Alternating tip splitting in directional solidification

We report experimental results on the tip splitting dynamics of seaweed growth in directional solidification of succinonitrile alloys. Despite the random appearance of the growth, a tip splitting morphology was observed in which the tip alternately splits to the left and to the right. The tip splitting frequency f was found to be related to the growth velocity V as a power law f~V1.5. This finding is consistent with the predictions of a tip splitting model that is also presented. Small anisotropies are shown to lead to different kinds of seaweed morphologies.     

Thermal gradient induced sidebranching in directional solidification

The polycrystalline perovskitelike manganese oxides La_1-xA_xMnO (A = Na, and K, ) have been fabricated by sol-gel technique. For all the compositions explored in this work, the average manganese oxidation state is practically constant, at for A = Na, and for A = K, respectively. A close relationship is confirmed to hold between the Curie temperature (T_c) and the bond distance of Mn-O. Results of magnetic measurements show that these materials can be utilized as suitable candidates for magnetic refrigerants with wide applied temperature span, for their significant entropy change and the easily tuned Curie temperature. Received: 12 September 1997 / Revised: 18 December 1997 / Accepted: 21 January 1998     

Seaweed to dendrite transition in directional solidification

We simulate directional solidification using a phase-field model solved with adaptive mesh refinement. For small surface tension anisotropy directed at 45 degrees relative to the pulling direction we observe a crossover from a seaweed to a dendritic morphology as the thermal gradient is lowered, consistent with recent experimental findings. We show that the morphology of crystal structures can be unambiguously characterized through the local interface velocity distribution. We derive semiempirically an estimate for the crossover from seaweed to dendrite as a function of thermal gradient and pulling speed.     

A prepared pattern with wavelength selection in directional solidification

As crystal growth is a vital link in the long chain of processes leading to state-of-the-art technological devices, a great deal is known about patterns formed at the solid-liquid interface of a growing crystal. However, some basic questions are still unanswered concerning macroscopic features exhibited by a moving solid-liquid interface. Even for the first instability, the cellular instability, a unique steady-state wavelength does not emerge from theory. Furthermore, while wavelength selection is observed in many different materials, its origin is still to be discovered. By breaking continuous rotational symmetry of the flat solid-liquid interface about the pulling direction v, we prepared a cellular pattern with a well-defined wavelength by front propagation into the unstable uniform state. The material is succinonitrile and the rectangular interface geometry is formed by loading it into a flat capillary. The capillaries are chosen to provide a sample thicknessy ₀ = 100n , and width 10y ₀ and 20y ₀. We use a high-resolution directional solidification apparatus and grow the crystal from grain-boundary-free seed crystals. Surprisingly, the shape of the groove next to the uniform state is initially well-described by nearly self-similar Gaussians. This suggests that the initial perturbation of the interface is localized to a region /2 around a groove. A pattern with a well-defined wavelength is established when the half-width of the Gaussians ₀16m is small compared to 80m so there is little overlap between a groove and its predecessor or successor. When overlap is significant, the pattern is time-dependent. These results suggest that wavelength selection in this prepared pattern is a consequence of front propagation of a localized perturbation.     

A WKB type analysis of marginal stability in directional solidification

We propose a simple and physical approach to the marginal stability criterion of pattern selection in directionally solidifying systems. The technique involves a WKB type analysis of instability caused by perturbations on the steady state shape of the cell.     

晶体取向对定向凝固枝晶生长的影响

采用类金属透明模型合金丁二腈-1.0 wt%乙醇(SCN-1.0 wt% Eth)合金, 考察了晶体取向对定向凝固过程中晶粒的平界面失稳孕育时间、枝晶形态演化以及枝晶一次间距的影响. 结果表明, 随着枝晶择优生长方向与温度梯度方向夹角的增大, 晶粒的平界面失稳孕育时间增加, 界面的稳定性增强; 对于不同晶体取向的枝晶形态演化, 枝晶择优生长方向与温度梯度方向夹角越大, 枝晶二次臂不对称生长越严重, 同时, 具有生长优势的枝晶二次臂对相邻枝晶的生长的抑制越强烈; 至于不同晶体取向的枝晶一次间距, 随着枝晶择优生长方向与温度梯度方向夹角的增大, 枝晶一次间距增大. 关键词： 定向凝固 平界面失稳 枝晶间距 晶体取向     

Tip-splitting instability in directional solidification based on bias field method

Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α 3/2/π≈ 0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.     

Crossover scaling of wavelength selection in directional solidification of binary alloys

We simulate cellular and dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with adaptive-mesh refinement. The spacing of primary branches is examined for a wide range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a nontrivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers. This result is further validated using published experimental data, which obeys the same scaling function.