Initial oxidation behavior of a single crystal superalloy during stress at 1150 °C
单晶高温合金在 1150 °C 应力下的初始氧化行为

Nickel-based single crystal superalloys have been widely used in turbine blades and other hot-end components of modern aeroengines due to their excellent creep and mechanical properties^1,2. To improve turbine efficiency, increasing turbine entry temperature is challenging superalloy’s operational limits³. Such high temperature also causes the rotating components (turbine discs and blades) to bear high centrifugal stresses⁴. Actually, except for high temperature and heavily stress, oxidation and hot corrosion unavoidably degrade the performance of turbine blades during service condition^5,6. Though thermal barrier coating (TBC) technology has been developed to avoid direct contact between high-temperature gas and turbine blades⁷ and also prevent the direct contact between oxygen and blades to some degree, the oxidation is still inevitable especially when the spallation or cracking of the TBC occurs. In many cases oxidation has been described as the precursor to fatigue damage⁸ and cause of inferior creep performance of thin wall superalloy⁹. Hence for better understanding the oxidation process is of great importance.
镍基单晶高温合金因其优异的蠕变和机械性能而被广泛用于涡轮叶片和现代航空发动机的其他热端部件^1,2。为了提高涡轮机效率，提高涡轮机入口温度对高温合金的运行极限提出了挑战³。这种高温还导致旋转部件（涡轮盘和叶片）承受高离心应力⁴。实际上，除了高温和重应力外，氧化和热腐蚀不可避免地会降低涡轮叶片在使用状态下的性能^5,6。尽管已经开发了热障涂层 （TBC） 技术来避免高温气体和涡轮叶片之间的直接接触⁷，并在一定程度上防止氧气与叶片之间的直接接触，但氧化仍然是不可避免的，尤其是当 TBC 发生剥落或开裂时。在许多情况下，氧化被描述为疲劳损伤⁸ 的前体，也是薄壁高温合金⁹ 蠕变性能较差的原因。因此，为了更好地了解氧化过程非常重要。

Though there are extensive researches focusing on oxidation behavior of superalloy during intermediate and high temperature^10,11,12, the initial oxidation process has not been observed clearly considering the rapid formation of adherent oxide scale. Through in-situ environmental transmission electron microscopy (ETEM), initial oxidation at only thermal exposure was observed by Ding¹³, and gave the proof that oxygen diffusion path is more inclined to be the interface rather than matrix channels¹⁴. However, considering the real service condition, the temperature of turbine blades can reach about 1150 °C even 1200 °C during emergency regimes¹⁵, and the loadings in [001] direction caused by thermal stress vary by around 400 MPa¹⁶. Researches of initial oxidation combining both thermal and stress are rarely reported until now.
尽管对高温合金在中高温下的氧化行为进行了广泛的研究^{10,11,12，但}考虑到粘附氧化皮的快速形成，尚未清楚地观察到初始氧化过程。通过原位环境透射电子显微镜 （ETEM），Ding¹³ 观察到仅在热暴露下发生初始氧化，并证明氧扩散路径更倾向于成为界面而不是基质通道¹⁴。然而，考虑到实际使用条件，在紧急情况下，涡轮叶片的温度可以达到1150°C左右甚至1200°^C15，并且[001]热应力引起的载荷方向的变化约为400^MPa16。到目前为止，结合热和应力的初始氧化的研究很少报道。

In this paper, microstructure evolution during oxidation of a nickel-based single crystal superalloy during only thermal exposure and thermal-stress pattern was studied by carrying out in-situ experiments in scanning electron microscope (SEM) at 1150 °C and 1150 °C/330 MPa under an oxygen partial pressure of 2 × 10⁻⁹ atm. The oxide scale was characterized by transmission electron microscopy (TEM) qualitatively. The mechanism of oxide nucleation and growth was discussed.
本文通过在 1150 °C 和 1150 °C/330 MPa 的扫描电子显微镜 （SEM） 中在 2 × 10⁻⁹ atm 的氧分压下进行原位实验，研究了镍基单晶高温合金在仅热暴露和热应力模式下氧化过程中的微观组织演变。透射电子显微镜 （TEM） 对氧化皮进行定性表征。讨论了氧化物成核和生长的机制。

Materials 材料

The [001] orientation nickel-based single crystal superalloy bar is 170 mm in length and 15 mm in diameter and its chemical composition are 4.3 wt% Cr, 9.1 wt% Co, 8.0 wt% W, 5.2 wt% Al, 6.0 wt% Ta, 2.5 wt% Re, 1.5 wt% Mo, 0.1 wt% Hf, 0.5 wt% Nb and others is Ni. Standard heat treatment is performed referring to the previous articles^17,18. Then, the alloy bar was processed into in-situ test specimens along [001] direction and perpendicular to [010] direction, the shape of specimen is shown as Fig. 1(a) and the dimension is marked as Fig. 1(b). The narrow region in the middle of the specimen is used for microstructure observation in SEM. The specimen is mechanically polished up to a mirror, then etched in a solution made of HNO₃(40%)+ H₃PO₄(12%)+ H₂SO₄(48%) for 10 seconds. Figure 1(c) shows the specimen global micrograph in low magnification, and γ microstructure is illustrated in Fig. 1(d). it shows that the γ′ cuboids (ordered L12 phase, average cube edge length: 450 nm) are separated by thin brighter γ channels (fcc crystal structure, average channel width: 80 nm) and distribute uniformly all over the material.
[001] 取向镍基单晶高温合金棒的长度为170 mm，直径为15 mm，其化学成分为4.3 wt% Cr、9.1 wt% Co、8.0 wt% W、5.2 wt% Al、6.0 wt% Ta、2.5 wt% Re、1.5 wt% Mo、0.1 wt% Hf、0.5 wt% Nb等为Ni。标准热处理参照前文第^17、18 条进行。然后，将合金棒沿[001]方向和垂直于[010]方向加工成原位试样，试样的形状如图1所示。1（a） 的，尺寸标记为图 1。1（b） 的。样品中间的狭窄区域用于 SEM 中的微观结构观察。将样品机械抛光至镜面，然后在 HNO₃ （40%） + H₃PO₄ （12%） + H₂SO₄ （48%） 制成的溶液中蚀刻 10 秒。图 1（c） 显示了低倍率下的标本整体显微照片，γ微观结构如图 1（d） 所示 。它表明 γ' 长方体（有序 L12 相，平均立方体边长：450 nm）被较亮的薄γ通道（FCC 晶体结构，平均通道宽度：80 nm）隔开，并均匀分布在整个材料中。

In-situ heating tensile specimen. (a) shape, (b) dimension, (c) micrograph of low-magnification and (d) micrograph of high-magnification.
原位加热拉伸试样。（a） 形状，（b） 尺寸，（c） 低倍显微照片和 （d） 高倍显微照片。

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Instrument 仪器

In-situ tensile test equipment developed by coauthors consists of the high-temperature tensile test machine shown as Fig. 2(b) and SEM (TESCAN S8000) shown as Fig. 2(a). The nickel-based single crystal superalloy specimen is fixed on a loading frame grip and is right above the heater’s surface shown as Fig. 2(b). The heating area is 8 mm in diameter at center of the specimen and a thermocouple contacts the back surface of specimen. In-situ experiment under thermal exposure at 1150 °C and thermal exposure with 330 MPa was carried out in the SEM vacuum chamber, chamber pressure is kept at 10⁻³ Pa, the oxygen partial pressure is about 2 × 10⁻⁹ atm, the real-time observation was conducted during the experiment.
合著者开发的原位拉伸试验设备由如图 2（b） 所示 的高温拉伸试验机和如图 2 所示的 SEM （TESCAN S8000） 组成。2（a） 项。镍基单晶高温合金试样固定在加载框架夹具上，位于加热器表面的正上方，如图 2（b） 所示。样品中心的加热区域直径为 8 mm，热电偶接触样品的背面。在 SEM 真空室中进行了 1150 °C 热暴露和 330 MPa 热暴露下的原位实验，腔室压力保持在 10⁻³ Pa，氧分压约为 2 × 10⁻⁹ 个大气压，实验过程中进行了实时观察。

(a) In-situ tensile test equipment, (b) High-temperature tensile test machine.
（a） 原位拉伸试验设备，（b） 高温拉伸试验机。

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Element distribution before and after the experiment was characterized in FEI Titan G2 TEM by OXFORD X-Max energy dispersive spectrum (EDS), samples were extracted by FEI Helios NanoLab FIB from the specimen.
采用 OXFORD X-Max 能量色散谱 （EDS） 对 FEI Titan G2 TEM 中实验前后的元素分布进行了表征，并通过 FEI Helios NanoLab FIB 从样品中提取样品。

The pattern of heating and stress loaded
加热和应力加载的模式

In this paper, the heating process was realized through electrical heating by adjusting input voltage in a range of 0 ~ 8.3 V, and the stress loaded process was achieved by uniaxial tensile, the details of equipment has been reported in our previous study¹⁹, Fig. 3 shows the temperature, displacement, and loading stress at different time during the experiment. In the beginning, temperature increased by increasing the voltage, turning points in temperature curve is caused by a sudden increase in voltage. The temperature reached 1150 °C after heating for 140 min. Then, it kept at 1150 °C and this period could be called thermal exposure. After thermal exposure for 100 min, Stress was loaded with a tensile displacement which was 1 μm/s, shown as the red and blue dashed lines in Fig. 3. Although a force about 50 N was preloaded before heating, the stress didn’t increase immediately with stress loading process considering the effect of thermal expansion. When the stress reached 330 MPa, the displacement was quitted to keep stress stable. In-situ observing time was located in the rage of 160 ~ 340 min. In the end, the specimen was cooled in furnace to room temperature, and stress was unloaded before specimen was taken out.
在本文中，通过在 0 ~ 8.3 V 范围内调节输入电压，通过电加热实现加热过程，通过单轴拉伸实现应力加载过程，设备的详细信息已在我们之前的研究 19 中报道，图¹⁹。3 显示了实验过程中不同时间的温度、位移和加载应力。开始时，温度通过增加电压而升高，温度曲线的转折点是由电压的突然增加引起的。加热 140 min 后温度达到 1150 °C。然后，它保持在 1150 °C，这段时间可以称为热暴露。热暴露 100 分钟后，应力加载了 1 μm/s 的拉伸位移，如图 1 中的红色和蓝色虚线所示。3. 虽然在加热前预加载了约 50 N 的力，但考虑到热膨胀的影响，应力加载过程并没有立即增加。当应力达到 330 MPa 时，停止位移以保持应力稳定。原位观测时间位于 160 ~ 340 min 左右。最后，试样在炉中冷却至室温，并在取出试样之前卸下应力。

The pattern of heating process and stress loaded during experiment.
实验过程中的加热过程和应力加载模式。

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Microstructure evolution 微观结构演变

Figure 4 shows a series of microstructure of superalloy during 1150 °C thermal exposure condition for different times. After 20 min of thermal exposure, the microstructure of specimen is the same as the initial one. Small precipitates appear on the origin interface of γ′/γ phase after thermal exposure for 40 min and prefer gathering along [001] direction, as indicated by red arrows in Fig. 4(c). After specimen oxidized for 80 min, the small precipitates also emerge and locate along [100] direction, shown by blue arrows in Fig. 4(d). With thermal exposure time increasing, the precipitates grow slowly on the interface. Also, the precipitates on γ′ phase show the trend of nucleation and growth, clearly shown in Fig. 4(e,f).
图 4 显示了高温合金在 1150 °C 热暴露条件下不同时间的一系列微观组织。热暴露 20 min 后，样品的微观结构与初始相同。热暴露 40 分钟后，小沉淀物出现在 γ′/γ 相的起始界面上，并且喜欢沿 [001] 方向聚集，如图 4（c） 中的 红色箭头所示。样品氧化 80 分钟后，小沉淀物也出现并沿 [100] 方向定位，如图 4（d） 中的 蓝色箭头所示。随着热暴露时间的增加，沉淀物在界面上缓慢生长。此外，γ' 相上的沉淀物显示出成核和生长的趋势，如图 4（e，f） 中 清楚地显示。

SEM images showing the microstructure evolution at 1150 °C during thermal exposure for (a) 20 min, (b) 40 min, (c) 50 min, (d) 80 min, (e) 100 min and (f) 120 min.
SEM 图像显示了在热暴露期间 （a） 20 min、（b） 40 min、（c） 50 min、（d） 80 min、（e） 100 min 和 （f） 120 min 期间在 1150 °C 下的微观结构演变。

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After thermal exposure oxidation for 120 min, stress was loaded to the same specimen along [001] direction and increased gradually to 330 MPa. Although the stress dose not increase immediately, the displacement (or more precisely of the strain) of specimen has increased with time, as displayed in Fig. 3. It appears the precipitates grow more rapidly while the stress was loaded. Precipitates are well advanced after 135 min thermal exposure and 15 min stress loading, they have fully occupied the original interface, as shown in Fig. 5(b). The growth of precipitates observed in Fig. 5(c) is more obvious, and it shows the direction of precipitate’s growth is outward, which makes the area marked as dashed lines in Fig. 4(a) become small. Then, the growth of precipitates tends to be slow after 175 min, shown as Fig. 5(d–f).
热暴露氧化 120 min 后，应力沿 [001] 方向加载到同一试样上，并逐渐增加到 330 MPa。虽然应力剂量不会立即增加，但试样的位移（或更准确地说是应变）随着时间的推移而增加，如图 3 所示 。当应力加载时，沉淀物似乎增长得更快。沉淀物在 135 min 的热暴露和 15 min 的应力加载后进展良好，它们已经完全占据了原始界面，如图 5（b） 所示 。图 5（c） 中观察到的沉淀物的增长更为明显，它表明沉淀物的增长方向是向外的，这使得该区域在图 5 中标记为虚线。4（a） 变小。然后，沉淀物在 175 分钟后生长趋于缓慢，如图 1 所示。5（d-f）。

SEM images showing the microstructure evolution with stress loaded during thermal exposure at 1150 °C for (a) 120 min, (b) 135 min, (c) 150 min, (d) 175 min, (e) 190 min and (f) 200 min.
SEM 图像显示了在 1150 °C 热暴露期间 （a） 120 min、（b） 135 min、（c） 150 min、（d） 175 min、（e） 190 min 和 （f） 200 min 期间应力加载下的微观结构演变。

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Element distribution 元素分布

Figure 6(a) presents a HAADF STEM overview image of surface of the specimen before the experiment, typical and cuboidal γ/γ′ microstructure can be seen clearly, and the interface of them is obvious. Figure 6(b–f) show a representative element distribution maps of the specimen characterized by EDS, the Ni₃Al γ′ phase displays concentrations of Al and Ni. The γ phase mainly contains Ni (at lower level compared with γ′ phase), Cr, Co and Re, those elements are separated in γ channels uniformly.
图 6（a） 显示了实验前样品表面的 HAADF STEM 概览图像，可以清楚地看到典型的立方体 γ/γ' 微观结构，它们的界面很明显。图 6（b–f） 显示了以 EDS 为特征的样品的代表性元素分布图，Ni₃Al γ' 相显示 Al 和 Ni 的浓度。γ相主要包含 Ni（与 γ′ 相相比含量较低）、Cr、Co 和 Re，这些元素均匀地分离在 γ 通道中。

(a) HAADF STEM image of surface of the specimen before oxidation, (b–f) EDS element distribution for Al, Cr, Co, Ni and Re on the surface of specimen before oxidation.
（a） 氧化前试样表面的 HAADF STEM 图像，（b–f） 氧化前试样表面 Al、Cr、Co、Ni 和 Re 的 EDS 元素分布。

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After the oxidation experiment, the element distribution of air-cooling specimen was mapped in Fig. 7(a–f) by EDS, Al and O elements show almost the same distribution, it indicates the precipitate are mainly Al₂O₃, which is also found in γ channel reported by Weiser²⁰. In this paper, more precisely, nucleation on the original interface of the two phases or called the side surface of γ phase was clearly observed. The diffusion toward γ′ phase of elements Cr, Co and Re occur slightly. While the γ phase is covered with an Al₂O₃ oxide layer, Al is being depleted next to the oxide-alloy interface. Then Ni becomes enriched at Al depleted zone shown in Fig. 4(e), and this phenomenon is analogous to Wagner’s experiments on Cu-Pt and Cu-Pd alloys²¹. Actually, the original interface of γ/γ′ phase, side surface of γ phase and oxide-alloy interface is the same interface.
氧化实验后，用 EDS 绘制了图 7（a-f） 中 风冷样品的元素分布，Al 和 O 元素的分布几乎相同，表明沉淀物主要是 Al₂O₃，这也存在于 Weiser²⁰ 报道γ通道中。在本文中，更准确地说，清楚地观察到两相的原始界面上或称为γ相的侧面上的成核。元素 Cr、Co 和 Re 向 γ' 相的扩散略有发生。虽然 γ 相覆盖着 Al₂O₃ 氧化层，但 Al 在氧化物-合金界面旁边被耗尽。然后 Ni 在图 4（e） 所示的 Al 耗尽区富集，这种现象类似于 Wagner 对 Cu-Pt 和 Cu-Pd 合金的实验²¹。实际上，γ/γ' 相的原始界面、γ相的侧面和氧化物-合金界面是相同的界面。
氧化实验后，风冷样品的元素分布如图 1 所示。EDS 的 7（a–f） 、Al 和 O 元素显示出几乎相同的分布，表明沉淀物主要是 Al₂O₃，这也存在于 Weiser²⁰ 报道的γ通道中。在本文中，更准确地说，清楚地观察到两相的原始界面上或称为γ相的侧面上的成核。元素 Cr、Co 和 Re 向 γ' 相的扩散略有发生。虽然 γ 相覆盖着 Al₂O₃ 氧化层，但 Al 在氧化物-合金界面旁边被耗尽。然后 Ni 在 Al 耗尽区富集，如图 1 所示。4（e） 的，这种现象类似于瓦格纳对 Cu-Pt 和 Cu-Pd 合金的实验²¹。实际上，γ/γ' 相的原始界面、γ相的侧面和氧化物-合金界面是相同的界面。

(a–f) EDS element distribution for O, Al, Cr, Co, Ni and Re on the surface of specimen after oxidation.
（a-f）氧化后样品表面 O、Al、Cr、Co、Ni 和 Re 的 EDS 元素分布。

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In order to quantify the composition at different positions after oxidation, several EDS line scans were taken from the surface of specimen and crossed both γ and γ′ phases, which is shown by the horizontal red dashed line in both Fig. 7(b) and Fig. 5. The alloy-oxide surface is marked as the blue dashed lines in Fig. 8 according to the high content of Al and O elements caused by diffusion and adsorption, respectively. The width of γ channel is about 70 nm close to the average width 80 nm described in Fig. 1(d). Moreover, Ta, W, Co, Cr, and even Re show slightly diffusion in oxide scale, which is caused by concentration gradient. Also, some compound oxide might form nearby new surface of oxide scale, but it could be negligible. The new surface is displayed by the yellow dashed lines in Fig. 8. It can be seen the thickness of oxide scale in sideway direction could reach almost 90 nm. This value was little higher than that analyzed in discussion section since the oxidation was more likely proceeding during the cooling period and also different zone was selected.
为了量化氧化后不同位置的成分，从样品表面采集了几次 EDS 线扫描，并穿过 γ 和 γ' 相，如图 7（b） 和图 7（b） 和图 7 中的水平红色虚线所示。 5. 合金氧化物表面在图 5 中标记为蓝色虚线。8 根据 Al 和 O 元素含量高分别由扩散和吸附引起。γ通道的宽度约为 70 nm，接近图 1（d） 中描述的平均宽度 80 nm。此外，Ta、W、Co、Cr 甚至 Re 在氧化物标度中表现出轻微的扩散，这是由浓度梯度引起的。此外，一些化合物氧化物可能会在氧化皮的新表面附近形成，但可以忽略不计。新表面由图 8 中的黄色虚线显示。可以看出，侧向氧化皮的厚度可以达到近 90 nm。该值略高于讨论部分中分析的值，因为氧化更有可能在冷却期间进行，并且还选择了不同的区域。

EDS line scans taken across the surface of specimen after oxidation experiment.
氧化实验后在样品表面进行的 EDS 线扫描。

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Figure 9(a–f) shows the element distribution for O, Al, Cr, Co, Ni and Re in depth direction of specimen after oxidation. It can be seen on the bottom interface γ/γ′ phase also occurred oxidation. And the severely oxidized zone circled by the white dashed line in Fig. 9(a) analogies that in Fig. 7(b), which indicates the oxidation occurred on both side and bottom interfaces of γ/γ′ phase. It also could be deduced from the change of original side interfaces morphology in Fig. 5(c–f). The oxide scale thickness formed on the bottom is about 50 nm. The diffusion of Cr, Co, Ni, and Re elements seems week in depth direction.
图 9（a-f） 显示了氧化后样品深度方向上 O、Al、Cr、Co、Ni 和 Re 的元素分布。可见在底部界面上 γ/γ′ 相也发生氧化。图 9（a） 中由白色虚线环绕的严重氧化区与图 9（a） 中的相似性。7（b） 中，这表明氧化发生在 γ/γ′ 相的侧面和底部界面上。它也可以从图 5（c-f） 中原始侧界面形态的变化中推断出来。底部形成的氧化皮厚度约为 50 nm。Cr、Co、Ni 和 Re 元素的扩散似乎是每周的深度方向。

(a–f) EDS element distribution for O, Al, Cr, Co, Ni and Re in depth direction of specimen after oxidation.
（a-f）氧化后样品深度方向上 O、Al、Cr、Co、Ni 和 Re 的 EDS 元素分布。
（a-f）氧化后样品深度方向上 O、Al、Cr、Co、Ni 和 Re 的 EDS 元素分布。

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Figure 10 shows the element distribution crossed both γ and γ′ phases in the depth direction, the scanning line is shown as the red dashed line in Fig. 9(b). It can be seen clearly that the diffusion happened only at the area closest to the surface. There is a quite thin layer oxidation laying on the interface of γ/γ′ phase, it corresponds exactly to the severely oxidized region in Fig. 9(a) and its value is about 30 nm.
图 10 显示了在深度方向上穿过 γ 和 γ' 相的元素分布，扫描线如图 9（b） 中的 红色虚线所示。可以清楚地看到，扩散只发生在最靠近表面的区域。在 γ/γ' 相的界面上有一个相当薄的氧化层，它与图 1 中的严重氧化区域完全对应。9（a） 及其值约为 30 nm。

EDS line scans in the depth direction of specimen after oxidation experiment.
氧化实验后样品深度方向的 EDS 线扫描。

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To be more accurate in analyzing the formed oxide scale, a detail TEM experiment was carried out. Figure 11(a) is the HAADF-STEM image of oxide scale and superalloy, it should be noted that the other elements including Cr, Co and Re are in the matrix superalloy instead of oxide scale, those elements are not shown in Fig. 11(b). The ratio of O and Al (the zone marked in red box of Fig. 11(b)) counted by EDS is 1.44, which is extremely close to the elemental ratio of Al₂O₃. Besides, the high-resolution STEM images (Fig. 11c) further supports the findings. The crystal plane spacing of blue dashed box zone marked in Fig. 11c is calculated and the value is 2.3 Å, which corresponds with the [110] crystal plane spacing of α-Al₂O₃²². The crystal plane spacing of red dashed box zone is 1.77 Å, corresponding with the [200] crystal plane spacing of Ni (fcc crystal structure).
为了更准确地分析形成的氧化皮，进行了详细的 TEM 实验。图 11（a） 是氧化皮和高温合金的 HAADF-STEM 图像，应该注意的是，包括 Cr、Co 和 Re 在内的其他元素都在基体高温合金中，而不是氧化皮，这些元素没有显示在图 11（b） 中。O 和 Al 的比率（图 1 中红色框标记的区域）。11（b））EDS 计算为 1.44，这与 Al₂O₃ 的元素比例非常接近。此外，高分辨率 STEM 图像 （图 11c） 进一步支持了这些发现。图 1 中标记的蓝色虚线框区的晶面间距。计算出 11c，值为 2.3 Å，对应于 α-Al₂O₃²² 的 [110] 晶面间距。红色虚线箱区的晶面间距为 1.77 Å，对应于 Ni 的 [200] 晶面间距（fcc 晶体结构）。

Composition and structure of oxide scale. (a) HAADF-STEM image of oxide scale and superalloy. (b) EDS mapping of oxide scale and superalloy. (c) High-resolution STEM images of oxide scale and superalloy.

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Oxide scale mechanism 氧化垢机制

After admitting oxygen, O₂ molecules dissociate and diffuse on the surface of γ phases, that process also reported on the surface of Cu-Au alloy²³. Compared with Ni elements, Al shows greater affinity for O, then Al atoms diffuse toward the alloy-oxygen interface, and may also transport through cation vacancy²⁴. Once Al₂O₃ precipitates nucleated on the original surface of γ phase as shown in Fig. 4(b–d). Al ion can transport by dislocations in oxide scale and boundaries between Al₂O₃ grains, the scale grows in form of outward transport²⁵, such a process is shown in Fig. 12(a).
进入氧后，O₂ 分子在 γ 相的表面解离并扩散，该过程也报道在 Cu-Au 合金的表面²³。与 Ni 元素相比，Al 对 O 表现出更大的亲和力，然后 Al 原子向合金-氧界面扩散，并且也可能通过阳离子空位传输²⁴。一旦 Al₂O₃ 沉淀成核γ 相的原始表面，如图 4（b-d） 所示 。Al 离子可以通过氧化皮的位错和 Al₂O₃ 晶粒之间的边界进行传输，氧化皮以向外传输的形式增长²⁵，这样的过程如图 12（a） 所示 。

Oxidation mechanism of γ phase in single crystal superalloy. (a) only thermal exposure, (b) thermal exposure and stress loaded.

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When stress is loaded, the dislocation in γ phase will increase and gather in the interface of γ and γ′ phases, which leads to the increase of vacancy^26,27. The vacancies and channels formed by dislocation will enhance the diffusion of Al atoms, as illustrated by Fig. 12(b). Also, the dislocation in Al₂O₃ grain and defects on grain boundaries in oxide scale is likely to increase during loading stress, the Al ions transport along those defects will enhance too, which caused the growth of oxide scale showed an accelerating trend, as evident from Fig. 5(a–f).
当应力加载时，γ相的位错会增加并聚集在 γ 相和 γ' 相的界面上，从而导致空位增加^26,27。位错形成的空位和通道将增强 Al 原子的扩散，如图 12（b） 所示 。此外，在加载应力作用下，Al₂O₃ 晶粒的位错和氧化皮中晶界上的缺陷可能会增加，沿这些缺陷的 Al 离子传输也会增强，这导致氧化皮的增长呈加速趋势，如图 5（a–f） 所示 。

Oxide scale kinetics 氧化皮动力学

To quantify the degree of oxidation, the oxide-oxygen interface was outlined using red dashed lines shown as Fig. 4(a). In this paper, four zones were selected, changes in each area were measured by Software Image J at different times, as outlined in Fig. 13(a). In thermal exposure period, slightly moving is founded, shown as the black outline and blue outline in Fig. 13(a). Once stress is loaded, the growth of oxide becomes considerable, displayed as green and red outline in Fig. 13(a). Since the shape is almost square, the slightly zigzag of outlines could be ignored compared with the whole shape. Therefore, the thickness of oxide at different times could be described as
为了量化氧化程度，用红色虚线勾勒出氧化物-氧界面，如图 4（a） 所示。在本文中，选择了四个区域，每个区域在不同时间通过软件图像 J 测量，如图 13（a） 所示 。在热暴露期间，会发现轻微移动，如图 13（a） 中的 黑色轮廓和蓝色轮廓所示。一旦应力加载，氧化物的增长就会变得相当大，如图 13（a） 所示 为绿色和红色轮廓。由于形状几乎是正方形的，因此与整个形状相比，可以忽略略微锯齿形的轮廓。因此，不同时期的氧化物厚度可以描述为

Where d(t) is the thickness of oxide, S_t and S₀ are the area of surrounded by oxide at t moment and initial time. L_t and L₀ are the side length of the surrounding area at t moment and initial time, respectively.
其中 d（t） 是氧化物的厚度，S_t 和 S₀ 是在 t 时刻和初始时间被氧化物包围的面积。L_t 和 L₀ 分别是周围区域在 t 时刻和初始时间的边长。

(a) Surrounding areas by oxide, (b) thickness of oxide at different times.
（a） 氧化物的周围区域，（b） 不同时间的氧化物厚度。

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The thickness of oxide in sideway direction at different times is shown as scatter graph in Fig. 13(b). At early stage of initial oxidation, oxidation of metal proceeds at a constant rate, which obeys the “linear rate law”, this period is well verified especially for the thickness of area 3 increasing during 180 min to 260 min. In that stage, chemisorption of oxygen is the rate-controlling step studied by Pettit²⁸ and has been described by Neil²⁹. However, in this paper, the rate during thermal exposure period is quite small, since the probability of oxygen molecules colliding with surface of alloy is low caused by high vacuum in SEM chamber. Once stress is loaded, the oxidation rate shows exceptional increase possibly triggered by diffusion enhancement of Al atom or ion in alloy and oxide scale. Moreover, logarithmic model (d(t) = A + k_ln(t + B)) still fits well with the oxidation process during thermal exposure with stress loaded, which indicates the stress doesn’t make the oxide scale deform to a large extent, and diffusion is still the rate-controlling step.
不同时间侧向氧化层的厚度如图 13（b） 中的 散点图所示。在初始氧化的早期阶段，金属的氧化以恒定的速率进行，这遵循“线性速率定律”，这个时期得到了很好的验证，特别是对于区域 3 的厚度在 180 min 到 260 min 期间增加。在该阶段，氧的化学吸附是 Pettit²⁸ 研究的速率控制步骤，Neil²⁹ 已经描述了这一步骤。然而，在本文中，由于 SEM 室中的高真空导致氧分子与合金表面碰撞的可能性很低，因此热暴露期间的速率非常小。一旦加载应力，氧化速率就会异常增加，这可能是由合金和氧化皮中 Al 原子或离子的扩散增强引发的。此外，对数模型 （d（t） = A + k_ln（t + B）） 仍然与应力加载热暴露过程中的氧化过程拟合良好，这表明应力不会使氧化皮在很大程度上变形，扩散仍然是速率控制步骤。

The value of fitting parameters for the four areas were compared in Table 1. It can be appreciated that the value of k_ln increase with the area increasing, which means the larger area or the longer side appears more oxidized phenomenon. This is mainly caused by higher density of dislocation in longer side of γ phase, and the high density of dislocation enhancing the diffusion process of Al atoms.
表 1 比较了四个区域的拟合参数值。可以理解，k_ln 的值随着面积的增加而增加，这意味着面积越大或边越长，出现氧化现象越多。这主要是由于γ相较长侧的位错密度较高，而位错的高密度增强了Al原子的扩散过程。

Oxide nucleation and growth on a nickel-based single crystal superalloy during only temperature of 1150 °C and thermal-stress pattern (1150 °C and /330 MPa) was observed. The oxide scale grown on the interface of γ/γ′ phase was constituted of α-Al₂O₃ precipitates. Loading stress enhanced the diffusion of Al atom in γ phase and Al ion in the oxide scale and caused high oxidation rate. Logarithmic model fitted well with the oxidation process during thermal exposure with stress loaded
在仅 1150 °C 的温度下观察到镍基单晶高温合金上的氧化物成核和生长和热应力模式（1150 °C 和 /330 MPa）。在 γ/γ' 相界面上生长的氧化皮由 α-Al₂O₃ 沉淀物组成。负载应力增强了 Al 原子在 γ 相中的扩散和 Al 离子在氧化皮中的扩散，并导致高氧化速率。对数模型与应力加载热暴露期间的氧化过程拟合良好
在仅 1150 °C 的温度下观察到镍基单晶高温合金上的氧化物成核和生长和热应力模式（1150 °C 和 /330 MPa）。在 γ/γ' 相界面上生长的氧化皮由 α-Al₂O₃ 沉淀物组成。负载应力增强了 Al 原子在 γ 相中的扩散和 Al 离子在氧化皮中的扩散，并导致高氧化速率。对数模型与应力加载热暴露期间的氧化过程拟合良好