Cu-Co-Fe合金雾化合金液滴凝固过程研究*

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赵雷, 江鸿翔, AHMAD Tauseef, 赵九洲. Cu-Co-Fe合金雾化合金液滴凝固过程研究^* . 2015, 51(7): 883-888[Lei ZHAO, Hongxiang JIANG, Tauseef AHMAD, et al. STUDY OF SOLIDIFICATION FOR GAS-ATOMIZED DROPLET OF Cu-Co-Fe ALLOY[J]. AMS, 2015, 51(7): 883-888] 复制到剪切板

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Cu-Co-Fe合金雾化合金液滴凝固过程研究^*

赵雷^1,², 江鸿翔², AHMAD Tauseef², 赵九洲²

1 辽宁石油化工大学机械工程学院, 抚顺 113001

2 中国科学院金属研究所, 沈阳 110016

赵雷, 男, 1981年生, 讲师, 博士

收稿日期:2015-01-16

基金:*国家自然科学基金项目51271185,51031003和51471173资助;

摘要

对Cu-10%Co-10%Fe (质量分数)亚稳液态组元不混溶合金开展了气体雾化快速凝固实验, 制备了富Fe-Co相球形粒子均匀分布于基体Cu的复合粉末, 建立了Cu-Co-Fe合金雾化液滴冷却过程中的温度场、浓度场和液-液相变动力学控制方程, 研发了耦合合金热力学和相变动力学的模拟方法, 模拟分析了Cu-10%Co-10%Fe合金雾化液滴的凝固组织形成过程. 实验和模拟结果表明, 在气体雾化快速凝固条件下, 液-液相变过程中富Fe-Co相液滴Marangoni迁移和Ostwald熟化的影响很弱, 粉末中心绝大部分区域内富Fe-Co相粒子的空间分布均匀. 对于直径小于220 mm的Cu-10%Co-10%Fe合金粉末, 富Fe-Co相粒子的平均半径R_a和数量密度N与雾化粉末直径d之间符合指数关系.

关键词: Cu-Co-Fe合金; 液相分离; 快速凝固; 建模及模拟

中图分类号:TG111.4, TF83

STUDY OF SOLIDIFICATION FOR GAS-ATOMIZED DROPLET OF Cu-Co-Fe ALLOY

Lei ZHAO^1,², Hongxiang JIANG², Tauseef AHMAD², Jiuzhou ZHAO²

1 School of Mechanical Engineering, Liaoning Shihua University, Fushun 113001

2 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016

Correspondent: ZHAO Jiuzhou, professor, Tel: (024)23971918, E-mail:jzzhao@imr.ac.cn

Fund:Supported by National Natural Science Foundation of China (Nos.51271185, 51031003 and 51471173);

Abstract

Keyword: Cu-Co-Fe alloy; liquid phase decomposition; rapid solidification; modeling and simulation

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Cu-Co-Fe合金具有高强度、高导电和巨磁电阻效应等特性, 在电接触材料、集成电路引线框架材料、电线电缆材料和铁磁性材料等领域具有重要的潜在应用前景^[1,2]. 然而, 该合金存在亚稳液态组元不混溶温度区, 合金熔体冷却时发生液-液相变, 极易形成偏析严重的凝固组织^[3,4]. 近年来, Cu-Co-Fe合金体系常被作为一种研究具有亚稳液态组元不混溶温度区间合金凝固行为的模型合金^{[5,6,7,8,9,10,11,12,13,14]}. 以往研究工作主要集中在热力学上. Kim和Abbaschian^[5]测定了Cu-Co-Fe合金的液相线温度和亚稳液相分离温度, 发现当Co和Fe的含量在一定范围内时, 合金具有亚稳液态组元不混溶温度区. Cao和G?rler^[6]对Cu-Co-Fe合金进行了差热分析(DTA)实验, 测定了Cu组元的原子分数在10%~84%之间且Co和Fe原子比为1∶3, 1∶1和3∶1 时的液相线温度和亚稳液相分离温度. Curiotto等^[7]采用差示扫描量热法(DSC)测定了Cu-Co-Fe合金液相线温度和亚稳液相分离温度. Munitz等^[8]对Cu-Co-Fe合金体系的热力学参数进行优化, 并计算了亚稳液相分离温度. Turchanin等^[9]利用量热法研究了Cu-Co-Fe合金的液相混合焓, 并利用计算相图方法评价了该体系的热力学参数. Bamberger等^[10]、Wang等^[11]和Palumbo等^[12]也分别对该体系的热力学参数进行了优化和评价, 并计算了相图. 在动力学上, Munitz等^[8]对Cu-Co-Fe合金开展了深过冷凝固实验, 研究了过冷度和冷却速率对合金凝固组织的影响, 结果表明, 当过冷度较高时合金发生了液-液相变, 富Fe-Co相形貌随过冷度增大的变化顺序为: 枝晶组织→枝晶+球状的混合组织→球状组织. Munitz和Abbaschian^[13]利用电子束表面熔化方法研究了高冷却速率下Cu-Co-Fe合金的液-液相分离行为. 代富平等^[14]利用落管研究了Cu-Co-Fe合金的液-液相分离过程. 研究表明, 快速凝固技术可以使Cu-Co-Fe合金快速通过液态组元不混溶区, 能有效地抑制液相分离和偏析组织的形成.

通常, 液-液相变过程中的组织演变是弥散相液滴形核、长大、粗化及空间迁移等共同作用的结果, 影响因素多, 且各影响因素间又相互作用, 十分复杂, 仅通过实验手段很难深入探索其凝固过程, 计算机模拟可以有效地揭示难混溶合金的凝固机理^[15,16]. 本工作以Cu-10%Co-10%Fe合金为对象, 用气体雾化快速凝固技术和计算机模拟相结合的方法, 研究快速凝固条件下Cu-10%Co-10%Fe合金的组织形成过程.

1 实验方法

以质量分数大于或等于99.9%的Cu, Co和Fe为原料配制合金, 成分为Cu-10%Co-10%Fe (质量分数). 实验过程如下: 首先将原料在KGPS100/2.5真空中频感应炉中加热到1420 ℃, 保温15~20 min, 确保组元完全互溶, 形成均一熔体; 然后用N₂气体将由安放于坩埚底部导流管流出的合金熔体雾化成液滴, 实现快速冷却凝固, 雾化气体压力为3 MPa; 最后对雾化粉末进行筛分、镶嵌和抛光处理, 利用Axiovert 200MAT光学显微镜(OM)和S-3400N扫描电子显微镜(SEM)观察凝固组织, 并进行能谱(EDS)分析. 利用SISC IAS V8.0定量金相分析软件对微观组织中第二相粒子尺寸和分布进行统计分析.

2 结果与分析

2.1 显微组织

图1为不同直径Cu-10%Co-10%Fe合金粉末的显微组织和数量密度分布. 由Cu-Co-Fe体系的垂直截面相图^[5]和EDS分析(图2)可知, 深色第二相为富Fe-Co相, 浅色基体为富Cu相. 当雾化粉末直径小于220 μm时, 粉末的显微组织由富Fe-Co相球形粒子和富Cu基体相组成, 随着粉末尺寸的增加, 富Fe-Co相球形粒子尺寸逐渐增大. 由文献[5]可知, 当Cu-10%Co-10%Fe合金熔体的过冷度大于24 K时, 雾化液滴发生液-液相变, 富Fe-Co相液滴在富Cu液相中形核、长大. 由于Cu-Co-Fe合金体系中组元互溶温度线(binodal line)位于液相线(liquidus)下方, 因此, 在亚稳液-液相变过程中, 富Fe-Co相小液滴形成后即处于过冷状态, 倾向于凝固. 如果雾化液滴的冷却速率足够快, 以致在雾化液滴冷却通过组元不混溶区时富Fe-Co相小液滴尚未凝固, 则这些富Fe-Co相小液滴将在包晶反应温度以下凝固, 形成富Fe-Co相球形粒子, 雾化液滴凝固后将呈现图1所示的凝固组织. 此外, 富Fe-Co相球形粒子在粉末中基本呈现均匀分布, 只是在除雾化粉末表面很小的区域内富Fe-Co相球形粒子数量密度减少(图1b和d).

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	Fig.1 SEM images of Cu-10%Co-10%Fe powders with diameters of 88~100 mm (a), 125~150 μm (b), 200~220 mm (c) and distribution of number density (N) of Fe-Co-rich phase particles along radial direction (r) of the Cu-10%Co-10%Fe powder with diameter of 125~150 mm (d)图1 不同直径Cu-10%Co-10%Fe合金粉末的SEM像和数量密度分布

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	Fig.2 EDS analysis of light (a) and dark (b) phases in Cu-Co-Fe alloy图2 Cu-Co-Fe合金的EDS分析

2.2 雾化液滴凝固过程模型

2.2.1 模型建立在凝固过程中, 雾化液滴表面热量通过与周围气体环境进行对流换热, 雾化液滴内部热量通过扩散和弥散相液滴运动进行传输, 雾化液滴温度场满足:

(1)	$\begin{matrix} ? ? (k ? T) + Q_{S / L} - Q_{d} - \\ \frac{4 π}{3} ? ? [\int_{0}^{\infty} u_{M} F (ρ_{β} C_{P}^{β} - ρ_{m} C_{P}^{m}) T R^{3} d R] = ρ C_{P} \frac{? T}{? t} \end{matrix}$

式中, $\begin{matrix} T \end{matrix}$ 为热力学温度; $\begin{matrix} ρ \end{matrix}$ , $\begin{matrix} C_{P} \end{matrix}$ 和 $\begin{matrix} k \end{matrix}$ 分别为合金密度、比热容和热导率; $\begin{matrix} ρ_{m} \end{matrix}$ 和 $\begin{matrix} ρ_{β} \end{matrix}$ 分别为基体和弥散相的密度; $\begin{matrix} C_{P}^{m} \end{matrix}$ 和 $\begin{matrix} C_{P}^{β} \end{matrix}$ 分别是基体和弥散相的比热容; $\begin{matrix} Q_{S / L} \end{matrix}$ 为固/液界面上凝固潜热释放速率; $\begin{matrix} Q_{d} = \end{matrix}$ $\begin{matrix} h (T_{d s} - T_{g}) \end{matrix}$ 为液滴表面对流换热速率^[17], 其中, $\begin{matrix} T_{d s} \end{matrix}$ 为雾化液滴的表面温度, $\begin{matrix} T_{g} \end{matrix}$ 为雾化气体的温度^[18], $\begin{matrix} h = k_{g} (2 + 0.6 \sqrt{R e} ? \sqrt[]{P r}) / d \end{matrix}$ 是雾化液滴表面与雾化气体间的界面换热系数^[17], $\begin{matrix} d \end{matrix}$ 为雾化液滴的直径, $\begin{matrix} k_{g} \end{matrix}$ 为雾化气体的热导率, $\begin{matrix} P r \end{matrix}$ 为气体的Prandtl数, $\begin{matrix} R e \end{matrix}$ 为Reynolds数; $\begin{matrix} u_{M} \end{matrix}$ 为由温度梯度导致的弥散相液滴的Marangoni迁移速度, $\begin{matrix} R \end{matrix}$ 为弥散相液滴的半径, $\begin{matrix} F \end{matrix}$ 为弥散相液滴的半径分布函数, $\begin{matrix} F (R, r, t) d R \end{matrix}$ 给出 $\begin{matrix} t \end{matrix}$ 时刻、位置 $\begin{matrix} r \end{matrix}$ 处单位体积熔体内半径在 $\begin{matrix} R \end{matrix}$ 到 $\begin{matrix} R + d R \end{matrix}$ 范围内弥散相液滴的数量. 温度场方程左边第1项表示热传导的贡献, 第2项表示固/液界面上凝固潜热释放的影响, 第3项表示表面对流换热的影响, 第4项表示弥散相液滴迁移导致的热量传输; 温度场方程右边为熔体温度随时间的变化.

合金液-液相变过程中溶质通过扩散和弥散相液滴的空间运动进行传输. 根据溶质守恒关系, 组元i的浓度场满足下面偏微分方程:

(2)	$\begin{matrix} ? ? [φ_{l} D_{i} ? S_{i}] - \frac{4 π}{3} ? ? [\int_{0}^{\infty} u_{M} F (C_{β}^{i} - C_{m}^{i}) R^{3} d R] = \frac{? C_{m i x}^{i}}{? t} \end{matrix}$

式中, $\begin{matrix} S_{i} = C_{m}^{i} - C_{m e}^{i} \end{matrix}$ 为基体熔体中组元i的过饱和度, $\begin{matrix} C_{m}^{i} \end{matrix}$ 为基体熔体中溶质i的摩尔浓度, $\begin{matrix} C_{m e}^{i} \end{matrix}$ 为溶质i在基体熔体中的平衡摩尔浓度, $\begin{matrix} C_{β}^{i} \end{matrix}$ 为弥散相液滴中溶质i的摩尔浓度, $\begin{matrix} φ_{l} \end{matrix}$ 为基体液相的体积分数, $\begin{matrix} D_{i} \end{matrix}$ 为溶质i的扩散系数, $\begin{matrix} C_{m i x}^{i} \end{matrix}$ 为合金(两液相混合物)中组元i的浓度. 浓度场方程左边第1项描述溶质原子在基体中扩散, 第2项描述弥散相液滴运动对浓度场的影响; 等式的右边描述合金浓度随时间的变化.

在弥散相液滴形核、扩散长大以及空间运动等因素共同作用下, 弥散相液滴半径分布函数满足如下连续方程:

(3)	$\begin{matrix} \frac{? F}{? t} + ? ? (u_{M} F) + \frac{?}{? R} (v F) = {\frac{? I}{? R}\|}_{R = R^{*}} \end{matrix}$

式中, $\begin{matrix} v \end{matrix}$ 和 $\begin{matrix} I \end{matrix}$ 分别为弥散相液滴的扩散长大速度和形核率^[19,20], $\begin{matrix} R^{*} \end{matrix}$ 为弥散相液滴的临界形核半径. 方程左侧第1项描述弥散相液滴分布函数随时间的变化, 第2项描述弥散相液滴运动对其分布函数的影响, 第3项描述弥散相液滴长大对其分布函数的影响; 方程右侧为源项, 描述弥散相液滴形核的影响. 由于在雾化液滴快速冷却过程中弥散相液滴间的碰撞凝并作用较弱^[21], 因此计算中忽略了弥散相液滴间碰撞凝并的影响.

采用有限体积法对温度场、浓度场和弥散相液滴半径分布函数连续性方程进行离散、数值求解, 并与Cu-Co-Fe热力学相图计算程序相耦合, 可模拟Cu-Co-Fe合金亚稳液-液相变过程.

2.2.2 计算中所用的主要物性参数模拟采用文献[9,22~25]中给出的有关Cu-Co-Fe合金系的热力学数据计算相图, 计算中采用液-液界面能的通用表达式^[26]:

(4)	$\begin{matrix} σ = σ_{0} {(1 - \frac{T}{T_{C}})}^{1.26} \end{matrix}$

式中, $\begin{matrix} σ \end{matrix}$ 为液-液界面能; $\begin{matrix} T_{C} \end{matrix}$ ≈(1620±10) K, 为Cu-10%Co-10%Fe合金的临界温度; 拟合计算表明, 常数 $\begin{matrix} σ_{0} \end{matrix}$ =1.78 J/m².

液态金属的动力学黏度随温度的变化关系满足下式^[27]:

(5)	$\begin{matrix} η = η_{0} e x p (\frac{Q}{R_{g} T}) \end{matrix}$

式中, $\begin{matrix} η_{0} \end{matrix}$ 为常数, Q为流动活化能, $\begin{matrix} R_{g} \end{matrix}$ 为气体常数. 富Cu液相的动力学黏度近似采用纯Cu的动力学黏度, 富Fe-Co液相的动力学黏度近似采用纯Fe和纯Co的动力学黏度的算术平均值.

溶质的扩散系数可以通过Stokes-Einstein方程与基体熔体的黏度 $\begin{matrix} η_{m} \end{matrix}$ 相联系, Fe和Co溶质原子在液相Cu基体中的扩散系数 $\begin{matrix} D_{i}^{} \end{matrix}$ 可如下计算^[28]:

(6)	$\begin{matrix} D_{i}^{} = \frac{k_{B} T}{6 π η_{m} r_{i}} \end{matrix}$

式中, $\begin{matrix} k_{B} \end{matrix}$ 是Boltzmann常数; i=Fe, Co; $\begin{matrix} r_{i} \end{matrix}$ 为Fe和Co的离子半径, 2种组元的离子半径分别取为 $\begin{matrix} r_{F e} = 0.055 \end{matrix}$ nm和 $\begin{matrix} r_{C o} = 0.53 \end{matrix}$ nm. 雾化气体的初速度取为300 m/s^[29].

2.2.3 模拟与讨论根据实验条件模拟计算了雾化液滴的快速凝固过程, 图3为直径为138 μm雾化液滴中心处温度和冷却速率随时间的变化关系. 可见, 雾化液滴冷却速率的变化与雾化液滴表面对流换热系数的变化规律一致.

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Fig.3 Variation of temperature (T) and cooling rate at the center of an atomized Cu-Co-Fe droplet of 138 μm in diameter with time (t) (The inset shows the variation of the convective heat-transfer coefficient (h) at the surface of an atomized Cu-Co-Fe droplet of 138 mm in diameter with time)图3 直径为138 mm的 Cu-Co-Fe雾化液滴中心处温度(T)和冷却速率随时间(t)的变化关系

图4给出了雾化液滴中心处液-液相转变的相变驱动力、富Fe-Co相液滴的形核率和数量密度随时间变化关系. 当驱动力达到一临界值时, 富Fe-Co相液滴开始形核, 发生亚稳液-液相变. 形核过程持续时间很短. 形核期间, 富Fe-Co相液滴数量密度迅速上升、平均半径缓慢增大(图5), 形核刚结束时基体熔体的过饱和度仍然很高, 富Fe-Co相液滴迅速长大, 此后, 随过饱和度的降低, 富Fe-Co相液滴长大速度逐渐减小.

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	Fig.4 Number density (N), nucleation rate (I) and driving force (DG) for nucleated Fe-Co-rich phase droplets at the center of an atomized drop of 138 μm in diameter vs time图4 直径为138 μm的雾化液滴中心处富Fe-Co相液滴的数量密度(N)、形核率(I)和形核驱动力(DG)随时间的变化关系

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	Fig.5 Average radius (R_a) of Fe-Co-rich phase droplets at the center of an atomized drop with different diameters vs time图5 不同直径雾化液滴中心处富Fe-Co相液滴的平均半径(R_a)随时间的变化关系

图6给出了直径为138 μm雾化粉末中富Fe-Co相粒子平均半径和数量密度沿粉末径向位置的变化曲线. 由于雾化液滴表面区域内温度梯度较大, 富Fe-Co相液滴Marangoni迁移作用较强, 且弥散相液滴迁移后得不到补充, 因此, 富Fe-Co相液滴持续减少, 最终导致粉末表面富Fe-Co相粒子数量密度减少(图1b); 在雾化液滴其它区域内, 在弥散相液滴形核结束后液滴的数量密度几乎不再变化, 这也表明快凝条件下富Fe-Co相液滴的Ostwald熟化作用很弱. 粉末中心绝大部分区域内富Fe-Co相粒子的空间分布非常均匀. 通过对比图5和6中计算结果和实验统计结果, 可见, 实验和模拟结果吻合得很好, 表明所建模型的合理性和有效性.

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	Fig.6 Variations of average radius and number density of Fe-Co-rich phase particles along the radial direction r in an atomized powder with diameter of 138 μm图6 直径为138 mm的雾化粉末中富Fe-Co相粒子的平均半径和数量密度随径向位置r变化的曲线

图7为富Fe-Co相液滴最大形核率 $\begin{matrix} I_{m a x} \end{matrix}$ 随形核阶段冷却速率的变化关系. 雾化液滴的尺寸越小, 形核阶段雾化液滴的冷却速率越大, 熔体获得的过冷度越大, 富Fe-Co相液滴的最大形核率 $\begin{matrix} I_{m a x} \end{matrix}$ 和液滴的数量密度越大, 液滴的平均半径越小. $\begin{matrix} I_{m a x} \end{matrix}$ 与形核阶段冷却速率 $\begin{matrix} {\dot{T}}_{N u c} \end{matrix}$ 符合 $\begin{matrix} I_{m a x} = B {\dot{T}}_{N u c}^{2.18} \end{matrix}$ 的指数关系, B为常数. 进一步分析表明, 当雾化粉末直径小于220 mm时, 富Fe-Co相粒子的平均半径R_a和数量密度 $\begin{matrix} N \end{matrix}$ 与雾化粉末直径d之间分别满足 $\begin{matrix} R_{a} = C_{1} d^{0.71} \end{matrix}$ 和 $\begin{matrix} N = C_{2} d^{- 2.1} \end{matrix}$ 的指数关系(图8), 式中, C₁和C₂为常数. 由这2个关系式可得弥散相体积分数 $\begin{matrix} φ \propto N R_{a}^{3} \approx \end{matrix}$ 常数, 进一步证明模型的有效性.

	Figure Option View Download New Window
	Fig.7 Relationship between the maximum nucleation rate (I_max) of Fe-Co-rich phase droplets and the cooling rate during the nucleation period (B—constant)图7 富Fe-Co相液滴的最大形核率I_max随形核阶段冷却速率的关系

	Figure Option View Download New Window
	Fig.8 Variation of average radius and number density of Fe-Co-rich particles vs powder diameter (d)图8 富Fe-Co相粒子的平均半径和数量密度随雾化粉末直径(d)变化关系

3 结论

(1) 对Cu-10%Co-10%Fe亚稳液态组元不混溶合金开展了气体雾化快速凝固实验, 建立了Cu-Co-Fe合金雾化液滴亚稳液-液相变过程的温度场、浓度场和液-液相变动力学控制方程, 并实现了合金热力学和相变动力学的耦合计算. 实验和模拟结果吻合得很好, 验证了所建模型的合理性.

(2) 在气体雾化快速凝固条件下, Cu-10%Co-10%Fe合金能够过冷至亚稳液态组元不混溶温度区而发生液-液相变. 当雾化粉末直径小于220 mm时, 富Fe-Co相液滴的凝固发生在包晶反应温度以下, 形成富Fe-Co相以球形粒子形式均匀分布于Cu基体的复合粉末组织. 雾化粉末的尺寸越小, 富Fe-Co相粒子的平均半径越小. 富Fe-Co相粒子的平均半径R_a和数量密度 $\begin{matrix} N \end{matrix}$ 与雾化粉末直径d之间满足指数关系.

(3) 气体雾化快速凝固条件下Cu-10%Co-10%Fe合金雾化液滴除表面很小的区域外, 弥散相液滴形核后液滴的数量密度几乎不变, 富Fe-Co相液滴Marangoni迁移和Ostwald熟化作用很小, 粉末中心绝大部分区域内富Fe-Co相粒子的空间分布非常均匀.

参考文献

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2000

2.726

0.0

... Cu-Co-Fe合金具有高强度、高导电和巨磁电阻效应等特性, 在电接触材料、集成电路引线框架材料、电线电缆材料和铁磁性材料等领域具有重要的潜在应用前景^[1,2] ...

1992

7.728

0.0

2009

0.0

1.541

Dai

F P

, Cao

C D

, Wei

B B

. Chin Sci Bull, 2009;54: 402

(代富平, 曹崇德, 魏炳波. 科学通报, 2009;54: 402)

三元Cu₅₀Fe_37.5Co_12.5包晶合金液滴在自由落体过程中发生亚稳液相分离, 主要形成由L₁(Cu)和L₂(Fe,Co)两相构成的壳核组织. 在测定固相面和液相面温度以及液相分离临界过冷度的基础上分析了壳核组织形成机制, 发现分离两液相的界面能随温度降低而增大, 合金液滴沿着半径方向从内向外存在着由小变大的温度梯度. 作用于L₂(Fe,Co)相上的Marangoni力(F_M)随其尺寸增加而增大, L₂(Fe,Co)相小液滴在F_M力的作用下从外向内迁移过程中逐渐粗化, 同时发生碰撞和凝并, 进而形成壳核结构的凝固组织.

... 然而, 该合金存在亚稳液态组元不混溶温度区, 合金熔体冷却时发生液-液相变, 极易形成偏析严重的凝固组织^[3,4] ...

2005

0.548

0.835

, Zhao

J Z

. Acta Metall Sin, 2005;41: 407

(何杰, 赵九洲. 金属学报, 2005;41: 407)

Fine powders of the Cu-Fe alloy were manufactured by using thehigh-pressure gas atomization technique. The study of the powdermicrostructures indicated that the size and concentration of theatomized-droplets play important roles in the microstructureevolution. A smaller atomized-droplet has a finer dispersedmicrostructure. Alloys with composition close to the criticalcomposition of the alloy system are relatively easy to be undercooledinto the miscibility gap. The formation of Fe--poor layer on the surfaceof powder is mainly caused by two reasons. One is the Fe-rich droplets'Marangoni migration towards the center of the atomized-droplet due tothe radial temperature gradient, and the other is the repulsive effectof the advancing solid-liquid interface on the Fe-rich droplets.

Institute of Metal Research; The Chinese Academy of Sciences; Shenyang 110016

采用高压气体雾化技术制备了Cu--Fe合金粉末, 并对粉末的组织进行了观察分析。结果表明, 雾化液滴的尺寸与合金成分影响凝固组织的演变过程。雾化液滴尺寸越小, 其内部富Fe相越弥散；Fe含量越接近亚稳液态组元不混溶区域的临界成分, 越容易发生液--液相变。分析表明, 富Fe液滴的Marangoni迁移和富Fe粒子与固--液界面之间的相互作用是导致粉末外部形成贫Fe层的主要原因。

... 然而, 该合金存在亚稳液态组元不混溶温度区, 合金熔体冷却时发生液-液相变, 极易形成偏析严重的凝固组织^[3,4] ...

2000

0.0

Kim

D I

, Abbaschian

. J Phase Equilib, 2000;21: 25

The metastable liquid-phase separation (MLPS) in the Cu-Co-Fe system was investigated using an electromagnetic levitation melting and solidification technique. It was found that when ternary alloys containing more than 10wt.% (12 at.%)Co and 10wt.% (11at.%)Fe were undercooled below a certain temperature, T _sep, the homogeneous melt separated into two liquid phases. In alloys containing more than 54 to 57wt.% (49 to 54at.%)Cu (depending on the Co and Fe content), the phase separation generally appeared as dispersed (Fe, Co)-rich droplets (L₁) in a Cu-rich matrix, whereas for alloys containing less copper, the separation resulted in Cu-rich droplets (L₂) in a (Fe, Co)-rich matrix. The metastable liquid miscibility gap boundary of the Cu-Co-Fe ternary was determined using the measured T _sep and the composition of the separated phases. The ternary liquid-phase separated boundaries were found to be consistent with a cross-sectioned phase diagram in which one axis represents pure copper and the other Fe + Co.

1.Department of Materials Science and Engineering, Kunsan National University, 573-701 Kunsan, Chollabukdo, Korea 2.Department of Materials Science and Engineering, University of Florida, 32611 Gainesville, FL

... 近年来, Cu-Co-Fe合金体系常被作为一种研究具有亚稳液态组元不混溶温度区间合金凝固行为的模型合金^[5-14] ...

... Kim和Abbaschian^[5]测定了Cu-Co-Fe合金的液相线温度和亚稳液相分离温度, 发现当Co和Fe的含量在一定范围内时, 合金具有亚稳液态组元不混溶温度区 ...

... 由Cu-Co-Fe体系的垂直截面相图^[5]和EDS分析(图2)可知, 深色第二相为富Fe-Co相, 浅色基体为富Cu相 ...

2005

0.924

0.432

Cao

C D

, G?rler

G P

. Chin Phys Lett, 2005;22: 482

The metastable liquid--liquid phase separation in undercooled Fe--Co--Cu ternary alloy melts (X_Cu=0.10--0.84; X_Co:X_Fe=1:3, 1:1 and 3:1) is investigated by differential thermal analysis in combination with glass fluxing technique. In almost every case, the undercooling of the homogeneous alloy melt was sufficient to reach the boundary line of the submerged miscibility gap. The differential-thermal-analysis signals indicate that this separation into a (Fe,Co)-rich liquid phase L₁ and a Cu-rich liquid L₂ is exothermic and proceeds until the rapid solidification of the L₁ phase occurs. At a given Cu concentration and with the increase of Co content, the phase separation temperatures decrease monotonically between the corresponding values of the boundary systems Fe--Cu and Co--Cu. The boundary lines of the miscibility gap, which are determined for the three quasi-binary cross-sections of the (Fe,Co)--Cu alloy system, show remarkably flat domes. The occurrence of the liquid phase separation shows an evident influence on the subsequent γ-Fe(Co,Cu)→α-Fe(Co, Cu) solid phase transformation.

1Department of Applied Physics, Northwestern Polytechnical University, Xi’an 710072 2Institut für Raumsimulation, DLR, D-51170Köln, Germany

... Cao和G?rler^[6]对Cu-Co-Fe合金进行了差热分析(DTA)实验, 测定了Cu组元的原子分数在10%~84%之间且Co和Fe原子比为1∶3, 1∶1和3∶1 时的液相线温度和亚稳液相分离温度 ...

2008

2.305

0.0

Curiotto

, Battezzati

, Johnson

, Palumbo

, Pryds

. J Mater Sci, 2008;43: 3253

Cu–Co–Fe alloys undercooled below a certain temperature display demixing of the liquid, followed by coagulation before dendritic solidification. In this article high temperature phase equilibria in Cu–Co–Fe samples have been precisely determined by DSC. Special attention has been paid to the liquid–liquid phase separation and on its effect on the formation of microstructures. The measured transformation temperatures have also been used to update the description of the ternary phase diagram.

1.Università di Torino Dipartimento di Chimica IFM, Centro di Eccellenza NIS Via Giuria 9 10125 Torino Italy 2.CINaM-CNRS, Campus de Luminy Case 913 13288 Marseille France 3.University of Copenhagen Niels Bohr Institute, Nanoscience Centre Copenhagen Denmark 4.Risoe National Laboratory Materials Research Department Frederiksborgvej 399 DK-4000 Roskilde Denmark 5.Risoe National Laboratory Fuel Cell and Solid State Chemistry Department Frederiksborgvej 399 DK-4000 Roskilde Denmark

... Curiotto等^[7]采用差示扫描量热法(DSC)测定了Cu-Co-Fe合金液相线温度和亚稳液相分离温度 ...

2006

2.305

0.0

Munitz

, Bamberger

A M

, Wannaparhun

, Abbaschian

. J Mater Sci, 2006;41: 2749

The effects of supercooling and cooling rate on the microstructure of ternary Cu–Fe–Co alloys were investigated. Electromagnetic levitation was used to supercool the liquids down by 180 K. Alloys with 11 at.% Cu and less than 19 at.% Fe contained fcc (Fe, Co) and fcc Cu phases; those with 19 to 23 at.% Fe contained bcc (Fe, Co), fcc (Fe, Co) and fcc Cu; those with more than 23 at.% Fe contained bcc (Fe, Co) and fcc Cu. The primary dendrites contained 10 to 20 at.% Cu, with Fe and Co contents depending on the alloy composition. Supercooling the melt below a certain temperature resulted in metastable separation of the melt into two liquids, one (Co + Fe)-rich, the other Cu-rich. The metastable phase separation temperatures and the two liquid compositions were determined experimentaly, and compared with calculated ones. Isothermal cross-sections at various temperatures were constructed for stable and metastable cases based on thermodynamic and experimental data of the Cu–Co, Cu–Fe, and Co–Fe systems. A peritectic reaction for the ternary alloys was found at approximately 1100°C.

1.Nuclear Research Center-Negev P.O.Box 9001 Beer-Sheva Israel 2.Materials Science and Engineering, Technion Technion City, Haifa Israel 3.University of Florida Department of Materials Science and Engineering Gainesville Florida 32611 USA 4.University of California College of Engineering Riverside CA 92521

... Munitz等^[8]对Cu-Co-Fe合金体系的热力学参数进行优化, 并计算了亚稳液相分离温度 ...

... 在动力学上, Munitz等^[8]对Cu-Co-Fe合金开展了深过冷凝固实验, 研究了过冷度和冷却速率对合金凝固组织的影响, 结果表明, 当过冷度较高时合金发生了液-液相变, 富Fe-Co相形貌随过冷度增大的变化顺序为: 枝晶组织→枝晶+球状的混合组织→球状组织 ...

2011

0.202

0.0

Turchanin

M A

, Dreval

L A

, Abdulov

A R

, Agraval

P G

. Powder Metall Met Ceram, 2011;50: 98

The mixing enthalpies of ternary Cu–Fe–Co liquid alloys are studied by the calorimetric method at 873 K and x _Co = 0–0.55. Thermodynamic assessments of the Fe–Co and Cu–Fe–Co systems are carried out with the CALPHAD method. A set of self-consistent thermodynamic parameters of the phases is obtained using data on the mixing enthalpies established in this study and published information on phase transformations. Isothermal and vertical sections of the phase diagram, liquidus and solidus surfaces, and metastable miscibility gap for overcooled liquid alloys are calculated. The undercooling degrees for the metastable liquid phase separation and temperature–composition ranges of the formation of the supersaturated solid solutions during the liquid quenching have been assessed.

1.Donbass State Mechanical Engineering Academy, Kramatorsk, Ukraine

... Turchanin等^[9]利用量热法研究了Cu-Co-Fe合金的液相混合焓, 并利用计算相图方法评价了该体系的热力学参数 ...

2002

1.394

0.0

Bamberger

, Munitz

, Kaufman

, Abbaschian

. Calphad, 2002;26: 375

Abstract

The thermodynamic description of the Cu-Co-Fe system was modified on the basis of experimental data obtained by electromagnetic levitation. Using the modified database, the solidus and liquidus temperatures were calculated. Very good agreement was obtained between the calculated and experimental data. The compositions of the metastable miscibility gap in the liquid were found to agree well with the observed values.

... Bamberger等^[10]、Wang等^[11]和Palumbo等^[12]也分别对该体系的热力学参数进行了优化和评价, 并计算了相图 ...

2002

0.0

Wang

C P

, Liu

X J

, Ohnuma

, Kainuma

, Ishida

. J Phase Equilib, 2002;23: 236

1.Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 02, 980-8579 Sendai, Japan

... Bamberger等^[10]、Wang等^[11]和Palumbo等^[12]也分别对该体系的热力学参数进行了优化和评价, 并计算了相图 ...

2006

1.394

0.0

Palumbo

, Curiotto

, Battezzati

. Calphad, 2006;30: 171

Abstract

The binary Co–Cu and the ternary Co–Cu–Fe systems have been optimized using the CALPHAD approach. Experimental data that have appeared recently in the literature have been used to improve the description of the metastable miscibility gap on both binary and ternary liquid phases. In the Co–Cu–Fe system, ternary parameters have been obtained to properly describe the miscibility gap. A significant improvement with respect to previous thermodynamic descriptions has been achieved. A set of model parameters for the liquid, f.c.c., and b.c.c. phases is given.

... Bamberger等^[10]、Wang等^[11]和Palumbo等^[12]也分别对该体系的热力学参数进行了优化和评价, 并计算了相图 ...

1998

2.305

0.0

... Munitz和Abbaschian^[13]利用电子束表面熔化方法研究了高冷却速率下Cu-Co-Fe合金的液-液相分离行为 ...

2007

0.0

... 近年来, Cu-Co-Fe合金体系常被作为一种研究具有亚稳液态组元不混溶温度区间合金凝固行为的模型合金^[5-14] ...

... 代富平等^[14]利用落管研究了Cu-Co-Fe合金的液-液相分离过程 ...

2010

0.845

1.101

Zhou

F M

, Sun

D K

, Zhu

M F

. Acta Phys Sin, 2010;59: 3394

(周丰茂, 孙东科, 朱鸣芳. 物理学报, 2010;59: 3394)

A two-dimensional (2D) lattice Boltzmann method (LBM) model was developed to simulate liquid-liquid phase separation of monotectic alloys, which is controlled by the diffusive growth, the collisions and coagulations, and the Ostwald ripening of the minority liquid droplets. The present model combines the features of the multiphase flow model proposed by Shan-Chen and the mesoscopic interparticle potentials developed by Oin. In addition, a source term is introduced in the LB evolution equations to account for the phase transformation. The proposed LBM model was applied to simulate single droplet growth, coagulation of two droplets and multi-droplet growth during the liquid-liquid phase separation process of a monotectic alloy. The simulation shows that the single droplet growth in the two-liquid phase is controlled by diffusion and that the initial nonequilibrium composition approaches to equilibrium. The coagulation velocity of two droplets is influenced by surface tension, which is in accordance with the trend of the analytical prediction. It is found that the liquid-liquid phase separation process is obviously impacted by the collisions and coagulations and the Ostwald ripening of the droplets.

东南大学江苏省先进金属材料高技术研究重点实验室,南京 211189

本文建立了一个模拟在弥散相液滴的扩散长大、碰撞凝并和Ostwald熟化等因素的作用下偏晶合金液-液相分离过程的二维格子玻尔兹曼方法 (lattice Boltzmann method, LBM) 模型.该模型结合了Shan-Chen的两相流模型和Qin的介观粒子相互作用势模型的优点，并在LB演化方程中引入了反映相变的源项.应用该模型模拟研究了偏晶合金液-液相分离过程中单液滴的生长、两液滴的合并和多液滴的生长规律.结果表明在两液相区中第二相单个液滴的生长是一个通过扩散从非平衡态到平衡态过渡的过程.两液滴合并

... 通常, 液-液相变过程中的组织演变是弥散相液滴形核、长大、粗化及空间迁移等共同作用的结果, 影响因素多, 且各影响因素间又相互作用, 十分复杂, 仅通过实验手段很难深入探索其凝固过程, 计算机模拟可以有效地揭示难混溶合金的凝固机理^[15,16] ...

2007

0.548

0.835

Cui

H B

, Guo

J J

, Su

Y Q

, Wu

S P

, Li

X Z

, Fu

H Z

. Acta Metall Sin, 2007;43: 907

(崔红保, 郭景杰, 苏彦庆, 吴士平, 李新中, 傅恒志. 金属学报, 2007;43: 907)

Cahn-Hilliard equation coupling with thermodynamic data is solved by Fourier transformation spectrum method due to the high efficiency and accuracy to simulate particle growth and Ostwald ripening for Cu-Pb monotectic alloy at the isothermal condition. The simulation results show that particle growth and Ostwald ripening for specific Cu-Pb monotectic alloy can be realized by the adjustment of gradient coefficient and mobility ratio. The growth of singular nucleated particles in a supersaturated matrix depends on the adjustment of free energy function and the smaller gradient coefficient, the more distinct steepness of concentration profile is. Growth rate of particle radius is in good agreement with the well accepted Zener’s law. Size distribution of reduced particle radius is computed and the peak of radius distribution changes from approaching the average radius to exceeding it.

哈尔滨工业大学材料科学与工程学院

采用计算效率和计算精度较高的Fourier变换谱分析方法求解Cahn-Hilliard相场方程, 并耦合热力学数据, 对Cu-Pb过偏晶合金在等温情况下液相分离过程中的颗粒生长和Ostwald 熟化进行了模拟研究. 结果表明, 合金体系中两液相区中的第二相颗粒生长和Ostwald 熟化过程可以通过调节能量梯度系数和迁移率系数实现.在过饱和基体中第二相单个颗粒生长的计算结果表明, 颗粒生长的扩散过程主要是系统自由能作用的结果, 能量梯度系数γ对颗粒与基体之间的浓度梯度起调节作用.随着γ的减小, 两液相之间的浓度梯度增大, 颗粒轮廓线的斜率增加. 颗粒半径的生长速率与经典的Zener理论良好吻合. 模拟了Cu-Pb过偏晶合金不混溶区析出第二相颗粒半径的分布情况, 随着粗化过程的进行, 归一化颗粒半径的尺寸分布峰值由初始的小于平均尺寸逐渐向平均尺寸靠近, 且最终超过平均尺寸。

1952

0.632

0.0

... Qd=h(Tds-Tg)为液滴表面对流换热速率^[17], 其中, Tds为雾化液滴的表面温度, Tg为雾化气体的温度^[18], h=kg(2+0 ...

... 6Re?Pr)/d是雾化液滴表面与雾化气体间的界面换热系数^[17], d为雾化液滴的直径, kg为雾化气体的热导率, Pr为气体的Prandtl数, Re为Reynolds数 ...

1993

0.0

... Qd=h(Tds-Tg)为液滴表面对流换热速率^[17], 其中, Tds为雾化液滴的表面温度, Tg为雾化气体的温度^[18], h=kg(2+0 ...

2013

1.815

0.0

... 式中, v和 I分别为弥散相液滴的扩散长大速度和形核率^[19,20], R*为弥散相液滴的临界形核半径 ...

1993

0.0

... 式中, v和 I分别为弥散相液滴的扩散长大速度和形核率^[19,20], R*为弥散相液滴的临界形核半径 ...

2007

0.5

0.0

... 由于在雾化液滴快速冷却过程中弥散相液滴间的碰撞凝并作用较弱^[21], 因此计算中忽略了弥散相液滴间碰撞凝并的影响 ...

1991

1.394

0.0

2007

0.202

0.0

Turchanin

M A

, Agraval

P G

. Powder Metall Met Ceram, 2007;46: 77

The mixing enthalpies and activities of components in liquid and solid alloys as well as the parameters of stable and metastable transformations are used for the thermodynamic evaluation of the Cu-Co system within the CALPHAD approach. The thermodynamic parameter for the (εCo) phase is evaluated within the Miedema model. The thermodynamic model of the system provides a self-consistent description of all thermodynamic quantities and phase transformations, including metastable ones. The description is in close agreement with experimental data. The thermodynamic model of system is used to explain the extension of the concentration range of supersaturated fcc solutions prepared by melt quenching.

1.Donbass State Mechanical Engineering Academy Kramatorsk

2003

0.0

Turchanin

M A

, Agraval

P G

, Nikolaenko

I V

. J Phase Equilib, 2003;24: 307

Together with previous values at 1873 K, new measurements of the enthalpies of formation of liquid Cu-Fe alloys, carried out by high-temperature calorimetry at 1673 K, have revealed a temperature dependence of ΔH, corresponding to a negative excess heat capacity of mixing. Our calorimetric results were combined with critically selected values of the enthalpies of alloying and activities of components in liquid and solid solutions, as well as parameters of stable and metastable phase transitions, to perform a thermodynamic evaluation of the system. The latter was carried out in the spirit of the CALPHAD approach, using Thermo-Calc software. The thermodynamic model generates a self-consistent description of all thermodynamic properties and phase equilibria, including metastable solidification, in close agreement with reliable experimental data. In particular, a very satisfactory representation of stable (L+δ)/γ, (L + γ)/ε, γ/(ε + α) and metastable (L₁/L₂), (L₁ + L₂)/ε phase boundaries has been achieved. The occurrence of a monotectic reaction L₂ ↔ L₁ + δ is suggested in the region of the metastable precipitation of δ-phase. A comprehensive thermodynamic model of the Cu-Fe system is used to explain the widening of the concentration limits of formation of supersaturated bcc and fcc solutions prepared by highly nonequilibrium methods of synthesis.

1.Donbass State Engineering Academy, Kramatorsk, Ukraine 2.University of Natal, Pietermaritzburg, South Africa

2002

3.94

0.0

Ohnuma

, Enoki

, Ikeda

, Kainuma

, Ohtani

, Sundman

, Ishida

. Acta Mater, 2002;50: 379

Abstract

α (A2)/γ (A1) phase equilibria of the Fe–Co system between 400 and 800°C were determined by means of lattice parameter measurement using thin film specimens. Bulk specimens were also analyzed to compare the extent of attainment to the equilibrium. The thin film technique was found to be greatly advantageous for obtaining the phase equilibria at lower temperatures where solid-state reactions are too slow to reach the equilibrium state in the conventional methods using bulk specimens. It was confirmed that the α+γ two-phase region extends below the temperature at which the α (A2)/α′ (B2) transus meets the α/α+γ boundary. Thermodynamic analysis was also conducted by taking the magnetic and chemical ordering contributions of the B2 structure into account, findings of which confirmed the extension of the α+γ two-phase region below the α/α′ ordering temperature.

1985

9.478

0.0

... 2 计算中所用的主要物性参数模拟采用文献[9,22~25]中给出的有关Cu-Co-Fe合金系的热力学数据计算相图, 计算中采用液-液界面能的通用表达式^[26]: ...

1992

0.0

... 液态金属的动力学黏度随温度的变化关系满足下式^[27]: ...

1988

0.0

... 溶质的扩散系数可以通过Stokes-Einstein方程与基体熔体的黏度 ηm相联系, Fe和Co溶质原子在液相Cu基体中的扩散系数 Di可如下计算^[28]: ...

1993

0.5

0.0

... 雾化气体的初速度取为300 m/s^[29] ...