Physical parameters used in the calculation .
Rapid solidification and microstructure evolution of deeply undercooled bulk concentrated Ni-20%at.Cu and Co-20%at.Pd alloys are strictly and systematically evaluated. First, thermodynamics of the undercooled melt is discussed. Consideration is provided for not only the systematic microstructure evolution within a broad undercooling range, but also the dendrite growth mechanism and the rapid solidification characteristics. The dendrite growth in the bulk undercooled melts was captured by a high speed camera. The first kind of grain refinement occurring in the low undercooling regimes was explained by a current grain refinement model. Besides for the dendrite melting mechanism, the stress originating from the solidification contraction and thermal strain in the first mushy zone during rapid solidification could be a main mechanism causing the second kind of grain refinement above the critical undercooling. This internal-stress led to the distortion and breakup of the primary dendrites and was semi-quantitatively described by a corrected stress accumulation model. It was found that the stress induced recrystallization could make the primary microstructures refine substantially after recalescence.
- rapid solidification
- grain refinement
Grain refinement is an interesting phenomenon that has an important scientific significance and has been numerously investigated [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. In order to understand of grain refinement phenomenon better, numerous studies have been extensively executed and many different grain refinement mechanisms were suggested separately, such as dynamic nucleation , critical growth velocity [5, 6], kinetics induced growth instabilities [2, 3, 4], dendrite fragmentation [7, 9], dendrite remelting and [8, 9] recrystallization . In 1959, Walker [1, 2, 3, 4, 5, 6, 7, 8] had been firstly investigated the grain refinement event occurring in the rapid solidification of deeply undercooled pure Nickel melt. He found that the grain size would abruptly refine when the initial undercooling Δ
In the present study, we choose Ni-20at.%Cu alloy and Co-20at.%Pd alloy. The authors experimentally investigated the microstructural evolution of the Ni-20at.%Cu alloys as a function of initial undercooling and the physical mechanisms of the grain refinements occurring at low undercooling regimes. In combination with the current dendrite growth model, we theoretically analyzed the dendrite remelting in the undercooled alloys by an extended chemical superheating model for non-equilibrium solidification of undercooled binary single phase alloys.
2. Material and methods
Ni-20at.%Cu (atomic percent) alloy and Co-20at.%Pd (atomic percent) alloy samples each weighing about 3 g, were prepared by
3. Solidification process
In the present study, we used a high speed camera to capture the solidification process, i.e., to capture the heat releasing process upon solidification. It can be seen from Figure 1 that for ∆
4. Dendrite growth analysis
Firstly, we need to use the BCT model by Boettinger, Coriell and Trividi  to calculate the solidification parameters. According to the models, the initial undercooling Δ
Using the physical parameters of the Ni-20at.%Cu alloy listed in Table 1, the undercooling components, the crystal growth velocity and the tip radius at the growing dendrite tip, can be calculated. The results are illustrated in Figures 2 and 3. It should be clarified that the table is original and we are using only data from Ref. .
|Parameters||Value of Ni-20at.%Cu alloys|
|Heat of fusion ∆
|Specific heat of the liquid
|Dynamic viscosity of the liquid
|Molar volume of the liquid /m3 mol−1||8.06 × 10−6|
|Molar volume of the solid /m3 mol−1||7.08 × 10−6|
||1680 K (1407°C)|
|Solute diffusivity in the liquid
||3 × 10−9|
||7 × 10−6|
||4 × 10−10|
|Speed of sound in the melt
|Equilibrium liquidus slope
|Equilibrium solute partition coefficient
|Size of the mushy zone
||3.25 × 10−7|
|Solid fraction at the dendrite coherency point
|Solidification shrinkage of the primary phase
|Atomic diffusive speed
It is well known that [13, 14, 15], in a single phase alloy, the condition of diffusional equilibrium is gradually becoming less important with the increase of solidification velocity and undercooling in front of the dendrite tip. Therefore, solute rejection is reduced and solutal undercooling decreases as the interface concentration approaches the melt composition. This ultimately causes partitionless solidification, which is solely controlled by thermal gradient. For Ni-20at.%Cu alloys (Figure 2), when the initial undercooling Δ
5. Structure evolution of undercooled alloys
As the increasing of undercooling, the Ni-20%at.Cu alloys undergo two kinds of grain refinements: one taking place at low undercoolings, and the other occurring at high undercoolings. The grain sizes and the corresponding typical microstructures at various undercoolings are shown in Figure 4. Pioneer investigations [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] have shown that as the initial undercooling increases, the microstructures of the deeply undercooled binary single phase solid solution alloys evolves as: coarse dendrites → fine equiaxed grains →coarse dendrites plus fine equiaxed grains → fine equiaxed grains. In the present investigation, we found that the microstructural evolution of the deeply undercooled Ni-20%at.Cu alloys was basically follows the above law. Subjected to small undercoolings, e.g., at Δ
When an alloy melt solidifies at a small undercooling, e.g., Δ
Three typical temperature profiles corresponding to the solidification of Co-20%at.Pd alloy melts in different undercooling regimes are shown in Figure 6. It was found that when Δ
6. Grain refinement mechanism of first refinement
The equilibrium phase diagram shows that the molten fraction of a solid alloy that has been heated into the solid-liquid binary phase regime is related to the chemical superheating . Here, due to the non-equilibrium effect involved in rapid solidification of undercooled melts, it is reasonable to speculate that the non-equilibrium kinetic phase diagram can deal with the remelted fraction of the solid phase more realistically and practically. Then, extension of Li’s model  will give a non-equilibrium chemical superheating model that can predict the remelted dendrite fraction by the following equation:
This model is similar to Li’s model , however it is an extended chemical superheating model considering the relaxation effect in undercooled liquid phase. In this extended model,
The remelted fraction of the primary dendrite is shown in Figure 4. The obvious difference between Li’s model and the present model is that the present model incorporates local non-equilibrium effect (i.e., the relaxation effect in the undercooled bulk liquid phase) in the model derivation. Thus, it can be further inferred that the remelted fraction of the primary dendrite of the present model is mainly influenced by the composition of liquid phase of the present model, in which the relaxation effect plays an important role . In the present experiments, the first kind of grain refinement of rapidly solidified Ni-20%at.Cu alloy emerged in the undercooling range of about 40 K (∆
7. Stress induced recrystallization mechanism (Δ
T > Δ T *)
Many researches [7, 8, 9, 15, 16, 17] have revealed that the stress induced recrystallization process mainly during recalescence period should be responsible for the grain refinement at high undercooling range. However, few strong and direct evidences have been found to support this speculation. We also have revealed this phenomenon in hypercooled Co-20at.%Pd alloys and found strong and direct evidences, see Ref. .
When the fraction of the solid phase exceeds about 10% during recalescence, the coherent dendrite networks are usually established [7, 9]. During rapid recalescence, as the dendrite fraction increases, the inter-dendritic permeability correspondingly decreases [7, 9]. Consequently the pressure gradient in the first mushy zone (FMZ) increases. The pressure gradient induces the inter-dendritic flow of liquid phase and therefore stress accumulated in the solid phase in the FMZ . Considering inter-dendritic flow of melt induced by both solidification contraction and thermal strain, we will build a corrected stress accumulation model for rapid solidification of an undercooled melt was established. According to Ref. , the liquid volume flux
is the size of FMZ in which primary growth or recalescence occurs,
The thermal strain induced inter-dendritic flow of liquid phase in the mushy zone can be expressed as :
where is the accumulated strain rate in the dendrites and can be defined as :
where is the strain rate in the dendrites and .
where is the temperature gradient ahead of the liquid/solid interface. is.
We define average thermal strain as:
In order to estimate the accumulated stress in the dendrites, we consider the one dimensional case. Then the momentum equation in solid phase is, as demonstrated in Ref. :
where is the dissipation of stress of interface and can be expressed by Darcy Eq., as demonstrated in Ref. :
At the start of the coherent part of the first mushy zone, which is abbreviated as FMZ, the solid stress is equal to the hydrostatic pressure, i.e.,
Considering inter-dendritic flow of liquid induced by both solidification contraction and thermal strain, an analytic model of stress accumulation during rapid solidification of undercooled melts was established in the present work. According to this model, the stress accumulated in the dendrite coherency can be calculated by Eq. (19).
It can be seen from Figure 8 that, with increasing Δ
Generally, recrystallization is a physical process and consists of two basic processes: the site saturation nucleation which proceeds by atomic thermal activation and the growth of the new strain free grains, when being annealed at temperatures above a proper recrystallization temperature, which is the atomic thermal activation temperature. In order to reveal the recrystallization process in the rapid solidification microstructures of the Ni-20at.%Cu alloys, recrystallization annealing experiments were performed for the quenched and naturally cooled alloys, see in the reference . Compared to the naturally cooled alloys which did not undergo recrystallization. However, as a comparison, the recrystallization drives the microstructures of the quenched alloys to transform into completely newly formed microstructures.
Applying molten glass purification method combined with cyclic superheating method, non-equilibrium microstructural evolution and grain refinement mechanisms of Ni-20at.%Cu and Co-20at.%Pd alloy were investigated systematically. The main conclusions are as follows:
Ni-20at.%Cu and Co-20at.%Pd alloy were undercooled by means of fluxing method. Two grain refinement events of the solidification microstructures were observed. The first grain refinement was attributed to chemical superheating induced dendrite remelting. The second grain refinement was ascribed to stress induced recrystallization of the rapidly solidified dendrites.
The relationship between the dimensionless superheating and the undercooling indicates that the grain refinement occurring at low undercoolings results from the dendrite break-up owing to the dendrite remelting, but at high undercooling the dendrite remelting effect is weak.
With the help of incorporating the relaxation effect of solute diffusion in bulk undercooled liquid, an extended chemical superheating model for predicting dendrite remelting was developed to explain the two kinds of grain refinement events occurring in the low and high undercooling regimes respectively. It was found that the present dendrite remelting model could predict relatively good results in consistency with the grain refinement event observed in the experiments.
It can be inferred that the rapid dendrite growth, the dendrite deformation and the stress-induced dendrite break-up occur during recalescence stage; the solidification of the residual liquid phase, the remelting of dendrites, the recrystallization and the grain growth (secondary recrystallization) occur during post-recalescence period.
A corrected model was developed to semiquantitatively calculate the stress accumulation during rapid solidification of undercooled Ni-20at.%Cu alloys. When the undercooling is larger than a critical value, the stress due to solidification contraction and thermal strain will cause break-up of the primary dendrites. The strain energy stored in the broken dendrite pieces will drive recrystallization, leading to a grain refined recrystallization microstructures
The authors are grateful to the financial support of National Basic Research Program of China (973Program, 2011CB610403). This work is also supported by International Cooperation Project Supported by Ministry of Science and Technology of China (No. 2011DFA50520).
Conflicts of interest
The authors have no conflicts of interest
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