Study of Solute Effect on Grain Refinement of Aluminium Alloys

Anmol Rathi*, Shivangi Rohatgi*, Megha Tiwari*, Ashok Sharma**

*III Yr Students, **Professor;
Malaviya National Institute of Technology, Jaipur-302017(Rajasthan)
E-mail: shivangi23512@gmail.com, acmeanmol@gmail.com, meghatiwari1992@gmail.com,
ashok.mnit12@gmail.com

Abstract

Grain refinement is an important technique to produce fine equiaxed grain structure in order to obtain
desirable mechanical and foundryl properties. This is achieved by addition of grain refiner (Al -5Ti-1B)
in the form of master alloy. The mechanism of grain refinement is addressed by nucleant and solute
paradigm. In nucleant paradigm nucleating particles are held responsible for attaining finer grains.
However, grain refinement is very sensitive to the alloying elements present. This is explained by
solute paradigm. The growth restriction effects of the solute are quantified by two parameters, i.e.
Growth Restriction Factor, Q and the Undercooling Parameter, P. The growth restriction factor Q is
proportional to the initial rate of constitutional undercooling development and can be used directly as
a criterion for the grain refinement in the aluminium alloys. P gives the maximum undercooling which
can be generated by a particular concentration of grain refiner .Q is inversely related to the resultant
grain size. The nucleation paradigm is now recognized as a part of process. To fully explain the
mechanism of grain refinement, it is essential to study solute effect on grain refinement. In the present
study nucleant effect and solute effect have been studied on Al alloys to understand how Q, P, RGS
and grain size is related.

Key words: Constitutional Undercooling, Growth Restriction Factor, Undercooling Parameter, Solute
effect, Nucleation.

1. Introduction
Grain refinement is an imperative technique Solute effect [4]. These grain refiners contain
used in industries to reduce the size of grains inoculants particles (TiB , TiC )[4-6]which as
of the as-cast alloys. The main aim of grain heterogeneities in the melt provide nucleation
refinement is to suppress the growth of surfaces. This can be characterised as the first
columnar and twin columnar grains and step of grain refinement i.e. Nucleant Effect
encourage a structure having equiaxed grains [7]. The solute effect comes in to play once
[1-3]. This is because a structure having fine nuclei starts to grow. In pure aluminum, there
equiaxed grains will have desirable are no segregating elements present; hence
mechanical properties and better feeding there is no constitutionally undercooled zone in
characteristics [3]. Grain refinement has many front of the interface to promote nucleation of
benefits in direct chill casting operations too; aluminum on the nucleant particles (TiB2). But
this includes reduced hot tearing susceptibility when solute is present, TiB2 becomes an
and reduced homogenization time.[3] effective nucleant due to the constitutionally
undercooled zone. Therefore when Al-5Ti-1B
Finer grains are achieved by the addition of is added to an alloy, TiB2 particles which act
grain refiners which are generally added in the as nucleant particles will be coated with a thin
form of master alloys such as Al-5Ti-1B for layer of Al3Ti. Generally commercial alloys
aluminium alloys. The effect of grain refiners containing 5 to 10 % Ti are primarily a mixture
can be divided into two: Nucleant effect and
of α-aluminum and crystalline TiAl3. α- 2. The Two Parameters
aluminum forms at the surface of the TiAl3 1. Growth Restriction Factor, Q
particle at temperature below the melting point
of the bulk metal. Once solid has formed, the It is the build-up of solute at the Solid liquid
TiAl3 particle becomes engulfed in the solid interface that restricts the growth of grains and
phase, and further growth becomes limited. therefore it becomes necessary to quantify its
Therefore, TiAl3 helps in improving the ratio of effect using GRF. The growth-restriction
nucleation rate to growth rate. Hence fine parameter Q is inversely proportional to the
grains are produced. Solute theory says solute growth rate [11]. The constitutional
elements like titanium segregate to the undercooling (∆ ) produced due to solute
inoculants/melt interface and affect the growth segregation can be related to the solid fraction
of dendrites and also affect the constitutional ( ) i.e fraction of solid formed in the melt or
undercooling at the solid–liquid interface. It is the amount of solid formed in the melt by
expressed by GRF which is a measure of the solidification of molten metal, by Scheilian
growth restricting effect of solute elements on solidification relation which is given as [15,8]
the growth of solid–liquid interface.The growth
restriction effects of solute can be quantified ∆ = 1−( )
by Growth Restriction Parameter (GRF)
represented by Q and Undercooling Parameter Where is the slope of liquidus curve in
represented by P. [8-10] P is the maximum binary phase diagram , is the bulk
degree of undercooling that can be generated concentration and k is a constant known as
and can be given by: portioning coefficient.

P= (k-1)/k Differentiating above equation with respect to

(w.r.t) fraction solid,
Where is the slope of liquidus curve in
binary phase diagram , is the bulk ( )
∆ ( ) ( )
concentration and k is a constant known as = – =0− (1-
portioning coefficient. k) (1 − ) = (k-1) (1 − )
The growth-restriction parameter Q is in In the beginning of solidification fraction of
inverse proportion to the growth rate. The solid formed is very little such that = 0.
concentration of Ti with other elements leads Therefore
to a constitutionally undercooled zone in front
of the growth interface and interrupt the growth ∆
= ( − 1)(1 − 0) = (k-1) which
of the previous grains.Being inversely
proportional to growth rate it is also affected by is growth restriction factor, Q.
the segregating ability of solute and
The rate at which the undercooled zone
concentration of bulk and is given by:
develops at the beginning of solidification is
Q= (k-1) equal to the Growth Restriction factor. From
the above relation it can be said that as Q
Q can be taken as a parameter to measure the increases the maximum undercooling which
grain size. Higher the Q for a solute lesser is can be generated increases, also there’s an
the grain size for that alloy.[11-13]. The increase in the development rate of the
following paper briefly studies the relationship constitutional undercooling zone and with it the
between Q, P, relative grain size and grain time required for the nucleation to begin on the
size for aluminium alloys. The work by Easton present heterogeneities within the undercooled
and St John [14, 2] proposed that the grain region decreases, this will result in a structure
refinement is simply related to the potency of a with desired finer grains.
nucleant and the degree and rate of
development of constitutional undercooling
generated by solute rejection during growth of
previously nucleated grains.
2. Undercooling Parameter, P

P is the maximum amount of undercooling

which can be generated by a growing grain
due to segregation of solute. If the grain refiner
added is strongly effective then the maximum
undercooling which can be achieved by it is
more. It is used to compare the effects of
different solute elements at different
concentrations and can be denoted as: [8]

P= (k-1)/k

Where symbols used have their usual

meaning.

3. Why Q is Preferred Over P?

Figure 1.b.
Both of the above two factors, P and Q,can be
used as a measure of grain size. But in
practical cases GRF is preferred over P. This
is because the deviation obtained in the values
Figure 1.a and 1.b shows the plot of P and Q
of P for varying solute content comes out to be
much greater that the deviation shown by Q values with the grain size respectively. It can
values for the same. It can be understood from be seen that for the binary alloys inoculated
the following figures 1.a and 1.b. [10,16] with a grain refiner, decrease in grain size with
increasing P and Q values follows same trend
but the degree of scatter in P values is much
greater than in Q values. For example: at grain
size of 200 m the data range for Q=1.5-4K
and for P=0.25 to 30K [16]. Therefore both
factors give the accurate estimate of grain size
but GRF is more precise than P.

4. Relation between GRF, Grain Size

and Nucleant Potency

Nucleant potency can be described as the

ability of a substrate to facilitate the nucleation
on its surface. [11] The degree of undercooling
required by a substrate decides whether it is a
strong or weak nucleant. Following is the
Figure 1.a. [16] phase diagram for the dilute binary system
where k and are assumed to be
independent of solute content.
 = =k ..................... (4)

Substituting values from eq.4

=
........... (5)

From the solid redistribution equation [nucleant

14],

= .....(6)

Where is the diffusion coefficient of solute in

liquid phase, x is the solid growth distance and
v is the growth rate of solid-liquid interface.
Figure.2 [4, 11,17] Putting the value of from eq.6 in eq.5

Here it is assumed that the thermal gradient in = = (1 - )....

front of solid-liquid interface is zero and thus,
(7)
there’s no thermal undercooling and latent
heat. [11,18] therefore the maximum From this equation it can be seen that in the
undercooling can be given by: initial stages of solidification as the growth
distance increases the undercooling generated
ahead of front increases is less.
................... (1)
The variation of constitutional undercooling
Where, is the maximum undercooling,
with the solid growth distance can be depicted
is the liquidus temperature at which from the above figure for AlTi0.05, AlTi0.10
solidification begins , is the actual and AlTi0.15 alloys. It can be seen that the
temperature of the melt, are the initial increase rate in ∆Tc is much faster for
slopes of liquidus and solidus respectively , AlTi0.15 alloy than that of the AlTi0.10 alloy,
are the concentration of solute in while it is faster for AlTi0.10 alloy than that of
bulk and the solid formed and k is the solute AlTi0.05 alloy. Thus, as the amount of solute
partitioning coefficient which is given by: (Ti) increases Q (slope of the curve) increases
and so is the rate with which maximum
K= ............ (2) undercooling, P, is achieved. Therefore, for a
certain nucleant let the undercooling required
From above figure we can see that both for its activation is , this degree of
are negative therefore eq.1 undercooling will be achieved at a lower grain
changes to: [4,11] size in that case where the solute
concentration is higher as for it Q will be more
as compared to when the solute concentration
= ................... (3)

Now, using equation of line i.e. y=mx+c ,

(where m is the slope of line and c is a
constant) for the above figure it can be written
that
 =- ]=

- .....(13)

Here, the effects of latent heat and thermal

gradient has been neglected which tends to
reduce the effective undercooling and the size
of undercooled zone. If the nucleant shows a
strong potential for nucleation the required
by it will be less and can be achieved easily at
a smaller grain size (fig.3) The Q can be taken
as a direct measure of RGS for the case
where strong potential nucleants are used this
Figure 3.Development of the constitutional
is because for them it can be assumed
undercooling zone with solid growth
that . When this assumption is applied
distance x for AlTi0.05, AlTi0.10 and AlTi0.15
to eq.13 it comes out that
alloys.

Let be the solid growth distance at which =- =- ) ... (14)

the undercooling generated reaches to ,
the amount of undercooling needed for the Since ,therefore and hence
nucleation to begin on the adjacent nucleant the rule of limits can be applied here which
substrates. Can be taken as the measure of gives the following:
the grain size up to which grain will grow
before subsequent nucleation on the adjacent RGS= = ............... (15)
nucleants will begin as the distance between
adjacent effective nucleation determines the Hence RGS has a direct relation with Q and
grain size in the final microstructure. To therefore the above stated fact is proved. The
compare the effect of solute content and the eq.15 also shows that as the GRF increases
potential of the nucleants is taken as the the RGS decreases for a strong nucleant. But
relative grain size (RGS) which is different the same cannot be said for weak potent
from average grain size as RGS gives us a an nucleants as for them P ,so ,unlike
estimate of the average grain size for a strong nucleants Q cannot be related directly
microstructure containing weak nucleants. with RGS for weak nucleants and therefore
When the undercooling generated reaches to only RGS ,which shall be the function of P, can
.RGS can be given by: be used as an appropriate measure of grain
size. It can also be concluded that strong
= (1 - )........ (8) nucleants require lower degree of
undercooling for their activation as
=1 - ................. (9) heterogeneous nucleation sites and their
addition results in finer grain structure when
compared.
=1- ................. (10)

Taking logarithm to the base e, on both the

sides of eq.10

= ............. (11)

=- .................. (12)
 5. Relationship between Grain Size
And Q
The relationship between the grain size and
growth restricting parameter can also be
empirically given as [19-21]:

..............(16)

Where a and b are constants and d is the grain

size. It should be noted that this relationship is
different from the one between RGS and GRF
which was previously stated in section 4. The
relationship between grain size and GRF
shows that the grain size varies linearly with
the inverse of growth restricting parameter and
Figure 4a.
therefore eq.16 can be compared to the
equation of line

......(17)

On comparing both the equations it can be

said that a-term is the intercept whereas b -
term is the slope of line and hence along with
Q both of these factors are also important in
determining the grain size.

Easton and StJohn [19,14]suggested that after

the initial nucleation of grains in the thermally
undercooled region at a mould wall, a wave of
nucleation events occurs from the edge of a
casting to the thermal centre as the
constitutional undercooling reaches the
Figure 4b.
undercooling needed by the nucleant to
to weak nucleants. Figure 4a shows predicted activate i.e. .this requires, although small,
value of relative grain size with Ti content in but growth of already nucleated particles which
Al-Si alloys and figure 4b. gives the actual is related to the fraction solid as [19]:Q=
grain size for the same alloy at two different ,from this relationship we can conclude that
concentration of .[16] it can be seen that
both RGS and actual grain size follows same
trend with varying Ti content except the actual
grain size becomes constant at higher values
of Ti concentration therefore RGS can be Therefore, nucleation of grains in a
taken as an appropriate measure of actual constitutionally undercooled zone indicates
grain size. The decrease in RGS for strong that the b-term is related to the nucleation
nucleants (low undercooling needed) undercooling, or potency of the substrates in
increases with increase in Ti content is greater the melt.[19]. Whereas a-term, unlike b-term,
that for weak nucleants. It is also seen that depends upon the nucleant particle
with increase in content there’s a drastic concentration, because a-term is that grain
decrease in grain size and hence, it is size at which the grain refinement effect of
concluded that presence of both Ti and is solute is maximum. Hence, the intercept is
important for effective grain refinement. dependent on the distances between the
active nucleation sites. a-term represents the
maximum number of particles within a set
addition of a particular type of refiner that are For Al alloys with Al-5Ti-B master alloy
able to facilitate nucleation which in turn following relationship can be used to
affects the grain size. More the number of determine the grain size[19]:
active nucleation sites smaller will be the grain
size. By assuming that the grain density is = + .............(19)
proportional to the nucleant particle density, it
would be expected that the linear intercept
The value of b term for this grain refiner is
grain size, a, is proportional to 1 , where lower when compared to b term value for Al-
is the density of particles and is the 3Ti-B which is 650 but at the same time the
value of a term is higher for the former grain
fraction of those particles that are active and
refiner. This shows that Al-5Ti-B will be more
can nucleate a grain. Hence there is an
effective for low solute concentrations as
inverse cube root relationship between the
number of particles present and the grain compare to Al-3Ti-B,as it has numerically
greater coefficient for the first term. This kind
diameter, which is proportional to the grain
of analysis may provide a tool for comparing
size. The complete relation can be denoted
and optimizing the effectiveness of grain
by[19]
refiners.
′∆
= 1 + ......... (18)

6. Conclusions the literature. Metall Mater Trans 30A:1613–

1623
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6. YÜCEL B. Grain refining efficiency of Al-Ti-C
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