Effect of Solid/Liquid and Eutectic Front Velocities on Microstructure Evolution in Al-20%Cu Alloys

Abstract

During the solidification process, microstructures are affected by the experimental conditions, the thermophysical characteristics of the alloy, and the type of grain-refining particles. Unidirectional solidification experiments were performed in a vertical Bridgman-type furnace to investigate the effect of the solidification front velocity on the solidified microstructure of a non-refined and refined Al-20%Cu alloy. The samples were solidified by rapidly increasing the sample velocity (v) range from 0.02 mm/s to 0.2 mm/s while maintaining an almost constant temperature gradient (~5 K/mm). As a result, despite changes in the solid/liquid front velocity along the sample, the microstructure of the non-refined alloys remained columnar. In the refined alloy, the columnar structure changed into an equiaxed structure at two different front velocities.

1. Introduction

The microstructures formed during solidification are directly related to the characteristics of alloys [1]. Identifying how the microstructure forms as the material solidifies and, also, how to control it is still a fascinating topic. This is because the final material’s properties depend on the microstructures, so maintaining the quality and performance of materials requires knowing the mechanism of developing the microstructure. Depending on the solidification conditions, the alloys’ microstructure can be columnar or equiaxed [2,3].

The columnar-to-equiaxed transition (CET) is a morphological transition that occurs during industrial procedures, including welding, additive manufacturing, and ingot casting [4]. It is generally known that materials with an equiaxed microstructure have better isotropic macroscopic mechanical properties than those with a columnar microstructure. The interaction between growing, equiaxed grains and the columnar front leads to the CET [5,6,7,8,9,10,11], and eventually, equiaxed grains will grow [12,13,14]. CET develops when the amount and size of equiaxed grains, which develop in front of the columnar front, reach a point where they restrict the continuing development of columnar dendrites. This phenomenon is referred to as mechanical blocking [4,14,15].

Mechanical effects, thermal interactions, and solute interactions contribute to the complex topic of dendrite competition at the solidification front [7,10]. Furthermore, gravity-caused flow can significantly affect microstructures and CET [3,14,16,17].

Hunt proposed the first analytical model [5]. In this model, equiaxed grains form by heterogeneous nucleation ahead of the dendritic columnar front, and when there is enough equiaxed volume fraction to stop columnar growth, equiaxed growth occurs. The predictions of this model are highly influenced by two key parameters: the nucleation undercooling and the nucleus density. In this model, the undercooled region depends on the thermal gradient and growth rate. The CET can be easily investigated through the directional solidification of the alloys.

The pulling velocity of the sample is a parameter used to control the solid/liquid front velocity (which is not the same as the pulling velocity). It is defined as the velocity at which the sample is pulled away from the hot zone of the furnace. H. Jung et al. [15] investigated how the pulling velocity affects CET. His experimental results agreed with the Hunt model in that equiaxed growth dominates at a given pulling velocity at the low-temperature gradient, and the high pulling velocity is advantageous to CET at a given temperature gradient. However, the Hunt model does not consider the solutal interaction between the columnar front and the equiaxed grains. This can lead to a new blocking phenomenon at the CET named “solutal blocking” [7,18].

Materials with fine, equiaxed grains have enhanced strength, ductility, and formability [19]. These objectives can be achieved using many techniques, such as heterogeneous nucleation during casting, severe plastic deformation (SPD) and recrystallization, as well as high-pressure torsion (HPT) [20,21,22]. Adding solute content to the melt is also a method for achieving efficient grain refining [23].

The finely equiaxed grain structure can be produced using grain refinement materials during the alloys’ solidification processes. The grain refinement material has a crucial impact on reducing the possibility of hot tearing, enhancing the distribution of porosity, and improving the directional feeding during the solidification process [24]. The grain refinement material’s particles are very effective nucleation sites introduced into a melt through different methods. Titan diboride (Al-5%TiB₂) is a grain refinement material that is commonly used for both shape casting and direct chill (DC) casting methods for aluminum alloys [25]. TiB₂ increases the number of grains produced during solidification, resulting in epitaxial growth originating from the particles [26]. Researchers agree that the heterogeneous nucleation of grains by the grain refinement’s particles is deterministic [2,27,28,29,30,31]. However, the type, size distribution, and amount of inoculant particles, as well as the chemical composition of the alloys, significantly impact the grain refinement material [2,31,32].

Studies have been conducted to determine various mechanisms that influence CET [33,34,35,36,37,38]. These studies emphasize the multiple mechanisms that influence CET in different situations. Studies [33,34] have highlighted the significance of the pulling velocity, temperature gradient, and grain refiner addition in shaping the grain structure. They have employed a CA-FE model to validate the progressive nature of CET. H. Nguyen-Thie et al. [35] delineate the prerequisites for CET, encompassing temperature fluctuations, the dissociation of dendritic side branches, and initiating equiaxed grain formation [36]. The process of dendritic fragmentation in the mushy zone, which is affected by convection, constitutional remelting, and capillary pinching, has been investigated [37]. A simulation model was introduced that replicates the movement and melting of dendritic fragments, highlighting particular circumstances that result in unwanted grains [38]. Fragmentation has been presented as a possible mechanism for CET, examining real-time instances and emphasizing its effectiveness in adjusting the dendritic network to the buildup of solutes. These findings provide insight into the intricate mechanisms influencing the columnar-to-equiaxed transition (CET) in different alloy systems.

The influence of temperature gradients on CET has been the subject of extensive research. As part of this research, modeling studies [5,6,7,8,11,18,39], well-controlled unidirectional solidification experiments in Bridgman furnaces, and non-steady-state directional solidification experiments using chill casting methods have all been conducted. The conclusion is that a lower temperature gradient in the melt promotes CET [15,40,41,42].

This study is part of the European Space Agency (ESA) project involving unidirectional solidification experiments using a Bridgman-type furnace. During the process of solidification, the velocity of the sample (also known as the pulling velocity) varied between 0.02 mm/s and 0.2 mm/s in these studies. After etching, we evaluated the impact of the rapid and sudden increase in sample velocity at the solid–liquid interface and the influence of grain refinement material on the microstructure of Al-20%Cu alloys that were either refined or non-refined.

2. Materials and Methods

2.1. Alloy

Alloy 1 was non-refined, while Alloy 2 was refined. Both alloys consisted of highly pure Al (99.95 wt%) and Cu (99.95 wt%). An alloy with grain refinement properties, specifically Al-5wt%Ti-1wt%B, was incorporated. Al-5wt%Ti-1wt%B, a grain refinement material, was added.

2.2. Solidification Facility

2.2.1. Furnace

The investigations were conducted in a vertical Bridgman-type tube furnace with four heating zones (Figure 1). The furnace had an inner diameter of 20 mm and a length of 200 mm. Water was used to cool the boiler wall to prevent the inductor from overheating. The furnace had a maximum temperature of 1000 °C and a maximum temperature gradient of about 10 K/mm. The velocity of the sample (pulling) varied from 0.002 mm/s to 1 mm/s. Under the furnace’s body is a water-cooling chamber in which the cooling core was immersed during the investigations.

2.2.2. Sample and Sample Holder

The diameter of the sample was 8 mm, and its length was 100 mm (Figure 2). The sample was contained in an alumina capsule (Figure 2) (1, 3). Using K-type thermocouples, the temperature distribution was measured at 12 places. On the surface of the alumina capsules, there was a groove that each thermocouple was put into (4). A quartz tube (5) was used to contain the alumina capsule with thermocouples. A cooling core made of copper (6) was connected to the alumina capsule (3) at the base of the quartz tube to enhance the unidirectional heat removal.

2.3. Solidification Experiment

The method was demonstrated by conducting multiple experiments on a single sample [43]. The samples were solidified under the following conditions for examination: the sample velocity was v_s = 0.02 mm/s during the first part of the sample, and it was rapidly increased to v_s = 0.2 mm/s when the solid/liquid front reached 35 mm from the bottom. The velocity of the sample increased from 0.02 mm/s to 0.2 mm/s within a time range of 2 s.

2.4. Determination of Solidification Parameters

The temperature gradient (G) and thermal parameters (solid/liquid and eutectic front velocities (v_liq and v_eut)) at the liquidus (604 °C) and eutectic (548 °C) temperatures were calculated as a function of the sample distance from the cooling curve, as measured by 13 thermocouples. The temperature gradient was G ≈ 5 K/mm, and the parameters were consistent across both samples. The solid/liquid and eutectic front velocities (v_liq and v_eut) refer to the velocities of the liquidus and eutectic isotherm at different points along the samples (Figure 3). The liquidus and the eutectic temperature were measured by differential scanning calorimetry (DSc) with 1.5, 2.5, 5, and 10 K/min cooling rates for both base materials. There was no significant difference between them.

At a sample velocity of 0.02 mm/s, the values of v_liq and v_eut were consistent and approximated the sample velocity. As a result of the sudden increase in sample velocity (from 0.02 mm/s to 0.2 mm/s), the v_liq and v_eut experienced a precipitous increase, initially from 0.02 mm/s to approximately 0.075 mm/s (Figure 3). At 110 mm, the v_liq (i.e., the start of solidification) and the v_eut (the end of solidification) were both approximately 0.27 mm/s and 0.32 mm/s, respectively. These values exceeded the sample velocity of 0.2 mm/s. The solidification process resulted in a slight reduction in the temperature gradient. The temperature gradient was G ~5 k/mm.

Solidification Path of the Alloy

The solidification of the alloy began with the α aluminum solid solution at a temperature of 604 °C and was completed by α + Al₂Cu eutectic at a temperature of 548 °C. The mushy zone is a mixed solid–liquid region where solidification begins and proceeds [44].

The formation of the mushy zone during solidification is influenced by various factors, including the presence of a magnetic field, temperature gradient, and front velocities [45,46,47].

3. Results and Discussion

3.1. Grain and Dendritic Structures

The micro- and macrostructure of the samples were made visible by etching an aqueous solution of HF and by barker etching.

The grain and dendritic structures of the unidirectionally solidified Al-20%Cu alloys are shown in Figure 4 (dendritic structure of alloy without (I) and with (II) grain refinement; grain structure with grain refinement (III)).

The dendritic structure of Alloy 1 is columnar independently from the solid/liquid front velocity, and the nature of the structure does not change during the solidification experiment.

The grain and the dendritic structure of Alloy 2 are complicated and strongly depend on the solid/liquid front velocity. The first part between lines X and A is columnar due to the very slow front velocity. The mushy zone was between lines A and C when the sample velocity jumped. The eutectic front (548 °C) represents the end of the mushy zone, as shown by line A, and the solid/liquid front (604 °C) represents the beginning of the mushy zone, as shown by line C, at which the sample velocity increased greatly from 0.02 mm/s to 0.2 mm/s.

The weight percentage of the liquid phase calculated from the Al-Cu equilibrium phase diagram was changed from 53 wt% at the end of the mushy zone to 100 wt% by the dendrite tips at the moment of the rapid change in sample velocity. The mushy zone (the first transient zone) can be divided into two parts.

The grain structure is finely equiaxed between lines A and B, and the grain structure between lines B and C is again mainly columnar after the complete solidification. This area contains some equiaxed grain as well. The change in v_eut at line A is rapid, so there is a sharp border between the columnar and equiaxed grain structures. At line B, the change in v_eut is continuous, and there is no sharp border between the equiaxed and columnar grain structures.

The second transient zone is in front of the mushy zone between two macro-segregated curves (lines C and D), which are, again, equiaxed. At line C, the v_liq also changed rapidly, and the border is sharp between the columnar and equiaxed grain structure, while at line D, the v_liq changed continuously, so the border is, again, not sharp.

The values of v_liq and v_sol at these points, from X to E, are presented in Table 1.

In our opinion, the following happened during the jump-like acceleration in the mushy zone of the sample: The sudden change in v_eut resulted in a significant solutal undercooling of the liquid in the mushy zone in front of the eutectic. Because of this undercooling, before the eutectic front, which is richer in alloying elements, is enough for heterogeneous nucleation, many nuclei are formed on the surface of the TiB₂ particles and grow as many small dendrites as possible. Due to this fact, the Cu concentration in the liquid phase locally increased because the solid phase concentration was lower than that in the liquid phase (C_sol = kC_liq, where k < 1). The increased concentration forced a remelting of the initial columnar dendrites. The partial remelting caused solutal fragmentation [2] in the solid dendrites. This remelting caused by a change in local composition is supported by the fact that the change has not appeared in the sample solidified with the same parameters without refinement material and the shape of the equiaxed dendrite between A and B points. If we compare the dendrite shape between this area and the area after Point C, we can see that their shapes are not the same (Figure 5). In Figure 5B, the dendrites are equiaxed; the dendrite arms were grown in any direction with a similar length. On the other hand, in Figure 5A, the dendrites seem like fragmented arms of bigger dendrites; they are not really equiaxed.

Moving away from the bottom of the original mushy zone to line C, the v_eut increases, but not as fast as it would immediately after a sudden change in v_eut. As a result, solutal undercooling decreases, just fewer new nuclei can be developed, solutal fragmentation cannot occur, and columnar grains solidify again.

In front of the mushy zone, from line C, the sudden change in the v_liq also produced a bigger solutal undercooling, which is enough to form the heterogenous nucleation. New, equiaxed grains were formed and grown. In contrast to the mushy zone, the v_liq is high enough to maintain the necessary solutal undercooling for heterogeneous nucleation.

The microstructures of the non-refined samples (Figure 4 (I)) remained columnar even though velocity changed along the sample. The difference between the microstructures of the two samples comes from the formation of new nuclei, which required significantly less undercooling in the case of heterogeneous nucleation in the inoculated sample.

Previous studies on changes in velocity and how they affect microstructure have given us a good understanding of how velocity affects the microstructural properties of different materials [48,49,50]. However, none of these studies specifically looked at how grain refinement materials and changes in velocity affect the dynamics of solutal undercooling and nucleation. Ref. [50] addresses structural transitions and interface evolution. The study shed light on how changes in processing conditions affect the overall morphology and characteristics of materials. In contrast, the study does not provide the same level of detail regarding the specific conditions and resulting microstructures in various velocity zones as this research did, detailing how these transitions occur and their impact on grain structure, including the formation of equiaxed grains and columnar to equiaxed transitions.

3.2. Size of Grains

The average L/W ratio was determined by measuring the length (L) and width (W) of the grains after they were counted. The findings are illustrated in Figure 6 and Figure 7. The grain is defined as columnar if the L/W ratio is above two and equiaxed if it is less than two [5,51].

4. Conclusions

This study investigated the effect of velocity variations on the micro- and macrostructure of non-refined and refined Al-20%Cu alloys during unidirectional solidification. In this experiment, the sample movement velocity in the mushy zone changed rapidly from 0.02 to 0.2 mm/s. The etching techniques revealed significant variations in the grain and dendritic structures among the samples. The dendritic structure in non-refined alloys was columnar, despite the solid/liquid front velocity. In contrast, refined alloys had a more complex structure that was dependent on the solid/liquid front velocity. This research proves that different solidification velocities produce different microstructural results when grain refinement material is present, which significantly impacts nucleation and growth dynamics. The results from the main investigation are as follows:

• For non-refined alloys, the structures are columnar at all different movement velocities, and there is no transition from columnar to equiaxed.

• Both non-refined and refined alloys form a columnar structure at a movement velocity of 0.02 mm/s.

• A columnar structure can develop in the refined alloy despite the presence of grain refinement material at lower movement velocities. However, the grain refinement material exerts its influence as the movement velocity increases. Consequently, the columnar structure undergoes a columnar-to-equiaxed transition (CET).

• The exceptional transition from columnar to equiaxed (CET) occurs at a low-movement velocity, and fine CET occurs at a high-movement velocity

• For refined alloys, the velocity of the solid/liquid front significantly affected the structure, and the columnar structure changed to an equiaxed structure when the movement velocity rapidly changed in the mushy zone.

Author Contributions

Conceptualization, A.R. (András Roósz) and Z.V.; methodology, A.R. (Arnold Rónaföldi) and A.A.; validation, A.R. (András Roósz), Z.V., and A.A.; formal analysis, A.A.; investigation, A.R. (Arnold Rónaföldi) and A.A.; resources, A.R. (András Roósz) and A.R. (Arnold Rónaföldi); data curation, Z.V. and A.A.; writing—original draft preparation, A.A.; writing—review and editing, A.R. (András Roósz) and Z.V.; visualization, A.A.; supervision, A.R. (András Roósz) and Z.V.; project administration, Z.V.; funding acquisition, A.R. (András Roósz). All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

The authors are grateful to the Hungarian National Research, Development, and Innovation Office for their assistance with the title ‘Formation of solidified microstructure during eutectic front velocity’.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study, in the collection, analysis, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. Schematic representation of the solidification facility, including the following items: (1) Sample; (2) Alumina capsule; (3) Quartz tube; (4) Copper cooling core; (5) Furnace with four heating zones; (6) Step motor; (7) RMF inductor; (8) Water cooling; and (9) Basement.

Figure 2. Representation of the sample and sample holder: 1 and 3, alumina capsule; 2, sample; 4, thermocouples; 5, quartz tube; 6, copper cooling core.

Figure 3. The velocities of solid/liquid and eutectic fronts as a function of distance from the bottom of the sample.

Figure 4. The microstructure changes with movement velocity points, represented by gray and black lines (M = 50 x). I. Microstructure of Al-20%Cu HF etching, II. Microstructure of Al-20% Cu + Gr HF Etching, III. The grain structure of Al-20%Cu barker etching.

Figure 5. Crystals form with different movement velocities (barker etching). (A) Fragmentation of the dendrite arm (0.016–0.128 mm/s). (B) Fine-equiaxed (0.128–0.0160 mm/s).

Figure 6. The grain length and width of the refined Al-20%Cu alloy at different movement velocities.

Figure 7. The types of grains in a refined Al-20%Cu alloy at different movement velocities.

Table 1

The distance from the solidification front is shown in Figure 4, as well as the eutectic front of the samples and the movement velocity at these points.

Name of Point	Distance from the Bottom of the Sample (mm)	Solid/Liquid Front Velocity (vliq, mm/s)
X	19	0.016
A	23	0.018
B	26	0.02
C	35
D	39	0.1
E	54	0.15

References

1. Spittle, J.A. Columnar to Equiaxed Grain Transition in as Solidified Alloys. Int. Mater. Rev.; 2006; 51, pp. 247-269. [DOI: https://dx.doi.org/10.1179/174328006X102493]

2. Dantzig, J.A.; Rappaz, M. Solidification: 2nd Edition—Revised & Expanded; EPFL Press: Lausanne, Switzerland, 2016; ISBN 978-2-940222-97-1

3. Li, Y.Z.; Mangelinck-Noël, N.; Zimmermann, G.; Sturz, L.; Nguyen-Thi, H. Comparative Study of Directional Solidification of Al-7 wt% Si Alloys in Space and on Earth: Effects of Gravity on Dendrite Growth and Columnar-to-Equiaxed Transition. J. Cryst. Growth; 2019; 513, pp. 20-29. [DOI: https://dx.doi.org/10.1016/j.jcrysgro.2019.02.050]

4. Kurz, W.; Bezençon, C.; Gäumann, M. Columnar to Equiaxed Transition in Solidification Processing. Sci. Technol. Adv. Mater.; 2001; 2, 185. [DOI: https://dx.doi.org/10.1016/S1468-6996(01)00047-X]

5. Hunt, J.D. Steady State Columnar and Equiaxed Growth of Dendrites and Eutectic. Mater. Sci. Eng.; 1984; 65, pp. 75-83. [DOI: https://dx.doi.org/10.1016/0025-5416(84)90201-5]

6. Gandin, C.-A. From Constrained to Unconstrained Growth during Directional Solidification. Acta Mater.; 2000; 48, pp. 2483-2501. [DOI: https://dx.doi.org/10.1016/S1359-6454(00)00070-7]

7. Martorano, M.A.; Biscuola, V.B. Predicting the Columnar-to-Equiaxed Transition for a Distribution of Nucleation Undercoolings. Acta Mater.; 2009; 57, pp. 607-615. [DOI: https://dx.doi.org/10.1016/j.actamat.2008.10.001]

8. Gäumann, M.; Trivedi, R.; Kurz, W. Nucleation Ahead of the Advancing Interface in Directional Solidification. Mater. Sci. Eng. A; 1997; 226–228, pp. 763-769. [DOI: https://dx.doi.org/10.1016/S0921-5093(97)80081-0]

9. Gandin, C.-A.; Rappaz, M. A Coupled Finite Element-Cellular Automaton Model for the Prediction of Dendritic Grain Structures in Solidification Processes. Acta Metall. Et Mater.; 1994; 42, pp. 2233-2246. [DOI: https://dx.doi.org/10.1016/0956-7151(94)90302-6]

10. Wang, C.Y.; Beckermann, C. A Unified Solute Diffusion Model for Columnar and Equiaxed Dendritic Alloy Solidification. Mater. Sci. Eng. A; 1993; 171, pp. 199-211. [DOI: https://dx.doi.org/10.1016/0921-5093(93)90407-6]

11. Dong, H.B.; Lee, P.D. Simulation of the Columnar-to-Equiaxed Transition in Directionally Solidified Al–Cu Alloys. Acta Mater.; 2005; 53, pp. 659-668. [DOI: https://dx.doi.org/10.1016/j.actamat.2004.10.019]

12. Liu, D.R.; Mangelinck-Noël, N.; Gandin, C.-A.; Zimmermann, G.; Sturz, L.; Nguyen-Thi, H.; Billia, B. Simulation of Directional Solidification of Refined Al–7wt%Si Alloys—Comparison with Benchmark Microgravity Experiments. Acta Mater.; 2015; 93, pp. 24-37. [DOI: https://dx.doi.org/10.1016/j.actamat.2015.03.058]

13. Liu, D.R.; Mangelinck-Noël, N.; Gandin, C.-A.; Zimmermann, G.; Sturz, L.; Nguyen Thi, H.; Billia, B. Structures in Directionally Solidified Al–7wt% Si Alloys: Benchmark Experiments under Microgravity. Acta Mater.; 2014; 64, pp. 253-265. [DOI: https://dx.doi.org/10.1016/j.actamat.2013.10.038]

14. Reinhart, G.; Gandin, C.-A.; Mangelinck-Noël, N.; Nguyen-Thi, H.; Spinelli, J.-E.; Baruchel, J.; Billia, B. Influence of Natural Convection during Upward Directional Solidification: A Comparison between in Situ X-Ray Radiography and Direct Simulation of the Grain Structure. Acta Mater.; 2013; 61, pp. 4765-4777. [DOI: https://dx.doi.org/10.1016/j.actamat.2013.04.067]

15. Jung, H.; Mangelinck-Noël, N.; Nguyen-Thi, H.; Billia, B. Columnar to Equiaxed Transition during Directional Solidification in Refined Al-Based Alloys. J. Alloys Compd.; 2009; 484, pp. 739-746. [DOI: https://dx.doi.org/10.1016/j.jallcom.2009.05.029]

16. Abou-Khalil, L.; Salloum-Abou-Jaoude, G.; Reinhart, G.; Pickmann, C.; Zimmermann, G.; Nguyen-Thi, H. Influence of Gravity Level on Columnar-to-Equiaxed Transition during Directional Solidification of Al—20 wt% Cu Alloys. Acta Mater.; 2016; 110, pp. 44-52. [DOI: https://dx.doi.org/10.1016/j.actamat.2016.03.007]

17. Rerko, R.S.; de Groh, H.C.; Beckermann, C. Effect of Melt Convection and Solid Transport on Macrosegregation and Grain Structure in Equiaxed Al–Cu Alloys. Mater. Sci. Eng. A; 2003; 347, pp. 186-197. [DOI: https://dx.doi.org/10.1016/S0921-5093(02)00592-0]

18. Martorano, M.A.; Beckermann, C.; Gandin, C.-A. A Solutal Interaction Mechanism for the Columnar-to-Equiaxed Transition in Alloy Solidification. Metall. Mater. Trans. A; 2003; 34, pp. 1657-1674. [DOI: https://dx.doi.org/10.1007/s11661-003-0311-x]

19. Murty, B.S.; Kori, S.A.; Chakraborty, M. Grain Refinement of Aluminium and Its Alloys by Heterogeneous Nucleation and Alloying. Int. Mater. Rev.; 2002; 47, pp. 3-29. [DOI: https://dx.doi.org/10.1179/095066001225001049]

20. Zhang, J.; Gao, N.; Starink, M.J. Microstructure Development and Hardening during High Pressure Torsion of Commercially Pure Aluminium: Strain Reversal Experiments and a Dislocation Based Model. Mater. Sci. Eng. A; 2011; 528, pp. 2581-2591. [DOI: https://dx.doi.org/10.1016/j.msea.2010.11.079]

21. Figueiredo, R.B.; Langdon, T.G. Processing Magnesium and Its Alloys by High-Pressure Torsion: An Overview. Adv. Eng. Mater.; 2019; 21, 1801039. [DOI: https://dx.doi.org/10.1002/adem.201801039]

22. Figueiredo, R.B.; Langdon, T.G. Grain Refinement and Mechanical Behavior of a Magnesium Alloy Processed by ECAP. J. Mater. Sci.; 2010; 45, pp. 4827-4836. [DOI: https://dx.doi.org/10.1007/s10853-010-4589-y]

23. Men, H.; Fan, Z. Effects of Solute Content on Grain Refinement in an Isothermal Melt. Acta Mater.; 2011; 59, pp. 2704-2712. [DOI: https://dx.doi.org/10.1016/j.actamat.2011.01.008]

24. Easton, M.A.; Qian, M.; Prasad, A.; StJohn, D.H. Recent Advances in Grain Refinement of Light Metals and Alloys. Curr. Opin. Solid State Mater. Sci.; 2016; 20, pp. 13-24. [DOI: https://dx.doi.org/10.1016/j.cossms.2015.10.001]

25. Xu, Y.; Kvam-Langelandsvik, G.; Bunaziv, I.; Li, Y. Understanding the Inoculation of Aluminium Grains during Welding under the Influences of High Cooling Rate and High Temperature Gradient. IOP Conf. Ser. Mater. Sci. Eng.; 2023; 1281, 012015. [DOI: https://dx.doi.org/10.1088/1757-899X/1281/1/012015]

26. Kennedy, J.R.; Davis, A.E.; Caballero, A.E.; Pickering, E.J.; Prangnell, P.B. β Grain Refinement during Solidification of Ti-6Al-4V in Wire-Arc Additive Manufacturing (WAAM). IOP Conf. Ser. Mater. Sci. Eng.; 2023; 1274, 012005. [DOI: https://dx.doi.org/10.1088/1757-899X/1274/1/012005]

27. Greer, A.L.; Quested, T.E. Heterogeneous Grain Initiation in Solidification. Philos. Mag.; 2006; 86, pp. 3665-3680. [DOI: https://dx.doi.org/10.1080/14786430500198486]

28. Greer, A.L.; Bunn, A.M.; Tronche, A.; Evans, P.V.; Bristow, D.J. Modelling of Inoculation of Metallic Melts: Application to Grain Refinement of Aluminium by Al–Ti–B. Acta Mater.; 2000; 48, pp. 2823-2835. [DOI: https://dx.doi.org/10.1016/S1359-6454(00)00094-X]

29. Quested, T.E.; Greer, A.L. The Effect of the Size Distribution of Inoculant Particles on As-Cast Grain Size in Aluminium Alloys. Acta Mater.; 2004; 52, pp. 3859-3868. [DOI: https://dx.doi.org/10.1016/j.actamat.2004.04.035]

30. Quested, T.E.; Greer, A.L. Athermal Heterogeneous Nucleation of Solidification. Acta Mater.; 2005; 53, pp. 2683-2692. [DOI: https://dx.doi.org/10.1016/j.actamat.2005.02.028]

31. Xu, Y.; Casari, D.; Mathiesen, R.H.; Li, Y. Revealing the Heterogeneous Nucleation Behavior of Equiaxed Grains of Inoculated Al Alloys during Directional Solidification. Acta Mater.; 2018; 149, pp. 312-325. [DOI: https://dx.doi.org/10.1016/j.actamat.2018.02.058]

32. Quested, T.E.; Dinsdale, A.T.; Greer, A.L. Thermodynamic Modelling of Growth-Restriction Effects in Aluminium Alloys. Acta Mater.; 2005; 53, pp. 1323-1334. [DOI: https://dx.doi.org/10.1016/j.actamat.2004.11.024]

33. Vandyoussefi, M.; Greer, A.L. Application of Cellular Automaton–Finite Element Model to the Grain Refinement of Directionally Solidified Al–4.15 Wt% Mg Alloys. Acta Mater.; 2002; 50, pp. 1693-1705. [DOI: https://dx.doi.org/10.1016/S1359-6454(02)00015-0]

34. Reinhart, G.; Mangelinck-Noël, N.; Nguyen-Thi, H.; Schenk, T.; Gastaldi, J.; Billia, B.; Pino, P.; Härtwig, J.; Baruchel, J. Investigation of Columnar–Equiaxed Transition and Equiaxed Growth of Aluminium Based Alloys by X-ray Radiography. Mater. Sci. Eng. A; 2005; 413–414, pp. 384-388. [DOI: https://dx.doi.org/10.1016/j.msea.2005.08.197]

35. Nguyen-Thi, H.; Reinhart, G.; Mangelinck-Noël, N.; Jung, H.; Billia, B.; Schenk, T.; Gastaldi, J.; Härtwig, J.; Baruchel, J. In-Situ and Real-Time Investigation of Columnar-to-Equiaxed Transition in Metallic Alloy. Metall. Mater. Trans. A; 2007; 38, pp. 1458-1464. [DOI: https://dx.doi.org/10.1007/s11661-007-9170-1]

36. Paradies, C.J.; Smith, R.N.; Glicksman, M.E. The Influence of Convection during Solidification on Fragmentation of the Mushy Zone of a Model Alloy. Metall. Mater. Trans. A; 1997; 28, pp. 875-883. [DOI: https://dx.doi.org/10.1007/s11661-997-1016-3]

37. Gu, J.P.; Beckermann, C.; Giamei, A.F. Motion and Remelting of Dendrite Fragments during Directional Solidification of a Nickel-Base Superalloy. Metall. Mater. Trans. A; 1997; 28, pp. 1533-1542. [DOI: https://dx.doi.org/10.1007/s11661-997-0215-2]

38. Ruvalcaba, D.; Mathiesen, R.H.; Eskin, D.G.; Arnberg, L.; Katgerman, L. In Situ Observations of Dendritic Fragmentation Due to Local Solute-Enrichment during Directional Solidification of an Aluminum Alloy. Acta Mater.; 2007; 55, pp. 4287-4292. [DOI: https://dx.doi.org/10.1016/j.actamat.2007.03.030]

39. Badillo, A.; Beckermann, C. Phase-Field Simulation of the Columnar-to-Equiaxed Transition in Alloy Solidification. Acta Mater.; 2006; 54, pp. 2015-2026. [DOI: https://dx.doi.org/10.1016/j.actamat.2005.12.025]

40. Kim, S.; Grugel, R.N. The Transition from Columnar to Equiaxed Dendritic Growth in Proeutectic, Low-Volume Fraction Copper, Pb−Cu Alloys. Metall. Mater. Trans. A; 1992; 23, pp. 1807-1815. [DOI: https://dx.doi.org/10.1007/BF02804373]

41. Siqueira, C.A.; Cheung, N.; Garcia, A. Solidification Thermal Parameters Affecting the Columnar-to-Equiaxed Transition. Metall. Mater. Trans. A; 2002; 33, pp. 2107-2118. [DOI: https://dx.doi.org/10.1007/s11661-002-0042-4]

42. Pineda, D.A.; Martorano, M.A. Columnar to Equiaxed Transition in Directional Solidification of Inoculated Melts. Acta Mater.; 2013; 61, pp. 1785-1797. [DOI: https://dx.doi.org/10.1016/j.actamat.2012.12.002]

43. Rónaföldi, A.; Kovács, J.; Roósz, A. A Suggested Effective Method for Unidirectional Solidification under Rotating Magnetic Field in the Space Experiments. Trans. Indian Inst. Met.; 2009; 62, pp. 475-477. [DOI: https://dx.doi.org/10.1007/s12666-009-0078-x]

44. Han, Q.; Hassan, M.I.; Saito, K.; Viswanathan, S.; Das, S.K. The Reheating-Cooling Method: A Technique for Measuring Mechanical Properties in the Nonequilibrium Mushy Zones of Alloys. Metall. Mater. Trans. A; 2005; 36, pp. 2073-2080. [DOI: https://dx.doi.org/10.1007/s11661-005-0328-4]

45. Niu, C.; Ren, W.; Ding, B.; Zhong, Y.; Yu, J. The Change of Mushy-Zone Length of a Nickel-Based Single-Crystal Superalloy During the Static-Magnetic-Field-Assisted Directional Solidification. Cryst. Res. Technol.; 2018; 53, 1700187. [DOI: https://dx.doi.org/10.1002/crat.201700187]

46. He, X.; Fuerschbach, P.; DebRoy, T. Heat Transfer and Fluid Flow during Laser Spot Welding of 304 Stainless Steel. J. Phys. D Appl. Phys.; 2003; 36, 1388. [DOI: https://dx.doi.org/10.1088/0022-3727/36/12/306]

47. Li, M.; Mori, T.; Iwasaki, H. Effect of Solidification Rate and Temperature Gradient on the Changes of Mushy Zone Length in Pb-36mass% Sn Binary Alloys during Upward Directional Solidification. ISIJ Int.; 1999; 39, pp. 341-345. [DOI: https://dx.doi.org/10.2355/isijinternational.39.341]

48. Aljaghtham, M.; El Habashi, S.; Premnath, K.; Alsulami, R.A. Solidification of Electrically Conducting Liquid Flow Driven by Shear and Pressure Gradients Subject to Viscous and Joule Heating. Heat Transf.; 2023; 52, pp. 2074-2099. [DOI: https://dx.doi.org/10.1002/htj.22775]

49. Palmieri, B.; Ward, C.A.; Dejmek, M. Effects of Nonlinear Interfacial Kinetics and Interfacial Thermal Resistance in Planar Solidification. Phys. Rev. E; 2012; 86, 051605. [DOI: https://dx.doi.org/10.1103/PhysRevE.86.051605]

50. Kang, J.; Zhao, M. Solid/Liquid Interface Evolution Including Seaweed Morphology during Directional Solidification of Co-Sn Alloys. Mater. Sci. Technol.; 2022; 38, pp. 191-197. [DOI: https://dx.doi.org/10.1080/02670836.2022.2031489]

51. Sun, Y.; Muta, H.; Kurosaki, K.; Ohishi, Y. Thermal and Electrical Conductivity of Liquid Al–Si Alloys. Int. J. Thermophys.; 2019; 40, 31. [DOI: https://dx.doi.org/10.1007/s10765-019-2497-1]