3.1. Effect of Fe Content on the Microstructure of Single Crystal
First, we studied the growth of the single grain. In the process of the alloy growing, the solute concentration in the liquid phase at the front of the solid–liquid interface decreased with the increase in distance from the interface, and the corresponding liquidus temperature TL changed from low to high. When the curve of the liquidus temperature TL was higher than the actual temperature TQ line in the liquid phase, the composition supercooled zone will be formed in the liquid phase at the front of the solid–liquid interface.
With the solidification layer moving inward, the heat dissipation ability of the solid phase was gradually weakened. The internal temperature gradient tended to be gentle. The solute atoms in the liquid phase were enriched, so the component supercooling in front of the interface increased. As the distribution coefficient of Al and V elements is close to that of Ti and their content is relatively low, the alloy is similar to pure metal if there is no Fe element in the alloy. Therefore, the component supercooling was not obvious and the grain was nearly plane growth, as shown in
Figure 2a (the color bar represents the field parameters field parameters
, and 0 and 1 represent the liquid phase and solid phase respectively). When the Fe content increased to 0.9 wt%, the component supercooled region at the front of the interface was larger. The protruding part continued to grow into the supercooled liquid phase. At the same time, branches grew on its side, and the grain growth tended to be dendrite. With the increase in Fe content, the growth rate of the whole grain decreased. In a certain concentration range, Fe content has a great influence on the morphology of Ti–6Al–4V grains. As shown in
Figure 3, in the early stage of solidification, the grain surface was relatively stable. The solid surface formed a bulge and gradually extended with time to the supercooled zone. Due to the small temperature gradient (5 K/cm) of the suspension melting, equiaxed grains were finally formed.
The influence of the increase in Fe content on the component supercooling was discussed. The existence of supercooling zone depends on the temperature gradient at the solid–liquid interface determined by the external heat flux,
where
G is the temperature gradient at the solid–liquid interface determined by the external heat flux;
TL is the actual temperature of the liquid phase at the front of the interface; and
x’ is the direction of the temperature gradient. In equilibrium, there is
G =
−mGc, where
Gc is the concentration gradient. When
G ≥
Gc, the liquid phase in the front interface is in the state of component supercooling. According to the study of Kurz et al. [
23], by assuming that there is no convection in the liquid phase and only diffusion, the critical condition of component supercooling can be rewritten as
where
m is the slope of liquidus;
D is the diffusion coefficient of liquid phase;
v is the migration rate of interface;
C0 is the initial composition; and
k0 is the distribution coefficient. For the Ti–6Al–4V–xFe alloy in this paper, if Ti is the solvent and Al, V, and Fe are the solute, then the liquid surface is a function of the concentration of Al, V, and Fe in the liquid phase,
. The temperature gradient of the liquid melting point at the solid–liquid interface is:
where
is slope of the liquidus of
CAl,
,
, and
.
In the equilibrium state, the solute mass at the solid–liquid interface is conserved. Assuming that there is no interaction between Al, V, and Fe, there is
where
,
, and
are the liquid diffusion coefficients of the corresponding element;
,
, and
are the initial concentrations of the corresponding element;
,
, and
are the partition coefficients of the corresponding elements. Substitute Equations (7), (8), and (9) into Equation (6), and the actual temperature gradient G is greater than or equal to
:
According to Equation (10), due to < 1, the component supercooling is easier to achieve when increases. Therefore, the increase in Fe content will promote the formation of the component supercooling zone, which will affect the morphology of the grains.
3.2. Effect of Fe Content on the Microstructure of Multiple Grains
The growth of several grains with different Fe content was simulated by MICRESS.
Figure 4 shows the effect of Fe content on grain size (the color bar represents the mass fraction of Al). With higher Fe content, the shape of grains is more complex and the grain size is more refined. Due to the low directional temperature gradient in the levitation melting, the overall appearance of equiaxed crystal appears. The crystal interface is always composed of crystal faces with smaller interface energy. The interface energy is smaller at the wide crystal face, while the energy of narrow crystal face at the edge is larger. Therefore, the crystal morphology tends to be spherical polyhedron in a stable state.
Figure 5 shows as the time goes on, the liquid phase almost disappeared at 0.85 s, and an equiaxed crystal with larger grains was obtained. For the titanium alloy, the BCC phase of the cubic crystal system was first formed during solidification, and the optimal growth direction was the <001> crystal direction.
For the Ti–6Al–4V–xFe alloy, there was a large solute concentration gradient in the solid–liquid interface at the front edge of the polyhedron, and its diffusion rate was faster than that of the large plane crystal surface with a small solute concentration gradient at the front edge of the interface, resulting in the gradual change of the crystal from an octahedron to a star. This trend was more obvious at the region with a higher Fe content. Compared with
Figure 4d, the segregation of Fe at the front of the solid–liquid interface in
Figure 4f was stronger, and the resulting local supercooling slowed down the interface migration rate.
The microstructure of each direction was very different due to the different influence of the solute diffusion field and temperature diffusion field in four <001> directions.
Figure 6 shows the effect of Fe content on the grain growth rate. When the Fe content exceeds 0.3 wt%, the growth rate of the alloy begins to decrease significantly. If the Fe content reaches 0.9 wt%, more time is needed for the liquid phase to disappear.
In the growth process, the gap between the grains is large, and the growth speed of the grains is slow, which may provide more space for the growth of small grains and reduce the annexation of grains. Therefore, the increase of Fe in the experiment made the grains more refined.
Figure 7 shows the grain size of the alloy obtained by levitation melting. In a certain range, with the increase in Fe content, the grain size of the alloy gradually decreases. According to the number of grains and the cut-off area, the average grain radius is simply estimated, as shown in
Figure 8. Compared with the simulated grain size, the experimental result was larger, which is due to the limited simulation time, while the experimental grains completed the grain growth. When there was no Fe in the alloy, as shown in
Figure 7a, the grain size was the largest and the grain distribution was relatively uniform. The grain radius was about 2.29 mm, and the shape of the grain was close to circular. With the increase in Fe content, the grain size of the alloy decreased gradually, while the overall decreasing trend was mitigated. When the Fe content was 0.9 wt%, the average grain radius was the smallest (about 1.03 mm).
With the increase in Fe content, the distribution of grains was no longer uniform. Some small grains were distributed at the junction of larger grains, and the morphology of grains was close to a complex polygon. It can be considered that the addition of Fe changes the size and distribution of the grains and affects the shape of the grains, which verifies the simulation results.
3.3. Element Distribution in Ti–6Al–4V–xFe Alloy
As shown in
Figure 9, the Fe composition distribution along the green lines was obtained and demonstrated in
Figure 9e. As the Fe content increased from
Figure 9a–d, the maximum solute concentration
CL* of Fe in the liquid phase at the solid–liquid boundary continued to rise (here represented by mass fraction), which were 0.67, 1.12, 1.48, and 1.63 wt%, respectively, corresponding to the four peaks in
Figure 9e. The segregation ratio S
R was 4.01, 4.15, 4.00, and 3.54, respectively, and the overall segregation trend was reduced. Within a certain range, the diffusion distance
δn of Fe (
Figure 9f) in the liquid phase had a linear relationship with the Fe content in the alloy, and the relationship can be fitted as:
According to classical theory, for convective solute distribution, under directional solidification conditions, there is:
when
x = 0,
=
* <
C0/
k0, and when
x =
δn,
.
Defining
,
, then
. After inserting the boundary conditions into the function, we can obtain:
where
k0 is the partition coefficient;
x is the diffusion distance;
v is the interface moving rate; and
DL is the liquid diffusion coefficient.
Three assumptions were made: (1) there is only diffusion (no convection) in the liquid phase; (2) the diffusion distance
δn at the thin solid–liquid interface are infinity; and (3) the components of the liquid phase outside the solute enrichment layer keep the original concentration
C0 unchanged during the solidification process. Under these assumptions, the maximum solute concentration is
CL* =
C0 /
K0 in the stable liquid phase, and the solute distribution equation of the stable state can be simplified as:
The composition of the liquid phase outside the solute enrichment layer is no longer
C0, but gradually increases in the case of limited liquid volume due to convection in the outer diffusion layer during the actual solute redistribution process. As the actual
CL* <
C0/
K0, the solute concentration calculated by Equation (13) is higher, as shown in
Figure 10. In this work, since the solidification process of levitation melting was not directional solidification, the direction of the temperature gradient has little effect on the grain morphology. As shown in
Figure 9, the grain growth speed was slow in the direction perpendicular to the larger plane of the grain, which had an angle of 45° with the relative temperature gradient direction. The solute distribution value should be between Equations (13) and (14). For the levitation melting of the Ti–6Al–4V–xFe alloy with a slow growth rate, the modified distribution equation of solute in the steady state can be proposed according to the results of phase field simulation:
The agreement of Equation (14) with the simulation results was close to 90%, while the agreement of the modified equation with the simulation results was close to 97%.
The composition at the triangular grain boundaries of Ti–6Al–4V–0.5Fe and Ti–6Al–4V–0.9Fe alloys were scanned by EPMA, and the results are shown in
Figure 11. The segregation of Ti at the grain boundary was not obvious. The overall distribution presents a homogeneous contrast due to the matrix material of Ti. Compared with
Figure 11a,
Figure 11b shows that there was a certain segregation of the Al element in α lamellae. The most serious segregation was in the β grain boundary, while the lowest content was at the edges of the β grain boundary.
In the solidification process of the titanium alloy, the solid–liquid phase transformation first occurs, forming β original grains, and growing continuously with the decrease in temperature. The amount of liquid phase gradually decreases and concentrates at the boundary of β grains at the end of the solid–liquid phase transformation, as presented in
Figure 5d. As the solidification proceeded, the liquid phase finally disappeared, forming the original β grain, as indicated in
Figure 4a. With the slow decrease in temperature (i.e., non-quenching), the BCC phase in the high temperature state of the Ti alloy was gradually transformed into the HCP phase (i.e., β/α transformation, forming primary α phase). The α lamellar structure (about 0.5–2 μm) was formed in the original β grain; and the remaining β phase was distributed at the boundary of the α lamellar. The morphology of the β original grain was retained without any deformation in the end. As a result, the microstructure shown in
Figure 11a was formed. During the cooling process, a relatively wide α lamellar structure (about 2–3 μm) was formed from the β grain boundaries. The remaining β phase was distributed at the edges.
In the same way, V and Fe, as β stable elements, concentration increased from the inner area to the edges of α lamellae. Due to the wide β grain boundary, the segregation at the edge of the β grain boundary was more obvious. Since Fe is a stronger β stable element than V, the segregation of Fe was more obvious. Comparing the β grain boundaries in
Figure 11a,c,
Figure 11c was finer (about 1–2 μm), which may be attributed to the grain refinement of Fe. The distribution trend of
Figure 11b was the same as in
Figure 11d.
Figure 12 compares the simulated with the experimental values of the Fe composition distribution. As the simulation process does not complete the β/α transformation, the segregation of Fe is mainly concentrated in the residual liquid phase between β grains. Comparing the segregation degree of the simulated and experimental values, the segregation degree of Fe in the simulation was not more than three times that of the nominal composition, whereas the segregation degree of the experimental value was close to six times the nominal composition. This may be attributed to the decrease in β phase amount in β/α transformation and the further compression of the range of Fe segregation distribution.
Through line scans crossing the grain boundaries of Ti–6Al–4V–0.5Fe, Ti–6Al–4V–0.7Fe, and Ti–6Al–4V–0.9Fe alloys, it can be seen from
Figure 13b that the fluctuation range of Al composition in the alloy ranged from 9.78 to 11.07 at%, V ranged from 2.19 to 7.98 at%, and Fe from 0.18 to 1.81 at%. Compared with the average composition, the fluctuation values of Al, V and Fe were 8%, 91%, and 202%, respectively. Obviously, the segregation of Fe was greater than V, while the segregation of V was greater than Al.
For three samples, the mean values of Fe composition were 0.60 at%, 0.76 at%, and 0.87 at% with the standard deviations of 0.31, 0.39, and 0.40, respectively. Considering that the grain boundary of the Ti–6Al–4V–0.9Fe sample was less and the overall element distribution was more uniform, the segregation of Fe was still slightly larger. It can be seen that in a certain range, with the increase in Fe content in the alloy, the segregation of Fe tended to increase; however, the influence of Fe content on the segregation of Al and V elements was negligible. With the increase in Fe content, the trends of Fe segregation in the simulation and experiment were the opposite. It is considered that the segregation of Fe mainly occurs in the stage of grain growth or solid-state phase transformation, which needs further study.