{'fraction_non_alphanumeric': 0.024348403519451053, 'fraction_numerical': 0.023518344308560677, 'mean_word_length': 4.619402985074627, 'pattern_counts': {'":': 0, '<': 1, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Direct formation of peritectic phase but no primary phase appearance within Ni83.25Zr16.75 peritectic alloy during free fall

Ni83.25Zr16.75 peritectic alloy was containerlessly solidified in a drop tube. When the droplet diameter exceeds a critical value (Dcrit), Ni7Zr2 phase primarily solidifies, followed by the peritectic reaction of Ni7Zr2 + L → Ni5Zr. Once the droplet diameter is smaller than the critical value (Dcrit), peritectic phase Ni5Zr directly solidifies from the undercooled melt by completely suppressing the nucleation and growth of Ni7Zr2 phase, which is ascribed to high undercooling and cooling rate. Additionally, peritectic phase Ni5Zr grows equiaxially in the sample solidified in a DSC at a cooling rate of 0.167 K/s.

Peritectic reaction, in which the primary phase reacts with a liquid phase at a triple junction on cooling to produce the peritectic phase, is observed in many binary alloys systems, such as Ti-Al, Fe-Co, Fe-Ni, etc [1][2][3] . Peritectic reaction terminates once the primary phase is enwrapped by the peritectic phase. Then, the primary phase transforms to the peritectic phase by peritectic transformation. Due to the sluggishness of long-range solid-state diffusion, peritectic transformation could not proceed completely, leading to the existence of primary phase in the final microstructure after peritectic solidification. Recently, microstructures containing only peritectic phase with no primary phase were reported during the solidification of highly undercooled peritectic alloys, which has aroused great interest [4][5][6][7][8][9] . Wei et al. 6 reported that once the undercooling exceeds a critical value of about 220 K, peritectic phase forms directly from the metastable liquid phase by suppressing the nucleation of primary phase for Cu-70%Sn alloy, which is hyperperitectic composition. Phanikumar et al. 8 found that the microstructure is nearly phase-pure peritectic phase when Fe-25%Ge peritectic alloy is undercooled up to 110 K using electromagnetic levitation technique, in which the primary phase is a solid solute phase of α -Fe. Löser et al. 9 reported that beyond a critical undercooling, the equilibrium solidification can be replaced by the direct growth of peritectic phase for Co 75 Si 25 peritectic alloy. Although some study results have been reported, fundamental and deep understanding of different aspects of peritectic solidification is still poor. These investigations mainly focus on the effect of undercooling on phase selection and microstructure evolution. It is not clear how the peritectic phase could directly form from liquid alloys, especially for some complicated peritectic alloys, for example, both the primary phase and the peritectic phase are intermetallic compounds.
The Ni-Zr binary alloy system contains abundant metallic compounds and amorphous alloys, which have been studied extensively [10][11][12][13][14][15][16] . However, most works concentrate on the atomic structure and glass forming ability. Ni 83.25 Zr 16.75 alloy is a typical peritectic composition in Ni-Zr binary alloy system. The primary phase Ni 7 Zr 2 and peritectic phase Ni 5 Zr are both intermetallic compounds. Phase selections between primary phase and peritectic phase have great influence on the final solidified microstructures, which directly relate to the materials characteristics. Therefore, the objective of this work is to investigate effects of undercooling and cooling rate on phase selection and microstructure evolution of Ni 83.25 Zr 16.75 peritectic alloy by a 3 m drop tube. Meanwhile, the effect of cooling rate on peritectic growth is also studied. Figure 1 shows the left part of Ni-Zr binary phase diagram 17 , in which the studied Ni 83.25 Zr 16.75 peritectic alloy is marked with an arrow. As can been seen, the solidification of Ni 83.25 Zr 16.75 peritectic alloy starts with the formation of primary Ni 7 Zr 2 phase and a peritectic reaction of Ni 7 Zr 2 + L → Ni 5 Zr occurs at 1573 K under the equilibrium condition. 100% peritectic phase is obtained when peritectic solidification is accomplished.

Results and Discussion
Drop tube processing has the advantage to achieve high cooling rate and undercooling, which is quite suitable to investigate the phase selection. However, it is hard to measure and record the temperature experimentally due to the short time of free fall. Under this condition, heat transfer theory 18,19 is applied to calculate the cooling rate and undercooling of droplets. The calculated results are shown in Fig. 2, and Table 1 lists the physical parameters used in the calculation 20 . It can be seen that the cooling rate and undercooling strongly depend on droplet diameter. Figure 3 illustrates the solidified microstructures of Ni 83.25 Zr 16.75 peritectic droplets with different diameters, in which the primary phase Ni 7 Zr 2 and the peritectic product Ni 5 Zr have been marked. In the droplet of   1120 μm, the solidified microstructures are composed of primary Ni 7 Zr 2 dendrites, peritectic phase Ni 5 Zr and inter-dendritic eutectic, as show in Fig. 3(a). Evidently, the primary phase Ni 7 Zr 2 is characterized by coarse, developed dendrites and surrounded by peritectic phase Ni 5 Zr. Figure 3(b) is the enlargement of inter-dendritic eutectic microstructure in Fig. 3(a). It must be noticed that there is no any prediction of eutectic transformation for this composition according to the equilibrium phase diagram. This will be discussed in the following parts.
With the decrease of droplet diameter, the refinement and fragment of primary Ni 7 Zr 2 dendrites occur. When the droplet diameters decrease to 226 μm, the microstructure consists of two regions, as presented in Fig. 3(c). Clearly, one is primary Ni 7 Zr 2 dendrites surrounded by peritectic phase Ni 5 Zr, which locate at the rim of the droplet. The other is Ni 5 Zr phase with no primary phase Ni 7 Zr 2 locating at the center of the droplet, as illustrated in Fig. 3(d). The peritectic phase Ni 5 Zr is the predominant phase. When the droplet diameter is very small like 67 μm, only peritectic phase Ni 5 Zr grows within the whole droplet and no Ni 7 Zr 2 dendrites can be observed, as presented in Fig. 3(e,f). According to Kerr and Kurz's description 21 , peritectic solidification consists of two processes, one is the solidification of primary phase and the other is the growth of peritectic phase. Meanwhile, three stages have been identified during a peritectic growth process, namely, peritectic reaction, peritectic transformation, and direct solidification of the peritectic phase. Different solidification pathway of Ni 83.25 Zr 16.75 peritectic droplets can be concluded based on the solidified microstructure presented in Fig. 3. In the droplets whose diameters are large, the primary phase Ni 7 Zr 2 is expected to nucleate at temperature below the liquidus temperature and grows into the manner of dendrites. With the decrease of droplets temperature, the peritectic phase Ni 5 Zr starts to nucleate at the surface of primary phase Ni 7 Zr 2 when the temperature below the peritectic temperature. The requirement of peritectic reaction, which is primary phase, peritectic phase and liquid must be in contact with each other at a triple junction, is satisfied after the nucleation of peritectic phase Ni 5 Zr. Then, peritectic reaction starts and peritectic phase Ni 5 Zr grows along the surface of primary Ni 7 Zr 2 dendrites to form a thin layer. Since peritectic reaction is controlled by short-range atomic diffusion in the liquid ahead of primary Ni 7 Zr 2 dendrites and peritectic phase Ni 5 Zr, it is able to accomplish rapidly at the initial stage of the peritectic growth process 21 . Once the primary Ni 7 Zr 2 dendrites are enveloped by the peritectic phase, the primary phase and liquid are separated by the peritectic phase, which results in the disappearance of the triple junction and the termination of peritectic reaction. After peritectic reaction, the peritectic phase Ni 5 Zr grows into the primary Ni 7 Zr 2 dendrites by peritectic transformation and into the liquid by direct solidification. Peritectic transformation is controlled by long-range solid-state diffusion and the cooling rate in drop tube processing is always high, leading that peritectic transformation could hardly take place. Therefore, the primary Ni 7 Zr 2 dendrites are retained in the microstructure, as illustrated in Fig. 3(a). Simultaneously, peritectic phase Ni 5 Zr grows into the liquid by direct solidification, which results in the deviation of residual liquid composition. As a consequence, the residual liquid solidifies as eutectic when the temperature decreases below the eutectic temperature, as illustrated in Fig. 3(b). The morphology in Fig. 3(b) is characterized by lamellar eutectic structure, where the bright one is (Ni) phase and the other is Ni 5 Zr phase.
With the decrease of droplet diameters, the possibility for a droplet to contain heterogeneous nucleation site is reduced. Therefore, droplets with small diameters can obtain high undercoolings. The enhancement of undercooling greatly promotes the nucleate rate of primary phase Ni 7 Zr 2 , which results in the refinement of primary Ni 7 Zr 2 dendrites. Meanwhile, the release of latent heat remelts the primary phase leading to the fragment of Ni 7 Zr 2 dendrites. As a result, the contact area between primary Ni 7 Zr 2 dendrites and liquid increases. This apparently promotes the peritectic reaction and thus more primary Ni 7 Zr 2 dendrites are decomposed. Similarly, residual liquid directly solidifies as Ni 5 Zr phase and a small amount of eutectic successively. According to the above analysis, it can be speculated that the volume fractions of peritectic phase increase with the decrease of droplet diameters. In order to validate the conclusion, the volume fractions of peritectic phase have been measured, which is illustrated in Fig. 4. Apparently, with the decrease of droplet diameters, the volume fraction of peritectic phase Ni 5 Zr increases, which is consistent with the speculation.
When the droplet diameter is 226 μm, the microstructure consists of only a small amount of primary Ni 7 Zr 2 dendrites near the rim of droplet and predominant Ni 5 Zr phase without any Ni 7 Zr 2 phase in the center, as presented in Fig. 3(c,d). The possibility for the formation of such a microstructure is that the peritectic phase Ni 5 Zr homogeneously nucleates at the center of the undercooled droplet and then starts to grow. Unfortunately, the peritectic phase Ni 5 Zr grows into a faceted way, the growth velocity of which is sluggish. The release of crystallization heat leads to a rise of temperature and a decrease of interface undercooling of Ni 5 Zr phase. Therefore, the growth of peritectic phase Ni 5 Zr will be terminated. At this small undercooling, the primary phase Ni 7 Zr 2 is preferred to nucleate and grow. Following that, peritectic reaction takes place when the temperature drops below the peritectic temperature T P . As for Ni 83.25 Zr 16.75 peritectic alloy, the liquidus temperature of Ni 7 Zr 2 phase is larger than that of Ni 5 Zr phase about 39 K, which leads to a high driving force for the nucleation of Ni 7 Zr 2 phase. Therefore, Ni 7 Zr 2 phase is preferred to nucleate. However, this is not the case under high undercooling condition. From a thermodynamic point of view, the change in Gibbs free energy, dG, determines which phase is thermodynamically stable at given temperature and pressure, expressed as  If the droplet is undercooled below the peritectic temperature T P , the formation of a new phase is determined by the competitive nucleation of Ni 7 Zr 2 phase and Ni 5 Zr phase. Clusters are the initial stage of nucleation. The formation of clusters needs atoms diffuse and attach together. When the attachment rate of atoms to the cluster is larger than the detachment rate of atoms to the same cluster, this cluster can form stable within the undercooled droplet. The concentration of droplet is the same as that of peritectic phase Ni 5 Zr. As a consequence, large chemical potential is required to form the clusters of Ni 7 Zr 2 phase compared with the formation of Ni 5 Zr clusters, resulting in large Gibbs free energy barrier to nucleation of Ni 7 Zr 2 phase. Thus, compared with the nucleation of Ni 5 Zr phase, high undercooling is required to nucleate the Ni 7 Zr 2 phase. Fortunately, the undercooling of Ni 7 Zr 2 phase ΔT is always larger than the undercooling of Ni 5 Zr phase ΔT p about 39 K, which is beneficial to the nucleation of Ni 7 Zr 2 phase. Therefore, Ni 7 Zr 2 phase is still preferred to nucleate when the droplet is undercooled just below the peritectic temperature T p . However, the ΔT/ΔT p ratio is decreased with the further increase of undercooling ΔT, leading to the disappearance of the advantage of the nucleation of Ni 7 Zr 2 phase. The undercooling is up to 120 K for the droplet whose diameter is 226 μm. Hence, peritectic phase Ni 5 Zr may primarily nucleates from the undercooled droplet when the droplet diameter is 226 μm.
With the further decease of droplet diameter, the peritectic phase Ni 5 Zr is more preferred to nucleate. A heat flux from the melt to the surroundings is required during the solidification process, which changes the free energies and therefore the relative thermodynamic stability, of the phases present 23 . Actually, the heat flux from the melt to the surrounding is absolutely dominated by the cooling rate. In the droplets whose diameter is 67 μm, the cooling rate is up to 1.8 × 10 5 K/s, which leads that the crystallization heat is rapidly transformed to the surroundings during the peritectic growth. Therefore, the peritectic Ni 5 Zr phase can continually grow, resulting in the formation of phase-pure Ni 5 Zr microstructure, as shown in Fig. 3(e-f). The EDS analysis demonstrates that it is peritectic phase Ni 5 Zr which contains about 81 at% Ni and 19 at% Zr. This indicates that high undercooling and cooling rate may totally suppress the formation of Ni 7 Zr 2 phase and results in the directly nucleation and growth of peritectic phase Ni 5 Zr from the undercooled melt. Besides, the critical diameter for obtaining phase-pure Ni 5 Zr microstructure is in the range of 226 to 67 μm.
In order to further investigate the effects of cooling rates on peritectic growth, DSC experiment was employed to perform a comparative analysis. 20 mg of Ni 83.25 Zr 16.75 samples was completely melted by heating to 1723 K and then solidified at a cooling rate of 0.167 K/s. The DSC curves are shown in Fig. 5, in which the upper curve is the heating curve and the other is the cooling curve. It can be seen that there are two peaks during the solidification, which represent the solidification of primary phase Ni 7 Zr 2 and the growth of peritectic phase Ni 5 Zr, respectively. The solidified sample has a undercooling of 67 K and the microstructure is illustrated in Fig. 6(a). Obviously, the microstructure consists of predominate peritectic phase Ni 5 Zr and a small amount of primary phase Ni 7 Zr 2 . Besides, a majority of peritectic phase Ni 5 Zr grows equiaxially. This indicates that peritectic transformation proceeds for a relatively long time duo to the low cooling rate in the DSC. Figure 6(b) shows the microstructure solidified in the drop tube at the similar undercooling level but with a high cooling rate of about 2.8 × 10 3 K/s. The microstructure are composed of primary phase Ni 7 Zr 2 , peritectic phase Ni 5 Zr and eutectic, which shows completely different morphology compared with that in Fig. 6(a). The Ni 5 Zr phase exhibits faceted morphology, indicating that peritectic phase grows mainly by peritectic reaction and direct solidification under high cooling rate condition. This reveals a different peritectic growth mechanism under different cooling rate condition.

Conclusion
In summary, Ni 83.25 Zr 16.75 peritectic alloy was rapidly solidified in a 3 m drop tube. The microstructure evolution with the decrease of droplet diameter is investigated. For large droplets, solidified microstructures are composed of primary Ni 7 Zr 2 dendrites, peritectic phase Ni 5 Zr and eutectic. The competitive nucleation and growth between Ni 7 Zr 2 phase and Ni 5 Zr phase become intensive as droplet diameter decreases. The solidified microstructure consists of only peritectic phase Ni 5 Zr once the droplet diameter less than a critical value, D crit , which is determined in the range of 226 to 67 μm. For D > D crit , Ni 7 Zr 2 phase primarily solidified, followed by the peritectic reaction of Ni 7 Zr 2 + L → Ni 5 Zr. For D < D crit, peritectic Ni 5 Zr phase directly solidifies from the undercooled melt by completely suppressing the nucleation and growth of Ni 7 Zr 2 phase, which is ascribed to high undercooling and cooling rate. Ni 83.25 Zr 16.75 sample solidified in the DSC contains no eutectic and the morphologies of peritectic phase Ni 5 Zr is equiaxial, indicating that peritectic phase grows mainly by peritectic reaction and peritectic transformation under low cooling rate condition.

Experimental Details
Containerless rapid solidification of Ni 83.25 Zr 16.75 peritectic alloy was performed in a 3 m drop tube. The master alloy samples were prepared by 99.99% pure Ni and 99.9% pure Zr mixtures in an argon atmosphere, and each of samples has a mass of 1.0 g. When the experiment began, the sample was placed in a silica tube, which has a Φ0.2 mm orifice at bottom and was installed at the top of 3 m drop tube. The drop tube was evacuated to 10 −5 Pa and backfilled with 20% Ar and 80% He gas mixture to 1 atm. After melted by induction heating, the sample was ejected out from the orifice and dispersed into many fine droplets by exerting argon gas flow. The droplets were solidified rapidly in a containerless state during free fall. After that, the droplets were collected and sieved into several groups according to their sizes. The solidified samples were analyzed by FEI Sirion SEM and Oxford INCA 300 EDS.