Article Type : Research Article
Authors : Xu R and Kim Y
Keywords : Modelling; TiAl; 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 29 K/s in
speed of 2060mm/hr. The gap is bigger between 1560mm/h with drawing speed v
than that of 1060mm/h. For engineering use the speed is better when the speed
is higher like 2060mm/h when the cooling rate attains from 0.4K/s to 29K/s with
the composition difference increasing with the maximum value. When cooling rate
is 2060mm/hr the biggest one in these three conditions will happen with 29K/s
when it is pure Al. 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. TiAl as a promise materials has been searched and developed for many
years. However the cooling rate with compositions is not much yet, so in this
study the equation is established through temperature and composition according
to the phase diagram. It is modelled with cooling rate and composition
difference too in directional solidification test. The detail value is combined
through phase equilibrium line and it is compared with thermal dynamics. The
research scope is from 0 to pure Al here [2]. 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 [3-5].
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.
Figure 1: The relations of dentrite and equilibrium state.
Figure 2: The relationship between temperature ad compositions in dentrite.
It shows two phases
decrease below the liquids 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).
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 with the drawing speed from 1060mm/hr, 1560mm/hr and
2060mm/hr. Drawing speed increases so that cooling rate increases a certain.
The period one of cooling rate is from 0.5K/s to 22 K/s in speed of 1560mm/hr.
The gap is bigger between 1560mm/h with drawing speed v than that of 1060mm/h.
For engineering use the speed is better when the speed is higher like 2060mm/h.
When the cooling rate attains from 0.5K/s to 29K/s with the composition
difference increasing with maximum value in speed of high value. When cooling
rate is 2060mm/hr the biggest one in these three conditions will happen with
29K/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 entropy 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 1560mm/h. 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 and DH is enthalpy
[3]. It is supposed that enthalpy is constant in this study.
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).
(a) 1060mm/hr.
(b) 1560mm/hr.
(c) 2060mm/hr.
Figure 3: The relation between cooling rate and ? composition under different speed in directional solidification.
(a) DS=1.2J/(mol•K).
(b) 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 [5].
The concentration of Al under the reaction will be
known in Figure 5. The interface stability is highly expected because of the
constitutional supercoiling. Well-developed dendrites are found at relatively
high solidification rate with 25~100?m/s. As for 44Al at% it uses ?????+? to
measure Al concentration while for above 46Al at% it uses ???. From the line it
will be increased from 44 to56 Al at% for ? phase. 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 [4].
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 29 K/s in speed of 2060mm/hr. The
gap is bigger between 1560mm/h with drawing speed v than that of 1060mm/h. For
engineering use the speed is better when the speed is higher like 1160mm/h when
the cooling rate attains from 0.3K/s to 29K/s with the composition difference
increasing with maximum value. When cooling rate is 2060mm/hr the biggest one
in these three conditions will happen with 29K/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.