Multi-phase field simulation of competitive grain growth for directional solidification

The multi-phase field model of grain competitive growth during directional solidification of alloy is established. Solving multi-phase field models for thin interface layer thickness conditions, the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt% camphor model alloy bi-crystals are investigated. The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed. The obtained results are shown below. In the competitive growth of convergent bi-crystals, when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large, the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite, blocking the unfavorably oriented dendrite, and the grain boundary is along the growth direction of the favorably oriented dendrite. When the pulling speed becomes small, the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite, eliminating the favorably oriented dendrite. In the process of competitive growth of divergent bi-crystal, when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small, the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains, and as the orientation angle of unfavorably oriented dendrites becomes larger, the unfavorably oriented grains are more likely to have stable secondary dendritic arms, which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space, but the grain boundary direction is still parallel to favorably oriented dendrites. In addition, the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes, this blocking of the tertiary dendritic arms has a random nature, which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.     

Heat and mass transfer characteristics during rapid solidification of Fe-Cu peritectic alloys

The viscose flow and microstructure formation of Fe-Cu peritectic alloy melts are investigated by analyzing the velocity and temperature fields during rapid solidification, which is verified by rapid quenching experiments. It is found that a large temperature gradient exists along the vertical direction of melt puddle, whereas there is no obvious temperature variation in the tangent direction of roller surface. After being sprayed from a nozzle, the alloy melt changes the magnitude and direction of its flow and velocity rapidly at a height of about 180 μm. The horizontal flow velocity increases rapidly, but the vertical flow velocity decreases sharply. A thermal boundary layer with 160–300 μm in height and a momentum boundary layer with 160–240 μm in thickness are formed at the bottom of melt puddle, and the Reynolds number Re is in the range of 870 to 1070 in the boundary layer. With the increase of Re number, the cooling rate increases linearly and the thickness of thermal boundary layer increases monotonically. The thickness of momentum boundary layer decreases slowly at first, then rises slightly and decreases sharply. If Re < 1024, the liquid flow has remarkable effects on the microstructure formation due to dominant momentum transfer. The separated liquid phase is likely to form a fiber-like microstructure. If Re>1024, the heat transfer becomes dominating and the liquid phase flow is suppressed, which results in the formation of fine and uniform equiaxed microstructures. Supported by the National Natural Science Foundation of China (Grant Nos. 50121101 and 50395105)     

强磁场对Mn-Sb包晶合金相变及凝固组织的影响

以Mn-56.5 wt%Sb包晶合金为研究对象, 进行了不同磁场、不同冷速条件下的凝固实验. 通过对液相线温度、包晶温度的考察, 发现强磁场可以提高Mn-56.5 wt%Sb合金的液相线温度, 且该上升值随磁感应强度的增加而增加, 当所施加的磁感应强度为11.5 T时, 液相线温度升高大约3 ℃, 但施加磁场后包晶反应温度没有明显改变. 对该合金的凝固组织进行定量金相分析发现, 施加磁场后MnSb相明显减少, 该结果与磁场对相变温度的影响相一致. 另外通过X射线衍射分析发现, 强磁场诱发包晶反应生成相MnSb的c轴垂直于磁场方向取向, 而Mn₂Sb相的(311)面平行于磁场方向取向. 对不同冷速凝固的Mn-56.5 wt%Sb合金组织进行定量金相分析结果显示, 强磁场对合金凝固过程的作用效果受到冷却速度的影响. 随着冷却速度的增加, 强磁场对该合金凝固组织中MnSb相的相对含量变化影响效果减弱. 关键词： 强磁场 包晶合金 凝固 相变温度     

Tunable zeroth-order resonator based on a ferrite metamaterial structure

This paper proposes a tunable zeroth-order resonator on a composite right/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. Based on the propagation theory of edge guided modes, the analysis procedure of this structure is introduced. The numerical results demonstrate the tunability of the resonant frequency by changing the DC bias magnetic field applied to the ferrite. In contrast to previous work, the proposed structure is easy to design and fabricate and does not require a chip component.     

Five-parameter crystallographic characteristics of the interfaces formed during ferrite to austenite transformation in a duplex stainless steel

The crystallography of interfaces in a duplex stainless steel having an equiaxed microstructure produced through the ferrite to austenite diffusive phase transformation has been studied. The five-parameter interface character distribution revealed a high anisotropy in habit planes for the austenite–ferrite and austenite–austenite interfaces for different lattice misorientations. The austenite and ferrite habit planes largely terminated on (1 1 1) and (1 1 0) planes, respectively, for the austenite–ferrite interfaces associated with Kurdjumov–Sachs (K–S) and Nishiyama–Wasserman (N–W) orientation relationships. This was mostly attributed to the crystallographic preference associated with the phase transformation. For the austenite–ferrite interfaces with orientation relationships which are neither K–S nor N–W, both austenite and ferrite habit planes had (1 1 1) orientations. Σ3 twin boundaries comprised the majority of austenite–austenite interfaces, mostly showing a pure twist character and terminating on (1 1 1) planes due to the minimum energy configuration. The second highest populated austenite–austenite boundary was Σ9, which tended to have grain boundary planes in the tilt zone due to the geometrical constraints. Furthermore, the intervariant crystallographic plane distribution associated with the K–S orientation relationship displayed a general tendency for the austenite habit planes to terminate with the (1 1 1) orientation, mainly due to the crystallographic preference associated with the phase transformation.     

Computer simulation of the carbon diffusivity in austenite

Tracer carbon diffusion in austenite is formulated in terms of a f.c.c. lattice gas model in which carbon interstitials repel at the distance of nearest neighbors. A Monte Carlo method is used to calculate the tracer carbon diffusivity as a function of composition and interaction energy. The computed diffusivities are discussed in relation to the experimentally determined diffusivities and the results of a model investigated by Parris and McLellan.     

钢铁材料中形变诱导相变超细化机理研究

通过计算机编程建立奥氏体相中12[1 1 0]刃位错、奥氏体相中非形变区和形变区奥氏体/铁 素体相界模型.用实空间的连分数方法计算了非形变区和形变区奥氏体/铁素体相界界面能， 计算了碳、氮及微合金元素在完整晶体及位错区引起的环境敏感镶嵌能，进而讨论形变过程 中铁素体形核的难易程度，碳、氮及合金元素在位错区的偏聚及析出与铁素体细化的关系. 计算结果表明：α-Fe易于在高密度位错区（形变带、亚晶界、晶界）形核，在奥氏体形变 过程中，就会大大提高α-Fe形核率，细化铁素体晶粒；碳、氮和微合金元素易于单独或共 同 关键词： 奥氏体/铁素体相界 刃位错 形变 晶粒细化     

Effect of prior austenite grain size on the formation of carbide-free bainite in low-alloy steel

ABSTRACT

Inconsistencies exist in literature regarding the effect of prior austenite grain size (PAGS) on the extent and kinetics of bainite transformation. Attempts have been made in the present work to address these issues in a low-alloy carbide-free bainitic steel using dilatometry, over a range of PAGS. The bainite transformation kinetics in the above-mentioned conditions have been analysed quantitatively using established kinetic model to extract information related to the transformation mechanisms in such conditions. Greater obstruction from grain boundaries in fine-grained austenite restricts sheaves of bainite to develop completely and thereby reduces the volume fraction of bainite in comparison with coarse-grained austenite. Initial nucleation rate of bainite transformation increases with decreasing PAGS due to an increase in the nucleation site density. However, the maximum nucleation rate decreases consistently with decreasing PAGS due to gradual reduction in the autocatalytic factor.     

铸造奥氏体不锈钢中铁素体与奥氏体位向关系及其对声衰减的影响

研究了铸造奥氏体不锈钢中铁素体与奥氏体位向关系及其对超声散射衰减的影响.利用电子背散射衍射技术表征了两相的晶体取向及其位向关系,基于真实的铁素体形貌建立了二维声传播各向异性模型并利用时域有限差分法进行了计算,分析了不同位向关系、铁素体形貌特征对声衰减系数的影响规律并进行了实验验证.结果表明：铸造奥氏体不锈钢奥氏体晶粒中散布着形状复杂的铁素体,典型铁素体形貌为条状和岛状;铁素体与奥氏体的位向关系以Kurdjumov-Sachs关系为主,少量满足Nishiyama-Wassermann关系.对声传播过程进行计算,发现两相位向关系和铁素体形貌协同作用影响超声波传播,在较高检测频率（15 MHz）下对散射衰减的影响不能忽略.结合“原位”实验对奥氏体<101>柱状晶粒的声衰减影响因素进行了定量分析,发现对于单一铸造奥氏体晶粒,晶粒内部取向不均匀性、奥氏体-铁素体位向关系以及奥氏体晶粒内铁素体形态都是超声散射衰减的主要原因.     

Effect of boundary heat flux on solidification in a forced liquid metal flow: a phase-field simulation

A phase-field model coupling with velocity field is employed to study the effect of boundary heat flux on the microstructure formation of a Ni-40.8%Cu alloy with liquid flow during the solidification, and an anti-trapping current is introduced to suppress the solute trapping due to the larger interface width used in simulations than a real solidifying material. The effect of the flow field coupling with boundary heat extractions on the microstructure formation as well as distributions of concentration and temperature fields are analyzed and discussed. The forced liquid flow can significantly affect the heat and solute diffusions, thus influencing morphology formation, concentration and temperature distributions during the solidification. The solute segregation and concentration diffusion are changed by boundary heat extractions, and the morphology, concentration and temperature distributions are significantly influenced by increasing the heat extraction, which relatively makes the effect of liquid flow constrained. By increasing the initial velocity of liquid flow, the lopsided rate of the primary dendrite arm is enlarged and the growth manner of dendrite arms gets changed, and the transition of the microstructure from dendrite to cellular moves to the large heat extraction direction. Therefore, there exists the competition between the heat flux, temperature gradient and forced liquid flow that finally determines the microstructure formation during directional solidification.     

Influence of environment and grain size on magnetic properties of nanocrystalline Mn–Zn ferrite

Nanocrystalline Mn_1−xZn_xFe₂O₄ (0.2?x?0.9) was prepared by mechanical alloying of the concerned oxide precursors and subsequent annealing in air and Ar atmosphere, respectively. Milling and annealing in air produces Zn-ferrites (ZnFe₂O₄) instead of Mn–Zn ferrites as MnO converts to higher oxides at higher oxygen partial pressure and fails to dissolve in the spinel phase. This is confirmed by careful quantitative X-ray diffraction analysis using Rietvelt profile matching and also by the non-saturating paramagnetic nature of the magnetization response with very low saturation level of these spinels milled and annealed in air. On the other hand, single-phase Mn–Zn ferrite results from the identical precursor oxide blend when milling and annealing are carried out under controlled (Ar) atmosphere. The average grain size of the as-milled and annealed powders, measured by Rietvelt refinement, varies between 6–8 and 14–18 nm, respectively. Further investigations performed with Mn_0.6Zn_0.4Fe₂O₄ reveal that a careful selection of annealing parameters may lead to an early superparamagnetic relaxation. Therefore, the blocking temperature can be significantly reduced through proper heat treatment schedule to ensure superparamagnetism and negligible hysteresis at low temperature.     

Terahertz power splitter based on ferrite photonic crystal

In this paper, we design a novel Y-junction power splitter which is optimized according to coupled mode theory. Two rods are added in the junction. One rod is a silicon rod and another one is a ferrite rod, the refractive index of which can be varied by adjusting the external magnetic field. So, it not only can split the power, but also controls the output energy of the two branches automatically. The transmission spectrum is calculated by finite difference time domain (FDTD) method, which shows that the output energy of the two branches is closely related to the frequency of the incident terahertz (THz) wave and the refractive index of the ferrite rod. The device is a good candidate for integrated optical circuit, the tuning rate of which is about a few microseconds.     

Fe-Pb合金凝固多相体系内偏析形成过程的三维数值模拟

基于Eulerian-Eulerian方法和流体体积技术,建立了三维多相流体动力学凝固模型,并将其与质量、动量、溶质和热焓守恒方程相耦合,对Fe-Pb合金侧向凝固过程进行了数值模拟.首先,分析了分布面积二次梯度((SPb))和浓度二次梯度((CPb))对偏析模式的影响,结果表明:液、气两相的流动相变使偏析模式表现为上端X形下端V形,X偏析由气相相变驱动力和多取向相变作用下的"散射"形成;ttc时,随(SPb)和(CPb)曲线降低,X偏析的下偏析角增大,上偏析角和V偏析角减小,Pb收得率增大,有利于获得含量稳定弥散的凝固组织.此外,还研究了液、气两相交互流动下通道偏析的形成机理,结果表明:通道偏析仅存在于流动-相变交互作用(ul·cl和ug·cg)为负值的区域,该区域的流动扰动抑制合金的局部凝固,促进偏析通道生长;流动-相变交互作用负值越小,偏析通道持续增长越稳定.模拟结果与实验结果相符合,验证了模型的准确性.     

Numerical simulation of quasisurface magnetostatic waves in a ferrite film with two magnetic channels

Quasisurface magnetostatic waves propagating in a ferrite film along two magnetized channels are simulated numerically. It is shown that the interaction between the channels is manifested differently, depending on the wavelength. In the long-wavelength region the interaction between the channels has a distributed character; in the short-wavelength region the interaction between the channels appears as if it takes place at their boundary. The magnetized region of the ferrite film between the channels behaves both as a conductor of the alternating field and as a medium with eigenmodes, so that under certain conditions the waveguide can be transformed into a three-channel structure. The dispersion curves of the magnetostatic wave modes of a two-channel waveguide lie in zones bounded by the dispersion curves of the corresponding modes of a one-channel waveguide of double width. As the gap between the channels increases, the dispersion curves of the odd modes shift toward shorter wavelengths, and those of the even modes shift toward longer wavelengths. Zh. Tekh. Fiz. 68, 91–96 (February 1998)     

Molecular dynamics simulation of the solidification of liquid gold nanowires

The solidification behavior of liquid gold nanowires with about 1.84 nm in diameter has been studied by using molecular dynamics simulation with an embedded atom potential. It is found the cooling rate has great effect on the final structure of the gold nanowires during solidification from liquid. With the decrease of cooling rates, the final structure of the gold nanowires varies from amorphous to crystalline via helical multi-shelled structure. The face-centered cubic structure of the gold nanowires is proven energetically the most stable form.     

Atomistic simulation of slow grain boundary motion

Existing atomistic simulation techniques to study grain boundary motion are usually limited to either high velocities or temperatures and are difficult to compare to realistic experimental conditions. Here we introduce an adapted simulation method that can access boundary velocities in the experimental range and extract mobilities in the zero driving force limit at temperatures as low as ～0.2T(m) (T(m) is the melting point). The method reveals three mechanistic regimes of boundary mobility at zero net velocity depending on the system temperature.