Cu-2.0Fe合金等温处理过程中富Fe析出相的形态演变

图1 空冷凝固态Cu-2.0Fe合金中富Fe析出相显微组织及EDS分析

Fig.1 Characterization of Fe-rich precipitates in the air-cooled Cu-2.0Fe alloy (a, b) SEM (a) and TEM (b) images showing the cuboidal and petal-like precipitates (c) HRTEM image showing a petal-like precipitate (Inset shows the SAED pattern of the precipitate) (d) TEM-EDS result of the petal-like precipitate in Fig.1c

与图1中空冷凝固态Cu-2.0Fe合金显微组织相比较，水冷凝固态Cu-2.0Fe合金组织中的析出相特征发生了显著变化，如图2所示。由图2a中SEM像可知，未在铜合金基体中发现析出相颗粒，但在TEM高倍下观察时发现大量尺寸为10 nm左右的球状小颗粒弥散分布在基体中，如图2b所示。结合图2c中HRTEM和FFT斑点分析可知，这些球状颗粒为fcc结构的富Fe相。经TEM-EDS检测进一步确认球状纳米小颗粒为富Fe成分，如图2d所示，但由于颗粒尺寸太小，EDS检测过程中受到颗粒周边基体中Cu元素的干扰较大，导致检测结果中球状小颗粒的Fe含量明显低于图1中的花瓣状颗粒。

图2

图2 水冷凝固态Cu-2.0Fe合金中富Fe析出相表征

Fig.2 Characterization of Fe-rich precipitates in the water-cooled Cu-2.0Fe alloy

(a) SEM image showing no precipitate

(b) HAADF-STEM image showing the nano-sized spherical precipitates

(d) TEM-EDS result of the spherical precipitate marked by the arrow in Fig.2b

对比空冷凝固态和水冷凝固态Cu-2.0Fe合金中富Fe相特征可知，富Fe析出相可以在铜合金熔体中呈球状析出，如图2所示，在高温时Fe在Cu中的固溶度较高，而低温时基本不溶^[26]，说明将空冷凝固态合金在1200℃进行重熔保温时，由于温度较高，大部分的Fe重新溶入到合金熔体中；从1200℃降温至1084℃的熔融态阶段，富Fe颗粒形核析出但是没有充分长大；温度为1084℃时将高温熔体直接水淬，由于合金熔体从高温迅速冷却，Fe来不及扩散，富Fe颗粒不能长大从而保持为尺寸较小的球状纳米颗粒。而在空冷凝固态Cu-2.0Fe合金中，富Fe析出相在慢速冷却过程中扩散长大，并在长大过程中发生形态转变，产生了立方状和花瓣状的形态，如图1所示，说明1084~1200℃的高温熔融阶段Cu-2.0Fe合金中的富Fe颗粒不会发生球状→立方状→花瓣状的演变，该形态演变必然发生在凝固后的固相Cu基体中。

2.2 等温过程中富Fe相形态演变

在水冷凝固态Cu-2.0Fe合金中，富Fe颗粒以纳米级的球状形态弥散分布在Cu基体中，将水冷凝固态合金在高温下做进一步的等温处理，将促进富Fe颗粒的粗化和形态演变。对水冷凝固态Cu-2.0Fe合金在924、964和984℃进行等温处理后的显微组织进行观察分析，并对其微米级花瓣状颗粒周边的富Fe小颗粒的尺寸分布和数量密度进行统计，结果如图3~6所示。可以看出，富Fe相发生了明显的粗化，且从水冷凝固态的球状演变为不同尺寸的立方状和花瓣状。

图3

图3 水冷凝固态Cu-2.0Fe合金等温处理后富Fe析出相的SEM像和EDS面扫图

Fig.3 SEM images (a, d, g) and corresponding EDS mappings of Cu (b, e, h) and Fe (c, f, i) elements showing Fe-rich precipitates in the isothermal-treated Cu-2.0Fe alloy (a-c) 924^oC, 6 h (d-f) 964^oC, 6 h (g-i) 984^oC, 6 h

图4

图4 图3中水冷凝固态Cu-2.0Fe合金等温处理后SEM像局部放大图

Fig.4 Magnified SEM images of the square zones in Fig.3 of the isothermal-treated Cu-2.0Fe alloys

(a) 924^oC, 6 h (b) 964^oC, 6 h (c) 984^oC, 6 h

图5

图5 等温处理6 h后微米级花瓣状颗粒周边的富Fe小颗粒的尺寸分布和数量密度

Fig.5 Size distributions of the precipitates after 924^oC, 6 h (a), 964^oC, 6 h (b), and 984^oC, 6 h (c) isothermal treatments, and number density of the small precipitates after isothermal treatments for 6 h (d) (d_mean—mean diameter)

图6

图6 水冷凝固态Cu-2.0Fe合金在964℃等温处理不同时间后富Fe析出相的SEM像和EDS面扫图

Fig.6 SEM (a, d, g) images and corresponding EDS mappings of Cu (b, e, h) and Fe (c, f, i) elements showing Fe-rich precipitates in the isothermal-treated Cu-2.0Fe alloys at 964^oC for 1 h (a-c), 6 h (d-f), and 12 h (g-i)

2.2.1 等温温度对富Fe相形态演变的影响

对水冷凝固态Cu-2.0Fe合金在924、964和984℃进行6 h的等温处理，SEM表征发现每个温度下都出现微米级尺寸且具有多个分支的花瓣状颗粒，如图3a、d和g所示。将图3a、d和g中的矩形框区域放大后，发现在微米级多分支花瓣状颗粒的周围弥散分布着亚微米级的立方状和花瓣状颗粒，如图4所示，其形态和尺寸特征与图1a~c中空冷凝固态Cu-2.0Fe合金的富Fe析出相类似。对图3a、d和g进行EDS面扫分析，可以看出，花瓣状颗粒对应的区域存在Fe元素富集，如图3b、c、e、f、h和i所示，说明这些花瓣状颗粒是富Fe析出相。需要指出的是，由于SEM样品事先进行了侵蚀处理，花瓣状富Fe颗粒发生局部脱落，所以在EDS面扫图中颗粒的Fe元素成分比较微弱。

将水冷凝固态与等温处理态的富Fe相形态、尺寸对比分析可知，相对于水冷凝固态，924、964和984℃等温处理6 h的Cu-2.0Fe合金中富Fe析出相发生了明显的粗化，且粗化过程中伴随着球状(纳米级，图2)→立方状(亚微米级，图4)→四分支花瓣状(亚微米级，图4)→多分支花瓣状(微米级，图3)的形态演变。924、964和984℃均处于富Fe相的fcc温度区间，相场模拟研究^[22]表明，fcc富Fe颗粒在界面能、弹性能和化学驱动力的综合作用下经历球状→立方状→四分支花瓣状的多重形态演变。首先，生长初期(颗粒尺寸< 100 nm)，弹性能和界面能的交互作用促使颗粒沿着弹性“软”取向生长，颗粒由球状转变为具有平坦界面的立方状，其中平坦界面为{001}_γ_-Fe晶面；接着，化学驱动力使立方状颗粒拐角沿<111>_γ_-Fe晶向快速生长，立方颗粒失去稳定性并转变为具有凹陷界面的花瓣状。立方形态的不稳定性取决于富Fe颗粒周边Fe元素的过饱和度。水冷凝固态Cu-2.0Fe合金等温处理过程中球状→立方状→四分支花瓣状形态演变的实验结果与前期相场模拟结果^[22]十分吻合，可以明确富Fe相的形态演变发生在高温固相Cu基体中，而发生形态演变的温度区间是Fe相的fcc温区。

富Fe析出相在等温处理过程中的粗化与Fe元素在Cu基体中的扩散有关，其中扩散系数D是描述元素扩散能力的参数，D强烈地依赖于温度，其中关系由Arrhenius方程表示^[27]：

D = D_{0} e x p (\frac{- Q}{R T})

(1)

式中，D₀为扩散常数；Q为扩散激活能；R为理想气体常数；T为绝对温度。由此可知，等温温度越高，Fe在Cu基体中的扩散能力越强，球状富Fe析出相粗化程度越高，导致微米级花瓣状富Fe颗粒的尺寸随着等温温度的升高而增大。此外，随着颗粒尺寸的逐步增大，花瓣状富Fe颗粒的分支数量逐步增加，后面2.3节将结合相场模拟对多分支的现象进一步分析讨论。

对微米级花瓣状富Fe颗粒周边的小颗粒进行了尺寸分布和数量密度统计，结果如图5所示。假设在区域面积为A μm²的范围内有N个富Fe颗粒，数量密度N_s即为每平方米区域内的颗粒个数，其计算公式为：

N_{s} = \frac{N}{A} \times 10^{12}

(2)

根据式(2)计算得到图5d中的结果。由图5a~c中颗粒尺寸分布图可知，随着等温温度的升高，直径< 100 nm和直径> 400 nm的富Fe颗粒数量占比逐渐减小，直径100~400 nm的富Fe颗粒数量占比逐渐增大，且随着等温温度从924℃升高至984℃，微米级花瓣状颗粒周围小颗粒的平均尺寸从225.2 nm降至207.6 nm。图5a~c中富Fe颗粒尺寸特征演变的原因可以从以下几点分析：(1) 等温温度的升高导致直径< 100 nm的富Fe颗粒快速长大，转变为直径100~400 nm的颗粒，导致直径< 100 nm和直径100~400 nm的富Fe颗粒数量占比分别减小和增大；(2) 随着等温温度的升高，微米级花瓣状富Fe颗粒尺寸逐步增大，说明该类颗粒粗化速率增大。根据Ostwald熟化机制^[28]，为减少体系的界面能，大颗粒的长大以吞并小颗粒的方式进行。等温温度升高时，直径> 400 nm的富Fe颗粒通过吞并周边的小颗粒(如< 100 nm的颗粒)快速粗化转变为微米级的花瓣状颗粒，引起直径< 100 nm和直径> 400 nm的颗粒数量占比同时减小。需要说明的是，等温处理过程中大颗粒吞并小颗粒必然引起Cu基体中富Fe颗粒数量密度的降低，这与图5d中微米级以下的富Fe颗粒数量密度随温度演变的趋势一致，证明以上分析的合理性。

2.2.2 等温时间对富Fe相形态演变的影响

图6为水冷凝固态Cu-2.0Fe合金在964℃分别进行1、6和12 h等温处理后富Fe颗粒的形态特征。可以看出，964℃等温处理1 h后，Cu基体中出现四分支花瓣状富Fe颗粒，颗粒尺寸约3.5 μm，如图6a所示。当等温时间延长到6 h时，颗粒由四分支花瓣状演变为多分支且分支明显的花瓣状，颗粒尺寸约4.3 μm，如图6d所示。当等温时间达到12 h时，等温时间的延长进一步促进了花瓣状颗粒分支的延伸和新分支的萌生，颗粒尺寸达到5.6 μm，如图6g所示。结合Cu、Fe元素EDS面扫分析可知图6a、d和g中的花瓣状颗粒均为富Fe成分。综上分析表明，随着等温时间的延长，Cu-2.0Fe合金中的富Fe颗粒不断长大，形态由图2中水冷凝固态的球状转变为图6a中四分支花瓣状，以及图6d和g中分支明显的多分支花瓣状，分支的数量随着等温时间的延长而增多。

2.3 等温过程中富Fe相形态演变的相场模拟

本工作基于前期研究^[22]采用相场法解析Cu-Fe二元系中富Fe析出相的形态不稳定性，为厘清动力学因素的影响，求解浓度场c(r, t)的相场方程，c(r, t)与体系中Fe原子的成分相关，其中 r 和t分别为空间坐标和时间。前期工作考虑了在界面能、弹性能和化学驱动力的综合作用下，富Fe析出相颗粒的形态演变机制，经理论推导、简化变量以及显式描述化学能和弹性能，得到动力学方程的无量纲形式^[22]：

\begin{array}{l} \frac{\partial c (r^{*}, t^{*})}{\partial t^{*}} = \nabla^{*} {M^{*} \nabla^{*} [2 a_{2}^{*} c (r^{*}, t^{*}) + 4 a_{4}^{*} c^{3} (r^{*}, t^{*}) - \\ α^{*} (\nabla^{*})^{2} c (r^{*}, t^{*})] + \\ μ^{*} \int V_{e l}^{*} (\frac{k^{*}}{k^{*}}) c (r^{*}, t^{*}) e^{i k^{*} r^{*}} \frac{d^{3} k^{*}}{{(2 π)}^{3}}} \end{array}

(3)

式中，r^* = r / l₀，其中，r为空间长度，l₀为网格步长；t^*为无量纲时间；k^* = kl₀， k^*和 k 为取向矢量； $\nabla$ ^* = $\nabla$ l₀；M^* = M|Δf |t / $l_{0}^{2}$ ，其中，Δf为热力学驱动力，M为结构弛豫的迁移系数；α^* = α / (|Δf| $l_{0}^{2}$ )，α为梯度系数且正比于界面能； $V_{e l}^{*}$ (n) = B(n)c₁₁ / [(c₁₁ + 2c₁₂)² $ε_{0}^{2}$ ] (n 为 k 取向的单位矢量)，函数B(n)包含了体系中弹性性能的所有信息，取决于弹性常数c₁₁、c₁₂和c₄₄以及成分变化引起的晶格膨胀系数ε₀；μ^* = (c₁₁ + 2c₁₂)² $ε_{0}^{2}$ / (|Δf |c₁₁)； $a_{2}^{*}$ 和 $a_{4}^{*}$ 是一定温度下的活性常数。

为研究Cu-Fe合金中富Fe相的析出动力学，利用Spectral-Eyre方法求解非线性方程(3)得到数值解^[29]。前期在512³的三维模拟盒子中进行的相场模拟结果^[22]显示，随着颗粒尺寸的增大，在弹性能各向异性的主导下其形态逐渐趋近立方状；随着模拟时间的进一步延长，立方颗粒出现凹陷形态，随之沿着立方颗粒的<111>取向快速生长，颗粒形态从立方状演化为花瓣状，接着颗粒的8个分支进一步发展形成稳定的花瓣状形态，以上模拟结果与图2和4中等温实验观察到的结果一致。然而，由于前期相场模拟盒子的空间限制，更大尺寸(如微米级尺寸)花瓣状颗粒的演变并未进行模拟分析^[22]。本工作在1024²模拟盒子中进行二维相场模拟，分析了花瓣状富Fe颗粒在更大尺寸下的形态演变行为，如图7所示。相场模拟所需的无量纲建模参数参照前期实验检测和热力学计算结果评估得到，参见文献[22]中的参数值。模拟结果显示，富Fe颗粒在984℃等温状态下不断长大，其形态由图7a中球状转变为图7b中棱边凹陷的立方状，接着产生<111>取向的一次分支形成图7c中四分支花瓣状，与前期三维模拟结果^[22]以及本工作图2和4所示的等温实验结果一致；随着等温时间的延长，四分支花瓣状颗粒进一步长大，一次分支继续延伸，同时在一次分支上生长出二次分支，产生了多分支的花瓣状，如图7d~f所示，该模拟结果与图3、图6d和g中等温处理态Cu-2.0Fe合金微米级尺度的多分支花瓣状富Fe颗粒的形态特征相吻合。分析表明，弹性应变能和化学驱动力相互角逐控制亚微米和微米尺度富Fe颗粒的形态，富Fe颗粒一次和二次分支的萌生和生长过程由化学驱动力(即颗粒周边Fe元素的过饱和度不同)主导产生。综合比较可知，等温实验结果与相场模拟结果一致，进一步证明了所采用相场模型^[22]的可靠性。

图7

图7 相场模拟结果显示Cu-Fe体系(平均Fe浓度 $\bar{c}$ = 0.02)在984℃下单个富Fe析出相的二维形态演变(初始状态为半径R = 4Δx (Δx为栅格间距)的球状纯Fe晶核，模拟盒子尺寸为1024²)

Fig.7 Morphological evolutions of the Fe-rich single precipitate in Cu-Fe system with an average Fe concentration $\bar{c}$ of 0.02 at 984^oC obtained in phase field modeling (The figures show the concentration fields of Fe-rich precipitate at different time steps t*. Initial configuration contains an iron pure spherical nucleus of radius R = 4Δx, in which Δx is the grid spacing. The size of the simulation box is 1024²)

(a) t^* = 1000 (b) t^* = 20000 (c) t^* = 70000 (d) t^* = 100000 (e) t^* = 150000 (f) t^* = 200000

3 结论

(1) 水冷凝固态Cu-2.0Fe合金中仅存在尺寸为10 nm左右的球状富Fe相，而在空冷凝固态富Fe相出现了亚微米尺度的立方状和花瓣状形态。水冷凝固态Cu-2.0Fe合金在富Fe相的fcc温区(即924~984℃)保温过程中，富Fe相发生球状(纳米级)→立方状(亚微米级)→四分支花瓣状(亚微米级)→多分支花瓣状(微米级)的演变，表明富Fe相的形态演变发生在高温固相Cu基体中。

(2) 随着等温温度和保温时间的增加，多分支花瓣状富Fe颗粒的尺寸逐渐增大，分支数量逐步增加。此外，随着等温温度的升高，多分支花瓣状颗粒周边小颗粒的数量密度下降，说明多分支花瓣状颗粒的长大需吞并周边纳米~亚微米尺度的小颗粒。

(3) 等温实验中富Fe相的形态演变行为与相场模拟结果相吻合。其中，弹性应变能和化学驱动力相互角逐控制亚微米和微米尺度富Fe相的形态，且在四分支花瓣状进一步长大过程中诱发二次分支在一次分支上的萌生和生长，产生多分支的花瓣状形态。

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DOI PMID

Phase separation of gamma' precipitates determines the microstructure and mechanical properties of nickel-based superalloys. In the course of ageing, disordered gamma spheres form inside ordered (L1(2)) gamma' precipitates, undergo a morphological change to plates and finally split the gamma' precipitates. The presence of gamma particles inside gamma' affects coarsening kinetics and increases alloy hardness. Here we use atom probe tomography to visualize phase separation in a Ni86.1Al8.5Ti5.4 alloy in three dimensions and to quantify the composition of all the phases with near-atomic resolution. We find that gamma' precipitates are supersaturated in nickel, thereby driving the formation of gamma particles and observe a compositional evolution of the gamma particles, which accompanies their morphological change. Our results suggest that by controlling nickel supersaturation we can tailor the phase separation and thereby the properties of nickel-based superalloys.

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The mechanical properties of metallic materials are determined by their microstructure, and in particular, the different morphologies of precipitates lead to distinct strengthening effects. Usually, the shape of precipitates changes during growth and coarsening regimes, leading to modification of the macroscopic properties of the materials. Thus, understanding of this phenomenon is key to tailoring the precipitate strengthening of industrial alloys. In this article, a general approach to explain the shape instability of iron-rich nanoparticles in Cu-Fe-Co alloys during casting and ageing processes is proposed. The evolution of particle shape from sphere to cuboid to petal and finally splitting into eight subnanoparticles is observed using transmission electron microscopy. Phase-field modelling and thermodynamic calculations are combined into a general model that describes and elucidates the morphological evolution of precipitates in alloys in terms of particle size, interfacial and elastic strain energy, and chemical driving force. These findings have the potential to promote new microstructural design approaches for a wide range of materials. (C) 2018 Acta Materialia Inc. Published by Elsevier Ltd.

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The development of Cu-based alloys with high-mechanical properties (strength, ductility) and electrical conductivity plays a key role over a wide range of industrial applications. Successful design of the materials, however, has been rare due to the improvement of mutually exclusive properties as conventionally speculated. In this paper, we demonstrate that these contradictory material properties can be improved simultaneously if the interfacial energies of heterogeneous interfaces are carefully controlled. We uniformly disperse γ-Al2O3 nanoparticles over Cu matrix and then we controlled atomic level morphology of the interface γ-Al2O3//Cu by adding Ti solutes. It is shown that the Ti dramatically drives the interfacial phase transformation from very irregular to homogeneous spherical morphologies resulting in substantial enhancement of the mechanical property of Cu matrix. Furthermore, the Ti removes impurities (O and Al) in the Cu matrix by forming oxides leading to recovery of the electrical conductivity of pure Cu. We validate experimental results using TEM and EDX combined with first-principles density functional theory (DFT) calculations, which all consistently poise that our materials are suitable for industrial applications.

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