Mechanism of grain refinement in Al-Cu alloy by adding trace La and Al-5Ti-1B

Yang Lin-Jie; Zhang Li-Li; Jiang Hong-Xiang; He Jie; Zhao Jiu-Zhou

doi:10.7498/aps.72.20222334

Abstract

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1. 引　言
2. 研究方法
3. 结果与讨论
3.1 实验验证
3.2 a-C薄膜厚度对SEY的影响
3.3 不同a-C厚度的电子散射轨迹
3.4 入射角度对SEY的影响
3.5 不同入射角度的电子散射轨迹
3.6 二次电子能量分布
4. 结　论

References

Abstract

Grain refinement of aluminium alloys can not only reduce the defects (such as segregation and hot tearing) but also improve the mechanical properties. Adding Al-5Ti-1B master alloy to the melt has become a common method to refine the solidification microstructure of aluminium alloys. A lot of researches have been carried out to uncover the grain refining mechanisms as well as to show the microstructure formation under the effect of grain refiner. These researches demonstrated that the grain refining efficiency is closely related to the number density of TiB₂ particles as well as the solute Ti concentration in the melt. However, there exist still problems to be resolved, such as the limited grain refinement potency of Al-5Ti-1B master alloy. Recently, the addition of trace La to the melt has attracted much attention to control the microstructure of aluminium alloys. The Al-Cu alloys are widely applied to the automobile and aerospace fields due to their high strength, good ductility and high temperature properties. It has been reported that Cu can segregate to Al/TiB₂ interface in the Al-Cu melt inoculated with Al-5Ti-1B master alloy. But the effect of Cu segregation on the grain refinement result is not clear yet. Meanwhile, whether the grain refinement effect of Al-5Ti-1B master alloy on Al-Cu alloy can be improved by the addition of trace La has not been reported.Solidification experiments are carried out for Al-2Cu alloy with the addition of Al-5Ti-1B master alloy+ trace La. The synergistic effect of trace La and Al-5Ti-1B on the solidification microstructure of Al-2Cu alloy is investigated. It is found that trace La can effectively enhance the refinement result of Al-2Cu alloy and further diminish the nucleation undercooling. Experimental and calculated results demonstrate that solute Cu segregates to the Al/TiB₂ interface and thus increases the interatomic spacing mismatch between Ti (0001) plane of the TiB₂ particles and the interfacial monolayer, while La segregation reduces the interatomic spacing mismatch. The trace La addition reduces the interfacial energy between α-Al and TiB₂ particles, improves the potency of TiB₂ particles to nucleate α-Al, and thus enhances the grain refinement result of Al-5Ti-1B master alloy.

Keywords:

PACS:

79.20.Hx	(Electron impact: secondary emission)
79.60.Dp	(Adsorbed layers and thin films)
52.65.Pp	(Monte Carlo methods)

Authors and contacts

1.
Shi-changxu Innovation Centre for Advanced Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
2.
School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

Corresponding author: Zhang Li-Li, llzhang@imr.ac.cn ; Zhao Jiu-Zhou, jzzhao@imr.ac.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2021YFA0716303), the China Manned Space Station Project, and the National Natural Science Foundation of China (Grant Nos. 51901231, 51971227).

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1. 引　言

二次电子发射现象是引起高能粒子加速器、真空微波元器件和其他电子设备异常放电的重要因素^[1–3], 受到相关领域研究人员的广泛关注. 例如, 在高能粒子加速器的真空室中, 由残留气体电离产生的电子束与真空腔壁碰撞产生二次电子, 从而形成电子云, 并导致束流损失或真空恶化^[4,5]. 二次电子发射系数(secondary electron yield, SEY)定义为二次电子数目与入射电子数目之比, 是表征二次电子发射现象的重要特征参数. 因此, 抑制二次电子发射现象或降低金属表面SEY是提高真空微波部件和设备放电阈值的重要途径.

二次电子一般从材料表面纳米深度中出射, 对表面状态非常敏感^[6,7], 因此通过表面镀膜能够有效抑制二次电子发射^[8,9]. 近年来, 非晶态碳(amorphous carbon, a-C)薄膜被发现在抑制二次电子发射方面具有巨大潜力^[10,11]. Larciprete等^[12]在Cu基底上制备纳米厚的a-C薄膜, 使Cu的SEY峰值从1.4降低到1.2. Li等^[13]在实验中发现a-C薄膜不但能够使不锈钢基片的SEY降低30.6%, 同时可以增大第一和第二临界能量, 从而降低微波器件异常放电风险. 除此之外, a-C薄膜还具有成本低、化学性质稳定、易制备等特点, 促进了该材料在抑制二次电子发射领域方面的应用. 然而, 有学者在实验中观察到了这种薄膜结构的SEY曲线在某些特定情况下呈现出了双峰形态, 这一现象很可能引起微波管内额外损耗, 从而影响器件性能、工作寿命和传输质量^[14,15].

有关a-C薄膜对二次电子发射的影响规律大多仍停留在实验阶段, 相关的理论研究仍然匮乏. 并且, 实验中观察到的双峰现象及其形成原因尚未得到充分的理论解释. Monte Carlo (MC)方法在粒子碰撞动力学模拟方面具有天然的优势, 通过MC模拟可以获得材料内部的电子散射过程以及二次电子发射特性的详细信息, 非常适合从微观层面解释二次电子发射特性的形成规律^[16–18]. Nguyen等^[19]采用MC方法模拟了石墨烯薄膜的二次电子发射过程, 其中电子的弹性散射和非弹性散射分别采用经典的Rutherford弹性散射截面^[20]和Bethe能量损失公式^[21]描述.

本文在已有电子与金属基底散射模型基础上, 采用MC方法建立了Cu表面a-C薄膜的二次电子发射数值计算模型, 模拟了电子在a-C薄膜和Cu基底内的散射过程及二次电子发射过程, 其中弹性散射和非弹性散射分别采用Mott微分散射截面法和Penn介电函数方法描述. 通过记录电子散射轨迹和统计二次电子信息, 探讨a-C薄膜对Cu的二次电子发射效应的抑制规律和双峰现象形成的原因.

2. 研究方法

根据a-C的厚度和入射电子能量, 电子在a-C/Cu内的散射可以分三种情况讨论, 如图1所示. 情况1: 如果a-C极薄, 电子可以直接穿透a-C并与Cu基底散射, 因此a-C几乎不会影响散射过程; 情况2: 如果a-C较厚且入射电子能量较低, 电子只能在a-C内散射, 无法到达Cu基底; 但如果入射电子能量较高, 电子会同时在a-C和Cu中散射(情况3). 电子无论在a-C或Cu中均可能发生电离散射事件, 并产生新电子, 这些新电子与入射电子同时被追踪, 直到电子出射到真空中或其能量耗尽在材料中. 此外, a-C薄膜还会通过影响金属表面功函数而改变电子出射概率, 因此真空/ a-C界面和a-C/Cu界面对电子散射和出射的影响需要在模型中予以考虑.

$图 1 a-C/Cu的二次电子发射示意图\r\nFig. 1. Schematic diagram of the secondary electron emission of a-C/Cu.$

图 1 a-C/Cu的二次电子发射示意图

Fig. 1. Schematic diagram of the secondary electron emission of a-C/Cu.

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基于MC方法的a-C/Cu二次电子发射数值模拟流程如图2所示. 首先, 根据电子的位置判断发生散射的材料种类. 若在Cu中, 电子与Cu原子的散射过程通过之前报道的模型进行模拟^[22]. 若在a-C中, 首先根据散射截面确定电子与C原子的散射类型. 若为弹性散射, 只改变电子运动方向, 若为非弹性散射, 还需更新电子能量, 并确定是否生成新的电子, 这些新电子也同样被追踪. 然后, 根据电子下一次的散射位置判断其是否从表面出射. 若出射, 则记录其信息, 包括出射能量、出射角度、出射点位置和电子散射轨迹; 否则, 电子将在材料内继续执行散射.

$图 2 基于MC方法的a-C/Cu二次电子发射模拟流程图\r\nFig. 2. Flow chart of secondary electron emission from a-C/Cu based on the MC method.$

图 2 基于MC方法的a-C/Cu二次电子发射模拟流程图

Fig. 2. Flow chart of secondary electron emission from a-C/Cu based on the MC method.

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电子的单步自由程 ${S_{\text{n}}}$ 可以通过一个均匀分布在[0, 1)之间的随机数 ${R_{1}}$ 获取:

${S_{\text{n}}} = - {\lambda _{\text{T}}}\ln {R_1} ,$

(1)

其中 ${\lambda _{\text{T}}}$ 为总平均自由程, 有 $\lambda _{\text{T}}^{ - 1} = ({\lambda _{{\text{el}}}} + {\lambda _{{\text{in}}}})^{ - 1} = \rho {\sigma _{\text{T}}}$ , $\lambda _{{\text{el}}}^{}$ 和 $\lambda _{{\text{in}}}^{}$ 分别表示弹性和非弹性散射的平均自由程. ${\sigma _{\text{T}}}$ 为总散射截面, $\rho$ 为材料的分子密度.

电子的散射类型可以用另一个[0, 1)之间的随机数 ${R_2}$ 确定. 如果当 ${R_2} < {{{\lambda _{{\text{in}}}}} \mathord{\left/ {\vphantom {{{\lambda _{{\text{in}}}}} {{\lambda _{\text{T}}}}}} \right. } {{\lambda _{\text{T}}}}}$ 时, 则进行弹性散射; 否则进行非弹性散射. 展示了根据散射截面计算的在不同能量 ${E_0}$ 下, 电子与Cu和a-C发生弹性和非弹性散射的概率P.

$图 3 电子与a-C和Cu原子的弹性和非弹性散射概率P和电子能量E0的关系\r\nFig. 3. Relationship between the elastic and inelastic scattering probability P of electron and a-C or Cu atoms and electron energy E0.$

图 3 电子与a-C和Cu原子的弹性和非弹性散射概率P和电子能量E₀的关系

Fig. 3. Relationship between the elastic and inelastic scattering probability P of electron and a-C or Cu atoms and electron energy E₀.

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对于电子能量低于10 keV的情况, 用量子力学分波法求解Schrödinger方程可以得到Mott弹性散射截面, 在物理意义上更为严格^[23]. 然而, Mott散射微分截面 ${{{\mathrm{d}}\varphi } / {{\mathrm{d}}\varOmega }}$ 的数值解计算非常复杂, 本文参考Czyzewski等^[24]的计算结果, 利用查表与插值结合的方法预先获得在不同能量和散射角度下的Mott散射截面值, 弹性散射角度可通过随机数 ${R_3}$ 获得:

${R_3} = \frac{{\displaystyle \int_0^\vartheta {\frac{{{\mathrm{d}}\varphi }}{{{\mathrm{d}}\varOmega }}\sin {\vartheta '}{{\mathrm{d}}}{\vartheta '}} }}{{\displaystyle \int_0^\pi {\frac{{{\mathrm{d}}\varphi }}{{{\mathrm{d}}\varOmega }}\sin {\vartheta '}{{{\mathrm{d}}}}{\vartheta '}} }},$

(2)

其中 $\varphi$ 为散射截面; $\varOmega$ 为立体角; $\vartheta$ 为两次散射事件间电子运动方向的夹角.

Penn介电函数法是研究现代电子非弹性散射事件的标准方法, 采用Penn介电函数近似方法^[25]计算非弹性散射微分截面和非弹性散射平均自由程. 对于非弹性散射微分截面:

$\frac{{{{\mathrm{d}}^2}\lambda _{{\text{in}}}^{ - 1}}}{{{\mathrm{d}}(h\omega ){\text{d}}q}} = \frac{1}{{\pi {a_0}{E_0}}}{{\mathrm{Im}}} \left\{ {\frac{{ - 1}}{{\varepsilon (q,w)}}} \right\}\frac{1}{q},$

(3)

其中, ${{\mathrm{Im}}} \left\{ {\dfrac{{ - 1}}{{\varepsilon (q, w)}}} \right\}$ 为能量损失函数; ${a_0}$ 为波尔半径; $h\omega$ 和 $hq$ 分别为非弹性散射中的能量损失和动量转移. 能量损失函数来源于Da等^[26]的计算结果, 是在通过非晶态碳的光学测量数据库^[27]所获得的光学介电常数 $\varepsilon (w)$ 实验数据的基础上, 从光学极限外推至有限波长区域得到的近似拓展. 非弹性散射中的能量损失 $\Delta E$ 可通过 ${R_4}$ 获得

${R_4} = \frac{{\displaystyle \int_0^{\Delta E} {\frac{{{\mathrm{d}}\lambda _{{\text{in}}}^{ - 1}}}{{{\mathrm{d}}(\Delta E')}}{\mathrm{d}}(\Delta E')} }}{{\displaystyle \int_0^{{E_0} - {E_{\text{F}}}} {\frac{{{\mathrm{d}}\lambda _{{\text{in}}}^{ - 1}}}{{{\mathrm{d}}(\Delta E')}}{\mathrm{d}}(\Delta E')} }},$

(4)

其中, ${E_{\text{F}}}$ 为电子所处材料的费米能级. 类似地, 非弹性电子散射角度 $\vartheta$ 可通过 ${R_5}$ 获得

${R_5} = \frac{{\displaystyle \int_0^\vartheta {\frac{{{{\mathrm{d}}^2}\lambda _{{\text{in}}}^{ - 1}}}{{{\mathrm{d}}\varOmega {\mathrm{d}}(\Delta E)}}\sin {\vartheta '}{\text{d}}{\vartheta '}} }}{{\displaystyle \int_0^\pi {\frac{{{{\mathrm{d}}^2}\lambda _{{\text{in}}}^{ - 1}}}{{{\mathrm{d}}\varOmega {\mathrm{d}}(\Delta E)}}\sin {\vartheta '}{\text{d}}{\vartheta '}} }}.$

(5)

在进行非弹性散射后, 原电子能量变为 $E_0' = {E_0} - \Delta E$ , 新电子能量为 ${E_{{\text{new}}}} = \Delta E - {E_{\text{B}}}$ , 其中 ${E_{\text{B}}}$ 表示内壳层电子束缚能.

当电子遇到界面势垒时, 一些电子会被反弹进入材料中, 而另一些电子则能跨越界面势垒. 以一维阶跃状势垒为例, 能量为E₁角度为 $\beta$ 的电子在材料内部、势垒区和真空区的电子波函数都满足薛定谔方程, 通过求解这三个区域的电子态密度, 根据势垒两侧电子态密度之比, 电子跨越高度为U₀的界面势垒的概率可以由()式中的穿透系数 ${T_{{\text{in}}}}$ 确定^[16]:

${T_{{\text{in}}}} = \left\{ \begin{aligned} &\frac{{4\sqrt {1 - \dfrac{{{U_0}}}{{{E_1}{{\cos }^2}\beta }}} }}{{{{\left[ {1 + \sqrt {\left(1 - \dfrac{{{U_0}}}{{{E_1}{{\cos }^2}\beta }}\right)} } \;\right]}^2}}}, & &{E_1}{\cos ^2}\beta \geqslant {U_0}, \\ &{\text{ }}0{\text{ }}, & &{E_1}{\cos ^2}\beta < {U_0}, \end{aligned} \right.$

(6)

其中, ${E_1}$ 代表电子跨越界面势垒前的能量; $\beta$ 是电子运动方向与界面法线方向的夹角. 只有当同时满足条件 ${E_1}{\cos ^2}\beta \geqslant {U_0}$ 和 ${T_{{\text{in}}}} > {R_{6}}$ ( ${R_{6}}$ 为(0, 1]随机数)时, 电子才能克服界面势垒.

克服势垒后的电子能量变为 $E_1' = {E_1} - {U_0}$ . 电子运动方向与界面法线方向之间的夹角 $\beta '$ 可以通过以下公式求得:

$\sqrt {E_1'} \sin \beta ' = \sqrt {{E_1}} \sin \beta .$

(7)

如果电子无法克服界面势垒, 则认为电子继续在当前材料内散射, 其能量不会改变, 但角度会变为 $\beta '' = {\text{π }} - \beta$ .

3. 结果与讨论

3.1 实验验证

为了验证模型的可靠性, 将计算结果与已报道的实验结果^[28,29]进行对比. 由于实验结果很容易受到表面状态和测试误差的影响, 有必要对SEY进行归一化处理, 相对SEY记为 ${\delta _{\text{r}}} = {\delta \mathord{\left/ {\vphantom {\delta {{\delta _{\max, {\text{Cu}}}}}}} \right. } {{\delta _{\max, {\text{Cu}}}}}}$ , 其中 ${\delta _{\max, {\text{Cu}}}}$ 为Cu的SEY最大值. 图4显示了a-C薄膜厚度L分别为0, 0.6和2.1 nm的a-C/Cu的相对SEY计算结果和实验结果的对比. 由图4可以看出, 本模型的计算结果与实验结果非常接近, 最大误差不超过12%, 验证了模型的可靠性.

$图 4 MC模拟结果与文献实验结果的对比\r\nFig. 4. Comparison of our MC simulation results and the reported experimental results.$

图 4 MC模拟结果与文献实验结果的对比

Fig. 4. Comparison of our MC simulation results and the reported experimental results.

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3.2 a-C薄膜厚度对SEY的影响

为了系统探讨a-C薄膜对Cu的SEY的影响, 计算了不同薄膜厚度L的SEY曲线, 并与纯a-C材料的SEY进行比较, 如图5(a)所示. 随着L从0 nm增加到1.5 nm, SEY最大值从1.14降至0.93, 但低能段的SEY略微上升. 然而, 当L从1.5 nm增加到3 nm, SEY最大值达到饱和, 且与a-C的SEY最大值几乎重合. 值得注意的是, 当L ≥ 1.5 nm时, SEY曲线呈现出明显的第二峰, 并且随着L的增加, 第二峰减弱并消失, SEY曲线从低能段到高能段逐渐与a-C的重叠. 此外, 随着L从0 nm增大至0.3 nm, 第一临界能量从211 eV降低至191 eV, 对应第二临界能量从503 eV增高至1020 eV. 当L > 0.3 nm时, SEY峰值小于1, 因此不会存在异常放电风险. 进一步展示了SEY第一峰值 ${\delta _{\max1}}$ 和第二峰值 ${\delta _{\max2}}$ 以及它们对应的入射能量 ${E_{\max1}}$ 和 ${E_{\max2}}$ 随L的变化规律.

$图 5 厚度L对SEY $\delta $的影响　(a)不同L下, $\delta $与$ {E_{{\text{PE}}}} $的关系; (b) ${\delta _{\max1}}$, ${\delta _{\max2}}$, ${E_{\max1}}$和${E_{\max2}}$与L的关系\r\nFig. 5. Effects of the thickness L on the SEY $\delta $: (a) $\delta $vs.$ {E_{{\text{PE}}}} $at different L; (b) ${\delta _{\max1}}$, ${\delta _{\max2}}$, ${E_{\max1}}$ and ${E_{\max2}}$vs. L.$

图 5 厚度L对SEY

$\delta$

的影响　(a)不同L下,

$\delta$

与

${E_{{\text{PE}}}}$

的关系; (b)

${\delta _{\max1}}$

${\delta _{\max2}}$

${E_{\max1}}$

和

${E_{\max2}}$

与L的关系

Fig. 5. Effects of the thickness L on the SEY

$\delta$

: (a)

$\delta$

vs.

${E_{{\text{PE}}}}$

at different L; (b)

${\delta _{\max1}}$

${\delta _{\max2}}$

${E_{\max1}}$

and

${E_{\max2}}$

vs. L.

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3.3 不同a-C厚度的电子散射轨迹

MC模拟能够还原电子在材料内部的散射过程, 从微观层面解释双峰现象. —展示了1000个 ${E_{{\text{PE}}}}$ = 500 eV的电子垂直入射到不同a-C薄膜厚度的电子散射轨迹分布, 即入射电子和电离电子在不同时刻的位置分布图, 不同颜色代表电子的深度. 随着L从0 nm增大至2.4 nm, 电子在材料内部的散射范围逐渐缩小, 并且最可几深度(most probable depth, MPD)从Cu转移至a-C中(图6(a)—(d)), 其中MPD表示与最大电子密度相对应的深度z. 这意味着, 当电子散射范围涉及两种材料时, SEY特性表现为两者的合成, 因此会有两个峰同时出现的情况. 此外, 较厚的a-C会显著限制电子的散射范围, 这是由于电子在a-C中的非弹性散射概率大于在Cu中的概率, 大部分电子没有足够能量跨越表面势垒出射, 导致SEY降低.

$图 6 不同厚度L下的电子散射轨迹分布及规律　(a) L = 0 nm; (b) L = 0.9 nm; (c) L = 1.5 nm; (d) L = 2.4 nm; (e) MPD和${P_{{\text{a-C}}}}$与L的关系. 图(a)—(d)中, 灰色点线表示MPD的位置, 红色曲线表示归一化的电子密度分布\r\nFig. 6. Distribution and pattern of electron scattering trajectories with different L: (a) L = 0; (b) L = 0.9 nm; (c) L = 1.5 nm; (d) L = 2.4 nm; (e) MPD and ${P_{{\text{a-C}}}}$ vs. L. In panels (a)–(d), the gray dot line represents the position of the MPD, and the red curve represents the normalized electron density distribution.$

图 6 不同厚度L下的电子散射轨迹分布及规律　(a) L = 0 nm; (b) L = 0.9 nm; (c) L = 1.5 nm; (d) L = 2.4 nm; (e) MPD和

${P_{{\text{a-C}}}}$

与L的关系. 图(a)—(d)中, 灰色点线表示MPD的位置, 红色曲线表示归一化的电子密度分布

Fig. 6. Distribution and pattern of electron scattering trajectories with different L: (a) L = 0; (b) L = 0.9 nm; (c) L = 1.5 nm; (d) L = 2.4 nm; (e) MPD and

${P_{{\text{a-C}}}}$

vs. L. In panels (a)–(d), the gray dot line represents the position of the MPD, and the red curve represents the normalized electron density distribution.

下载: 全尺寸图片幻灯片

进一步展示了MPD和a-C中电子数量比例 ${P_{{\text{a-C}}}}$ 随a-C厚度L的变化规律. 定义 ${P_{{\text{a-C}}}} = {{{N_{{\text{a-C}}}}}/{{N_{{\text{total}}}}}}$ , ${N_{{\text{a-C}}}}$ 和 ${N_{{\text{total}}}}$ 分别表示a-C和a-C/Cu中的电子数量. 当L从0 nm增加到0.3 nm时, MPD从1.46迅速下降至0.24; 进一步增大L会使MPD增大, 即向更深方向移动. 此外, ${P_{{\text{a-C}}}}$ 随着L的增加而增加, 当L ≥ 0.6 nm时, ${P_{{\text{a-C}}}}$ 甚至大于0.5, 意味着在a-C内的电子数目超过在Cu内的电子数. 以上结果均表明a-C/Cu界面势垒是阻止电子进入Cu的关键因素之一.

3.4 入射角度对SEY的影响

在实际应用中, 大多数电子的入射角度与材料表面并不是垂直的. 以L = 1.5 nm为例, 显示了不同入射角度 $\theta$ 下的a-C/Cu的SEY曲线. 随着 $\theta$ 的增加, SEY显著增大, 并且第二峰也逐渐减弱至消失. 此外, 随着 $\theta$ 从30°增大至80°, 第一临界能量从168 eV降低至68 eV, 对应第二临界能量从284 eV增高至2840 eV. 从观察到 ${\delta _{\max1}}$ 和 ${\delta _{\max2}}$ 均呈指数增大, 而 ${E_{\max1}}$ 和 ${E_{\max2}}$ 略微增加. 为了定量分析第二峰的变化, 定义了第二峰的高度 ${\delta _\Delta }$ 和宽度 ${E_\Delta }$ , 如所示. ${\delta _\Delta }$ 和 ${E_\Delta }$ 随着 $\theta$ 明显减小, 直到 $\theta$ ≥70°时完全消失. 这是因为 $\theta$ 越大, 进入Cu的电子比例减少, 双峰现象就会减弱; 其次, 根据()式, 电子在a-C/Cu界面处的夹角 $\beta$ 随 $\theta$ 的增大而增大, 导致电子跨越界面势垒的概率降低.

$图 7 入射角度$\theta $对SEY $\delta $的影响　(a) 不同$\theta $下, $\delta $与$ {E_{{\text{PE}}}} $的关系; (b) ${\delta _{\max1}}$, ${\delta _{\max2}}$, ${E_{\max1}}$和${E_{\max2}}$与$\theta $的关系; (c) ${\delta _\Delta }$和${E_\Delta }$与$\theta $的关系. 其中, 图(c)中的内插图为${\delta _\Delta }$和${E_\Delta }$的示意图\r\nFig. 7. Effects of incident angle $\theta $ on the SEY $\delta $: (a) $\delta $ vs. $ {E_{{\text{PE}}}} $ at different $\theta $; (b) ${\delta _{\max1}}$, ${\delta _{\max2}}$, ${E_{\max1}}$and ${E_{\max2}}$ vs. $\theta $; (c) ${\delta _\Delta }$ and ${E_\Delta }$ vs. $\theta $. In panel (c), the interpolation diagram is a schematic diagram of ${\delta _\Delta }$ and ${E_\Delta }$.$

图 7 入射角度

$\theta$

对SEY

$\delta$

的影响　(a) 不同

$\theta$

下,

$\delta$

与

${E_{{\text{PE}}}}$

的关系; (b)

${\delta _{\max1}}$

${\delta _{\max2}}$

${E_{\max1}}$

和

${E_{\max2}}$

与

$\theta$

的关系; (c)

${\delta _\Delta }$

和

${E_\Delta }$

与

$\theta$

的关系. 其中, 图(c)中的内插图为

${\delta _\Delta }$

和

${E_\Delta }$

的示意图

Fig. 7. Effects of incident angle

$\theta$

on the SEY

$\delta$

: (a)

$\delta$

vs.

${E_{{\text{PE}}}}$

at different

$\theta$

; (b)

${\delta _{\max1}}$

${\delta _{\max2}}$

${E_{\max1}}$

and

${E_{\max2}}$

vs.

$\theta$

; (c)

${\delta _\Delta }$

and

${E_\Delta }$

vs.

$\theta$

. In panel (c), the interpolation diagram is a schematic diagram of

${\delta _\Delta }$

and

${E_\Delta }$

下载: 全尺寸图片幻灯片

3.5 不同入射角度的电子散射轨迹

—绘制了不同 $\theta$ 下的电子散射轨迹和沿深度z方向的电子密度分布. 随着 $\theta$ 的增大, 电子的散射范围显著缩小. 同时, MPD向表面方向移动. 定量地给出了MPD和 ${P_{{\text{a-C}}}}$ 随着 $\theta$ 的变化规律. 首先, ${P_{{\text{a-C}}}}$ 增大甚至接近0.97, 意味着更多电子集中在a-C区域内散射, Cu对SEY的影响逐渐减弱, 因此双峰现象减弱; 其次, MPD减小表明电子散射位置向表面转移, 更多电子仅在浅表层散射, 此时电子更容易出射, SEY随着 $\theta$ 的增大因而显著增大.

$图 8 不同入射角度$\theta $下的电子的散射轨迹分布及规律(L = 1.5 nm)　(a) $\theta $= 0°; (b) $\theta $= 30°; (c) $\theta $= 60°; (d) $\theta $= 80°; (e) MPD和${P_{{\text{a-C}}}}$与$\theta $的关系. 图(a)—(d)中, 灰色点线表示MPD的位置, 红色曲线表示归一化的电子密度分布\r\nFig. 8. Distribution and pattern of electron scattering trajectories with different $\theta $ (L = 1.5 nm): (a) $\theta $= 0°; (b) $\theta $= 30°; (c) $\theta $= 60°; (d) $\theta $= 80°; (e) the MPD and ${P_{{\text{a-C}}}}$ vs. $\theta $. In panels (a)–(d), the gray dot line represents the position of the MPD, and the red curve represents the normalized electron density distribution.$

图 8 不同入射角度

$\theta$

下的电子的散射轨迹分布及规律(L = 1.5 nm)　(a)

$\theta$

= 0°; (b)

$\theta$

= 30°; (c)

$\theta$

= 60°; (d)

$\theta$

= 80°; (e) MPD和

${P_{{\text{a-C}}}}$

与

$\theta$

的关系. 图(a)—(d)中, 灰色点线表示MPD的位置, 红色曲线表示归一化的电子密度分布

Fig. 8. Distribution and pattern of electron scattering trajectories with different

$\theta$

(L = 1.5 nm): (a)

$\theta$

= 0°; (b)

$\theta$

= 30°; (c)

$\theta$

= 60°; (d)

$\theta$

= 80°; (e) the MPD and

${P_{{\text{a-C}}}}$

vs.

$\theta$

. In panels (a)–(d), the gray dot line represents the position of the MPD, and the red curve represents the normalized electron density distribution.

下载: 全尺寸图片幻灯片

3.6 二次电子能量分布

二次电子能量分布(secondary electron spectrum, SES)包含了更丰富的表面信息, 是表征二次电子发射的另一个重要参数^[30,31]. 为此, 展示了 ${E_{{\text{PE}}}}$ = 500 eV的电子束垂直照射不同厚度a-C薄膜的本征SES与其半峰宽(full width at half maximum, FWHM)和最可几能量(most probable energy, MPE)的变化情况. 随L的增加, SES的本征峰逐渐降低, 并向a-C的靠拢, 并且MPE向高能段移动, FWHM展宽. 可见a-C会使MPE和FWHM显著增大, 表明a-C薄膜会导致电子发生更频繁的非弹性碰撞, 从而损失能量, 导致低能电子比例减少, MPE增大及FWHM向高能段展宽.

$图 9 L对SES的影响　(a) 不同L下的SES; (b) MPE和FWHM与L的关系\r\nFig. 9. Effects of L on the SES: (a) SES curves with different L; (b) MPE and FWHM vs. L.$

图 9 L对SES的影响　(a) 不同L下的SES; (b) MPE和FWHM与L的关系

Fig. 9. Effects of L on the SES: (a) SES curves with different L; (b) MPE and FWHM vs. L.

下载: 全尺寸图片幻灯片

4. 结　论

本文开发了一种a-C/Cu双层材料的二次电子发射MC数值模型, 用于研究a-C薄膜对Cu的二次电子发射的影响. 其中, 电子与目标原子之间的弹性散射和非弹性散射过程分别采用Mott理论和Penn介电函数模型描述. 为了精确重现电子在a-C/Cu内的散射过程, 模型还考虑了a-C引起的功函数的变化以及电子在a-C/Cu界面及真空/a-C界面处的多次散射过程. 基于本模型的计算结果, 得到以下结论.

1) a-C薄膜可以使Cu的SEY最大值从1.14降低到0.93. 这是因为a-C薄膜能够通过更多次的非弹性散射事件降低电子的能量, 并且a-C/Cu界面能够限制电子的散射范围, 从而降低SEY.

2) 当a-C薄膜厚度大于0.9 nm时, SEY曲线开始呈现双峰现象. 然而, 继续增加a-C薄膜厚度, 第二峰减弱并向高能段移动. 通过增加a-C薄膜厚度和电子入射角度, 均会使第二峰减弱甚至消失.

3) 双峰现象是由电子在两种不同材料中的散射引起的, 表现为两种材料SEY特性的重合. 较厚的a-C薄膜或较大的电子入射角度都会将更多电子限制在a-C薄膜内, 减弱SEY的第二峰.

本文提出的模型有助于从微观层面理解多层结构的二次电子发射特性, 对于选择合适的薄膜厚度以抑制二次电子发射, 以及避免双峰现象引起的异常放电具有重要的理论指导意义.

References

[1]	张丽丽 2017 博士学位论文 (沈阳: 中国科学院大学) Zhang L L 2017 Ph. D. Dissertation (Shenyang: University of Chinese Academy of Sciences) (in Chinese)
[2]	Greer A L, Bunn A M, Tronche A, Evans P V, Bristow D J 2000 Acta Mater. 48 2823 Google Scholar
[3]	Quested T E, Greer A L 2004 Acta Mater. 52 3859 Google Scholar
[4]	Quested T E, Greer A L 2005 Acta Mater. 53 4643 Google Scholar
[5]	Easton M A, StJohn D H 2001 Acta Mater. 49 1867 Google Scholar
[6]	Easton M A, StJohn D H 2005 Metall. Mater. Trans. A 36 1911 Google Scholar
[7]	Easton M A, StJohn D H 2008 Mater. Sci. Eng. A 486 8 Google Scholar
[8]	Fan Z, Wang Y, Zhang Y, Qin T, Zhou X R, Thompson G E, Pennycook T, Hashimoto T 2015 Acta Mater. 84 292 Google Scholar
[9]	Cibula A 1951 J. Inst. Met. 80 1
[10]	Crossley F A, Mondolfo L F 1951 JOM. 3 1143 Google Scholar
[11]	Jones G P, Jones H 1987 Solidification Processing (Sheffield: University of Sheffield) p496
[12]	Mohanty P S, Gruzleski J E 1995 Acta Metall. Mater. 43 2001 Google Scholar
[13]	Fan Z Y 2013 Metall. Mater. Trans. A 44 1409 Google Scholar
[14]	Maxwell I, Hellawell A 1975 Acta Metall. 23 229 Google Scholar
[15]	Zhang L L, Zheng Q J, Jiang H X, Zhao J Z 2019 Scr. Mater. 160 25 Google Scholar
[16]	Li J H, Hage F S, Ramasse Q M, Schumacher P 2021 Acta Mater. 206 116652 Google Scholar
[17]	吴俊子, 贾锦玉, 姜佳鑫 2018 稀土信息 2 30 Wu J Z, Jia J Y, Jiang J X 2018 Rare Earth Inform. 2 30
[18]	韩延峰 2007 博士学位论文 (上海: 上海交通大学) Han Y F 2007 Ph. D. Dissertation (Shanghai: Shanghai Jiao Tong University) (in Chinese)
[19]	Zhang Z, Bian X, Wang Y, Liu, X 2003 Mater. Sci. Eng. A 352 8 Google Scholar
[20]	李克, 饶磊, 闫洪, 王俊, 孙宝德 2006 铸造 9 894 Li K, Rao L, Yan H, Wang J, Sun B D 2006 Foundry 9 894
[21]	董天顺, 崔春翔, 刘双进, 刘福才 2008 稀有金属材料与工程 1 29 Dong T S, Cui C X, Liu S J, Liu F C 2008 Rare Metal Mater. Eng. 1 29
[22]	Wang Z J, Si N C 2015 Rare Metal Mater. Eng. 44 2970 Google Scholar
[23]	Ma T F, Chen Z Y, Nie Z R, Huang H 2013 J. Rare Earths 31 622 Google Scholar
[24]	Wang K, Cui C X, Wang Q, Liu S, Gu C 2012 Mater. Lett. 85 153 Google Scholar
[25]	Wang K, Cui C X, Wang Q, Zhao L, Hu Y 2013 J. Rare Earths 31 313 Google Scholar
[26]	Zhang L L, Song Y, Yang L J, Zhao J Z, He J, Jiang H X 2022 Materials 15 600 Google Scholar
[27]	Zhang M X, Kelly P M, Easton M A, Taylor J A 2005 Acta Mater. 53 1427 Google Scholar
[28]	Wang Y, Fang C M, Zhou L, Hashimoto T, Fan Z 2018 Acta Mater. 164 428 Google Scholar
[29]	Iida T, Guthrie R I L 1993 The Physical Properties of Liquid Metals (Oxford: Clarendon Press) p71
[30]	Fan T X, Yang G, Zhang D 2005 Metall. Mater. Trans. A 36 225 Google Scholar
[31]	Dinsdale A T 1991 Calphad. 15 317 Google Scholar
[32]	李淑波, 杜文博, 王旭东, 刘轲, 王朝辉 2018 金属学报 54 911 Google Scholar Li S B, Du W B, Wang X D, Liu K, Wang C H 2018 Acta Metall. Sin. 54 911 Google Scholar
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图 1 Al-2Cu和不同La添加量下经0.4% Al-5Ti-1B中间合金细化处理的Al-2Cu合金晶粒平均尺寸和微观组织的OM像

Figure 1. Average size of α-Al grains and OM images of the Al-2Cu alloys without addition of inoculant, inoculated with 0.4% Al-5Ti-1B and inoculated with 0.4% Al-5Ti-1B + 0.08% La.

DownLoad: Full-Size Img PowerPoint

图 2 添加1% Al-5Ti-1B的Al-2Cu合金的TEM像及元素分布图　(a) 低倍TEM像; (b)—(e) 元素Al (b), Cu (c), Ti (d), B (e)分布图; (f) TiB₂粒子的高倍TEM像, 其中插图为元素Al, Cu和Ti在蓝框内的平均电子能量损失谱线

Figure 2. TEM image and elemental maps in the Al-2Cu alloy inoculated by 1% Al-5Ti-1B: (a) TEM image at low magnification; (b)–(e) elemental maps of Al (b), Cu (c), Ti (d), B (e); (f) TEM image at high magnification of TiB₂ particles, where inset shows the electron energy loss spectroscopy line profiles of elements Al, Cu and Ti averaged over the area indicated in Fig. (f) by blue box

DownLoad: Full-Size Img PowerPoint

图 3 (a) 添加1% Al-5Ti-1B + 0.08% La的Al-2Cu合金的高倍TEM像; (b)—(e) 元素Al (b), Cu (c), Ti (d), La (e)的X射线能量散谱图; (f) Al, Cu, Ti和La元素的电子能量损失谱线

Figure 3. (a) TEM image at high magnification in Al-2Cu alloy inoculated by 1% Al-5Ti-1B + 0.08% La; (b)–(e) energy dispersive X-ray spectroscopy maps of Al (b), Cu (c), Ti (d), La (e); (f) electron energy loss spectroscopy line profiles of elements Al, Cu, Ti and La averaged over the area indicated in (a) by pink box of TiB₂ particles.

DownLoad: Full-Size Img PowerPoint

图 4 添加1% Al-5Ti-1B + 0% La (a)和1% Al-5Ti-1B +0.08% La (b)的Al-2Cu合金HRTEM像; (c) TiB₂粒子中Ti (0001)面与界面单原子层间界面示意图

Figure 4. HRTEM images showing the basal plane (0001) of TiB₂ in Al-2Cu alloy inoculated with 1% Al-5Ti-1B + 0% La (a) and 1% Al-5Ti-1B +0.08%La (b), respectively; (c) schematic illustration of interface between the Ti (0001) plane of TiB₂ surface and the monolayer

DownLoad: Full-Size Img PowerPoint

图 5 经0.4% Al-5Ti-1B细化处理的Al-2Cu合金的DTA升温(虚线)和冷却(实线)曲线, 其中T_m 和T_n分别为合金的熔点和开始形核温度, T_m = 926.2K; 插图为α-Al的形核过冷度ΔT_Heter

Figure 5. DTA heating (dashed line) and cooling (solid line) curves for the Al-2Cu alloys with the addition of 0.4% Al-5Ti-1B master alloy. T_n and T_m = 926.2K are respectively the nucleation temperature of α-Al and the melting point temperature of Al. Inset shows the undercooling ΔT_Heter.

DownLoad: Full-Size Img PowerPoint

图 6 微量La添加量对经0.4%Al-5Ti-1B细化处理的Al-2Cu合金生长限制因子的影响

Figure 6. Effect of trace La addition on the growth restriction factor of Al-2Cu alloy inoculated with 0.4% Al-5Ti-1B master alloy.

DownLoad: Full-Size Img PowerPoint

表 1 (13)式中涉及的参数

Table 1. Parameters used in Eq. (13).

i k_i m_i/(K·%^–1) ${c'_{{\text{S}}i}}/\%$ ${c'_{{\text{L}}i}}/\%$ Reference

Ti 7.8 33.3 — — [12]
Cu 0.17 –3.4 5.69 32.5 [34]
La 0.004 –1.71 0.05 11.7 [35]

DownLoad: CSV

[1]	张丽丽 2017 博士学位论文 (沈阳: 中国科学院大学) Zhang L L 2017 Ph. D. Dissertation (Shenyang: University of Chinese Academy of Sciences) (in Chinese)
[2]	Greer A L, Bunn A M, Tronche A, Evans P V, Bristow D J 2000 Acta Mater. 48 2823 Google Scholar
[3]	Quested T E, Greer A L 2004 Acta Mater. 52 3859 Google Scholar
[4]	Quested T E, Greer A L 2005 Acta Mater. 53 4643 Google Scholar
[5]	Easton M A, StJohn D H 2001 Acta Mater. 49 1867 Google Scholar
[6]	Easton M A, StJohn D H 2005 Metall. Mater. Trans. A 36 1911 Google Scholar
[7]	Easton M A, StJohn D H 2008 Mater. Sci. Eng. A 486 8 Google Scholar
[8]	Fan Z, Wang Y, Zhang Y, Qin T, Zhou X R, Thompson G E, Pennycook T, Hashimoto T 2015 Acta Mater. 84 292 Google Scholar
[9]	Cibula A 1951 J. Inst. Met. 80 1
[10]	Crossley F A, Mondolfo L F 1951 JOM. 3 1143 Google Scholar
[11]	Jones G P, Jones H 1987 Solidification Processing (Sheffield: University of Sheffield) p496
[12]	Mohanty P S, Gruzleski J E 1995 Acta Metall. Mater. 43 2001 Google Scholar
[13]	Fan Z Y 2013 Metall. Mater. Trans. A 44 1409 Google Scholar
[14]	Maxwell I, Hellawell A 1975 Acta Metall. 23 229 Google Scholar
[15]	Zhang L L, Zheng Q J, Jiang H X, Zhao J Z 2019 Scr. Mater. 160 25 Google Scholar
[16]	Li J H, Hage F S, Ramasse Q M, Schumacher P 2021 Acta Mater. 206 116652 Google Scholar
[17]	吴俊子, 贾锦玉, 姜佳鑫 2018 稀土信息 2 30 Wu J Z, Jia J Y, Jiang J X 2018 Rare Earth Inform. 2 30
[18]	韩延峰 2007 博士学位论文 (上海: 上海交通大学) Han Y F 2007 Ph. D. Dissertation (Shanghai: Shanghai Jiao Tong University) (in Chinese)
[19]	Zhang Z, Bian X, Wang Y, Liu, X 2003 Mater. Sci. Eng. A 352 8 Google Scholar
[20]	李克, 饶磊, 闫洪, 王俊, 孙宝德 2006 铸造 9 894 Li K, Rao L, Yan H, Wang J, Sun B D 2006 Foundry 9 894
[21]	董天顺, 崔春翔, 刘双进, 刘福才 2008 稀有金属材料与工程 1 29 Dong T S, Cui C X, Liu S J, Liu F C 2008 Rare Metal Mater. Eng. 1 29
[22]	Wang Z J, Si N C 2015 Rare Metal Mater. Eng. 44 2970 Google Scholar
[23]	Ma T F, Chen Z Y, Nie Z R, Huang H 2013 J. Rare Earths 31 622 Google Scholar
[24]	Wang K, Cui C X, Wang Q, Liu S, Gu C 2012 Mater. Lett. 85 153 Google Scholar
[25]	Wang K, Cui C X, Wang Q, Zhao L, Hu Y 2013 J. Rare Earths 31 313 Google Scholar
[26]	Zhang L L, Song Y, Yang L J, Zhao J Z, He J, Jiang H X 2022 Materials 15 600 Google Scholar
[27]	Zhang M X, Kelly P M, Easton M A, Taylor J A 2005 Acta Mater. 53 1427 Google Scholar
[28]	Wang Y, Fang C M, Zhou L, Hashimoto T, Fan Z 2018 Acta Mater. 164 428 Google Scholar
[29]	Iida T, Guthrie R I L 1993 The Physical Properties of Liquid Metals (Oxford: Clarendon Press) p71
[30]	Fan T X, Yang G, Zhang D 2005 Metall. Mater. Trans. A 36 225 Google Scholar
[31]	Dinsdale A T 1991 Calphad. 15 317 Google Scholar
[32]	李淑波, 杜文博, 王旭东, 刘轲, 王朝辉 2018 金属学报 54 911 Google Scholar Li S B, Du W B, Wang X D, Liu K, Wang C H 2018 Acta Metall. Sin. 54 911 Google Scholar
[33]	Zhang L L, Jiang H X, He J, Zhao J Z 2020 Scr. Mater. 179 99 Google Scholar
[34]	Okamoto H 2013 J. Phase Equilib. Diffus. 34 493 Google Scholar
[35]	Elliott R P, Shunk F A 1981 Bull. Alloy Phase Diagrams 2 219 Google Scholar

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Vol. 72, Issue 8 - 2023-04-20

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