Pattern formation in solidification

Regular patterns form in many solidification processes. Examples occur during lamella and rod-like eutectic growth and when single-phase cells or dendrites are formed. The scale and regularity of the microstructure can determine the properties of the cast materials and is thus important practically. The purpose of the present paper is to show that common features occur in all processes.Steady-state analysis indicates that a wide range of possible spacings could occur during eutectic, cellular or dendritic growth. The degree of freedom is removed by considering the mechanism determining the minimum and maximum spacing on a specimen. It is found that the minimum spacing occurs when the array first becomes stable for a lamella or rod-like eutectic, for cell growth and for some dendrites. For low temperature gradient, high-velocity dendrites, the minimum spacing is determined by the spacing when the dendrites first become near enough to interact. The maximum spacing for eutectics and for cells is determined by tip splitting. The maximum spacing for dendrites occurs when a tertiary arm becomes a new primary. Good agreement is obtained between theory and experiment using this approach to predict spacing limits. The average spacing on a specimen can approach either limit depending on past history. The two extreme spacings are found to span the spacing of the minimum undercooling for eutectic and cellular growth and this allows an average spacing to be estimated using a single condition.It is concluded that three conditions are necessary to form regular structures. A mechanism must exist to eliminate members of the array when the spacing is too small. A mechanism must exist to form new members of the array when the spacing is too wide. The structure must be stable to fluctuations in the range of spacing between the two limits.     

A mechanism for the equalisation of primary spacing during cellular and dendritic growth

The Hunt and Lu [Metall. Mater. Trans. A 27A (1996) 611] model for the selection of primary spacing, , during cellular and dendritic growth predicts a range of spacings falling between minimum and maximum values of _min and _max respectively. Within the model _max/_min will be at least 2 and may, under certain circumstances, be significantly greater. In this paper we use a free boundary model of solidification within an array to demonstrate that interaction between the tips of the cells or dendrites leads to a transverse adjustment mechanism that will tend to equalise the spacing as growth proceeds. This transverse adjustment mechanism is shown to be rapid for the spacings characteristic of cellular growth but much more gradual for the spacings characteristic of dendritic growth. These findings are consistent with observations of the primary spacing of dendrites grown in alloys of the transparent casting analogue, succinonitrile.     

Growth of a Cellular/Dendritic Array

This paper describes a time dependent numerical model for the steady and non-steady growthof a cellular/dendritic array in a moving linear temperature field. The model gives fully selfconsistent solutions for axisymmetric interface shapes, predicts cellular and dendritic spacings,undercoolings and the transition between structures. An important feature of the model is thatthe spacing selection mechanism has been treated. The model predicts two different dendriticgrowth regions. One occurs at low dimensionless velocities where the dendrite array is uniform:a small stable range of spacings is predicted and the prediction agrees very well with existing experiments. The other occurs at high dimensionless velocities where the dendrite array is irregular, its minimum spacing is inversely proportional to velocity Experiment was carried out to verify the prediction. The irregular dendrite array was observed and the measured minimum spacing fitted extremely well with the prediction. By fitting the numerical results. Relatively simple analytic expressions are obtained which provide an insight into the cellular and dendritic growth processes and are useful for comparing theory with experiment.     

NiAl-W纳米多孔阵列制备方法研究

采用定向凝固与选择性腐蚀复合工艺,获得NiAl-W纳米多孔阵列。通过定向凝固速率可调节棒状NiAl-W共晶中棒状W相的间距和直径,电化学选择性腐蚀去除W相后,在NiAl基体表面上形成间距和孔径可调的多孔阵列。由于孔径尺度的限制,孔列在电势0.5V连续腐蚀2~3h后受到极大的阻力。     

Sn-9Zn无铅焊料合金凝固组织及其在时效中的演变

为了考察Sn-9Zn无铅焊料合金凝固组织及其在时效中的演变,制备了不同冷却条件及不同熔体过热度下Sn-9Zn/Cu焊点,并利用扫描电镜和光学显微镜观察了其组织形貌.观察发现:共晶组织随冷却速率提高而显著细化;同时,随炉缓冷凝固时合金形成完全的层片状共晶组织,而空冷和喷水冷却条件下合金除层片状共晶组织外,还形成了杆状富锌相.实验结果还表明,熔体过热度对出炉空冷合金的共晶组织有显著影响,较高的熔体过热度使共晶组织更细密.在空冷合金的时效过程中,杆状富锌相趋于逐渐溶解消失,90℃时效时还发生了共晶组织的显著粗化.     

Eutectic spacing and faults of directionally solidified Al–Al3Ni eutectic

The Al–Al₃Ni eutectic was directionally solidified at a thermal gradient of 4.5 K/mm in a vacuum Bridgman–type furnace in order to study eutectic spacing selection criterion.The microstructure was examined in transverse and longitudinal sections and the interrod spacings were measured at different growth velocity. It has been shown that the interrod spacing is not unique and displays a limited range for rodlike Al–Al₃Ni eutectic alloy. The initial growth velocities are not responsible for the eutectic spacing range, while such faults as branching, endingand diameter change have a significant influence on the eutectic spacing adjustment.     

Eutectic spacing and faults of directionally solidified Al–Al3Ni eutectic

The Al–Al₃Ni eutectic was directionally solidified at a thermal gradient of 4.5 K/mm in a vacuum Bridgman-type furnace in order to study eutectic spacing selection criterion. The microstructure was examined in transverse and longitudinal sections and the interrod spacings were measured at different growth velocity. It has been shown that the interrod spacing is not unique and displays a limited range for rodlike Al–Al₃Ni eutectic alloy. The initial growth velocities are not responsible for the eutectic spacing range, while such faults as branching, ending and diameter change have a significant influence on the eutectic spacing adjustment.     

Structure and mechanical Properties of Al-40% Cu Directionally Solidified Alloy

Commercial purity Al-40% Cu alloys were directionally solidified under a constant temperature gradient of 9 K/mm and growth rate (R) varying from 8 to 305 μm/sec. Cellular structure was obtained with a single primary CuAl₂ rod-like dendrite in the cell centre and a fanned-out eutectic structure surrounding it, while the boundary was composed of a coarser eutectic structure. The intercellular spacing and/or the CuAl₂ interdendritic spacing varied with (R)^?1/3. The UTS increased with R and was found to be lower than that of Al? CuAl₂ eutectics grown under similar conditions. The fracture strength of the primary CuAl₂ dendrites was calculated and was found to increase with decreasing their cross-sectional area.     

Growth mechanisms of modified eutectic silicon

Transmission electron microscopy has been used to study the growth mechanism of silicon in modified aluminium-silicon eutectic alloys. In agreement with earlier studies a high density of thin {1 1 1 } faults was observed in silicon modified by relatively large amounts of sodium or strontium. High-resolution microscopy showed that these faults were a mixture of thin twins and stacking faults, the inter-fault spacing being at least ten times the twin width. Because modified silicon is thought to grow by the twin re-entrant edge mechanism, the thin twins were examined in relation to the shape of the modified silicon dendrites and the solidified growth interfaces. It was concluded that the thin faults were not deformation twins resulting from either thermal contraction stresses or mechanical grinding during specimen preparation. No direct evidence was found to support the re-entrant edge mode of growth in modified silicon. Instead it is suggested that the interface may appear macroscopically non-faceted, as in the more general Lateral Microscopic Growth mechanisms.     

Cu-Cr合金初生相对共晶生长的影响机制研究

制备了定向凝固Cu-1.0%Cr亚共晶自生复合材料,研究了初生α相生长对共晶生长的影响机制,探讨了亚共晶合金中共晶的生长规律.研究结果表明,Cu-1.0%Cr合金定向凝固时,在初生α相间生长的共晶受到初生相生长的影响,在热场不定向和生长空间受限的双重作用下,共晶无定向地杂乱生长.初生α相的生长引起枝晶间液相溶质分布的变化,随着凝固速度的增大,初生α枝晶间液相溶质的浓度分布趋于平缓,成分趋近于CE.Cu-1.0%Cr合金在快速凝固条件下,初生α相生长改变了共晶的生长环境,致使形成非平衡凝固组织--离异共晶.     

Evaluation of the rodlike cu6sn5 phase in directionally solidified tin — 0.9 wt.% copper eutectic alloys

Sn — 0.9 wt.% Cu alloys were directionally solidified under controlled conditions after which diameters of the aligned and rodlike Cu₆Sn₅ eutectic phase were measured as a function of the imposed growth velocity. A rod diameter (d) and growth velocity (V) relation of d²V = constant was found, which is analogous to that established for eutectic phase spacings. A discussion is presented for using the fiber diameter, in lieu of or in addition to the interrod spacing, to evaluate the relation between solidification processing parameters and the observed microstructure.     

Measurement of fine pearlite interlamellar spacing by atomic force microscopy

Pearlite interlamellar spacing is an important parameter controlling ductility and strain hardening of carbon steels. Fine pearlite is the appropriate initial microstructure for drawing high carbon steel with exponential strain hardening rate, leading to high final tensile strengths. The majority of optical and electron microscopy methods for measuring interlamellar spacing present difficulties when applied to fine microstructures. Atomic force microscopy (AFM) was employed to investigate pearlitic steels lead patented at 510 °C and then cold drawn to 86% reduction in area. Conventional specimen preparation techniques for optical metallography were appropriated to produce high resolution AFM images, on which measurements of minimum interlamellar spacing, in good agreement with spacings estimated using the Embury–Fisher model, were easily performed. This revised version was published online in November 2006 with corrections to the Cover Date.     

凝固条件和镁对Al-Si11.0合金组织的影响

研究了宇向凝固时冷却条件和镁元素对Ａｌ－Ｓｉ１１．０合金树枝晶结构和共晶组织的影响。试验结果表明,随着冷却速度的增加,Ａｌ－Ａｉ１１．０合一次枝晶和二镒分枝间距都显著减小,在较小的冷却速度时,加入镁元素后合金的二镒分枝间距明显增大,而在冷却速度大于１６０Ｋ／ｍｉｎ时,则没有影响。试验还发现,加入镁元素后,冷却速度对共晶成分的影响显示减小,是合 共晶组织变细。在试验范围内,Ａｌ－Ｓｉ１１．０合金中加     

High frame rate imaging with a small number of array elements

Recently, a high frame rate imaging method has been developed to construct either 2-D or 3-D images (about 3750 frames or volumes/s at a depth of about 200 mm in biological soft tissues because only one transmission is needed). The signal-to-noise ratio (SNR) is high using this method because all array elements are used in transmission and the transmit beams do not diverge. In addition, imaging hardware with the new method can be greatly simplified. Theoretically, the element spacing (distance between the centers of two neighboring elements) of an array should be lambda/2, where lambda is the wavelength, to avoid grating lobes in imaging. This requires an array of a large number of elements, especially, for 3-D imaging in which a 2-D array is needed. In this paper, we study quantitatively the relationship between the quality of images constructed with the new method and the element spacing of array transducers. In the study, two linear arrays were used. One has an aperture of 18.288 mm, elevation dimension of 12.192 mm, a center frequency of 2.25 MHz, and 48 elements (element spacing is 0.381 mm or 0.591 lambda). The other has a dimension of 38.4 mmx10 mm, a center frequency of 2.5 MHz, and 64 elements (0.6 mm or 1.034 lambda element spacing). Effective larger element spacings were obtained by combining signals from adjacent elements. Experiments were performed with both the new and the conventional delay-and-sum methods. Results show that resolution of constructed images is not affected by the reduction of a number of elements, but the contrast of images is decreased dramatically when the element spacing is larger than about 2.365 lambda for objects that are not too close to the transducers. This suggests that an array of about 2.365 lambda spacing can be used with the new method. This may reduce the total number of elements of a fully sampled 128x128 array (0.5 lambda spacing) from 16384 to about 732 considering that the two perpendicular directions of a 2-D array are independent (ignoring the larger element spacing in diagonal directions of 2-D arrays).     

The growth of oriented ceramic eutectics

Controlled microstructures of the two eutectics in the alumina-titania system have been grown using a special electron beam heating technique. In the aluminium titanate-titania system, the eutectic interlamallar spacing varies with the freezing rate R as =AR ^–n where n=0.5 and the value of the constant A is 8.5×10^–6 cm^3/2sec^–1/2. Primary plate-like dendrites of aluminium titanate in a matrix of discontinuous aluminium titanate-titania eutectic are formed on solidifying a composition TiO₂-20 wt % Al₂O₃. These dendrites appear to deflect cracks in this ceramic. In the alumina-aluminium titanate system, primary rod-like dendrites of alumina were grown in a ribbon-like eutectic of alumina and aluminium titanate on solidifying a composition Al₂O₃–38.5% TiO₂.     

Three-dimensional reconstruction of anomalous eutectic in laser remelted Ni-30 wt.% Sn alloy

Abstract

Laser remelting has been performed on Ni-30 wt.% Sn hypoeutectic alloy. An anomalous eutectic formed at the bottom of the molten pool when the sample was remelted thoroughly. 3D morphologies of the α-Ni and Ni₃Sn phases in the anomalous eutectic region were obtained and investigated using serial sectioning reconstruction technology. It is found that the Ni₃Sn phase has a continuous interconnected network structure and the α-Ni phase is distributed as separate particles in the anomalous eutectic, which is consistent with the electron backscatter diffraction pattern examinations. The α-Ni particles in the anomalous eutectic are supersaturated with Sn element as compared with the equilibrium phase diagram. Meanwhile, small wavy lamella eutectics coexist with anomalous eutectics. The Trivedi–Magnin–Kurz model was used to estimate undercooling with lamellar spacing. The results suggest that the critical undercooling found in undercooling solidification is not a sufficient condition for anomalous eutectic formation. Besides, α-Ni particles in the anomalous eutectic do not exhibit a completely random misorientation and some neighboring α-Ni particles have the same orientation. It is shown that both the coupled and decoupled growth of the eutectic two phases can generate the α-Ni + Ni₃Sn anomalous eutectic structure.     

Hardness and mechanical property relationships in directionally solidified aluminium-silicon eutectic alloys with different silicon morphologies

Hardness and tensile property measurements made on directionally solidified Al-Si eutectic alloys show that definite but different hardness-growth velocity and hardness-silicon interparticle spacing relationships exist for alloys with different silicon eutectic phase morphologies. Tensile property measurements show that hardness and 0.2% proof stress follow silicon interparticle spacing relationships of the same form. It is suggested that hardness can only be used to measure proof stress when the eutectic structure displays a single silicon eutectic phase morphology.     

Effect of Solidification Rate on Microstructure and Solid/Liquid Interface Morphology of Nie11.5 wt% Si Eutectic Alloy

In this study NieN i3 Si eutectic in situ composites are obtained by Bridgman directional solidification technique when the solidification rate varies from 6.0 mm/s to 40.0 mm/s. At the low solidification rates the lamellar spacing is decreased with increasing the solidification rate. When the solidification rate is higher than 25 mm/s, the lamellar spacing tends to be increased, because the higher undercooling makes the mass transport less effective. The adjustments of lamellar spacing are also observed during the directional solidification process, which is consistent with the minimum undercooling criterion. Moreover, the transitions from planar interface to cellular, then to dendritic interface, and finally to cellular interface morphologies with increasing velocity are observed by sudden quenching when the crystal growth tends to be stable.     

Chill modification in AI–Si–Sb eutectic alloys

Abstract

Interface undercooling and Si interparticle spacing measurements and observations of the Si phase structure are presented for Al–12·7Si–0·2Sb (wt-%) alloys directionally solidified over the growth velocity range 20–820 μm S^?1 with a temperature gradient in the liquid of 32 K cm^?1. The undercooling measurements show that the undercooling decreases over the growth velocity range where chill modification occurs. Some cozonal twinning was observed in the fibres but the density of twinning decreased with increasing growth velocity and many fibres were observed to be twin free. The measured undercoolings and spacings are related to growth curves derived from the Jackson and Hunt analysis of eutectic growth, after allowance for a constitutional undercooling term due to Sb buildup at the growth interface during solidification. It is shown that the present measurements can be reconciled with a chill modification mechanism that assumes a faceted–non-faceted transition in the Si phase, but not with a mechanism that considers that the chill modified structure is a rapidly solidified flake structure.

MST/3164     

Critical splitting of the solidifying interface-geometrical model of spacing selection during directional solidification of lamellar eutectics

The steady-state coupling equations of directional solidification of Al-Al₂Cu (=0.94), Sn-Pb (=0.59)and Al-Si (=0.17)eutectics have been solved numerically. The profiles, splitting features and supercooling of the solidifying interface were investigated in detail as functions of the lamellar spacing. It was found that when supercooling, T ₀, at the three-phase conjunction point reaches its minimum value, min (T ₀), the solidifying interface profile of one lamellar phase was in the critical splitting state (marginally stable state) and that of the other lamella was super-stable. Langer's marginal stability theory of lamellar eutectic solidification with a planar interface was extended to the case with a curved interface, and a geometrical model of the spacing selection has been suggested (critical splitting state of one lamella's solidifying interface). The general scaling law of the spacing, derived according to this theory, was found to be consistent with the similarity law recently derived by Kassner and Misbah; it is also supported by experimental results. Another geometrical model of the spacing selection was found, where the solidifying interface profile of one lamella became split and other lamella's profile was in the critical splitting state. The experimental data for directional solidification of Al-Si eutectic showed that the irregular eutectics have a spacing selected according to this mode.