Article Type : Research Article
Authors : Run Xu and Kim Y
Keywords : Modelling; Dentrite; Analysis; Temperature; Cooling rate; Composition; Interface; Gibbs free energy
According to composition at solid and liquid interface in
solidification the line model of temperature and composition in dentrite has
been established. The equation is gained as T=-1000C+2273?Meantime
the cooling rate and time has been discussed. In the intersection the cooling
rate of solid and liquid ?T is gained. According to dentrite therefore the
composition can determine temperature. Y changes from pure X to pure Y ie. 0 to
100%Y the temperature will change from maximum to minimum at Al composition in
materials like TiAl. The period one of cooling rate is from 0.5K/s to 11 K/s in
speed of 360mm/hr. The gap is bigger between 720mm/h with drawing speed v than
that of 360mm/h. For engineering use the speed is better when the speed is
higher like 720mm/h when the cooling rate attains from 2K/s to 22K/s with the
composition difference increasing with maximum value. When cooling rate is
1160mm/hr the biggest one in these three conditions will happen with 35K/s.
When DS is 2J/ (mol•K) the DG changes from1500J to -500J with the temperature
increases same in TiAl. It means that when DS becomes big the DG will decrease.
From diagram the concentration of Al is measured to be 1.6at% in 46Al at%. The
calculation value is thought to be phase forming element due to the minus. That
has been the low concentration with and solid solution in TiAl.
The change of
temperature in the solid and liquid in solidification transformation can deduce
the their related formula. The curve expresses its trend better. From this
relation their composition will change when the transformation happens. It is
known that the temperature in solidification can solve their relationship. In
this study in terms of these equations the deduction and analysis is done and
the error analysis to them is done. Here the solid and liquid equation is
explored within line and find the simple formula which make us to calculate the
cooling rate rapidly [1,2]. Therefore in this study the model of temperature
and composition has been established to observe the trend and intrinsic
relationship between them. Then the error is checked with variance to both of
constant. On the other side the relationship with cooling rate and energy
difference & temperature has been investigated according to varied speed
and ?S respectively for the application. According to the solidified
crystalline and phase diagram the application will be known. In addition
relationship between cooling rate and energy difference & temperature are
drawn for further research in this study. To calculate the cooling rate is our
destination in the end in terms of the composition in TiAl alloys. Therefore
the establishment equation between temperature and cooing rate in terms of the
equilibrium diagram.
The
relationship between composition and temperature (Figure 1)
Figure 1 shows that the
two lines with liquid and solid phase meet in one point. The cooling rate ?T is
known. It shows two phases decrease below the liquidus phase line. It shows
these two line relations in constitutional super cool. We choose the certain
value to proceed experiment.Here C is the Al composition, Cl and Cs is the
liquid and solid composition of Al.
Let T=aC+b (1)
We have
Tl=aCl+b (2)
Ts=aCs+b (3)
According to Ti-Al
state equilibrium state we have supposed
Cl=0.44, Tl=1833K
and
Cs= 0.46, Ts=1813K
Substitute above
constant to (2) and (3), so
a=-1000, b=2273. The
formula (1) is
T=-1000C+2273 (4)
This is the equation to calculate temperature in terms of composition (Figure 2).
Figure 1: The relations of dentrite and equilibrium state.
Figure 2: The relationship between temperature ad compositions in dentrite.
(a) 360mm/hr.
(a) 760mm/hr.
(a) 1160mm/hr.
Figure 3: The relation between cooling rate and ? composition under different speed in directional solidification.
(a) DS=1.2J/(mol•K)
(a) DS=2J/ (mol•K).
Figure 4:
The relations between DG and temperature in solidified state.
Figure 5: Trend Fmol and CAl with Al content in ? TiAl?? and ? is formed and L is remained.
From Figure 2 we know
the distribution of temperature and composition in directional solidification.
When composition difference increases temperature decreased somewhat in term of
content in dentrite. When composition difference is from 0 to 1 the temperature
changes from 230K to 1300K respectively. It means Y changes from pure X to pure
Y ie. 0 to 100%Y the temperature will change from maximum to minimum at Al
composition in materials like TiAl.
Calculation of cooling rate (Figure 3)
As Figure 3 when
composition deference increases cooling rates rate increases properly at 20mm
solidified length. Drawing speed increases so that cooling rate increases a
certain. The period one of cooling rate is from 0.5K/s to 11 K/s in speed of
360mm/hr. The gap is bigger between 720mm/h with drawing speed v than that of
360mm/h. For engineering use the speed is better when the speed is higher like
720mm/h. When the cooling rate attains from 2K/s to 22K/s with the composition
difference increasing with maximum value. When cooling rate is 1160mm/hr the
biggest one in these three conditions will happen with 35K/s. This is the
result of concentration of liquid and solid in terms of composition.
DT=T1-T2=-1000(C1-C2)
=-150K (5)
t=L/v=20*3600/360=200s
So C= (T1-T2)/t (6)
Here C and DT is
cooling rate and temperature difference respectively (Figure 4).
From Figure 4 DG
decreases with temperature increasing. It decreases with enthalpy DS increasing
from 1, 2 to 2J/mol/K. It’s decreasing means cooling rate increases along the
dendrite. When speed increases it decreases like 1160mm/h. Here DS is entropy.
This is the result of concentration of liquid and solid in terms of
composition. When DS is 1.2J/ (mol•K) the DG changes from 2200J to 1000J with
the temperature increases from 850K to 1900K respectively. When DS is 2J/
(mol•K) the DG changes from1500J to -500J with the temperature increases same.
It means that in TiAl when DS becomes big the DG will decrease. G is Gibbs free
energy [3].
DG=DH-TDS (7)
In Ti-Al DH and DS are
to be
DH=3.3KJ/mol?DS=1.2 J/mol/K at 1492? [4] (Figure 5).
The concentration of Al
under the reaction will be known in Figure 5. The interface stability is highly
expected because of the constitutional super cooling. Well-developed dendrites
are found at relatively high solidification rate with 25~100?m/s. From diagram
the concentration of Al is measured to be 1.6at% in 46Al at%. The calculation
value is thought to be phase forming element due to the minus. That has been
the low concentration with and solid solution in TiAl. Maybe good result will
be obtained use the inferior solution model. They agreed with each other well.
So they are approximate value calculated with the method.
·
According
to composition at solid and liquid interface in solidification the line model
of temperature and composition in dentrite has been established. The equation
is gained as T=-1000C+2273?Meantime the
cooling rate and time has been discussed. In the intersection the cooling rate
of solid and liquid ?T is gained. Composition difference has been deduced and
analysed according to dentrite therefore the composition can determine
temperature. When composition difference is from 0.4 to 0.6 the temperature
changes from 1880K to 1680K. Y changes from pure X to pure Y ie. 0 to 100%Y the
temperature will change from maximum to minimum at Al composition in materials
like TiAl.
· The period one of cooling rate is from 0.5K/s to 11 K/s in speed of 360mm/hr. The gap is bigger between 720mm/h with drawing speed v than that of 360mm/h. For engineering use the speed is better when the speed is higher like 720mm/h when the cooling rate attains from 2K/s to 22K/s with the composition difference increasing with maximum value. When cooling rate is 1160mm/hr the biggest one in these three conditions will happen with 35K/s.
When DS is 2J/ (mol•K) the DG changes from1500J
to -500J with the temperature increases same. It means that in TiAl alloys when
DS becomes big the DG will decrease. From diagram the concentration of Al is
measured to be 1.6at% in 46Al at%. The calculation value is thought to be phase
forming element due to the minus. That has been the low concentration with and
solid solution in TiAl.