High Undercooling Research Articles

Peritectic solidification mechanism of substantially undercooled liquid Fe-Y-B ternary alloys

Liquid Fe84Y10B6 and Fe74Y16B10 peritectic type alloys were substantially undercooled up to 382 (0.25 TL) and 400K (0.26 TL) with drop tube technique. The molecular dynamics simulation results revealed that the former alloy was characterized by larger Fe, Y and B self-diffusion coefficients and activation energies. In low undercooling regime, γFe phase in Fe84Y10B6 alloy and Y2Fe17Bx phase in Fe74Y16B10 alloy formed preferentially, faceted τ1(Y2Fe14B) phase subsequently developed through peritectic transition. With the increase of undercooling, peritectic transition was promoted by the refined primary phases. Once liquid undercoolings reached certain critical values, a stronger nucleation driving force is provided for τ1 phase, resulting in its direct nucleation and growth by suppressing the formation of primary phases and the following peritectic transformations. If liquid undercooling rose further, there occurred the faceted to non-faceted growth mode transition of the main peritectic τ1 phase. This indicates that high undercooling and rapid solidification is an effective approach to modulate phase transition pathway and microstructural evolution of rare earth alloys.

Growth kinetics and microstructure transition of undercooled Fe7(CoNi)75B18 eutectic muti-principal element alloy

The mechanism of rapid solidification behavior of eutectic muti-principal element alloys (EMPEAs) is an eye-catching field. In this study, the novel Fe7(CoNi)75B18 EMPEA was undercooled via rapid solidification and B2O3 glass purification method and the maximum undercooling up to 190 K was achieved. A clear microstructure evolution path was identified with the undercooling: fully regular eutectic → primary dendrite and regular eutectic → primary dendrite and divorced eutectic. The orientation relationship (OR) between the primary (Fe, Co, Ni) phase and secondary B-rich phase was revealed both at low and medium undercoolings by electron backscatter diffraction (EBSD) analysis. The results show that the OR disappears at high undercooling (190 K) owing to the microstructure fragment and rotation during the post-recalescence. Furthermore, the growth velocity exponentially raised with the increase of undercooling. The maximum growth velocity of the primary phase was 1.152×10−1 m/s, which is significantly lower than binary alloys due to the sluggish kinetics effect of EMPEAs. This study helps to understand the solidification kinetics and microstructure transition of the novel EMPEA and has important implications for controlling the solidification process of more complex alloys.

Surface wave phenomenon and microstructure evolution mechanism of electromagnetically levitated ternary Ti-Al-Fe alloy

Electromagnetic levitation technique was performed to investigate the surface wave phenomenon and microstructure evolution mechanism of undercooled ternary Ti50Al30Fe20 alloy. Under the condition of high undercooling, the formation process of surface waves on the levitated alloy surface were directly detected by high-speed camera. The cooling gas provided the external perturbation that promoted surface nucleation, providing the suitable site for surface wave generation. On the rotating semisolid alloy surface, the competition between centrifugal force and surface tension caused the surface wrinkling, leading to the formation of surface waves. The residual liquid phase was solidified in the vortex circulation flow, and the vortex-shape pattern was preserved during rapid solidification. With the increases of undercooling, the microstructure evolved from dendrites and interdendritic lamellar eutectics into uniform anomalous eutectics because of the independent nucleation and competitive growth of (βTi) and TiFe phase. The surface wave was formed only at high undercoolings, indicating this phenomenon was related to the fluidity in eutectic growth. In this case, the uniform microstructure was closer to satisfying the continuum medium hypothesis, and the homogeneous medium reduced the energy damage during wave propagation. In addition, the micromechanical properties were remarkably increased as undercooling rose owing to the microstructural morphology and solute trapping effect.

Revealing the nucleation and growth modes upon rapid solidification of undercooled Co-24 at.% Sn eutectic alloy by the crystallographic orientation relations

In the realm of undercooled eutectic alloys, the nucleation (i.e., copious vs. single) and the growth (i.e., coupled vs. decouple) modes, particularly the formation of anomalous eutectics, remain subjects of intense debate. This study delves into the crystallographic orientation relationships (ORs) during rapid solidification of an undercooled Co-24 at.% Sn eutectic alloy, where the high-temperature eutectic phases (β-Co3Sn2 and α-Co) persist to room temperature. A significant finding is the consistent observance of the same eutectic OR, i.e., 112̅0β−Co3Sn2 // 11̅1α−Co and 0001β−Co3Sn2 // 110α−Co, across various undercooling conditions from low to high and eutectic morphologies from lamellar to anomalous. This consistency underscores a unified growth mode of coupled eutectic growth. Furthermore, the observance of twin OR, i.e., 112̅1<11̅26>, 112̅2<1123̅> or 112̅4<2243̅>, between β-Co3Sn2 phases in diverse eutectic colonies, spanning from low to intermediate undercooling, and would also be the case of high undercooling, reinforces a single nucleation mode except under exceedingly low undercooling. Building on these insights, the anomalous eutectic colonies are suggested to be formed from a single origin where coupled eutectic growth of eutectic seaweeds or eutectic dendrites instead of dual origins. This study not only illuminates the underlying mechanisms of rapid solidification in undercooled eutectic alloys but also paves the way for innovative microstructure modulation strategies.

Non-equilibrium solidification behavior and mechanical properties of undercooled Fe7(CoNi)77B16 muti-principal element alloy

Multi-principal element alloys (MPEAs) have attracted growing attention owing to the vast compositional field and the comprehensive properties. In this work, Fe7(CoNi)77B16 MPEA was undercooled by vacuum melting furnace with low (61 K, 95 K), medium (115 K, 148 K), and high undercoolings (200 K). The maximum growth velocity of the alloy was 0.21 m/s due to the sluggish kinetics effect. The regular eutectic transformed to anomalous eutectic and the primary dendrite refined from 9.1 μm to 3.5 μm with the increase of undercooling. Meanwhile, the phase selection behavior at high undercooling was observed between the stable (Fe, Co, Ni) phase and the metastable (Fe, Co, Ni)23B6 phase. The hardness of primary phase and compressive strength of the undercooled MPEAs were increased to 952.19 HV and 2061.72 MPa, which is much higher than the as-cast alloy. The enhancement of the mechanical properties was attributed to microstructure evolution. The decrease in plasticity resulted from the increasing volume fraction of brittle intermetallic phases. This study helps to theoretically understand the solidification mechanism of the Fe-Co-Ni-B MPEAs and provides a promising way to enhance the mechanical properties of the novel MPEAs.

Ni and Ni–P substrates inhibit Bi phase segregation and IMC overgrowth during the soldering process of Sn–Bi solder

In this paper, presents surface modification of Cu substrates by electroplating or chemical plating to obtain high-quality Ni and Ni–P coatings. The Sn58Bi solder reactions with Cu, Ni, and Ni–P UBMs at 180 °C, 250 °C, and 320 °C, respectively. Research has found that Ni and Ni–P substrates can inhibit Bi phase segregation and interfacial IMC overgrowth in Sn–Bi solder joints. Bi phase segregation occurs during the transition from Cu6Sn5 to Cu3Sn. There is Bi segregation at the interface of Sn58Bi/Cu solder joints to Cu3Sn/Cu interface, and IMC grows rapidly. However, Ni/Cu and Ni–P/Cu substrates can not only suppress the Bi phase segregation behavior of Sn58Bi solder joints during soldering, but also slow down the excessive growth of interfacial IMC; Even under the harsh soldering process of up to 320 °C for 600 s, it still has an effective blocking effect. In addition, at 320 °C, when Sn58Bi solder react with Cu, the interface directly crosses Cu6Sn5 to generate Cu3Sn, which exhibits the morphology characteristics of Cu6Sn5 due to high thermal conditions. During the soldering, Ni atoms continuously diffuse towards the interface, and Ni3Sn4 (Ni/Cu) grows from needle like in the early stage of soldering to rod like, and finally to block like; The block like appearance of Ni3Sn4 (Ni–P/Cu) occurs earlier than that of Ni3Sn4 (Ni/Cu), because the presence of columnar Ni3P layers provides a wider diffusion channel for Ni atoms, but the overall growth size is smaller than that on Ni/Cu. A higher undercooling can promote the growth of interfacial IMC, including Cu6Sn5 and Ni3Sn4. At the same time, the Bi phase inside the Sn58Bi solder joint is coarsened, and the substrate Ni/Ni–P can eliminate interfacial brittleness after eliminating Bi segregation.

Evolution mechanism of rapid solidification microstructure of an undercooled copper-based single phase alloy

Using undercooling technology combined with melt purification of glass and recirculation overheating, different undercoolings were successfully obtained for Cu60Ni38Co2 alloy samples. Applying high speed photography technique, the physical process of undercooled solidification was observed and relationship between undercooling and solidification rate was analyzed. Experimental results indicate the critical undercoolings exist in the structure evolution process. Electron backscatter diffraction (EBSD) analysis was applied to characterize the Cu60Ni38Co2 alloy sample with a maximum undercooling of 255K, revealing grain orientation and the corresponding orientation difference distribution. In addition, transmission electron microscopy (TEM) showed high density dislocation networks. Combining EBSD and TEM data analysis, an important conclusion was drawn: recrystallization is the main factor for grain refinement at high undercooling. This finding is of great significance for a deeper understanding of the structure evolution in the physical process of undercooled alloys.

Dendritic Si growth morphologies in highly undercooled Al–Si alloys

The morphology of primarily crystallizing Si in hypereutectic Al-(20, 40, 55) wt%Si alloys during conventional casting (nucleation undercooling ΔT<1 K) and solidification at high undercoolings (ΔT up to 335 K) has been investigated. As expected, at higher undercoolings a higher nucleation frequency and fast growth of primary Si is observed, leading to the formation of multiple microstructural zones. Instead of the well-known plate-like Si in the as-cast microstructure, various morphologies of primary Si such as faceted and non-faceted blocky morphologies as well as dendrites with aligned side branches showing constant spacing features are observed after solidification at high undercoolings. The special Si dendrites only grow in a limited range of melt concentrations and undercoolings. The transition from faceted to non-faceted growth appears to occur in several steps, as Si dendrites with similar features of the secondary arms as in non-faceted metal alloys are also observed.

Mechanical and electrical performances of ternary Cu-2.8%Ni-0.7%Si alloy modulated by ultrasonic solidification

One-dimensional (1D) and three-dimensional (3D) ultrasounds were introduced into the solidification process of ternary Cu-2.8wt%Ni-0.7wt%Si alloy together with the in-situ measurements of acoustic fields. In the case of 1D ultrasound, stable cavitation was the main form of acoustic energy transmission. The grain size of α-Cu dendrites was reduced because stable cavitation improved the wetting between impurities and alloy melt, which further promoted nucleation process. When 3D ultrasounds were applied, transient cavitation was the dominant mode of acoustic energy dissipation. This induced local high undercooling in alloy melt, causing a significant increase in bulk nucleation rates and the formation of numerous tiny α-Cu equiaxed grains. Meanwhile, as ultrasonic dimension increased, the strengthened acoustic streaming accelerated solute and thermal diffusion and weakened the preferred orientation of growing α-Cu grains. The proportion of low-angle grain boundaries (LAGBs) increased consequently, which suppressed the nucleation and growth of δ-Ni2Si discontinuous precipitates (DPs) during subsequent annealing treatment. The tensile strength and electrical conductivity of 3D ultrasonically solidified alloy after annealing reached 688.2 MPa and 2.7×107 S/m respectively, showing obvious advantages in synergetic mechanical and electrical performances.

Remarkable undercooling capability and metastable thermophysical properties of liquid Nb84.1Si15.9 alloy revealed by electrostatic levitation in outer space.

The stable manipulation, high undercooling, and thermophysical property measurement of the liquid Nb84.1Si15.9 refractory alloy were successfully achieved by the electrostatic levitation technique on board the China Space Station. By controlling the superheating temperature, a maximum liquid undercooling up to 421K (0.18 TL) was obtained in the space environment, and two distinct solidification paths with different recalescence features were realized at metastable undercooled states. The liquid density and the ratio of specific heat to emissivity were measured in a wide temperature range from 1841 to 2346K, which displayed linear and quadratic relations vs temperature, respectively. The liquid emissivity was further deduced from the specific heat of the liquid alloy calculated by molecular dynamics simulation. In addition, both the density and structural characteristics of the undercooled liquid alloy were also analyzed by MD calculations.

An Experimental Study on the Influence Solution Concentration and Nano-Additives on Cold Storage Performance of Tetrabutylammonium Bromide

Tetrabutylammonium bromide (TBAB) is considered a promising alternative cold energy storage material. Due to the high dissociation heat of phase transition at an atmospheric pressure of 278–293 K, which reaches 200–500 kJ/kg, this substance is considered an effective cold energy storage medium for air conditioning systems. In this paper, the cold storage crystallization process of TBAB solution with different concentrations was tested by conducting experiments and the phase transition’s temperature and latent heat were measured. Finally, the growth characteristics of TBAB hydrate crystals with different concentrations (10%, 20%, 30% and 40%) were analyzed. Considering the cold storage temperature, phase transformation temperature and latent heat, the cold storage effect is the best when 40% TBAB solution is used. Although single substance phase change materials have a long service life, they have problems with low thermal conductivity and high undercooling. Therefore, researchers usually improve the performance of phase change materials by adding other auxiliary materials, thereby enhancing their application prospects. Among these auxiliary materials, adding nano additives to phase change materials can significantly improve latent heat, thermal conductivity and nucleation ability, while also reducing undercooling. Therefore, we studied the influence of different nano-additives (Al2O3, SiC, TiO2 and ZnO) on phase change materials. The composites with excellent properties were screened by cooling step cooling curve and differential scanning calorimeter (DSC). Compared with pure TBAB solution, the phase transition latent heat of the composite phase change materials (PCMs) prepared by adding nanoparticles were significantly increased. The results show that adding nano-SiC into 40% TBAB solution can obtain better performance. This work not only provides reference for the further research, but also a sight to design the phase change materials for the application of new phase change cold storage materials.

Thermophysical properties and rapid solidification mechanism of liquid Zr&lt;sub&gt;60&lt;/sub&gt;Ni&lt;sub&gt;25&lt;/sub&gt;Al&lt;sub&gt;15&lt;/sub&gt; alloy under electrostatic levitation condition

In this study, the thermophysical properties and rapid solidification mechanism of highly undercooled liquid Zr&lt;sub&gt;60&lt;/sub&gt;Ni&lt;sub&gt;25&lt;/sub&gt;Al&lt;sub&gt;15&lt;/sub&gt; alloy are investigated through the electrostatic levitation technique. The maximum undercooling of this alloy reaches 316 K (0.25&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;L&lt;/sub&gt;). Both density and surface tension display a linear relationship with temperature, while viscosity is related to temperature exponentially. When alloy undercooling is less than 259 K, two significant recalescence events are observed during solidification, corresponding to the formation of pseudobinary (Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni + Zr&lt;sub&gt;5&lt;/sub&gt;Ni&lt;sub&gt;4&lt;/sub&gt;Al) eutectic and ternary (Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni + Zr&lt;sub&gt;5&lt;/sub&gt;Ni&lt;sub&gt;4&lt;/sub&gt;Al + Zr&lt;sub&gt;2&lt;/sub&gt;Ni) eutectic. The growth velocity of the binary eutectic phase gradually increases with further undercooling and reaches a maximum undercooling value of 259 K. In contrast, once undercooling exceeds 259 K, a single recalescence event occurs, leading to the independent nucleation of all three compound phases from alloy melt and the rapid growth of a ternary anomalous eutectic structure. Notably, the growth velocity of the ternary eutectic phase exhibits a gradual decline with further undercooling. This diminishing trend of the growth velocity suggests that further undercooling might entirely suppress crystal growth dynamically at a threshold of 385 K. With classical nucleation theory and the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, the onsets of crystallization for the three phases are calculated, thereby constructing a time–temperature-transformation (TTT) diagram. This diagram elucidates the competitive nucleation among the three phases in the undercooled melt. Both theoretical and experimental evidence reveal that Zr&lt;sub&gt;6&lt;/sub&gt;Al&lt;sub&gt;2&lt;/sub&gt;Ni phase is primarily nucleated at lower undercooling levels, whereas under higher cooling condition, it is possible for all three phases to nucleate simultaneously.

Study on structure refinement mechanism in rapid solidification of a deeply undercooled Cu60Ni38Co2 alloy

Employing molten glass purification and cyclic overheating technologies, a Cu60Ni40 alloy was modified by introducing trace amounts of Co element. Through this process, we aimed to understand how the addition of Co element influences the microstructure morphology of the alloy. By combining the BCT model and metallographic analysis, the intrinsic factors of microstructure transformation in the alloy were studied. In the case of small undercooling, solute diffusion dominates dendritic growth, but the undercooled melt is limited to a narrow range of growth, resulting in the formation of coarse dendritic morphology in Cu–Ni alloy. As the undercooling increases, the growth of dendrites is gradually controlled by both solute diffusion and thermal diffusion, and the remelting effect of dendrites is also gradually enhanced. During rapid solidification with lower undercooling, the dendrites formed by the undercooled melt can be remelted to form numerous crystal seeds. Within a moderate undercooling range, dendrites grow directionally due to thermal diffusion and exhibit specific characteristics. At high undercooling, the dendrites' directional growth, primarily driven by thermal diffusion, undergoes stress fragmentation.

In Situ Observation of P91 High‐Alloy Steel Solidification Characteristics at Different Cooling Rates

To clarify the effect of different radial cooling intensities on the formation of central cracks in large round bloom continuous casting, it is necessary to study the solidification characteristics and dynamics of P91 high‐alloy steel at different cooling rates (CRs) to improve the central defects. In this article, the solidification characteristics of P91 high‐alloy steel at different CRs are studied by using the Thermo‐Calc software, high‐temperature laser confocal microscopy, scanning electron microscopy, and optical microscopy. Meanwhile, the growth kinetics of δ‐Fe and γ‐Fe phases under different CRs are determined. In the results, it is shown that the solidification path of P91 high‐alloy steel is L(L + δ‐Fe) → (L + γ‐Fe + δ‐Fe) → (δ‐Fe + γ‐Fe). The δ‐Fe and γ‐Fe phase precipitation process is divided into two stages. Stage I is the nucleation and rapid growth phase, in which a high undercooling is required. Stage II is the slow growth stage, where the undercooling decreases and remains constant. The initial growth linear velocities of the δ‐Fe phase are 0.51, 2.72, and 2.09 μm s−1 at CRs of 10, 50, and 100 °C min−1, respectively, while those of the γ‐Fe phase are 0.10, 1.42, and 1.41 μm s−1.

Facile formation of a superalloy-like microstructure in Ni77Ga23 alloys by rapid solidification processing

Ni77Ga23 alloys were undercooled and rapidly solidified using glass fluxing treatment. An in situ diagnosis of dendrite growth velocity during rapid solidification processing suggests crystallization of a disordered solid solution from low to high undercoolings. While this diagnosis is consistent with an X-ray diffraction analysis, a neutron diffraction analysis suggests the formation of Ni3Ga phase in addition to the disordered solid solution. An EBSD analysis shows the formation of an equiaxed microstructure at a high undercooling. A HAADF-STEM study of equiaxed grains reveals a superalloy-like substructure, where cuboidal coherent precipitates of Ni3Ga phase are dispersed in the matrix of the disordered solid solution. A HRTEM study further reveals disordered nanodomains in the lattice of Ni3Ga phase. It is concluded that rapid solidification processing can lead to facile formation of a superalloy-like microstructure without an aging treatment.

Ultrasonic solidification mechanism and optimized application performances of ternary Mg71.5Zn26.1Y2.4 alloy

One dimensional (1D) and three dimensional (3D) ultrasound sources were applied to the solidification process of Mg71.5Zn26.1Y2.4 alloy. The acoustic spectra were in-situ measured, based on which the cavitation intensities and dynamic solidification mechanism were further investigated. With the increase of ultrasonic dimension and amplitude, the primary Mg3Zn6Y phase was significantly refined from petals to nearly pentagonal shape. The sound field measurements showed that the transient cavitation played a decisive role in generating a high local undercooling, which facilitated the formation of icosahedral clusters and promoted the nucleation of primary Mg3Zn6Y phase. The morphological transition of (α-Mg+Mg3Zn6Y) eutectic from lamellar to anomalous structure occurred under 3D ultrasonic condition. The stable cavitation took the main responsibility because the high pressure excited by nonlinearly oscillating bubbles induced the preferential nucleation of α-Mg phase rather than Mg3Zn6Y phase. As compared with its static values, the tensile strength and compression plasticity of this alloy were increased by the factors of 1.9 and 2.1, and its corrosion resistance was also improved with the corrosion current density decreased by one order of magnitude.

Subgrain-assisted spontaneous grain refinement in rapid solidification of undercooled melts

The grain refinement mechanism for rapid solidification of undercooled melts is still an open problem even after 60 years of on-going studies. In this work, rapid solidification of undercooled Ni and equi-atomic FeCoNiPd melts was studied and spontaneous grain refinement was found at both low and high undercooling. After a detailed electron backscattered diffraction analysis, subgrain-induced grain orientation scattering and splitting were found to occur along with the transition from coarse dendrites to fine equiaxed grains at low and high undercooling, respectively, indicating that subgrains play an important role during the formation of fine equiaxed grains. On this basis, a compromise mechanism of subgrain-assisted spontaneous grain refinement was proposed. Because the dendrite re-melting induced thermo-mechanical process and fluid flow induced dendrite deformation occur simultaneously during the post-recalescence stage, stress accumulation would be maximum at both low and high undercooling, thus inducing dynamic recrystallization, during which the formation and rotation of subgrains make the grain orientations scattering and even splitting. Furthermore, the grain/subgrain size of undercooled FeCoNiPd ascribing to its unique co-segregation behavior keeps almost invariable from low to high undercooling, indicating that the co-segregation strategy would be effective to inhibit grain growth after rapid solidification and would be useful in practice.

Investigation on solidification structure evolution of deeply undercooled single-phase Ni-Cu-Co alloys

In this work, the main focus was on exploring the effect of increasing the gradient content of Co element on the solidification process of Ni-Cu-Co alloy under deep undercooling conditions. The effects on its solidification rate, recalescence effect, and critical undercooling range were also explored. In the experiment, a combination of molten glass purification and cyclic superheating technology was mainly used to obtain gradient undercooling of Ni88Cu10Co2, Ni88Cu8Co4, and Ni88Cu6Co6 alloy samples at intervals of 10 K. By analyzing the microstructure evolution under different undercooling degrees through metallographic diagrams, and combining it with high-speed cameras to record the phenomenon of recalescence during the solidification process, the influence of the addition of Co element on the solidification rate, recalescence effect, and the critical undercooling range appearing in the microstructure during the overall solidification process was explored. Conduct EBSD analysis on the alloy samples under the maximum undercooling of Ni88CuCo6, and analyze the representative significance behind their characterization data. At the same time, TEM transmission analysis was conducted on the Ni88Cu6Co6 alloy sample with the highest Co content, and it was found that there are high-density dislocation and stacking fault networks as well as obvious twinning structures in the substructure area. The standard FCC diffraction pattern also represents that it is still a single-phase structure. Based on the above metallographic diagram, EBSD, and TEM data analysis, it is proven that the occurrence of grain refinement under high undercooling is mainly due to stress induced recrystallization.

Solidification Behavior of Undercooled Fe75B25 Alloy

The paper presents a study of the phase selection and microstructure evolution of Fe75B25 alloy subjected to solidification at various undercoolings. The alloy invariably solidifies into a primary Fe2B phase and α-Fe/Fe2B eutectic at all the experimental undercoolings up to 381 K. A metastable Fe3B phase does not precipitate, although its growth in this alloy is favored without large-scale solute diffusion involved. It is shown that the phase selection is nucleation-controlled. Solid sites existing in the alloy melt seem more favorable for the nucleation of the Fe2B phase. As undercooling increases, primary the Fe2B phase changes its morphology complexly. It solidifies into coarse faceted dendrites at low undercoolings, developed non-faceted dendrites at moderate undercoolings, seaweeds with dense branches at higher undercoolings, and refined granular grains at undercooling above 147 K.

Phase field modelling of hopper crystal growth in alloys

Here we use phase field to model and simulate “hopper” crystals, so named because of their underlying cubic structure but with a hopper-like depression on each of the six faces. Over the past three decades simulations of single phase solidification have successfully explored dendritic structures, in two and three dimensions, formed under high undercooling from a slight perturbation in anisotropy. More recently we see the modelling of faceted structures at near equilibrium, and also, under high undercooling, the formation of dendritic-like structures in two dimensions which retain some faceting in the dendrite arms. A cubic hopper crystal appears to be a hybrid structure, somewhere between a perfect cube and a dendrite, and, to date, has not appeared in the modelling literature. In this paper we describe a model for faceted cubic growth and explore results, necessarily in three dimensions, that include perfect cube, hopper and dendritic. We also touch briefly on one other morphology—octahedral.