or post-dynamic
recrystallization (PDRX) [18], which will not be further
discussed in this review due to the space limitation.
It has been realized for many years that the
nuclei of recrystallization are not produced by random
atomic fluctuations as for the case of phase
transformations, but small volumes which previously
exist in the distorted microstructure [1]. For these small
volumes, frequently subgrains, to effectively become
growing new grains, it is necessary to have a high angle
misorientation, as well as an energy advantage. The
classical theory of strain induced grain boundary motion
(SIBM) projected by Beck and Sperry [22], which
involves the bulging of part of pre-existing HAGB that
is associated with a single subgrain possessing great size
to provide the energy benefit, more confirmed this. For
SRX, this energy benefit can be built from side to side
SRV by subgrain growth [23] or subgrain coalescence
[24-26]. The time preferred to form the large subgrains
such that the motivating force appropriate to the stored
energy is enough to overcome the boundary curvature,
according to the classic work of Bailey and Hirsch [27],
is termed as incubation time to indicate the initiation of
recrystallization during SRX, This definition is, on the
other hand, no longer convenient for DRX, thus the
critical strain ( εcr ) or critical dislocation density ( ρcr ) is
often used to define the onset of recrystallization. After
defining the key terminology within the recrystallization
domain, the factors influencing DRX are now
summarized in the following section.
Summary
The three DRX processes, i.e., DDRX, CDRX
and GDRX, were taking place in dissimilar TMP
conditions at high temperatures for a variety of metallic
materials have been reviewed. The terminologies used
in DRX field were summarized, collectively with the
key factors influencing the DRX processes, in addition
to the investigational techniques to characterize them.
An importance was particular on the mechanisms and
the presented numerical models.
DDRX, moreover known as conventional
DRX, is evidently the most widely studied DRX
process. DDRX operates in low to medium SFE
materials at high temperatures (T > 0.5 Tm). At this
stage, generally DDRX initiates by strain of grain
boundaries along with a necklace structure composed of
fine recrystallized grain are produced. DDRX might
also take place at or near further heterogeneous sites
such as shear bands, kink bands; however these sites are
more commonly produced at low deformation
temperature or else high strain rates. It is obvious that
the new grains might be formed by twinning at high
strain levels. In general, the stable state of DDRX in
conditions of flow stress, recrystallized grain size as a
purpose of deformation temperature as well as
deformation strain rate is well established. The DDRX
at changeable TMP conditions, still, needs more
investigation. Because it is apparent from experiments
that different DRX mechanisms can perform together or
in series with changing TMP. It becomes further
complex if precipitation, which affects nucleation of
recrystallization as well as grain boundary migration,
takes place at the same time as with deformation. There
exist many of numerical models of DDRX; the majority
of them work well in some preferred situations. On the
other hand, none of these models is deemed as a general
model that takes all key ingredients of DDRX into
account and is capable to model DDRX in changeable
conditions for particle-containing materials.
In terms of CDRX, it was establish that this
DRX process takes place in all metals as well as alloys
irrespective of their SFE when the deformation
temperature is moderately low (T < 0.5 Tm), in severe
plastic deformation. At high temperatures, however,
CDRX is most often observed in high SFE materials.
The mechanism of CDRX is not also understood as for
DDRX, the main matter is how the LAGBs increase
their misorientation and convert into HAGBs. At low
deformation temperatures, it appears that LAGBs can
increase their misorientation consistently by the
misorientation saturates at relatively low values, and it is
the formation of microshear bands or kink bands that
ultimately leads to the formation of HAGBs. At high
deformation temperatures, microshear bands or kink
bands become less significant, the transformation of
LAGBs to HAGBs is done moreover by the equal
increase of misorientation or progressive lattice rotation
by grain boundaries. Experimentally, the arrangement of

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
30
HAGBs also depends on the grain orientation, and there
exist a number of stable orientations, in which the
increase in misorientation is not enough to form new
HAGBs even at large deformations. A whole systematic
study on CDRX by varying original grain sizes, grain
orientations, chemical compositions, deformation
temperatures and strain rates etc., providing quantitative
data on flow stress, crystal size and misorientation
evolutions, is still missing. CDRX are further complex
situations where precipitation or fine second-phase
particles are involved, or in varying TMP conditions,
also needs further development. In terms of numerical
modeling, only a sparse amount of CDRX models are
found in the literature. This is partly due to be short of
an apparent image on the CDRX process mechanisms.
As compared to the two DRX processes
mentioned above, GDRX appears rather simple. The
geometric shape alter due to deformation was studies
under different deformation modes such as hot rolling,
hot torsion and plane strain compression. It is concluded
that GDRX takes place once the thickness of the
HAGBs reaches 1-2 subgrain size distance. This
frequently means, even it is not clearly stated, that
GDRX occurs concurrently for each grain. Since the
rate of GDRX is infinitely dependent on the thickness of
HAGBs, the grain morphology is of greater significance
as compared to DDRX and CDRX. This includes the
local variations such as serrations, and the global shape,
i.e., spherical, cubic or any new shapes. HAGB
migration suitable to dislocation density variation or
grain boundary energy, also the introduction of new
HAGBs, needs to be considered to clarify the
discrepancies experimentally observed in conditions of
the evolution of the thickness of HAGBs.
Correspondingly to the further two DRX processes,
precipitation or fine second-phase particles influence the
GDRX process through retarding grain boundary
migration. Dissimilar models are developed,
furthermore at this stage, physically based models
combining the general geometric shape modify with the
local grain morphology (serrations) and HAGB
migration, as well as the formation of new HAGBs are
still missing. Since most of the above mentioned
phenomena are already modeled, it seems realistic to
combine them into a single model.
In summary, it can be said that although some
of the aspects related to DRX still need further
investigation, the existing knowledge obtained from
both experiments and simulations can already provide
valuable help on controlling the microstructure
evolution during thermomechanical processing. Fig. 35-
37 illustrates the various modes of dynamic
recrystallization. All the referenes mentioned in 5, 5.1,
5.2, 5.2.1 and 5.3 can be found in the original review
article by Huang and Logé [48].
Fig. 35: Typical flow curves during cold and hot
deformation [57].
Fig. 36: Evaluation of the microstructure during (a) Hot deformation of a material showing recovery. (b)
Continuous dynamic recrystallization (CDRX).

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31
Fig. 37: Graphical abstract. [48].
Grain Growth
Structure of Metals
Very often we presume that the reader
knows everything we are talking about. It is not so
simple. Sometimes the old books contain excellent
explanations/definitions of certain simple terms.
Before discussing grain growth, we are taking the
liberty of defining some grains-related terms.
“Metals are crystalline, i.e. they consist of
small crystals – They are thus polycrystalline. The
crystals in these materials are normally referred to as
its grains. Since the crystals/grains are small, optimal
microscoping, using up to 1000 magnifications, is
used to study the structural features associated with
the grains. This is known as sub-structure.
Furthermore, there is the basic structure inside the
grain themselves, i.e. the atomic arrangements inside
the crystals known as the crystal structure”. [14].
We will not be discussing the theory of
metals and related topics such as dislocations and
ship phenomena, but later grain boundaries and all
related phenomena.
Nucleation of sub-grains/cells
We know that the grains in metals and alloys
play very important roles in determining their various
properties. As we have mentioned earlier, all
metals/alloys are made up of crystals/grains. Their
shapes and sizes depend on the composition, on the
method of preparation (e.g. casting, rolling, swaging,
temperature, cooling rate etc.) of the materials. The
important factor is diffusion which depends on the
processing temperature of the material. The
significant direct result of a temperature rise in a
solid material is that it increases the diffusion rate of
self-diffusion and for the diffusion of the atoms
(alloying or impurities) that may be present.
Basically, diffusion is simply the spontaneous change
in location of individual atoms within an existing
material. Any process or reaction that involves
spontaneous rearrangement or redistribution of
individual atoms is done solely by diffusion. The role
of diffusion is important in almost all metallurgical
processes such as grain growth, recovery,
recrystallization etc. And any action that influences
diffusion rates directly affects all such processes and
hence is of vital interest to the material scientists,
solid state chemist and solid state physicists. The
probable mechanism of diffusion also depends on
vacant lattice points in the material. It means that
diffusion is accomplished by successive movements
of individual atoms, and the movement of any given
atom in a solid necessary involves certain energy of
activation. And whenever activitation energy is
involved, the Maxwell-Boltzmann probability
formula applies. (For detailed description please refer
to ref.21). It must be understood that physical and
chemical changes accomplished by diffusion can be
tremendously accelerated by relatively small
increases in temperature. For any activitation energy
per mole is required to initiate diffusion, is based

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32
upon the average behavior of a large number of
atoms. Individual atoms within a group/cluster of
atoms vary widely in energy at any given moment, so
that some of the atoms present will require for their
activation a relatively large increment of energy,
others a small one, and a few none at all. Any factor
that increases the initial energy of a specific atom
correspondingly diminishes the additional energy
required to activate it for diffusion. Therefore, the
potential energy available from a plastically
deformed area will be activated, increasing the
diffusion rate locally. It is thus important to
remember that diffusion is much more rapid in a
deformed high energy region of a grain boundary
than through the less important crystals which meet
to form the grin boundary and diffusion rates are
significantly higher for a deformed metal than for the
same undeformed metal free of the internal energy
stored by deformation. In 2.3 and 4.1.1 we have
briefly discussed the formation of sub-grains/cells
and polygonization structures. Doherty et al [33]
have discussed in some detail the nucleation of sub-
grains and grain growth during recrystallization.
“According to them, through deformation,
energy is stored in the material in the form of
dislocations. This energy is free in recovery,
recrystallization and grain growth when the material
is annealed at an adequately high temperature.
Recrystallization occurs by strain-induced boundary
migration of only a few grains. These a small number
of grains grow become very large at the expense of
the small grains in the matrix.
The growth of newly formed strain-free
grains at the expense of the polygonized matrix is
obtained by the relocation of high-angle boundaries.
The motivating force for recrystallization is the
remaining strain energy in the matrix following
recovery. This strain energy exists as dislocations
mainly in the sub-grain boundaries. Thus, the various
factors that control the mobility of the high-angle
boundary or the driving force for its migration will
influence the kinetics of recrystallization and
consequently the grain structure. In connection with
the driving force for recrystallization, a fine sub-
grained matrix has high strain-energy content than
does a coarse sub-grained matrix. Accordingly,
recrystallization (also grain size) occurs faster in a
fine-sub-grained matrix than in a coarse-sub-grained
matrix. During recrystallization, continued recovery
may occur in the matrix by sub-grain growth,
resulting in a reduction of the driving energy for
recrystallization and therefore a decrease in the
recrystallization rate (and retardation of grain
growth). From driving energy considerations, it is
understandable that the tendency for recrystallization
(and grain growth) is stronger in heavily deformed
than in moderately or lightly deformed materials. For
a given deformation, the finer the original grain size,
the stronger the tendency for recrystallization. Fig. 38
[17] shows effects in low carbon steels.
Fig. 38: Effect of penultimate grain size on the recrystallization kinetics of a low- carbon steel, cold rolled
60% and annealed at 540⁰C (1005⁰F). Note the incubation time is shortened as the penultimate grain
size before cold rolling is decreased. [17]

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
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“Sometimes a section of the initial boundary
of grain results grain-boundary nucleation from the
region of a high dislocation content and is observed
in large-grained materials deformed at low and
medium strains. This bulging mechanism of
nucleation for recrystallization is a consequence of
the strain-induced boundary migration. As shown in
Fig. 39 [17], the nucleus may be produced by
subgrain growth to the exact of the original grain
boundary in grain boundary migration to the right as
well as subgrain growth to the left forming a fresh
high angle boundary, and by grain boundary
migration to the right and subgrain growth to the left
but without forming a new high angle boundary.
Fig. 39: Schematic showing three types of grain-
boundary nucleation and the growth of the
nucleus (N) at the expense of the
polygonized subgrains. [17]
Grain Growth
According to Cahn [13], “when primary
recrystallization is complete, the material have grain
boundaries having fixed interfacial energies,
irrespective motivating force of retained energy is
used up and the grain structure is not so far stable.
Thus situation is at best metastable, with ideal
thermodynamic stability is simply attained as the
sample has been converted into a monocrystal. The
situation is closely similar to foam of soap bubbles
(Fig. 26) which progressively coarsen along with
become a single bubble (as discussed earlier in 4.2).
Fig 26 served to clarify the unsteadiness of grain
structures on geometrical foundation. Initially assume
that in two dimensions, the grains were collection of
perfectly regular hexagon. The sides of the grains
would next be flat and all triple points would be in
equilibrium, as grain boundaries (in two dimensions,
strictly grain edges) then all meet at 120o. Since all
boundaries are assumed to be high-angle boundaries,
as a result of equal energy, the triangle of forces at
the triple point is stable. On the other hand, if a
“rogue grain” has simply, say 5 sides, the standard
internal angle will exceed 120o unless the sides are
curved convex outwards – then the sides should be
unstable, and in search of shorten themselves during
straightening, they will concern the triple point
equilibria at the apex, therefore the grain in
progressively consumed. The smaller the quantity of
sides, the sharper is the curvature of the sides for a
certain grain size, and more rapidly is the procedure
of absorption. Once a rogue grain has vanished, the
new neighbors find themselves out of equilibrium,
and the process continues. Grains with over 6 sides
grow, those with smaller amount vanish. In a soap-
bubble array, it has been experimentally that the
bubble diameter D follows the time law:
=
The rate of boundary migration is inversely
proportion to the mean radius of curvature and that
this term is proportional to D”. For detailed
discussion, please consult Cahn [13].
In short, the phenomenon of grain growth is
rather complicated and a lot of work has been done
over many decades. There are many text books,
conferences proceedings, research articles and review
articles. They have been mentioned with references.
As stated earlier, the procedure of
recrystallization of plastically distorted metals and
alloys play very significant roles in the making,
shaping and usage of materials. Furthermore, during
deformation, energy is stored in the material in the
form of dislocations, stacking-faults, vacancies etc.
The main point to remember in the process
of grain growth is self-diffusion. Whenever a grain
boundary exists in a metal, the high energy offers a
sufficient thermodynamic reason for grain growth to
occur – to eliminate the boundary and so to reduce
free energy in the metal. The tendency toward grain
growth exists in all polycrystalline metals at any
(reasonable high) temperature. The rate at which it
actually occurs varies from unobservable show to
tremendously rapid according to environment and
internal structure.
“In the fifties, four variables were
considered of interest in their influence upon the rate
of grain growth [21].
(a) Difference in original grain size:
Difference size between adjacent grains
provides the diffusion-rate differential for active

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34
grain growth: the greater the size difference, the
higher is the rate differential, and rapid the growth of
the larger grain.
(b) Elevated temperatures:
A substantial increase in temperature
increases diffusion rates accelerates grain transfer
between adjacent grains, so increases the rate of
growth of the larger grain.
(c) Initial grain size:
“If there is a similar distribution of grain
sizes, the rate of grain growth at any given
temperature is higher if average grain size is fine than
if it is coarse.”
(d) Extent of cold work:
“Energy stored in a metal is effective in
increasing the rates of diffusion and grain growth and
is somewhat selective in this process. During cold
working, the smaller crystals within the aggregate are
formed to strain harden more rapidly than the larger
ones, and so to acquire a disproportional great share
of the total energy stored in the metal. The resulting
disproportional-energy differential reinforces surface-
energy differences in promoting growth of the larger
grains at the rate of smaller ones.
So far so good for the earlier knowledge:
There is a lot of literature available on the grain
growth, both normal and abnormal. But the process
starts first with cell formation. We explain it again
briefly. According to Cahn [13], the division of
dislocations, vacancies in a plastically deformed
metal is not identical. It was established that grains in
different deformed polycrystalline metals consist of
sub grains or cells, the interiors of which contain a
moderately low dislocation concentration which the
small-angle cell boundaries (cell walls) sharpen after
then the cells gradually grow larger as their interiors
happen to more drained of dislocations. After
recovery the cells are of same dimension in all
direction. Among all metals dislocation with more
than a few different burgers vectors are offered to
form cell wall and sharpness varies. There is a direct
selection among the stacking fault energy and
therefore the degree of dissociation of dislocations
with their capability to climb, and the sharpness of
cells walls. The cell formation is a rather compound
form of polygonization and the cell boundaries are
comparable to sub-boundaries formed by
polygonization. Fig 40 shows a family of etched in an
annealed aluminium sample. Cell structures are
formed mainly in effect through creep and fatigue. In
these cases the functional stress equally produces the
deformation and helps the dislocations to climb into
the cell walls. Cell walls are extreme mobile than
average large-angle grain boundaries. It is probable
that cell walls in metals move simply in the influence
of internal stress in all grain and that small-angle tilt
boundaries progress readily in the control of a
suitable sheer stress, creating thus a small plastic
strain. The recovery of yield stress/hardness of a
metal through progressive annealing behind plastic
deformation is about certainly due to cell
structure/size.
Fig. 40: Subgrains in annealed aluminium sheet.
X100. (After LaCombe and Beaujard
{1947}.) [13]
A general association has been established
between yield strength and cell size:
σ = σₒ +kd -1/2, where σ = yield stress
d = sub-grain or cell size, σₒ = friction stress when
dislocations glide on the slip plane and
k = stress concentration factor.
Such a relationship was found by Khan [50-
54] between yield stress and martensite plate size
(sub-structure) in Cu-Al-Zn martensites and the
growth of plates had followed the time law. These
papers were described by Prof. Walter S. Owen of
MIT and Prof. R. W. Cahn of Sussex/Cambridge as
excellent and most indigenous works. Some other
aspects pointed out by Cahn [13] of relationship
between yield stress and cell/subgrain structure are:

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
35
(a) Metals of low stacking fault energy, wherein
dislocations cannot readily climb, do not form
pointed cell structures; also no recovery of yield
stress is observed.
(b) A stress applied in recovery anneal accelerates
recovery of mechanical properties, also it
accelerates the increase in growth of the cell
structure.
(c) The mean sub-grain size and misorientation
inside a variety of grains in rolled iron depends
on the orientation of individual grains relative to
the rolling plane as well as direction, etc.
Role of grain boundary migration in grain growth
In brief, we know that grain boundaries has
significant role in grain growth properties of
engineering materials also this process has an
important function in recovery, recrystallization and
grain growth. Grain boundaries have been classified
as low angle grain boundaries, high angle grain
boundaries etc. Humphreys and Hatherly [19],
Mittemeijer [18], Cahn [13], Raabe [1], Doherty et
al. [33, 34], Burke and Turn-bull [37], Aust and
Rutter [55], Lücke and Stüwe [56], Hu Hsun [17] etc
etc have thoroughly discussed this process and can be
consulted for detailed information. This process can
be summarized in these words: “Recovery may be
defined as the low angle boundary migration and
during the nucleation of recrystallization, and
Recrystallization may be defined as the motion of
large angle boundaries. Humphreys and Hatherly [19]
have extensively discussed the various theories of the
mobility of low angle as well as large angle margins,
and all the various factors that effect both these
migrations. The various factors can have both
negative and positive effects on grain growth (or
retardation) and subsequently on the mechanical and
physical properties of engineering materials.
Humphreys and Hatherly [19] have also
discussed (Chapter 6) the sub-grain coarsening, the
motivating force for sub-grain growth, experimental
measurements of sub-grain coarsening, sub-grain
growth in boundary migration, sub-grain growth
through rotation and coalescence, the cause of
particles on the rate of sub-grain growth and the
particle limited and particle stimulated sub-grain size
and growth and the abnormal grain growth. It is this
last phenomenon that we briefly discuss.
Abnormal grain growth
“The process in which microstructure of
grains after recrystallization becomes unstable and
formation of some grain might extremely small Fig
41 (a+b) and even greater is called abnormal grain
growth”. It is a significant way for producing large-
grained materials for processing of Fe-Si alloys used
for electrical applications. The motivating force for
abnormal grain growth is generally the reduction in
grain boundary energy”. For further information
please see [19]. Fig 42 (a) shows abnormal grain
growth in Al - 1% Mg + 1% Mn alloy annealed at
600oC [19] and a polycrystalline Zr Specimen
showing individual grains with pronounced grain
boundaries, Fig. 42(b).
Fig. 41: (A) Growth kinetics of the phases in a series of Ti-Mn alloys containing different volume fractions at
973K, (a) α phase, (b) β phase. (After Grewel and Ankem) {1989}.) [19].

Iqra Zubair Awan and Abdul Qadeer Khan, J.Chem.Soc.Pak., Vol. 41, No. 01, 2019
36
Fig. 41: (b) schematic representation of the change in grain size distribution during (a) normal size growth. (b)
Abnormal grain growth. (After Detert {1978}.) [19].
Fig. 42: (A) Abnormal grain growth in Al-1% Mg-1%Mn annealed at 600⁰C. [19].

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Fig. 42: (b) Polycrystalline zirconium specimen
photographed with polarized light. In this
photograph, individual crystals can be
distinguished by a difference in shading, as
well as by the thin lines representing grain
boundaries. X350 (Photomicrograph by E.
R.. Buchanan).
Computer Modeling and Simulation
Humphreys and Hatherly [19] have also given
details of many simulation methods, viz., Monte Carlo
simulations, Cellular automatic, Molecular dynamics,
Vertex simulations, Computer Avrami models, Neural
net work modeling etc etc.
Measurement of Recrystallization
Humphreys and Hatherly [19] have mentioned
the following techniques and associated parameters:
Techniques for measuring recrystallization
(a) Optical microscopy
(b) Transmission electron microscopy
(c) Scanning electron microscopy
(d) Electron backscatter diffraction
(e) X-ray diffraction
(f) Ultrasonics
(g) Property measurements
Driving pressure for recrystallization
(a) Calorimetry
(b) X-ray diffraction
(c) Electron microscopy and diffraction
Fraction recrystallized
(a) Microscopically methods
(b) EBSD methods
Nucleation and growth rates
(a) Nucleation of recrystallization
(b) .2 Growth rates
Grain and subgrain size
(a) .EBSD measurements
(b) .Calculation of size
(c) .Precision of measurement
Grain boundary character d