-
Having a
$\gamma /\gamma′ $ microstructure similar to Ni-base superalloys and also including various alloying elements such as Al and W, new Co-base superalloy, namely Co-Al-W-base alloy, has been widely studied as a kind of potential alternative of Ni-base superalloy, which is the most important high-temperature structural material in industrial applications. Besides, Co-Al-W-base alloy has also excellent mechanical properties, for example, creep properties comparable to those of the first-generation Ni-base single crystal superalloys. In our previous work, the ideal composition formula of Ni-base superalloy has been obtained by applying the cluster-plus-glue-atom structure model of faced centered cubic solid solution, which shows that the most stable chemical short-range-order unit is composed of a nearest-neighbor cluster and three next-neighbor glue atoms. In this paper, the ideal cluster formula of Co-Al-W-base superalloy is addressed by using the same approach. Based on cluster-plus-glue-atom model theory, according to lattice constants and atom radii, calculations are carried out. The results show that the atom radius of Al is equal to Covalent radius (0.126 nm) and for$\gamma′ $ phase the atom radius of W changes obviously (0.1316 nm). After analyzing atomic radii, the chemical formula for Co-Al-W ternary alloy is calculated to be [Al-Co12](Co,Al,W)3, which signifies an Al centered atom and twelve Co nearest-neighbored cluster atoms plus three glue atoms, which is in good consistence with that for Ni-base single crystal superalloy. For multi-element alloy, the alloying elements are classified, according to the heat of mixing between the alloying elements and Co as well as partition behavior of alloying elements, as solvent elements-Co-like elements$\overline {{\rm{Co}}} $ (Co, Ni, Ir, Ru, Cr, Fe, and Re) and solute elements-Al-like elements$\overline {{\rm{Al}}} $ (Al, W, Mo, Ta, Ti, Nb, V, etc.). The solvent elements can be divided into two kinds according to partition behaves:${\overline {{\rm{Co}}} ^{\gamma }}$ (Cr, Fe, and Re) and${\overline {{\rm{Co}}} ^{\gamma′}}$ (Ni, Ir, and Ru). The latter is further grouped into Al,${\overline {\rm{W}} }$ (W and Mo, which have weaker heat of mixing than Al-Co ) and${\overline {{\rm{Ta}}} }$ (Ta, Ti, Nb, V, etc., which have stronger heat of mixing than Al-Co). Then all chemically complex Co-Al-W-base superalloys are simplified into$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ pseudo-binary or$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)$ pseudo-ternary system. Within the framework of the cluster-plus-glue-atom formulism and by analyzing the compositions of alloy, it is shown that the Co-Al-W-base superalloy satisfies the ideal formula$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.0}}{{\overline {{\rm{Al}}} }_{2.0}}} \right)$ (or$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.5}}$ =${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{9.375}}$ at.%). In the same way, those of$\gamma $ and$\gamma′ $ phases are respectively$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{1.5}}{{\overline {{\rm{Al}}} }_{1.5}}} \right)$ (or$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{1.0}}$ =${\overline {{\rm{Co}}} _{84.375}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{6.250}}$ at.%) and$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\left( {{{\overline {{\rm{Co}}} }_{0.5}}{{\overline {{\rm{Al}}} }_{2.5}}} \right)$ (or$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{0.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{2.0}}$ =${\overline {{\rm{Co}}} _{78.125}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{12.500}}$ at.%). For example, alloy Co82Al9W9 and its$\gamma $ and$\gamma′ $ phases are formulated respectively as [Al-Co12]Co1.1Al0.4W1.4 (~ [Al-Co12]Co1.0Al0.5W1.5), [Al-Co12]Co1.6Al0.4W1.0 (~ [Al-Co12]Co1.5Al0.5W1.0), and [Al-Co12]Co0.3Al0.5W2.2 (~[Al-Co12]Co0.5Al0.5W2.0).1. 引 言
Ni基高温合金[1]优异的高温性能源自由
$\gamma /\gamma′ $ 两相构成的微观结构, 其中金属间化合物L12-Ni3Al($\gamma′ $ )以立方形态在面心立方结构的Ni基体$(\gamma)$ 中共格析出. 2006年, Sato等[2]在Co-Al-W三元系中发现了类似的结构特征, 即L12结构的金属间化合物Co3(Al,W)在$\gamma $ -基体中以立方形态共格析出. 这种新型$\gamma′ $ 相强化的Co基高温合金拥有与第一代Ni基单晶高温合金相媲美的蠕变性能, 流变应力随温度同样存在异常变化阶段, 并且其合金熔点较Ni基高温合金高50—100 K. 但由于在Co-Al-W三元相图中,$\gamma /\gamma′ $ 两相区间十分狭小,$\gamma′ $ 相热稳定性差, 所以高温强度与Ni基高温合金相比仍有差距.通过合金化可以扩大
$\gamma /\gamma′ $ 两相区, 从而有效提高$\gamma′ $ 相固溶温度, 这类$\gamma /\gamma′ $ 合金逐渐发展为多元复杂成分体系. Sato等[2]以及Suzuki和Pollock[3]发现, Ta是$\gamma′ $ 相强稳定元素, 通过添加Ta元素可以使Co79.4Al8.8W9.8Ta2 (全文统一采用原子百分比表述, at.%)合金的$\gamma′ $ 相固溶温度与硬度值明显高于Ni基高温合金Waspaloy, Nb和Ti有相似作用. Bauer等[4]发现, 含B合金的蠕变强度可与Ni基高温合金IN713C相媲美, 在此基础上添加2 at.% Ti可以使该合金蠕变强度更好, 接近于IN100高温合金. Klein等[5]发现, Cr提高合金抗氧化性能, 但过多添加则会破坏$\gamma /\gamma′ $ 两相结构, 此时需添加一定量的Ni, Mo或Ta来稳定$\gamma′ $ 相. Ooshima等[6]利用热力学计算发现, 在多种合金元素中只有Re降低合金的$\gamma′ $ 相固溶温度; 而通过实验验证后发现Nb, Ta和Ti确实会提高$\gamma′ $ 相固溶温度. Chen和Wang[7]通过第一性原理计算发现, Mo, Ta, Ir可以稳定$\gamma′ $ 相. Bauer等[8]在2010年发现, W, Ta, Ti, Nb和V都会提高$\gamma′ $ 相体积分数与固溶温度; 而W含量的增加以及Ir的添加都会提高合金的液相线温度. Kobayashi等[9]通过实验发现, 少量的Hf添加可以稳定$\gamma′ $ 相, 而2.2 at.% Ta的添加不会改变Co-Al-W三元体系的相平衡. Meher等[10]发现, 相对于Co86Al7W7合金, Co59Al8W8Ni25合金中Ni有强烈配分到$\gamma′$ 相的趋势且$\gamma $ 基体中Ni的增加会提高其中W的固溶度, 在Co83Al10W5Ta2合金中Ta的添加则降低Al的配分系数; 关于原子占位, 通过成分分析发现Ni占据Co3(Al,W)中Co的位置, 而Al, W和Ta有相同的占位. 但是正如Ni基高温合金一样, 作为成分较为复杂的合金, Co-Al-W基高温合金多元合金化存在着成分设计与优化的重大挑战, 目前, 基于电子空穴理论的相计算法[11]以及基于d电子理论的新相计算法[12]都无法定量解决成分问题.近期, Ni基高温合金成分规律的研究有了重大进展, 其核心突破在于引入了适用于描述合金固溶体化学近程序结构的“团簇加连接原子”结构模型[13-15]. 该结构模型认为, 具有良好综合表现的固溶体合金是由特定的局域结构单元堆垛而成, 每个单元覆盖最近邻配位多面体团簇以及次近邻的若干连接原子, 可表述为团簇成分式: [团簇](连接原子). 对于具有高结构稳定性的单晶型Ni基高温合金, 其理想团簇成分式满足
$\left[ { {{\rm{Al}}} \text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\rm{A}}{{\rm{l}}_{1.0}}\left( {{\overline {{\rm{Cr}}} }^\gamma }_{0.5}\right.$ $ \left.{{\overline {{\rm{Cr}}} }^{\gamma′ }}_{1.5} \right)$ [16], 上横线元素表示同类元素的平均原子.在此基础上, 本文将该方法应用于Co-Al-W基高温合金的结构模型建立和成分解析. 下面首先介绍稳定固溶体的团簇加连接原子结构模型, 确立基础的Co-Al二元团簇结构单元, 根据团簇共振模型结合
$\gamma $ 和$\gamma′ $ 两相晶格常数与合金元素半径计算连接原子个数, 进而得到Co-Al-W基高温合金的团簇成分通式. 然后将合金元素分类, 置于团簇成分通式中, 用于解析现有Co-Al-W基高温合金成分. 最终根据解析结果和理论计算, 确定Co-Al-W基高温合金的理想团簇成分式为$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$ ${\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}} ,\;\overline {{\rm{Ta}}} } \right)_{1.5}}$ , 例如, Co81Al9W8Ta2合金的团簇成分式为[Al-Co12]Co1.0Al0.4W1.3Ta0.3 (~[Al-Co12]Co1.0Al0.5(W,Ta)1.5). 最后, 应用类似方法, 确定了$\gamma $ 基体和$\gamma′$ 析出相的理想成分式, 合金成分式为两者等比例混合而得.2. 固溶体的团簇加连接原子模型
众所周知, 工业金属材料发展自固溶体合金, 而由于对固溶体合金成分根源认识不足, 具有优异性能的固溶体合金成分都是经过长期和大量经验式探索得到的.
固溶体合金是指在溶剂原子中溶入一定量溶质原子后仍保持溶剂结构特征的合金. 描述固溶体合金就是确定溶质在溶剂中的分布特征, 也就是由于原子间相互的化学作用, 在近程序局域范围, 原子呈现出某种程度的有序行为, 称为化学近程序结构.
人们发展了多种描述固溶体化学近程序的方法, 包括Bragg和Williams[17,18]的长程有序参数、Bethe[19]改进的短程有序参数以及Cowly[20-22]提出的短程序参量数, 但这些参数都是从统计角度出发, 没有建立结构模型, 更无法解释合金成分规律. 在前期工作中, 我们提出了一种描述近程有序结构的方法, 即团簇加连接原子结构模型, 并且该模型已成功应用在准晶[23,24]、金属玻璃[25-28]和一些固溶体合金[29-33]中. 团簇加连接原子结构模型认为[34]: 任何一个合金相的近程序结构都可以看作是由团簇加上位于团簇间隙中的连接原子组成, 用团簇成分式可以表示为[团簇](连接原子), 其中的团簇特指以中心原子为中心的第一近邻配位多面体, 而连接原子则位于次近邻位置.
化学近程序只强烈地发生在最近邻和次近邻位置, 以Ni-Cr-Al基高温合金体系为例[34,35], 其基体为面心立方固溶体
$(\gamma) $ , 其最近邻团簇部分为配位数12的立方八面体, 次近邻最多有6个原子, 即连接原子个数的范围为1—6[36-38] . 团簇式结构单元体现了理想的化学近程序结构特征. 原子占位通常以混合焓为依据, 即在Ni-Cr-Al基合金中, 与溶剂呈强负混合焓的元素, 例如Al, 优先置于团簇中心位置, 余量进入连接原子位置, 而作用较弱的${\overline {{\rm{Cr}}} }$ 仅置于连接原子位置, 那么$\gamma $ 相的团簇式可以表述为$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\rm{A}}{{\rm{l}}_x}{\overline {{\rm{Cr}}} _y}$ (上横线元素表示同类元素的平均原子; Al,$\overline {{\rm{Cr}}} $ 均与基体溶剂组元Ni呈负混合焓; x, y分别表示连接原子中Al和$\overline {{\rm{Cr}}} $ 的原子个数). 根据文献[34], 单位团簇式中的原子个数Z表示为$Z = c \times {\rho _{\rm a}} \times r_1^3$ , c ≈ 11.476为无量纲常数,${\rho _{\rm{a}}}$ 表示平均原子密度 (单位体积原子个数, 为平均原子体积的倒数, 即有$1/{\rho _{\rm{a}}} = {V_{\rm{a}}} = \sum {f_i} \times {V_i}$ , fi和Vi分别是元素i的原子分数和原子体积), r1表示团簇半径 (第一近邻的平均距离), 这里r1 = (RNi + RAl) (RNi和RAl分别是Ni和Al原子的半径). 已知面心立方密堆率为0.74 (原子球体占总体积的比例), Ni-Cr-Al固溶体的平均原子体积$1/{\rho _{\rm{a}}}$ 及原子密度${\rho _{\rm{a}}}$ 为$\begin{split}\frac{1}{{\rho _{\rm{a}}}} = & \left( {\frac{4}{3}{{\text{π}} / {0.74}}} \right) \times \left(\frac{{1 + x}}{{13 + x + y}} \times R_{{\rm{Al}}}^3 \right.\\ & \left.+ \frac{{12}}{{13 + x + y}} \times R_{{\rm{Ni}}}^3 + \frac{y}{{13 + x + y}} \times R_{{\rm{Cr}}}^3\right)\!,\end{split}$
(1) ${\rho _{\rm{a}}} = \frac{Z}{{c \times {{\left( {R_{\rm{Al}} + R_{\rm{Ni}}} \right)}^3}}} = \frac{{13 + x + y}}{{c \times {{\left( {R_{\rm{Al}} + R_{\rm{Ni}}} \right)}^3}}}.$
(2) 将(2)式代入(1)式中, 并代入原子半径值RAl = 0.126 nm, RNi = 0.125 nm, RCr = 0.128 nm, 得x, y之间的关系为
$3.39 = 1.02x + 1.07y.$
(3) 求解(3)式的整数解, 则得到团簇成分式为
$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\overline {{\rm{Cr}}} _3}$ .析出相
$\gamma′ $ 相具有AuCu3结构, 为面心立方的完全有序结构, 团簇依然为[Al-Ni12], 而连接原子为3个Al, 达到理想相成分, 团簇式为$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\rm{A}}{{\rm{l}}_3}$ .Ni基高温合金成分式由两种成分式的等比例混合得到, 即50% ×
$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\overline {{\rm{Cr}}} _3}$ + 50% ×$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\rm{A}}{{\rm{l}}_3}$ =$\left[ {{\rm{Al}}\text{-} {{\overline {{\rm{Ni}}} }_{12}}} \right]{\rm{A}}{{\rm{l}}_{1.5}}{\overline {{\rm{Cr}}} _{1.5}}$ . 解析结果与第五代和第六代Ni基单晶高温合金成分高度一致, 确认了Ni基单晶高温合金的团簇成分式含有三个连接原子[34]. 下节将介绍Co-Al-W三元基础体系中的团簇模型.3. Co-Al-W基础体系的理想团簇成分式
Co-Al-W基合金也以
$\gamma′ $ -Co3(Al,W) +$\gamma $ -基体为结构特征, 与Ni基高温合金微观结构相似, 且Ni与Co元素性质相近. 下面分别阐述两相及合金的理想成分式.3.1
$\gamma $ 相的理想团簇成分式在Co-Al-W三元体系中, 对于
$\gamma $ 基体, 合金化元素Al, W和基体Co均呈负混合焓 ($\Delta {H_{{\rm{Co}} \text{-} {\rm{Al}}}}$ = –19 kJ/mol,$\Delta {H_{{\rm{Co}} \text{-} {\rm{W}}}}$ = –1 kJ/mol), 其中Al与Co的混合焓绝对值较大, 故而占据团簇中心位置, 过量Al将占据连接原子位置; W与Co的混合焓绝对值较小, 故而在有Al占据团簇中心的情况下, W占据连接原子位置. 因此Co-Al-W固溶体合金$\gamma $ 的团簇成分通式为以Al原子为中心原子的立方八面体团簇[Al-Co12]加上若干个Co, Al, W作为连接原子, 即[Al-Co12](Co,Al,W)x, 其中[Al-Co12]团簇如图1所示. 在添加合金化元素后, 各种元素将按照原子相互作用规律进行分类而置入该基础成分通式, 并通过计算确定连接原子个数.按照文献[34]所提供的方法, 将Co-Al-W合金中
$\gamma $ 相的化学结构单元设为[Al-Co12]CoxAlyWz, 其中x, y, z分别表示连接原子位置中三种元素的原子个数, 将三种原子半径代入(1)式, 得到平均原子体积 (单位体积原子个数${\rho _{\rm{a}}}$ 的倒数)为$\begin{split} \frac{1}{{{\rho _{\rm{a}}}}} = & \left( {{{\frac{{4{\text{π}}}}{3}} / {0.74}}} \right) \times \left(\frac{{12 + x}}{{13 + x + y + z}}R_{{\rm{Co}}}^3 \right.\\ & \left.+ \frac{{1 + y}}{{13 + x + y + z}}R_{{\rm{Al}}}^3 + \frac{z}{{13 + x + y + z}}R_{\rm{W}}^3\right)\!, \end{split}$
(4) 由
$Z = c \cdot {\rho _{\rm{a}}} \cdot r_1^3$ 以及r1 = (RCo + RAl)可知, 平均原子密度为${\rho _{\rm{a}}} = \frac{Z}{{c \times {{\left( {R_{\rm{Al}} + R_{\rm{Co}}} \right)}^3}}} = \frac{{13 + x + y + z}}{{c \times {{\left( {R_{\rm{Al}} + R_{\rm{Co}}} \right)}^3}}}.$
(5) 将(5)式代入(4)式中, 化简后得x, y, z之间的关系为
$\begin{split} & {\left( {{R_{{\rm{Al}}}} + {R_{{\rm{Co}}}}} \right)^3} \times 2.03 \\ = & \left( {12 + x} \right) R_{{\rm{Co}}}^{\rm{3}} + \left( {1 + y} \right) R_{{\rm{Al}}}^{\rm{3}} + z \times R_{\rm{W}}^3. \end{split}$
(6) 已知各原子的Goldschmidt半径为RCo = 0.125 nm, RNi = 0.125 nm, RW = 0.141 nm, RCr = 0.128 nm[39]. 由于Co与Al之间存在强烈的相互作用, Al原子呈共价半径RAl = 0.126 nm[34]. 但是元素半径有可能在
$\gamma $ 固溶体合金化后发生变化. 面心立方结构中晶格常数a与平均原子半径R之间的关系为$R = {{\sqrt 2 a} / 4}$ , 对于多元合金, 晶格常数可表示为每种元素半径Ri的原子百分比分数fi平均:$a = \frac{{\displaystyle\sum \left( {{R_i} \times {f_i}} \right) \times 4}}{{\sqrt 2 }}.$
(7) 例如, 对于合金Co82Al9W9, 其
$\gamma $ 相成分为Co81.7Al9.3W9.0, 将上述各元素半径及其含量fi代入(7)式, 则有$\gamma $ 相晶格常数 a = (0.125 × 0.817 + 0.126 × 0.093 + 0.141 × 0.090) ×$4/ {\sqrt 2} = $ 0.3579 nm.$\gamma $ 相晶格常数的计算结果如表1所列, 可以看到, 对于Co-Ni-Al-W四元合金, 根据(7)式计算所得的晶格常数值与各文献中实验所测值误差约为10–3量级, 而其他合金的误差均在10–4量级, 说明合金元素在固溶形成$\gamma $ 相时原子半径几乎无变化, 故而下文计算时原子半径均使用RCo = 0.125 nm, RW = 0.141 nm, RAl = 0.126 nm.合金成分/at.% $\gamma $相成分/at.% 晶格常数实验值/nm 晶格常数计算值/nm 绝对误差$\varDelta $ Co82Al9W9 Co81.7Al9.3W9 0.3580 0.3579 0.0001 Co83Al9W8 Co81.9Al10.0W8.1 0.3576 0.3575 0.0001 Co80Al9W11 Co80.7Al9.2W10.2 0.3586 0.3588 0.0002 Co74Al9W9Cr8 Co73.9Al8.0W6.8Cr11.2 0.3578 0.3575 0.0003 Co64Al9W9Ni18 Co69.1Al6.8W7.0Ni16.9 0.3577 0.3562 0.0015 Co65Al9W9Ni9Cr8 Co66.7Al7.8W6.7Ni8.3Cr10.7 0.3581 0.3584 0.0003 Co56Al9W9Ni18Cr8 Co59.2Al6.0W7.4Ni15.6Cr11.8 0.3583 0.3581 0.0002 Co72.5Ni10Al10W7.5 Co76.2Al8.7W5.4Ni9.7 0.3578 0.3562 0.0016 将Co, Al, W原子半径代入(6)式, 得x, y和z之间的关系为
$6.62 = 2.00x + 1.95y + 2.80z.$
(8) 由(8)式得到连接原子总数为x + y + z = 3.3 – 0.4z, 通过分析
$\gamma $ 相成分可知, 连接原子中W原子个数约为1, 即z ≈ 1, 则x + y + z ≈ 3, 因此$\gamma $ 相的成分式含有三个连接原子.3.2
$\gamma′ $ 相的理想团簇成分式在Co-Al-W三元体系中,
$\gamma′ $ 相为具有固定成分式的金属间化合物Co3(Al,W), 具有AuCu3结构. 据此,$\gamma′ $ 相的团簇同样为[Al-Co12] (图1). 下面按照类似方法, 根据原子半径与晶格常数计算连接原子个数.首先判断合金元素的原子半径固溶到Co3(Al,W)中是否会发生变化. 根据文献[43]中的数据可知, Co3(Al,W)与Ni3Al相的晶格常数分别为0.3565 nm 和0.3568 nm, 这说明原子半径较大的W原子加入后对
$\gamma′ $ 相的晶格常数并无过多影响, 即W原子半径变化最为明显. 根据$\gamma′ $ 相成分及其晶格常数重新计算W原子半径. 已知$\gamma′ $ 相为$\gamma $ 相的超结构, 其中类Al原子(包括W)位于顶点位置, 其平均原子半径为$\displaystyle\sum {R_i} \times {f_i}$ , 类Co元素位于面心位置, 其平均原子半径基本接近Co, 则晶格常数a为$a = \frac{{2 \times R_{\rm{Co}} + 2 \times \displaystyle\sum R_i \times {{f_i} / {\left( {100 - f_{\rm{Co}}} \right)}}}}{{\sqrt 2 }}.$
(9) 例如, 对于合金Co82Al9W9, 其
$\gamma′ $ 相成分为Co77.49Al10.03W12.48, 将77.49 at.% Co, 10.03 at.% Al以及12.48 at.% W代入(9)式, 已知测得的$\gamma′ $ 相晶格常数为0.3594 nm, 则W的原子半径为RW = [($\sqrt 2 $ × 0.3594 – 2 × 0.125)/2 – 0.126 × 10.03/22.51] × 22.51/12.48 = 0.1317 nm. 计算结果列于表2中.合金成分/at.% $\gamma′ $相成分/at.% 晶格常数实验值/nm W原子半径/nm Co82Al9W9 Co77.49Al10.03W12.48 0.3594 0.1317 Co83Al9W8 Co76.6Al9.4W14 0.3589 0.1306 Co80Al9W11 Co75.1Al9.1W15.8 0.3595 0.1311 Co74Al9W9Cr8 Co73.9Al9.4W10.4Cr6.3 0.3587 0.1314 Co64Al9W9Ni18 Co58.9Al10.8W11.0Ni19.3 0.3590 0.1317 Co65Al9W9Ni9Cr8 Co64.2Al10.1W9.9Ni9.4Cr6.4 0.3587 0.1317 Co56Al9W9Ni18Cr8 Co54.5Al10.5W9.7Ni19.7Cr5.6 0.3587 0.1319 Co72.5Ni10Al10W7.5 Co68.8Al10.8W9.9Ni10.5 0.3593 0.1324 根据表2所列结果的平均值, 假设在
$\gamma′ $ 相中, W原子的半径为RW = 0.1316 nm, 将Co, Al, W原子半径代入(4)式, 得x, y和z之间的关系为$6.62 = 2.00x + 1.95y + 2.28z.$
(10) 由(10)式得到连接原子总数为x + y + z ≈ 3.3 – 0.3z, 通过分析
$\gamma′ $ 相成分, 可知在连接原子中约有2个W原子, 则x + y + z ≈ 3, 即$\gamma′ $ 相的成分式亦含有三个连接原子.综上所述, 对于Co-Al-W三元合金, 其
$\gamma $ 和$\gamma′$ 两相的团簇式中均存在3个连接原子, 说明其合金的基础团簇成分式必然为[Al-Co12](Co,Al,W)3, 即与Ni基高温合金[16]和马氏体不锈钢[32]的情形十分类似. 因此合金成分解析可以简单地用16原子成分式进行, 但实际的Co-Al-W基高温合金往往含有多种其他合金化元素, 因此首先需要进行元素分类, 见下节.4. 合金元素分类
已知Co-Al-W基高温合金的团簇成分通式为[Al-Co12](Co,Al,W)3, 可以确定在团簇中存在三种不同的原子: 团簇中心原子、团簇壳层原子以及连接原子, 显然基体溶剂元素Co优先占据团簇壳层位置, 而余量填入连接原子位置, 并且由表1和表2可知,
$\gamma $ 基体相中的Co明显多于$\gamma′ $ 相. 在利用团簇加连接原子结构模型解析合金成分时, 主要根据添加的合金化组元与基体组元之间的混合焓来判断其在团簇式中的位置. 由于Co元素与Ni元素性质相近, 且有相同的原子半径, 又因为Co-Al-W基高温合金与Ni基高温合金的微观组织极为相似, 所以在对Co-Al-W基高温合金中元素进行分类时, 可以参考Ni单晶高温合金, 其元素分类以合金化元素与主要溶剂Ni元素之间的混合焓为依据[16].根据现有的Co-Al-W基高温合金成分, 向Co-Al-W三元基体中添加的合金化元素有Ta, Ti, Nb, V, Cr等, 本文根据合金化组元与基体组元Co之间的混合焓
$\Delta H$ 和合金元素在$\gamma $ 与$\gamma′ $ 相之间的配分行为将合金元素进行分类, 结果如表3所列.元素分类 合金化元素 混合焓$\Delta H$/kJ·mol 元素配分系数K ${\overline {{\rm{Co}}} ^{\gamma }}$ Cr –4 0.48—0.60 Fe –1 Re 2 ${\overline {{\rm{Co}}} ^{\gamma′ }}$ Ni –2 1.08—1.27 Ru –1 Ir –3 Al Al –19 0.93—1.60 ${\overline {\rm{W}} }$ W –1 1.03—6.21 Mo –5 ${\overline {{\rm{Ta}}} }$ V –14 1.57—8.67 Ta –24 Nb –25 Ti –28 Sc –30 Hf –35 合金元素首先分为两大类: 一类是溶剂元素, 称为类Co元素, 用符号
$\overline {{\rm{Co}}} $ 表示, 包括Co, Ni, Ir, Ru, Cr, Fe, Re等, 它们均与Co之间呈弱混合焓; 另一类是溶质元素, 称为类Al元素, 用符号${\overline {{\rm{Al}}} }$ 表示, 包括Al, W, Mo, Ta, To, Nb, V等, 它们与Co呈负混合焓. 以此可以将Co-Al-W基合金简化为$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ 伪二元合金体系, 其团簇成分通式为$\left[ {\overline {{\rm{Al}}} \text{-}{{\overline {{\rm{Co}}} }_{12}}} \right]{\left( {\overline {{\rm{Co}}} ,\overline {{\rm{Al}}} } \right)_3}$ .其中, 根据合金元素的配分行为, 溶剂元素
$\overline {{\rm{Co}}} $ 可以分为${\overline {{\rm{Co}}} ^{\gamma }}$ (Cr, Fe, Re, 优先配分至$\gamma $ 相)和${\overline {{\rm{Co}}} ^{\gamma′ }}$ (Ni, Ir, Ru, 优先配分至$\gamma′ $ 相); 溶质元素$\overline {{\rm{Al}}} $ 均倾向于形成$\gamma′ $ 相. 根据混合焓, 进一步分为Al (形成$\gamma′ $ 相的主要元素)、类W元素${\overline {\rm{W}} }$ (含W和Mo, 与Co之间呈弱于Al-Co的负混合焓)和类Ta元素${\overline {{\rm{Ta}}} }$ (含Ta, Ti, Nb, V等, 与Co之间呈强于Al-Co的负混合焓). 因此多元合金的团簇成分通式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\left( {\overline {{\rm{Co}}} ,{\rm{Al,}}\overline {\rm{W}} ,\;\overline {{\rm{Ta}}} } \right)_3}$ .综上所述, 合金化元素可以分为类Co的溶剂元素
$\overline {{\rm{Co}}} $ 和三种溶质元素Al,${\overline {\rm{W}} }$ ,${\overline {{\rm{Ta}}} }$ , 详述如下.1) 溶剂元素
$\overline {{\rm{Co}}} $ : 包括Co, Ni, Ir, Ru, Cr, Fe, Re等, 与Co形成连续或宽固溶体, 优先占据团簇的壳层位置, 余量填入连接原子位置. 其中${\overline {{\rm{Co}}} ^{\gamma }}$ (Ni, Ru, Ir)优先配分到$\gamma′ $ 相, 促进析出相形成, 它们在$\gamma′$ 相中占据Co的位置[2,10,53], 而${\overline {{\rm{Co}}} ^{\gamma′ }}$ (Cr, Fe, Re)优先配分到$\gamma $ 基体相中, 是稳定基体的元素. 对于Cr, Ping等[54]在一种Co基高温合金中发现了(Ni,Co,Cr)3(Ti,Al)相的存在, 说明Cr元素在$\gamma′ $ 相中占位与Co相同, 即优先占据团簇壳层位置.2) Al: 主要溶质元素, 与Co之间呈较强烈的负混合焓, 其含量一般足以占据CN12团簇的中心位置, 是形成团簇的主要元素, 构成
$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$ 立方八面体团簇, 余量进入连接原子位置. 它同时强化固溶体$\gamma $ 和析出相$\gamma′ $ , 在两相中的配分系数接近1. 它与Co只能形成亚稳$\gamma′ $ 相, 稳定的$\gamma′ $ 相是通过添加W来实现的[2].3) 类W元素
${\overline {\rm{W}} }$ : 主要溶质元素, 包括W和Mo, 与Co之间呈较弱的负混合焓, 与Co形成多种化合物, 它们占据连接原子位置. W是稳定$\gamma′ $ 相的主要元素[2], Mo也有类似作用, 但是需要与其他元素匹配[55,56], 它们优先配分到$\gamma′ $ 析出相, 主要起沉淀强化作用.4) 类Ta元素
${\overline {{\rm{Ta}}} }$ : 微量溶质元素, 包括Ta, Ti, Nb, V, Si, Sc以及Hf, 与Co之间呈强烈的负混合焓, 占据连接原子位置, 与Co形成多种化合物. 其作用类似于${\overline {\rm{W}} }$ , 但是几乎完全配分至$\gamma′ $ 析出相, 是更强的$\gamma′ $ 相形成元素, 因此可以把${\overline {{\rm{Ta}}} }$ 与${\overline {\rm{W}} }$ 合并考虑.由此, 多元Co-Al-W基合金均可表述为
$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ 伪二元体系或者$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-}\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)$ 伪三元体系.特别地, Ni3Al可以稳定存在, 但是在Co-Al相图中无稳定的Co3Al存在, 因此需要W, Mo元素辅助Al来稳定
$\gamma′ $ 相, 这里的元素分类与Ni基高温合金存在重大差别: W和Mo单独成为一类, 其作用在于同Al一起, 共同形成稳定的$\gamma′ $ 相, 这也是Co-Al-W基高温合金的独特之处, 其他元素的分类与Ni基高温合金一致.下节利用推出的团簇模型和元素分类, 分析现有典型Co-Al-W基高温合金的成分规律.
5. Co-Al-W基高温合金成分解析
5.1 合金成分解析原则及步骤
综上所述, 根据面心立方固溶体的团簇加连接原子结构模型可知, Co-Al-W三元合金以及
$\gamma $ 和$\gamma′ $ 相的团簇成分通式均为[Al-Co12](Co,Al,W)3, 即包括16个原子: 1个位于团簇中心位置的中心Al原子、12个位于团簇壳层位置形成立方八面体团簇的Co原子、以及3个混杂占位的连接原子.由此可以确定利用团簇加连接原子结构模型解析Co-Al-W基高温合金成分的步骤为: 1)首先将原子百分比换算成在团簇式所占个数, 即将原子百分比成分乘以0.16 ( = 16/100), 获得以Z = 16团簇式为基础的成分式; 2)将元素归类后放置在团簇成分通式中相应位置, 即得到该合金的团簇成分式.
以Co81.3Al9.2W9.5合金为例, 此时已经表述为原子百分比, 每个成分乘上0.16, 得到在16原子团簇式中分别有13.01个Co、1.47个Al以及1.52个W. 根据团簇模型, 1个Al原子占据团簇中心位置, 12个Co原子占据团簇壳层位置, 其余原子均占据团簇与团簇之间的连接原子位置, 即得到该合金的团簇成分式为: [Al-Co12]Co1.0Al0.5W1.5.
结合Co-Al-W合金的团簇成分通式[Al-Co12](Co,Al,W)3与表3中的合金元素分类, 对现有的Co-Al-W基多元合金的成分进行筛选, 通过解析得到对应的团簇成分式, 如表4所列. 同时统计了符合条件的合金两相成分并进行解析, 结果列于表5中, 筛选条件为: 1)合金中Co元素含量大于等于50 at.%; 2)合金的微观组织中
$\gamma′ $ 相为立方形态; 3)合金的微观组织中$\gamma′ $ 相的体积分数范围为40% ≤${V_{\gamma′ }}$ ≤ 90%; 4)合金中只存在$\gamma /\gamma′ $ 两相, 无其他析出相; 5)合金时效温度为1173 K.合金成分/at.% 团簇成分式-[团簇](连接原子)3 连接原子 Co78Al10W10Ta2 [Al-Co12]Co0.5Al0.6W1.6Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co78Al9W10Mo3 [Al-Co12]Co0.5Al0.4W1.6Mo0.5 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{2.1}}$ Co79Al9W10Ti2 [Al-Co12]Co0.6Al0.4W1.6Ti0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W10V2 [Al-Co12]Co0.6Al0.4W1.6V0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W10Si2 [Al-Co12]Co0.6Al0.4W1.6Si0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W8Ta2Nb2 [Al-Co12]Co0.6Al0.4W1.3Ta0.3Nb0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$ Co79Al9W8Ta2V2 [Al-Co12]Co0.6Al0.4W1.3Ta0.3V0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$ Co79Al8W9Ta2Ti2 [Al-Co12]Co0.6Al0.3W1.4Ta0.3Ti0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.3}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.6}}$ Co79.5Al9.7W10.8 [Al-Co12]Co0.7Al0.6W1.7 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.7}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.7}}$ Co79.9Al9.4W10.7 [Al-Co12]Co0.8Al0.5W1.7 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$ Co80Al9W11 [Al-Co12]Co0.8Al0.4W1.8 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.8}}$ Co80Al9W9Ti2 [Al-Co12]Co0.8Al0.4W1.4Ti0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$ Co80Al9W9V2B0.04 [Al-Co12]Co0.8Al0.4W1.4V0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$ Co80Al9W9Ta2 [Al-Co12]Co0.8Al0.4W1.4Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$ Co80.3Al9.3W10.4 [Al-Co12]Co0.8Al0.5W1.7 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$ Co80.5Al9W10Si0.5 [Al-Co12]Co0.9Al0.4W1.6Si0.1 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.9}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.1}}$ Co81Al9W9Mo1B0.04 [Al-Co12]Co1.0Al0.4W1.4Mo0.2 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$ Co81Al9W8Ta2 [Al-Co12]Co1.0Al0.4W1.3Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$ Co81.3Al9.2W9.5 [Al-Co12]Co1.0Al0.5W1.5 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.5}}$ Co81.5Al9W9Nb0.5 [Al-Co12]Co1.0Al0.4W1.4Nb0.1 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.1}}$ Co81.5Al9W5.5Ta2Mo2 [Al-Co12]Co1.0Al0.4W0.9Ta0.3Mo0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.2}}{\overline {{\rm{Ta}}} _{0.3}}$ Co82Al9W9 [Al-Co12]Co1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co72Al9W9Ni10 [Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co82Al9W7.5Mo1.5 [Al-Co12]Co1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co80Al9W9Cr2B0.04 [Al-Co12]Co0.8Cr0.3Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$ Co78Al9W9Cr4 [Al-Co12]Co0.6Cr0.6Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co73Al9W9Ni9 [Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co64Al9W9Ni18 [Al-Co10.2Ni1.8]Ni1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co81.8Al9.2W9 [Al-Co12]Co1.1Al0.5W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.4}}$ Co72.5Al10W7.5Ni10 [Al-Co11.6Ni0.4]Ni1.2Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.2}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co81.5Al9W5.5Ta2Ir2 [Al-Co2]Co1.0Al0.4W0.9Ta0.3Ir0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{0.9}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W8Ta2Cr2 [Al-Co12]Co0.6Cr0.3Al0.4W1.3Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$ 合金成分/at.% $\gamma $相团簇成分式 $\gamma′ $相团簇成分式 Co82Al9W9 [Al-Co12]Co1.6Al0.4W1.0 [Al-Co12]Co0.3Al0.5W2.2 Co78Al9W9Cr4 [Al-Co12]Co0.9Al0.3W0.9Cr0.9 [Al-Co12]Co0.2Al0.5W1.8Cr0.5 Co73Al9W9Ni18 [Al-Co11.1Ni0.9]Al0.1W1.1Ni1.8 [Al-Co9.4Ni2.6]Al0.7W1.8Ni0.5 Co79.5Al9.7W10.8 [Al-Co12]Co1.7Al0.4W0..9 [Al-Co12]Co0.4Al0.6W2.0 Co80Al9W9Ti2 [Al-Co12]Co1.6Al0.4W0.8Ti0.2 [Al-Co12]Co0.2Al0.4W1.9Ti0.4 Co80Al9W9Ta2 [Al-Co12]Co1.8Al0.4W0.7Ta0.1 [Al-Co12]Co0.2Al0.4W1.9Ta0.5 Co79Al8W9Ta2Ti2 [Al-Co12]Co2.0Al0.3W0.5Ta0.04Ti0.1 [Al-Co12]Co0.1Al0.4W1.9Ta0.3Ti0.3 Co78Al10W10Ta2 [Al-Co12]Co1.6Al0.7W0.7Ta0.1 [Al-Co12]Al0.7W1.9Ta0.4 Co78Al9W10Mo3 [Al-Co12]Co1.7Al0.1W0.8Mo0.4 [Al-Co12]Co0.2Al0.6W1.7Mo0.5 对于表4中所有合金, 将
$\overline {{\rm{Co}}} $ 含量范围78 at.%—83 at.%划分成宽度为1 at.%的等成分区间, 并统计处于每个区间内的合金数目, 绘制出$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ 二元成分图, 横坐标为$\overline {{\rm{Co}}} $ 含量, 纵坐标为处于每一成分区间内的合金数量, 结果如图2所示. 可以看出, 所有合金均处于Co成分78 at.%—83 at.%范围内, 根据图中合金数量随Co含量变化的趋势, 可以统计出平均Co含量约为80.76 at.%, 对应Al含量则为19.24 at.%, 解析后其团簇式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{0.9}}{\overline {{\rm{Al}}} _{2.1}}$ (~$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\;{\overline {{\rm{Co}}} _{1.0}}{\overline {{\rm{Al}}} _{2.0}}$ ).将表4中Co-Al-W基合金成分制作出
$\overline {{\rm{Co}}} \text{-}$ $ {\rm{Al}} \text{-} \left( {\overline {\rm{W}} ,\;\overline {{\rm{Ta}}} } \right)$ 伪三元成分图, 结果如图3所示, 其中红线为Sato等[2]制作的1173 K下Co-Al-W三元体系中富Co端的等温截面图,$\gamma /\gamma′ $ 两相区成分通常在9 at.% Al, 8 at.% W—11 at.% W之间, 可见通过筛选后的合金成分多数位于$\gamma /\gamma′ $ 两相区中. 根据表4中合金成分的解析结果, 多数合金成分式的连接原子中, Al原子个数接近于y = 0.5. 例如, Co81Al9W8Ta2合金的16原子成分式为[Al-Co12]Co1.0Al0.4W1.3Ta0.3, Co72Al9W9Ni10合金的16原子成分式为[Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4. 结合上文中得到的$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ 二元基础团簇成分式$\left[ {\overline {{\rm{Al}}}} \text{-}\right. $ $\left. {{\overline {{\rm{Co}}} }_{12}}\right]{\overline {{\rm{Co}}} _{1.0}}{\overline {{\rm{Al}}} _{2.0}}$ , 可以得到Co-Al-W基高温合金的理想团簇成分式为$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}$ $ {\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{1.5}}$ , 即理想合金成分应为${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}$ $ {\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{9.375}}$ , 这与表4中多元合金的解析结果高度一致, 该成分点在图3中用蓝色空心三角形点标出.5.2
$\gamma /\gamma′ $ 两相成分解析类似地, 分别绘制合金与两相的数量随Co含量的变化图以及
$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)$ 三元成分分布图, 结果如图4所示.由图4可知,
$\gamma $ 相中$\overline {{\rm{Co}}} $ 含量范围为84 at.%—88 at.%,$\gamma′ $ 相中$\overline {{\rm{Co}}} $ 含量范围为75 at.%—79 at.%. 根据图4中合金数量随Co含量的变化趋势, 可以统计出$\gamma $ 相的平均$\overline {{\rm{Co}}} $ 含量约为85.85 at.%, 对应$\overline {{\rm{Al}}} $ 含量则为14.16 at.%, 解析后其团簇式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.7}}{\overline {{\rm{Al}}} _{1.3}}$ (~$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.5}}{\overline {{\rm{Al}}} _{1.5}}$ ); 统计出$\gamma′$ 相的平均$\overline {{\rm{Co}}} $ 含量约为76.37 at.%, 对应$\overline {{\rm{Al}}} $ 含量则为23.63 at.%, 解析后其团簇式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$ ${\overline {{\rm{Co}}} _{0.2}}{\overline {{\rm{Al}}} _{2.8}}$ (~$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\;{\overline {{\rm{Co}}} _{0.5}}{\overline {{\rm{Al}}} _{2.5}}$ ). 继而从相图中读出$\gamma $ +$\gamma′ $ 三角形双相区的三个端点 (图3(b)中由大环标注), 分别为Co77Al9W14, Co78Al10W12 ($\gamma′ $ 相区的两个端点)和Co85Al9W6 ($\gamma $ 相区的最大固溶度). 根据前述方法, 解析得到这三点的16原子团簇成分式为[Al-Co12]Co0.3Al0.5W2.2, [Al-Co12]Co0.5Al0.6W1.9和[Al-Co12]Co1.6Al0.4W1.0, 可以近似为[Al-Co12]Co0.5Al0.5W2.0 ($\gamma ′$ 析出相成分式)和[Al-Co12]Co1.5Al0.5W1.0 ($\gamma $ 固溶体成分式).此外, 根据(8)和(10)式, 当团簇式中连接原子中Al的个数为0.5时, 对于
$\gamma $ 和$\gamma′ $ 两相分别有解(1.5, 0.5, 1)和(0.5, 0.5, 2), 与上述实验结果相符, 即得到$\gamma $ 固溶体理想团簇成分式为$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$ ${\overline {{\rm{Co}}} _{1.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{1.0}}$ ,$\gamma′ $ 析出相理想团簇成分式为$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\;{\overline {{\rm{Co}}} _{0.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{2.0}}$ , 而合金成分式正好为两者的等比例混合, 即$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}$ $ {\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{1.5}}$ .6. 结 论
金属间化合物-
$\gamma′ $ 析出强化的Co-Al-W基高温合金具有与Ni基高温合金相似的微观结构, 结合前期获得的Ni基高温合金的元素分类和团簇成分式, 本文得到了Co-Al-W基高温合金以及两相的成分式.1) 根据合金中
$\gamma′ $ 和$\gamma $ 两相成分与晶格常数的实验结果, 推断出W的原子半径在$\gamma′ $ 和$\gamma $ 两相中分别为0.1316 nm和0.141 nm (Goldschmidt半径); Al原子半径均为共价半径, 即0.126 nm. 计算得到两相的团簇结构单元均为[Al-Co12]团簇加上3个连接原子, 进而可以推断出, 合金的团簇成分通式为[Al-Co12](Co,Al,W)3;2) 对于多元合金, 共有溶剂及溶质元素两大类, 前者为类Co元素
$\overline {{\rm{Co}}} $ (Co, Ni, Ir, Ru, Cr, Fe, Re), 后者为类Al元素$\overline {{\rm{Al}}} $ (Al, W, Mo, Ta, Ti, Nb, V等). 其中, 溶剂元素可进一步分为${\overline {{\rm{Co}}} ^{\gamma }}$ (Cr, Fe, Re, 配分系数小于1)和${\overline {{\rm{Co}}} ^{\gamma′}}$ (Ni, Ir, Ru, 配分系数大于1), 溶质元素$\overline {{\rm{Al}}} $ 均倾向于形成$\gamma′ $ 相, 包含Al、类W元素$\overline {{\rm{W}}} $ (W, Mo, 与Co之间呈弱于Al-Co的负混合焓)和类Ta元素$\overline {{\rm{Ta}}} $ (Ta, Ti, Nb, V等, 与Co之间呈强于Al-Co的负混合焓). 由此, 任何复杂Co-Al-W基合金均可表述为$\overline {{\rm{Co}}} \text{-} \overline {{\rm{Al}}} $ 伪二元和$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)$ 伪三元体系;3) 通过解析典型Co-Al-W基合金成分, 得到了合金的理想团簇成分式:
$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\;\left( {{{\overline {{\rm{Co}}} }_{1.0}}{{\overline {{\rm{Al}}} }_{2.0}}} \right)$ (或$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}}, \overline {{\rm{Ta}}} } \right)_{1.5}}$ =$ {\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}$ ${\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{9.375}}$ at.%), 即以Al为中心,$\overline {{\rm{Co}}} $ 元素作为第一近邻的立方八面体团簇$\left[ {{\rm{Al}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$ 加上3个连接原子;$\gamma $ 相的成分式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]\;\left( {{{\overline {{\rm{Co}}} }_{1.5}}{{\overline {{\rm{Al}}} }_{1.5}}} \right)$ (或$\left[ {{\rm{Al}} \text{-}{{\overline {{\rm{Co}}} }_{12}}} \right]\;{\overline {{\rm{Co}}} _{1.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{1.0}}$ =$ {\overline {{\rm{Co}}} _{84.375}}{\rm{A}}{{\rm{l}}_{9.375}}$ ${\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{6.250}}$ at.%);$\gamma \prime $ 相的成分式为$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]$ $\left( {{{\overline {{\rm{Co}}} }_{0.5}}{{\overline {{\rm{Al}}} }_{2.5}}} \right)$ (或$\left[ {{\rm{Al}} \text{-}{{\overline {{\rm{Co}}} }_{12}}} \right]\;{\overline {{\rm{Co}}} _{0.5}}{\rm{A}}{{\rm{l}}_{0.5}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{2.0}}$ =${\overline {{\rm{Co}}} _{78.125}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)_{12.500}}$ at.%).[1] Sims C T, Hagel W C 1972 The Superalloys (New York: John Wiley & Sons) p1
[2] Sato J, Omori T, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2006 Science 312 90Google Scholar
[3] Suzuki A, Pollock T M 2008 Acta Mater. 56 1288Google Scholar
[4] Bauer A, Neumeiera S, Pyczakb F, Singer R F, Göken M 2012 Mater. Sci. Eng. 550 333Google Scholar
[5] Klein L, Shen Y, Killian M S, Virtanen S 2011 Corros. Sci. 53 2713Google Scholar
[6] Ooshima M, Tanaka K, Okamoto N L, Kishida K, Inui H 2010 J. Alloys Compd. 508 71Google Scholar
[7] Chen M, Wang C Y 2009 Scr. Mater. 60 659Google Scholar
[8] Bauer A, Neumeier S, Pyczakc F, Göken M 2010 Scr. Mater. 63 1197Google Scholar
[9] Kobayashi S, Tsukamoto Y, Takasugi T 2012 Intermetallics 31 94Google Scholar
[10] Meher S, Yan H Y, Nag S, Dye D, Banerjee R 2012 Scr. Mater. 67 850Google Scholar
[11] Morinaga M, Yukawa N, Ezaki H, Adachi H 1984 Superalloys (Warrendale, PA: The Metallurgical Society of AIME) p523
[12] 张继山, 崔华, 胡壮麟, 村田纯教, 森永正彦, 汤川夏夫 1993 金属学报 29 289Google Scholar
Zhang J S, Cui H, Hu Z L, Murata Y, Morinaga M, Yukawa N 1993 Acta Metall. Sin. 29 289Google Scholar
[13] Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D: Appl. Phys. 40 R273Google Scholar
[14] Han G, Qiang J B, Li F W, Yuan L, Quan S G, Wang Q, Wang Y M, Dong C, Häussler P 2011 Acta Mater. 59 5917Google Scholar
[15] Luo L J, Chen H, Wang Y M, Qiang J B, Wang Q, Dong C, Häussler P 2014 Philos. Mag. 94 2520Google Scholar
[16] 张宇, 王清, 董红刚, 董闯, 张洪宇, 孙晓峰 2017 金属学报 54 591Google Scholar
Zhang Y, Wang Q, Dong H G, Dong C, Zhang H Y, Sun X F 2017 Acta Metall. Sin. 54 591Google Scholar
[17] Bragg W L, Williams E J 1934 Proc. R. Soc. London, Ser. A 151 699
[18] Williams E 1935 Proc. R. Soc. London, Ser. A 152 231Google Scholar
[19] Bethe H 1935 Proc. R. Soc. London, Ser. A 150 552Google Scholar
[20] Cowly J 1950 Phys. Rev. 77 669Google Scholar
[21] Cowly J 1960 Phys. Rev. 120 1648Google Scholar
[22] Cowly J 1965 Phys. Rev. 138 A1384Google Scholar
[23] Chen H, Wang Q, Wang Y M, Qiang J B, Dong C 2010 Philos. Mag. 90 3935Google Scholar
[24] Chen H, Wang Q, Wang Y M, Wang Y, Dong C 2011 Isr. J. Chem. 51 1226Google Scholar
[25] Wang Y, Wang Q, Zhao J, Dong C 2010 Scr. Mater. 63 178Google Scholar
[26] Yuan L, Pang C, Wang Y M, Wang Q, Qiang J B, Dong C 2010 Intermetallics 18 1800Google Scholar
[27] Li F W, Qiang J B, Wang Q, Wang Y M, Dong X L, Dong C, Zhu S J 2012 Intermetallics 30 86Google Scholar
[28] Wang Z R, Dong D D, Qiang J B, Wang Q, Wang Y M, Dong C 2013 Sci. China: Phys. Mech. Astron. 56 1419Google Scholar
[29] Wang Q, Zhu C L, Li Y H, Wu J, Dong C, Qiang J B, Zhang W, Inoue A 2007 Mater. Sci. Forum 561−565 1275Google Scholar
[30] 谷俊杰 2011 硕士学位论文 (大连: 大连理工大学)
Gu J J 2011 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese)
[31] Wang Q, Li Q, Li X N, Zhang R Q, Gao X X, Dong C, Liaw P K 2015 Metall. Mater. Trans. A 46 3924Google Scholar
[32] 王清, 查钱锋, 刘恩雪, 董闯, 王学军, 谭朝鑫, 龚春俊 2012 金属学报 48 1201Google Scholar
Wang Q, Zha Q F, Liu E X, Dong C, Wang X J, Tan C X, Gong C J 2012 Acta Metall. Sin. 48 1201Google Scholar
[33] 马仁涛, 郝传璞, 王清, 任明法, 王英敏, 董闯 2010 金属学报 46 1034Google Scholar
Ma R T, Hao C P, Wang Q, Ren M F, Wang Y M, Dong C 2010 Acta Metall. Sin. 46 1034Google Scholar
[34] 董丹丹 2017 博士学位论文 (大连: 大连理工大学)
Dong D D 2017 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)
[35] 董闯, 董丹丹, 王清 2018 金属学报 54 293Google Scholar
Dong C, Dong D D, Wang Q 2018 Acta Metall. Sin. 54 293Google Scholar
[36] Hong H L, Wang Q, Dong C 2015 Sci. China: Mater. 58 355Google Scholar
[37] Hong H L, Wang Q, Dong C, Liaw P K 2014 Sci. Rep. 4 7065Google Scholar
[38] 洪海莲, 董闯, 王清, 张宇, 耿遥祥 2016 物理学报 65 036101Google Scholar
Hong H L, Dong C, Wang Q, Zhang Y, Geng Y X 2016 Acta Phys. Sin. 65 036101Google Scholar
[39] Pearson W B 1973 J. Appl. Cryst. 6 306Google Scholar
[40] Pyczak F, Bauer A, Göken M, Lorenz U, Neumeier S, Oehring M, Paul J, Schell N, Schreyer A, Stark A, Symanzik F 2015 J. Alloys Compd. 632 110Google Scholar
[41] Povstugar I, Zenk C H, Li R, Choi P P, Neumeier S, Dolotko O, Hoelzel M, Göken M, Raabe D 2016 Mater. Sci. Technol. 32 220Google Scholar
[42] Shinagawa K, Omori T, Sato J, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2008 Mater. Trans. 49 1474Google Scholar
[43] Wang Y J, Wang C Y 2009 Appl. Phys. Lett. 94 261909Google Scholar
[44] Bocchini P J, Lass E A, Moon K W, Williams M E, Campbell C E, Kattner U R, Dunand D C, Seidman D N 2013 Scr. Mater. 68 563Google Scholar
[45] Povstugar I, Choi P P, Neumeier S, Bauer A, Zenk C H, Göken M, Raabe D 2014 Acta Mater. 78 78Google Scholar
[46] Meher S, Banerjee R 2014 Intermetallics 49 138Google Scholar
[47] Lass E A, Williams M E, Campbell C E, Moon K W, Kattner U R 2014 J. Phase Equilib. Diffus. 35 711Google Scholar
[48] Zhong F, Li S S, Sha J B 2015 Mater. Sci. Eng. A 637 175Google Scholar
[49] Sauza D J, Bocchini P J, Dunand D C, Seidman D N 2016 Acta Mater. 117 135Google Scholar
[50] Zhou H J, Xue F, Chang H, Feng Q 2018 J. Mater. Sci. Technol. 34 799Google Scholar
[51] Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817Google Scholar
[52] Shinagawa K, Omori T, Oikawa K, Kainuma R, Ishida K 2009 Scr. Mater. 61 612Google Scholar
[53] Chen M, Wang C Y. 2010 Phys. Lett. A 374 3238Google Scholar
[54] Ping D H, Cui C Y, Gu Y F, Harada H 2007 Ultramicroscopy 107 791Google Scholar
[55] Makineni S K, Nithin B, Chattopadhyay K 2015 Scr.Mater. 98 36Google Scholar
[56] Makineni S K, Samanta A, Rojhirunsakool T, Alam T, Nithin B, Singh A K, Banerjee R, Chattopadhyay K 2015 Acta Mater. 97 29Google Scholar
[57] Pollock T M, Dibbern J, Tsunekane M, Suzuki 2010 JOM 62 58Google Scholar
[58] Yan H Y, Vorontsov V A, Dye D 2014 Intermetallics 48 44Google Scholar
[59] Xue F, Zhou H J, Ding X F, Wang M L, Feng Q 2013 Mater. Lett. 112 215Google Scholar
[60] Xue F, Zhou H J, Feng Q 2014 JOM 66 2486Google Scholar
[61] Titus M S, Suzuki A, Pollock T M 2012 High Temperature Creep of New L12 Containing Cobalt‐Base Superalloys (New York: John Wiley Sons. Inc.) p823
[62] Shi L, Yu J J, Cui C Y, Sun X F 2015 Mater. Lett. 149 58Google Scholar
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图 2 合金数量随Co含量的变化, 虚线表示平均成分式
$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\overline {{\rm{Al}}} _{2.0}}$ Figure 2. Statistical distribution of alloy compositions as a function of at.% Co. The dashed vertical line represents the ideal composition formula
$\left[ {\overline {{\rm{Al}}} \text{-} {{\overline {{\rm{Co}}} }_{12}}} \right]{\overline {{\rm{Co}}} _{1.0}}{\overline {{\rm{Al}}} _{2.0}}$ 图 3
$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}},\overline {{\rm{Ta}}} } \right)$ 伪三元成分分布 (a) 合金成分; (b)$\gamma $ 和$\gamma′ $ 两相成分; 图中虚线为 Co-Al-W三元相图中富Co端1173 K等温截面相图[2], 中心成分点${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}$ ${\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{9.375}}$ 用蓝色空心三角形标出Figure 3.
$\overline {{\rm{Co}}} \text{-} {\rm{Al}} \text{-} \left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)$ pseudo-ternary composition diagram: (a) Alloy compositions; (b)$\gamma $ and$\gamma′ $ two phases compositions, where the dashed lines represent the isothermal section of the Co-Al-W ternary system in the Co-rich portion at 1173 K[2], and the blue hollow triangle points to the center composition${\overline {{\rm{Co}}} _{81.250}}{\rm{A}}{{\rm{l}}_{9.375}}{\left( {\overline {\rm{W}} ,\overline {{\rm{Ta}}} } \right)_{9.375}}$ 表 1 实测的
$\gamma $ 相成分和晶格常数[40-42], 以及按照(7)式计算的晶格常数Table 1. Measured compositions and lattice constants of
$\gamma $ phase in Co-Al-W-base superalloys[40-42], in comparison with the calculated lattice constants合金成分/at.% $\gamma $相成分/at.% 晶格常数实验值/nm 晶格常数计算值/nm 绝对误差$\varDelta $ Co82Al9W9 Co81.7Al9.3W9 0.3580 0.3579 0.0001 Co83Al9W8 Co81.9Al10.0W8.1 0.3576 0.3575 0.0001 Co80Al9W11 Co80.7Al9.2W10.2 0.3586 0.3588 0.0002 Co74Al9W9Cr8 Co73.9Al8.0W6.8Cr11.2 0.3578 0.3575 0.0003 Co64Al9W9Ni18 Co69.1Al6.8W7.0Ni16.9 0.3577 0.3562 0.0015 Co65Al9W9Ni9Cr8 Co66.7Al7.8W6.7Ni8.3Cr10.7 0.3581 0.3584 0.0003 Co56Al9W9Ni18Cr8 Co59.2Al6.0W7.4Ni15.6Cr11.8 0.3583 0.3581 0.0002 Co72.5Ni10Al10W7.5 Co76.2Al8.7W5.4Ni9.7 0.3578 0.3562 0.0016 表 2 实测
$\gamma′ $ 相成分和晶格常数[40-42]以及根据(9)式计算的W原子半径Table 2. Atomic radii of W fitted from measured compositions and lattice constants
$\gamma′$ phases in different alloys[40-42]合金成分/at.% $\gamma′ $相成分/at.% 晶格常数实验值/nm W原子半径/nm Co82Al9W9 Co77.49Al10.03W12.48 0.3594 0.1317 Co83Al9W8 Co76.6Al9.4W14 0.3589 0.1306 Co80Al9W11 Co75.1Al9.1W15.8 0.3595 0.1311 Co74Al9W9Cr8 Co73.9Al9.4W10.4Cr6.3 0.3587 0.1314 Co64Al9W9Ni18 Co58.9Al10.8W11.0Ni19.3 0.3590 0.1317 Co65Al9W9Ni9Cr8 Co64.2Al10.1W9.9Ni9.4Cr6.4 0.3587 0.1317 Co56Al9W9Ni18Cr8 Co54.5Al10.5W9.7Ni19.7Cr5.6 0.3587 0.1319 Co72.5Ni10Al10W7.5 Co68.8Al10.8W9.9Ni10.5 0.3593 0.1324 表 3 合金化组元与基体组元Co之间的混合焓
$\Delta H$ (单位: kJ/mol)及在$\gamma / \gamma′ $ 两相中的配分系数(${K_x} = {C_x}^{\gamma′}/{C_x}^\gamma $ )[9,10,40-42,44-52]Table 3. Heats of mixing
$\Delta H$ (unit: kJ/mol) between alloying elements and matrix element Co and their partition coefficients (${K_x} = {C_x}^{\gamma′ }/$ ${C_x}^\gamma $ ) for$\gamma$ and$\gamma′$ [9,10,40-42,44-52]元素分类 合金化元素 混合焓$\Delta H$/kJ·mol 元素配分系数K ${\overline {{\rm{Co}}} ^{\gamma }}$ Cr –4 0.48—0.60 Fe –1 Re 2 ${\overline {{\rm{Co}}} ^{\gamma′ }}$ Ni –2 1.08—1.27 Ru –1 Ir –3 Al Al –19 0.93—1.60 ${\overline {\rm{W}} }$ W –1 1.03—6.21 Mo –5 ${\overline {{\rm{Ta}}} }$ V –14 1.57—8.67 Ta –24 Nb –25 Ti –28 Sc –30 Hf –35 表 4 Co-Al-W基多元合金的团簇成分式, 所列成分源自文献[2-4, 6, 8, 10, 39, 40-42, 44, 45, 48, 51, 57-62]
Table 4. Compositions formulas of Co-Al-W-base multi-element superalloys. The alloy compositions are taken from references [2-4, 6, 8, 10, 39, 40-42, 44, 45, 48, 51, 57-62]
合金成分/at.% 团簇成分式-[团簇](连接原子)3 连接原子 Co78Al10W10Ta2 [Al-Co12]Co0.5Al0.6W1.6Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co78Al9W10Mo3 [Al-Co12]Co0.5Al0.4W1.6Mo0.5 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.5}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{2.1}}$ Co79Al9W10Ti2 [Al-Co12]Co0.6Al0.4W1.6Ti0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W10V2 [Al-Co12]Co0.6Al0.4W1.6V0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W10Si2 [Al-Co12]Co0.6Al0.4W1.6Si0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W8Ta2Nb2 [Al-Co12]Co0.6Al0.4W1.3Ta0.3Nb0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$ Co79Al9W8Ta2V2 [Al-Co12]Co0.6Al0.4W1.3Ta0.3V0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.6}}$ Co79Al8W9Ta2Ti2 [Al-Co12]Co0.6Al0.3W1.4Ta0.3Ti0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\rm{A}}{{\rm{l}}_{0.3}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.6}}$ Co79.5Al9.7W10.8 [Al-Co12]Co0.7Al0.6W1.7 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.7}{\rm{A}}{{\rm{l}}_{0.6}}{\overline {\rm{W}} _{1.7}}$ Co79.9Al9.4W10.7 [Al-Co12]Co0.8Al0.5W1.7 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$ Co80Al9W11 [Al-Co12]Co0.8Al0.4W1.8 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.8}}$ Co80Al9W9Ti2 [Al-Co12]Co0.8Al0.4W1.4Ti0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$ Co80Al9W9V2B0.04 [Al-Co12]Co0.8Al0.4W1.4V0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$ Co80Al9W9Ta2 [Al-Co12]Co0.8Al0.4W1.4Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.3}}$ Co80.3Al9.3W10.4 [Al-Co12]Co0.8Al0.5W1.7 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.7}}$ Co80.5Al9W10Si0.5 [Al-Co12]Co0.9Al0.4W1.6Si0.1 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.9}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}{\overline {{\rm{Ta}}} _{0.1}}$ Co81Al9W9Mo1B0.04 [Al-Co12]Co1.0Al0.4W1.4Mo0.2 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$ Co81Al9W8Ta2 [Al-Co12]Co1.0Al0.4W1.3Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$ Co81.3Al9.2W9.5 [Al-Co12]Co1.0Al0.5W1.5 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.5}}$ Co81.5Al9W9Nb0.5 [Al-Co12]Co1.0Al0.4W1.4Nb0.1 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}{\overline {{\rm{Ta}}} _{0.1}}$ Co81.5Al9W5.5Ta2Mo2 [Al-Co12]Co1.0Al0.4W0.9Ta0.3Mo0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.0}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.2}}{\overline {{\rm{Ta}}} _{0.3}}$ Co82Al9W9 [Al-Co12]Co1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co72Al9W9Ni10 [Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co82Al9W7.5Mo1.5 [Al-Co12]Co1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co80Al9W9Cr2B0.04 [Al-Co12]Co0.8Cr0.3Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.8}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.6}}$ Co78Al9W9Cr4 [Al-Co12]Co0.6Cr0.6Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.6}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co73Al9W9Ni9 [Al-Co11.7Ni0.3]Ni1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co64Al9W9Ni18 [Al-Co10.2Ni1.8]Ni1.1Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co81.8Al9.2W9 [Al-Co12]Co1.1Al0.5W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.1}{\rm{A}}{{\rm{l}}_{0.5}}{\overline {\rm{W}} _{1.4}}$ Co72.5Al10W7.5Ni10 [Al-Co11.6Ni0.4]Ni1.2Al0.4W1.4 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.2}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.4}}$ Co81.5Al9W5.5Ta2Ir2 [Al-Co2]Co1.0Al0.4W0.9Ta0.3Ir0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{1.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{0.9}}{\overline {{\rm{Ta}}} _{0.3}}$ Co79Al9W8Ta2Cr2 [Al-Co12]Co0.6Cr0.3Al0.4W1.3Ta0.3 ${\overline {{\rm{Co}}} ^{\gamma′ }}_{0.6}{\overline {{\rm{Co}}} ^\gamma }_{0.3}{\rm{A}}{{\rm{l}}_{0.4}}{\overline {\rm{W}} _{1.3}}{\overline {{\rm{Ta}}} _{0.3}}$ 表 5 部分Co-Al-W基高温合金中
$\gamma $ 和$\gamma′ $ 两相团簇式[40,42,44,45]Table 5. Composition formulas of
$\gamma $ and$\gamma′ $ phases in some Co-Al-W-base superalloys[40,42,44,45]合金成分/at.% $\gamma $相团簇成分式 $\gamma′ $相团簇成分式 Co82Al9W9 [Al-Co12]Co1.6Al0.4W1.0 [Al-Co12]Co0.3Al0.5W2.2 Co78Al9W9Cr4 [Al-Co12]Co0.9Al0.3W0.9Cr0.9 [Al-Co12]Co0.2Al0.5W1.8Cr0.5 Co73Al9W9Ni18 [Al-Co11.1Ni0.9]Al0.1W1.1Ni1.8 [Al-Co9.4Ni2.6]Al0.7W1.8Ni0.5 Co79.5Al9.7W10.8 [Al-Co12]Co1.7Al0.4W0..9 [Al-Co12]Co0.4Al0.6W2.0 Co80Al9W9Ti2 [Al-Co12]Co1.6Al0.4W0.8Ti0.2 [Al-Co12]Co0.2Al0.4W1.9Ti0.4 Co80Al9W9Ta2 [Al-Co12]Co1.8Al0.4W0.7Ta0.1 [Al-Co12]Co0.2Al0.4W1.9Ta0.5 Co79Al8W9Ta2Ti2 [Al-Co12]Co2.0Al0.3W0.5Ta0.04Ti0.1 [Al-Co12]Co0.1Al0.4W1.9Ta0.3Ti0.3 Co78Al10W10Ta2 [Al-Co12]Co1.6Al0.7W0.7Ta0.1 [Al-Co12]Al0.7W1.9Ta0.4 Co78Al9W10Mo3 [Al-Co12]Co1.7Al0.1W0.8Mo0.4 [Al-Co12]Co0.2Al0.6W1.7Mo0.5 -
[1] Sims C T, Hagel W C 1972 The Superalloys (New York: John Wiley & Sons) p1
[2] Sato J, Omori T, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2006 Science 312 90Google Scholar
[3] Suzuki A, Pollock T M 2008 Acta Mater. 56 1288Google Scholar
[4] Bauer A, Neumeiera S, Pyczakb F, Singer R F, Göken M 2012 Mater. Sci. Eng. 550 333Google Scholar
[5] Klein L, Shen Y, Killian M S, Virtanen S 2011 Corros. Sci. 53 2713Google Scholar
[6] Ooshima M, Tanaka K, Okamoto N L, Kishida K, Inui H 2010 J. Alloys Compd. 508 71Google Scholar
[7] Chen M, Wang C Y 2009 Scr. Mater. 60 659Google Scholar
[8] Bauer A, Neumeier S, Pyczakc F, Göken M 2010 Scr. Mater. 63 1197Google Scholar
[9] Kobayashi S, Tsukamoto Y, Takasugi T 2012 Intermetallics 31 94Google Scholar
[10] Meher S, Yan H Y, Nag S, Dye D, Banerjee R 2012 Scr. Mater. 67 850Google Scholar
[11] Morinaga M, Yukawa N, Ezaki H, Adachi H 1984 Superalloys (Warrendale, PA: The Metallurgical Society of AIME) p523
[12] 张继山, 崔华, 胡壮麟, 村田纯教, 森永正彦, 汤川夏夫 1993 金属学报 29 289Google Scholar
Zhang J S, Cui H, Hu Z L, Murata Y, Morinaga M, Yukawa N 1993 Acta Metall. Sin. 29 289Google Scholar
[13] Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D: Appl. Phys. 40 R273Google Scholar
[14] Han G, Qiang J B, Li F W, Yuan L, Quan S G, Wang Q, Wang Y M, Dong C, Häussler P 2011 Acta Mater. 59 5917Google Scholar
[15] Luo L J, Chen H, Wang Y M, Qiang J B, Wang Q, Dong C, Häussler P 2014 Philos. Mag. 94 2520Google Scholar
[16] 张宇, 王清, 董红刚, 董闯, 张洪宇, 孙晓峰 2017 金属学报 54 591Google Scholar
Zhang Y, Wang Q, Dong H G, Dong C, Zhang H Y, Sun X F 2017 Acta Metall. Sin. 54 591Google Scholar
[17] Bragg W L, Williams E J 1934 Proc. R. Soc. London, Ser. A 151 699
[18] Williams E 1935 Proc. R. Soc. London, Ser. A 152 231Google Scholar
[19] Bethe H 1935 Proc. R. Soc. London, Ser. A 150 552Google Scholar
[20] Cowly J 1950 Phys. Rev. 77 669Google Scholar
[21] Cowly J 1960 Phys. Rev. 120 1648Google Scholar
[22] Cowly J 1965 Phys. Rev. 138 A1384Google Scholar
[23] Chen H, Wang Q, Wang Y M, Qiang J B, Dong C 2010 Philos. Mag. 90 3935Google Scholar
[24] Chen H, Wang Q, Wang Y M, Wang Y, Dong C 2011 Isr. J. Chem. 51 1226Google Scholar
[25] Wang Y, Wang Q, Zhao J, Dong C 2010 Scr. Mater. 63 178Google Scholar
[26] Yuan L, Pang C, Wang Y M, Wang Q, Qiang J B, Dong C 2010 Intermetallics 18 1800Google Scholar
[27] Li F W, Qiang J B, Wang Q, Wang Y M, Dong X L, Dong C, Zhu S J 2012 Intermetallics 30 86Google Scholar
[28] Wang Z R, Dong D D, Qiang J B, Wang Q, Wang Y M, Dong C 2013 Sci. China: Phys. Mech. Astron. 56 1419Google Scholar
[29] Wang Q, Zhu C L, Li Y H, Wu J, Dong C, Qiang J B, Zhang W, Inoue A 2007 Mater. Sci. Forum 561−565 1275Google Scholar
[30] 谷俊杰 2011 硕士学位论文 (大连: 大连理工大学)
Gu J J 2011 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese)
[31] Wang Q, Li Q, Li X N, Zhang R Q, Gao X X, Dong C, Liaw P K 2015 Metall. Mater. Trans. A 46 3924Google Scholar
[32] 王清, 查钱锋, 刘恩雪, 董闯, 王学军, 谭朝鑫, 龚春俊 2012 金属学报 48 1201Google Scholar
Wang Q, Zha Q F, Liu E X, Dong C, Wang X J, Tan C X, Gong C J 2012 Acta Metall. Sin. 48 1201Google Scholar
[33] 马仁涛, 郝传璞, 王清, 任明法, 王英敏, 董闯 2010 金属学报 46 1034Google Scholar
Ma R T, Hao C P, Wang Q, Ren M F, Wang Y M, Dong C 2010 Acta Metall. Sin. 46 1034Google Scholar
[34] 董丹丹 2017 博士学位论文 (大连: 大连理工大学)
Dong D D 2017 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)
[35] 董闯, 董丹丹, 王清 2018 金属学报 54 293Google Scholar
Dong C, Dong D D, Wang Q 2018 Acta Metall. Sin. 54 293Google Scholar
[36] Hong H L, Wang Q, Dong C 2015 Sci. China: Mater. 58 355Google Scholar
[37] Hong H L, Wang Q, Dong C, Liaw P K 2014 Sci. Rep. 4 7065Google Scholar
[38] 洪海莲, 董闯, 王清, 张宇, 耿遥祥 2016 物理学报 65 036101Google Scholar
Hong H L, Dong C, Wang Q, Zhang Y, Geng Y X 2016 Acta Phys. Sin. 65 036101Google Scholar
[39] Pearson W B 1973 J. Appl. Cryst. 6 306Google Scholar
[40] Pyczak F, Bauer A, Göken M, Lorenz U, Neumeier S, Oehring M, Paul J, Schell N, Schreyer A, Stark A, Symanzik F 2015 J. Alloys Compd. 632 110Google Scholar
[41] Povstugar I, Zenk C H, Li R, Choi P P, Neumeier S, Dolotko O, Hoelzel M, Göken M, Raabe D 2016 Mater. Sci. Technol. 32 220Google Scholar
[42] Shinagawa K, Omori T, Sato J, Oikawa K, Ohnuma I, Kainuma R, Ishida K 2008 Mater. Trans. 49 1474Google Scholar
[43] Wang Y J, Wang C Y 2009 Appl. Phys. Lett. 94 261909Google Scholar
[44] Bocchini P J, Lass E A, Moon K W, Williams M E, Campbell C E, Kattner U R, Dunand D C, Seidman D N 2013 Scr. Mater. 68 563Google Scholar
[45] Povstugar I, Choi P P, Neumeier S, Bauer A, Zenk C H, Göken M, Raabe D 2014 Acta Mater. 78 78Google Scholar
[46] Meher S, Banerjee R 2014 Intermetallics 49 138Google Scholar
[47] Lass E A, Williams M E, Campbell C E, Moon K W, Kattner U R 2014 J. Phase Equilib. Diffus. 35 711Google Scholar
[48] Zhong F, Li S S, Sha J B 2015 Mater. Sci. Eng. A 637 175Google Scholar
[49] Sauza D J, Bocchini P J, Dunand D C, Seidman D N 2016 Acta Mater. 117 135Google Scholar
[50] Zhou H J, Xue F, Chang H, Feng Q 2018 J. Mater. Sci. Technol. 34 799Google Scholar
[51] Takeuchi A, Inoue A 2005 Mater. Trans. 46 2817Google Scholar
[52] Shinagawa K, Omori T, Oikawa K, Kainuma R, Ishida K 2009 Scr. Mater. 61 612Google Scholar
[53] Chen M, Wang C Y. 2010 Phys. Lett. A 374 3238Google Scholar
[54] Ping D H, Cui C Y, Gu Y F, Harada H 2007 Ultramicroscopy 107 791Google Scholar
[55] Makineni S K, Nithin B, Chattopadhyay K 2015 Scr.Mater. 98 36Google Scholar
[56] Makineni S K, Samanta A, Rojhirunsakool T, Alam T, Nithin B, Singh A K, Banerjee R, Chattopadhyay K 2015 Acta Mater. 97 29Google Scholar
[57] Pollock T M, Dibbern J, Tsunekane M, Suzuki 2010 JOM 62 58Google Scholar
[58] Yan H Y, Vorontsov V A, Dye D 2014 Intermetallics 48 44Google Scholar
[59] Xue F, Zhou H J, Ding X F, Wang M L, Feng Q 2013 Mater. Lett. 112 215Google Scholar
[60] Xue F, Zhou H J, Feng Q 2014 JOM 66 2486Google Scholar
[61] Titus M S, Suzuki A, Pollock T M 2012 High Temperature Creep of New L12 Containing Cobalt‐Base Superalloys (New York: John Wiley Sons. Inc.) p823
[62] Shi L, Yu J J, Cui C Y, Sun X F 2015 Mater. Lett. 149 58Google Scholar
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