二维极化激元学近场研究进展

段嘉华; 陈佳宁

doi:10.7498/aps.68.20190341

摘要

极化激元学可以实现纳米尺度上的光子操控和光与物质相互作用的调控, 已经成为现代物理学中的一个重要分支. 与传统贵金属相比, 二维范德瓦耳斯原子晶体中极化激元具有更强的局域能力且可实现主观调控. 近期, 利用扫描式近场光学显微镜在二维体系中观察到了多种类型的极化激元, 为今后量子物理和纳米光子学的发展提供了新思路. 本文主要介绍通过近场光学手段揭示二维极化激元学的重要进展和实验结果. 在介绍近场光学及其成像原理的基础上, 总结了二维极化激元学中近场研究进展的几个重要研究方向, 包括等离极化激元、声子极化激元、激子极化激元和杂化型极化激元等. 最后提出了近场光学今后可能的发展方向.

关键词:

Abstract

Due to the capability of nanoscale manipulation of photons and tunability of light-matter interaction, polaritonics has attracted much attention in the modern physics. Compared with traditional noble metals, two-dimensional van der Waals materials provide an ideal platform for polaritons with high confinement and tunability. Recently, the development of scanning near-field optical microscopy has revealed various polaritons, thereby paving the way for further studying the quantum physics and nano-photonics. In this review paper, we summarize the new developments in two-dimensional polaritonics by near-field optical approach. According to the introduction of near-field optics and its basic principle, we show several important directions in near-field developments of two-dimensional polaritonics, including plasmon polaritons, phonon polaritons, exciton polaritons, hybridized polaritons, etc. In the final part, we give the perspectives in development of near-field optics.

Keywords:

PACS:

06.20.Dk	(Measurement and error theory)
06.30.Bp	(Spatial dimensions)
42.25.Hz	(Interference)
42.30.Lr	(Modulation and optical transfer functions)

作者及机构信息

段嘉华^1,2,
陈佳宁^1,2,3,4

1.
中国科学院物理研究所, 北京　100190

2.
中国科学院大学物理学院, 北京　100049

3.
北京凝聚态物理国家实验室, 北京　100190

4.
松山湖材料实验室, 东莞　523808

通信作者: 陈佳宁, jnchen@iphy.ac.cn

基金项目: 国家重点基础研究发展计划(批准号: 2016YFA0203500)、国家自然科学基金(批准号: 11874407)和中国科学院战略性先导专项(批准号: XDB 30000000)资助的课题.

Authors and contacts

1.
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

3.
Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China

4.
Songshan Lake Materials Laboratory, Dongguan 523808, China

Corresponding author: Chen Jia-Ning, jnchen@iphy.ac.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0203500), the National Natural Science Foundation of China (Grant No. 11874407), and the Strategic Priority Research Program of Chinese Academy of Science (Grant No. XDB 30000000).

文章全文

1. 引　言

耐事故燃料能提高反应堆核燃料系统在正常运行工况以及严重事故工况下的安全性和可靠性^[1]. 自福岛第一核电站事故发生以来, 耐事故燃料的研发一直是核燃料领域的研究热点, 而筛选高铀密度和高导热系数的燃料体系是耐事故燃料开发的重要思路^[2]. 选用高铀密度的燃料可以延长反应堆的换料周期, 提高核电站运行的经济性; 采用高导热系数的燃料可以降低燃料芯块和包壳的峰值温度, 增强燃料元件的抵御严重事故能力^[3–5]. 与传统UO₂燃料相比, UN, U₃Si₂燃料都具有铀密度高和导热系数高的优点, 且它们的导热系数随着温度的升高而增加^[6]. 然而, UN在氧气、水或蒸汽环境中容易发生氧化腐蚀, 而且其粉末制备和芯块烧结的条件也较为苛刻, 在低烧结温度下制得的UN芯块很难达到满足燃料应用的密度, 而高烧结温度则会对材料的微观结构造成不利影响; U₃Si₂具有更好的抗氧化能力, 但其较低的熔点会降低安全裕度^[7,8]. 因此, UN-U₃Si₂复合燃料充分利用两种燃料相的优点, 以其高抗氧化性、高熔点等优势, 成为了一种极具研发潜力的耐事故燃料.

近年来, 国外学者开展了一系列不同温度、不同时间、不同掺杂比例、多种烧结方式下的UN-U₃Si₂复合燃料的烧结实验^[6,9–11]. Ortega等^[9]采用液相烧结工艺制备UN-U₃Si₂复合燃料样品, 并通过延长烧结时间和进行后处理去除表面孔隙, 实验最终得到了致密度达到94%的样品, 且其铀含量比UO₂高出30%以上. Johnson等^[6]的放电等离子体烧结(spark plasma sintering, SPS)实验结果表明, 在常规烧结温度下得到的复合燃料样品中, 由于UN与U₃Si₂发生相互作用, 形成了一种未知的U-Si-N三元相. White等^[10]在1873—1973 K的温度范围内, 通过液相烧结制备出了U₃Si₂体积分数在10%到40%之间的多种复合燃料, 结果表明, 每种复合燃料的热导率均随温度的升高而增加, UN和U₃Si₂之间的热膨胀差异导致了微观结构中微裂纹的产生. Lopes等^[11]采用SPS方法在1723 K烧结温度和3 min烧结时间下得到了相对密度为98%的UN-10%U₃Si₂ (质量分数)复合燃料芯块, 并从静态蒸汽高压釜测试中得出结论: U₃Si₂相提高了UN基体的稳定性, 燃料芯块的腐蚀机制从晶间开裂转变为了晶内开裂. 然而, 现有的实验技术难以对烧结过程中的微观组织演变进行实时的观测, 导致了无法更加深入地理解两相复合燃料的烧结机理. 因此, 对UN-U₃Si₂复合燃料的烧结过程开展理论模拟研究具有十分重要的意义.

目前, 相场法已被成功应用于合金腐蚀行为^[12]、核燃料裂变气体释放行为^[13]、高熵合金富Cu相析出^[14]等各方面的模拟研究中, 而在陶瓷粉末烧结过程的相场模拟方面也同样取得了一些成果^[15–19]. Liu等^[15]建立了一种新型相场模型描述两相多孔组织的烧结过程. Kumar等^[16]通过相场模拟了两种不等尺寸颗粒的烧结过程, 分析了不同子过程的热力学驱动力. Biswas等^[17]开发出一种考虑方向依赖的界面扩散各向异性和晶粒取向依赖的晶界能各向异性的相场模型, 研究了各向异性性质对固态烧结过程中微观结构演化的影响. Du等^[18]采用相场方法进一步模拟了多孔陶瓷烧结过程中的孔隙变形和晶界迁移. Hötzer等^[19]提出了一种考虑体积扩散、表面扩散和晶界扩散的相场模型描述Al₂O₃颗粒的烧结过程. 然而, 两相烧结过程不仅涉及两相之间溶质元素的扩散, 而且烧结后期的晶粒长大同时受气孔及第二相的影响. 上述模型为两相烧结相场模型的开发提供了一些思路, 但完整准确地描述两相烧结过程的形貌演化等工作需要重新构建自由能泛函数, 并准确求解相场演化方程.

本工作以Wang^[20]提出的固态烧结相场模型为基础, 建立了包含气孔和两种固相的相场模型, 采用张量形式的扩散迁移率系数以及与表面能和晶界能相关的模型参数, 模拟了UN粉末与U₃Si₂粉末的两相烧结过程, 分别对烧结颈的形成与增长过程、三叉晶界的形成过程以及不同体积分数比的两相组织演变过程等进行了研究.

2. 相场模型

2.1 相场变量

本模型通过引入一系列取向场变量η₁, η₂, ···, η_p和浓度场变量ϕ_α, ϕ_β, ρ来描述不同取向的两种晶粒相和气孔相. η_i(i = 1, 2, ···, p)为非保守型相场变量, 其中η_i(i = 1, 2, ···, r)用来描述α相多晶中不同晶粒的取向, η_i(i = r + 1, r + 2, ···, p)用来描述β相多晶中不同晶粒的取向, 在第i个晶粒内部η_i的取值为1, 其余p – 1个取值为0; ϕ_α为保守型相场变量, 在α相取值为1, 在β相和气孔相取值为0; ϕ_β为保守型相场变量, 在β相取值为1, 在α相和气孔相取值为0; ρ为保守型相场变量, 在α相和β相取值为1, 在气孔相取值为0.

图1为扩散界面相场模型的示意图. 可以看出, 在晶界处η_i的取值从1连续变化为0 (或者从0连续变化为1), ϕ_α的取值从1连续变化为0, ϕ_β的取值从0连续变化为1, 在气孔边界处, ρ的取值从0连续变化为1. 已有研究^[21]表明, 当晶粒个数p > 36时, 晶粒组织演变对p取值的依赖性可以忽略.

$图 1 相场模型示意图 (ρ, ϕα, ϕβ —浓度场变量; η1—晶粒1的取向场变量; η2—晶粒2的取向场变量)\r\nFig. 1. Schematic of phase field model (ρ, ϕα, ϕβ —concentration field variable; η1—orientation field variable of grain 1; η2—orientation field variable of grain 2.)$

图 1 相场模型示意图 (ρ, ϕ_α, ϕ_β —浓度场变量; η₁—晶粒1的取向场变量; η₂—晶粒2的取向场变量)

Fig. 1. Schematic of phase field model (ρ, ϕ_α, ϕ_β —concentration field variable; η₁—orientation field variable of grain 1; η₂—orientation field variable of grain 2.)

下载: 全尺寸图片幻灯片

2.2 自由能泛函数

本工作两相烧结相场模型的总自由能泛函数F采用以下形式:

$\begin{split} &F = \int_V \Bigg[ f(\rho ,{\eta _1},{\eta _2}, \cdots ,{\eta _p},{\phi _\alpha },{\phi _\beta }) + \frac{{{\kappa _\rho }}}{2}{{\left| {\nabla \rho } \right|}^2}\\ &+ \frac{{{\kappa _\phi }}}{2}{{\left| {\nabla {\phi _\alpha }} \right|}^2} + \frac{{{\kappa _\phi }}}{2}{{\left| {\nabla {\phi _\beta }} \right|}^2} + \frac{{{\kappa _\eta }}}{2}\sum\limits_{i = 1}^p {{{\left| {\nabla {\eta _i}} \right|}^2}} \Bigg] {\mathrm{d}}V , \end{split}$

(1)

式中, 第1项f为局部自由能密度函数; 第2项、第3项、第4项和第5项为梯度自由能, 分别表示气孔表面、α相的相界面、β相的相界面和晶界处的额外自由能; κ_ρ, κ_ϕ和κ_η为梯度能系数, 取决于两种材料气孔表面、晶粒相界面和晶界处的能量和宽度, 单位J/m; V为空间体积.

本工作采用的f表达形式为

$\begin{split} & f(\rho ,{\eta _1},{\eta _2}, \cdots ,{\eta _p},{\phi _\alpha },{\phi _\beta }) \\ =\;& A{\rho ^2}{(1 - \rho )^2} + B\Bigg\{ \Big[ {\rho ^2} + 6(1 - \rho )\left( {{\phi^2 _\alpha } + \phi^2 _\beta } \right) - 4(2 - \rho )\left( {\phi _\alpha ^3 + \phi _\beta ^3} \right) + 3{{\left( {\phi _\alpha ^2 + \phi _\beta ^2} \right)}^2} \Big] \\ & + \Bigg[ \phi _\alpha ^2 + 6(1 - {\phi _\alpha })\sum\limits_{i = 1}^r {\eta _i^2} - 4(2 - {\phi _\alpha })\sum\limits_{i = 1}^r {\eta _i^3} + 3 \left( \sum\limits_{i = 1}^r {\eta _i^2} \right)^2 \Bigg] \\ & + \Bigg[ {\phi _\beta ^2 + 6(1 - {\phi _\beta })\sum\limits_{i = r + 1}^p {\eta _i^2} - 4(2 - {\phi _\beta })\sum\limits_{i = r + 1}^p {\eta _i^3} + 3{{\left( {\sum\limits_{i = r + 1}^p {\eta _i^2} } \right)}^2}} \Bigg] + {a_{{\text{GB}}}}\sum\limits_{i = 1}^p \sum\limits_{j > i}^p {\eta _i^2\eta _j^2} \Bigg\}\,, \end{split}$

(2)

式中, A和B为与两种材料气孔表面、晶粒相界面和晶界处能量和宽度有关的参数, 单位J/m³; a_GB为扩散界面参数, 取a_GB = 1.5^[22]; 方程右侧第1项为双势阱函数, 在晶粒内部与气孔内部取得极小值; 方程右侧第2项花括号中为多势阱函数, 在晶粒内部取得极小值. 本工作所采用的自由能泛函数能够保证在各个晶粒内部和气孔内部取得p + 1个极小值.

F中各参数与两种材料的物理参数之间的关系为^[23]

${\kappa _\eta } = \frac{{3\left( {{\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta } \right)\delta }}{4}$

(3)

${\kappa _\rho } = {\kappa _\phi } = \frac{{3\delta \left[ {2({\varphi _\alpha }\gamma _{\text{s}}^\alpha + {\varphi _\beta }\gamma _{\text{s}}^\beta ) - ({\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta )} \right]}}{4} ,$

(4)

$A = \frac{{12({\varphi _\alpha }\gamma _{\text{s}}^\alpha + {\varphi _\beta }\gamma _{\text{s}}^\beta ) - 7({\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta )}}{\delta } ,$

(5)

$B = \frac{{{\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta }}{\delta } ,$

(6)

式中, 插值函数 ${\varphi _\alpha } = {{\displaystyle \sum\nolimits_{i = 1}^r {\eta _i^2} } \Big/ {\displaystyle \sum\nolimits_{i = 1}^p {\eta _i^2} }}$ , ${\varphi _\beta } = {{\displaystyle \sum\nolimits_{i = r + 1}^p {\eta _i^2} } \Big/ {\displaystyle \sum\nolimits_{i = 1}^p {\eta _i^2} }}$ ; $\gamma _{{\text{gb}}}^\alpha$ 和 $\gamma _{\text{s}}^\alpha$ , $\gamma _{{\text{gb}}}^\beta$ 和 $\gamma _{\text{s}}^\beta$ 分别为两种材料的晶界能和表面能, 单位J/m²; δ为扩散界面的宽度, 单位m.

2.3 演化动力学方程

假设烧结过程中的质量守恒, 上述相场模型中ρ, ${\phi _\alpha }$ 和 ${\phi _\beta }$ 的演化动力学方程为Cahn-Hilliard方程^[24]:

$\frac{{\partial \rho }}{{\partial t}} = \nabla \cdot \left( {{\boldsymbol{M}}\nabla \frac{{\delta F}}{{\delta \rho }}} \right) = \nabla \cdot {\boldsymbol{M}}\nabla \left[ {\frac{{\partial f}}{{\partial \rho }} - {\kappa _\rho }{\nabla ^2}\rho } \right] ,$

(7)

$\frac{{\partial {\phi _\alpha }}}{{\partial t}} = \nabla \cdot \left( {{\boldsymbol{M}}\nabla \frac{{\delta F}}{{\delta {\phi _\alpha }}}} \right) = \nabla \cdot {\boldsymbol{M}}\nabla \left[ {\frac{{\partial f}}{{\partial {\phi _\alpha }}} - {\kappa _\phi }{\nabla ^2}{\phi _\alpha }} \right] ,$

(8)

$\frac{{\partial {\phi _\beta }}}{{\partial t}} = \nabla \cdot \left( {{\boldsymbol{M}}\nabla \frac{{\delta F}}{{\delta {\phi _\beta }}}} \right) = \nabla \cdot {\boldsymbol{M}}\nabla \left[ {\frac{{\partial f}}{{\partial {\phi _\beta }}} - {\kappa _\phi }{\nabla ^2}{\phi _\beta }} \right] ,$

(9)

式中, t为时间; ${\boldsymbol M}$ 为迁移率张量, 表达形式为^[23]

${\boldsymbol{M}} = \frac{{{\nu _{\text{m}}}({\varphi _\alpha }{{\boldsymbol{D}}_\alpha } + {\varphi _\beta }{{\boldsymbol{D}}_\beta })}}{{RT}} ,$

(10)

其中, ν_m为摩尔体积, R为气体常数, T为温度, ${{\boldsymbol{D}}_\alpha }$ 和 ${{\boldsymbol{D}}_\beta }$ 为两种材料的扩散系数张量.

本工作采取的体系扩散机制包括表面扩散和晶界扩散. 因此, 可以认为 ${{\boldsymbol{D}}_\alpha } = {\boldsymbol{D}}_\alpha ^{\text{s}} + {\boldsymbol{D}}_\alpha ^{{\text{gb}}}$ , ${{\boldsymbol{D}}_\beta } = {\boldsymbol{D}}_\beta ^{\text{s}} + {\boldsymbol{D}}_\beta ^{{\text{gb}}}$ , 其中, ${\boldsymbol{D}}_\alpha ^{\text{s}}$ 和 ${\boldsymbol{D}}_\alpha ^{{\text{gb}}}$ , ${\boldsymbol{D}}_\beta ^{\text{s}}$ 和 ${\boldsymbol{D}}_\beta ^{{\text{gb}}}$ 分别为两种材料的表面扩散系数张量和晶界扩散系数张量, 表达形式为^[23]

${\boldsymbol{D}}_\alpha ^{\text{s}} = D_\alpha ^{\text{s}}{\rho ^2}{(1 - \rho )^2}{{\boldsymbol{T}}^{\text{s}}} ,$

(11)

${\boldsymbol{D}}_\beta ^{\text{s}} = D_\beta ^{\text{s}}{\rho ^2}{(1 - \rho )^2}{{\boldsymbol{T}}^{\text{s}}} ,$

(12)

${{ {\boldsymbol{T}}}^{\text{s}}} = {\boldsymbol{I}} - {{\boldsymbol{n}}_{\text{s}}} \otimes {{\boldsymbol{n}}_{\text{s}}} ,$

(13)

${{\boldsymbol{n}}_{\text{s}}} = \frac{{\nabla \rho }}{{\left| {\nabla \rho } \right|}} ,$

(14)

式中, $D_\alpha ^{\text{s}}$ 和 $D_\beta ^{\text{s}}$ 为表面扩散系数标量, 取决于两种材料的性质; ${\boldsymbol T}^{\rm s}$ 为表面投影张量, 保证表面扩散在晶粒与气孔接触表面的切线方向; I为单位张量; 符号 $\otimes$ 为张量积; ${\boldsymbol n}_{\rm s}$ 为垂直于表面的单位法向量.

${\boldsymbol{D}}_\alpha ^{{\text{gb}}} = D_\alpha ^{{\text{gb}}}\sum\limits_{i = 1}^p {\sum\limits_{j > i}^p {{\eta _i}} {\eta _j}} {{\boldsymbol{T}}^{{\text{gb}}}} ,$

(15)

${\boldsymbol{D}}_\beta ^{{\text{gb}}} = D_\beta ^{{\text{gb}}}\sum\limits_{i = 1}^p {\sum\limits_{j > i}^p {{\eta _i}} {\eta _j}} {{\boldsymbol{T}}^{{\text{gb}}}} ,$

(16)

${{ {\boldsymbol{T}}}^{{\text{gb}}}} = {\boldsymbol{I}} - {{\boldsymbol{n}}_{{\text{gb}}}} \otimes {{\boldsymbol{n}}_{{\text{gb}}}} ,$

(17)

${{\boldsymbol{n}}_{{\text{gb}}}} = \frac{{\nabla {\eta _i} - \nabla {\eta _j}}}{{\left| {\nabla {\eta _i} - \nabla {\eta _j}} \right|}} ,$

(18)

式中, $D_\alpha ^{{\text{gb}}}$ 和 $D_\beta ^{{\text{gb}}}$ 为晶界扩散系数标量, 取决于两种材料的性质; ${\boldsymbol{T}}^{{\text{gb}}}$ 为晶界投影张量, 保证晶界扩散在晶界的切线方向; ${\boldsymbol{n}}_{{\text{gb}}}$ 为垂直于晶界的单位法向量.

η_i的演化动力学方程为Allen-Cahn方程^[24]:

$\begin{split} \frac{{\partial {\eta _i}}}{{\partial t}} =\;& - L\frac{{\delta F}}{{\delta {\eta _i}}} = - L\left[ {\frac{{\partial f}}{{\partial {\eta _i}}} - {\kappa _\eta }{\nabla ^2}{\eta _i}} \right]{,}\\ & i = 1,2, \cdots,p,\end{split}$

(19)

式中, L为表征晶界迁移率的系数, 与两种材料的物理参数之间的关系为^[25]

$L = \frac{{({\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta ){M_{\text{b}}}}}{{{\kappa _\eta }}} ,$

(20)

${M_b} = \frac{{{\nu _{\text{m}}}({\varphi _\alpha }D_\alpha ^{{\text{gb}}} + {\varphi _\beta }D_\beta ^{{\text{gb}}})}}{{10RT\delta }} ,$

(21)

其中, M_b为晶界迁移率.

根据(7)式、(8)式、(9)式的Cahn-Hilliard方程与(19)式的Allen-Cahn方程, 对所有相场变量进行求解, 可以计算出组织演变过程中任意时刻的微观结构与空间分布. 本工作通过编写程序进行模拟, 采用有限差分法求解相场方程, 在时间上采用显式Euler算法对非线性偏微分方程进行离散化, 在空间上采用五点差分法求解Laplace项^[26].

为了直观地表征两相烧结过程, 本工作中可视化变量φ为

$\varphi = 1.5\sum\limits_{i = 1}^r {\eta _i^2} + \sum\limits_{i = r + 1}^p {\eta _i^2} .$

(22)

3. 无量纲化处理

本工作相场模型的变量与参数采用无量纲形式. 根据(7)式、()式与()式, 保守场演化方程中含有量纲的量为t, $\boldsymbol M$ , F和 $\nabla$ , 通过选取参考空间长度 $l^*$ 、参考时间 $t^*$ 和参考能量密度 $\varepsilon^*$ 作为参考物理量, 可以得到无量纲Hamilton算符 $\tilde \nabla = {l^ * }\nabla$ 、无量纲时间 $\tau=t/t^*$ 和无量纲自由能 $\tilde F =F/\varepsilon^*$ . 将无量纲量代入(7)式、(8)式与(9)式, 得到变形后的方程为

$\begin{split} &\frac{{\partial \rho }}{{\partial \tau }} = \tilde \nabla \cdot \left( {\frac{{{\boldsymbol{M}}{\varepsilon ^ * }{t^ * }}}{{{l^{{ * 2}}}}}\tilde \nabla \frac{{\delta \tilde F}}{{\delta \rho }}} \right)\\ =\;&\tilde \nabla \cdot \frac{{{\boldsymbol{M}}{\varepsilon ^ * }{t^ * }}}{{{l^{{*2}}}}}\tilde \nabla \left[ {\frac{1}{{{\varepsilon ^ * }}}\frac{{\partial f}}{{\partial \rho }} - \frac{{{\kappa _\rho }}}{{{\varepsilon ^ * }{l^{{ * 2}}}}}{{\tilde \nabla }^2}\rho } \right] , \end{split}$

(23)

$\begin{split}&\frac{{\partial {\phi _\alpha }}}{{\partial \tau }} = \tilde \nabla \cdot \left( {\frac{{{\boldsymbol{M}}{\varepsilon ^ * }{t^ * }}}{{{l^{{ * 2}}}}}\tilde \nabla \frac{{\delta \tilde F}}{{\delta {\phi _\alpha }}}} \right)\\ =\;&\tilde \nabla \cdot \frac{{{\boldsymbol{M}}{\varepsilon ^ * }{t^ * }}}{{{l^{{*2}}}}}\tilde \nabla \left[ {\frac{1}{{{\varepsilon ^ * }}}\frac{{\partial f}}{{\partial {\phi _\alpha }}} - \frac{{{\kappa _\phi }}}{{{\varepsilon ^ * }{l^{{ * 2}}}}}{{\tilde \nabla }^2}{\phi _\alpha }} \right] , \end{split}$

(24)

$\begin{split} &\frac{{\partial {\phi _\beta }}}{{\partial \tau }} = \tilde \nabla \cdot \left( {\frac{{{\boldsymbol{M}}{\varepsilon ^ * }{t^ * }}}{{{l^{{ * 2}}}}}\tilde \nabla \frac{{\delta \tilde F}}{{\delta {\phi _\beta }}}} \right)\\ =\;&\tilde \nabla \cdot \frac{{{\boldsymbol{M}}{\varepsilon ^ * }{t^ * }}}{{{l^{{*2}}}}}\tilde \nabla \left[ {\frac{1}{{{\varepsilon ^ * }}}\frac{{\partial f}}{{\partial {\phi _\beta }}} - \frac{{{\kappa _\phi }}}{{{\varepsilon ^ * }{l^{{ * 2}}}}}{{\tilde \nabla }^2}{\phi _\beta }} \right] .\end{split}$

(25)

由此可得无量纲迁移率张量 $\tilde {\boldsymbol{M}} = {\boldsymbol{M}}{\varepsilon^*}{t^*}/l^{*2}$ .

根据(19)式, 非保守场演化方程含有量纲的量为t, L, F和 $\nabla$ . 将无量纲量代入(19)式, 得到变形后的方程为

$\begin{split}\frac{{\partial {\eta _i}}}{{\partial \tau }} = - L{\varepsilon ^ * }{t^ * }\frac{{\delta \tilde F}}{{\delta {\eta _i}}} =\;& - L{\varepsilon ^ * }{t^ * }\left[ {\frac{1}{{{\varepsilon ^ * }}}\frac{{\partial f}}{{\partial {\eta _i}}} - \frac{{{\kappa _\eta }}}{{{\varepsilon ^ * }{l^{{ * ^2}}}}}{\nabla ^2}{\eta _i}} \right],\\ & i = 1,2, \cdots ,p. \\[-1pt]\end{split}$

(26)

由此可得无量纲迁移系数 $\tilde L = L{\varepsilon ^*}{t^*}$ .

本工作取 ${t^*} = 1/\left( {L{\varepsilon ^*}} \right)$ , ${\varepsilon ^*} = B$ ; ${l^*}$ 的取值与δ有关, 对应无量纲化之后一个单位长度占有的界面宽度, 本工作取 ${l^*} = \delta /m$ ; m为扩散界面在模拟中占据的格点数, 本工作取m = 3.

根据所选取的参考物理量, 无量纲迁移率张量 $\tilde {\boldsymbol{M}}$ 与无量纲总自由能泛函数 $\tilde F$ 中A, B, ${\kappa _\rho }$ , ${\kappa _\phi }$ , ${\kappa _\eta }$ 等参数对应的无量纲形式分别为

$\tilde {\boldsymbol{M}} = \frac{{15[ {( {{\varphi _\alpha }D_\alpha ^{\text{s}} + {\varphi _\beta }D_\beta ^{\text{s}}} ) + ( {{\varphi _\alpha }D_\alpha ^{{\text{gb}}} + {\varphi _\beta }D_\beta ^{{\text{gb}}}} )} ]{m^2}}}{{2({\varphi _\alpha }D_\alpha ^{{\text{gb}}} + {\varphi _\beta }D_\beta ^{{\text{gb}}})}} ,$

(27a)

$\tilde A = \frac{A}{{{\varepsilon ^ * }}} = \frac{{12({\varphi _\alpha }\gamma _{\text{s}}^\alpha + {\varphi _\beta }\gamma _{\text{s}}^\beta ) - 7({\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta )}}{{{\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta }} ,$

(27b)

$\tilde B = {B}/{{{\varepsilon ^ * }}} = 1 ,$

(27c)

$\begin{split}& {\tilde \kappa _\rho } = \frac{{{\kappa _\rho }}}{{{\varepsilon ^ * }{l^{{ * 2}}}}} = {\tilde \kappa _\phi } = \frac{{{\kappa _\phi }}}{{{\varepsilon ^ * }{l^{{ * 2}}}}} = \\ & \frac{3}{4}\bigg[{\frac{{2({\varphi _\alpha }\gamma _{\text{s}}^\alpha + {\varphi _\beta }\gamma _{\text{s}}^\beta ) - ({\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta )}}{{{\varphi _\alpha }\gamma _{{\text{gb}}}^\alpha + {\varphi _\beta }\gamma _{{\text{gb}}}^\beta }}} \bigg]{m^2}, \end{split}$

(27d)

${\tilde \kappa _\eta } = \frac{{{\kappa _\eta }}}{{{\varepsilon ^ * }{l^{{ * 2}}}}} = \frac{3}{4}{m^2} .$

(27e)

本工作利用相场模型对UN粉末与U₃Si₂粉末在1823 K温度下的两相烧结过程进行了数值模拟, 以UN为α相, U₃Si₂为β相, 模拟中用到的UN和U₃Si₂的物理参数如表1和表2所列^[27–32].

表 1 UN的物理参数^[27–29]

Table 1. Physical parameters of UN at 1823 K^[27–29]

Parameter	Value	Unit	Ref.
$D_\alpha ^{\text{s}}$	7.5 × 10^–12	m²·s^–1	[27]
$D_\alpha ^{{\text{gb}}}$	$0.01D_\alpha ^{\text{s}}$	m²·s^–1	[28]
$\gamma _{\text{s}}^\alpha$	1.6	J·m^–2	[29]
$\gamma _{{\text{gb}}}^\alpha$	0.8	J·m^–2	[29]
δ	6	nm	[29]

下载: 导出CSV

| 显示表格

表 2 U₃Si₂的物理参数^[30–32]

Table 2. Physical parameters of U₃Si₂ at 1823 K^[30–32]

Parameter	Value	Unit	Ref.
$D_\beta ^{\text{s}}$	100 $D_\beta ^{{\text{gb}}}$	m²·s^–1
$D_\beta ^{{\text{gb}}}$	6.5923 × 10^–10	m²·s^–1	[30]
$\gamma _{\text{s}}^\beta$	2.0	J·m^–2	[31]
$\gamma _{{\text{gb}}}^\beta$	1.3	J·m^–2	[32]
δ	6	nm	[32]
Note: $D_\alpha ^{\text{s}}$ , $D_\beta ^{\text{s}}$ — surface diffusivity; $D_\alpha ^{{\text{gb}}}$ , $D_\beta ^{{\text{gb}}}$ — grain-boundary diffusivity; $\gamma _{\text{s}}^\alpha$ , $\gamma _{\text{s}}^\beta$ — surface energy; $\gamma _{{\text{gb}}}^\alpha$ , $\gamma _{{\text{gb}}}^\beta$ — grain-boundary energy; δ — diffuse interface width.

下载: 导出CSV

| 显示表格

将UN和U₃Si₂的物理参数代入上述方程中, 求得各无量纲参数的具体数值如表3所列.

表 3 模拟中的无量纲参数表

Table 3. Non-dimensional parameters used in simulation.

Parameter	Value	Parameter	Value
$\tilde A({\varphi _\alpha } = 1, {\text{ }}{\varphi _\beta } = 0)$	17	${\tilde \kappa _\eta }$	6.75
$\tilde A({\varphi _\alpha } = 0, {\text{ }}{\varphi _\beta } = 1)$	11.5	$\tilde {\boldsymbol{M}}({\varphi _\alpha } = 1, {\text{ }}{\varphi _\beta } = 0)$	6817.5
$\tilde B$	1	$\tilde {\boldsymbol{M}}({\varphi _\alpha } = 0, {\varphi _\beta } = 1)$	6817.5
${\tilde \kappa _\rho }({\varphi _\alpha } = 1, {\varphi _\beta } = 0)$	20.25	$\tilde L$	1
${\tilde \kappa _\rho }({\varphi _\alpha } = 0, {\text{ }}{\varphi _\beta } = 1)$	14	$\Delta x = \Delta y$	1
${\tilde \kappa _\phi }({\varphi _\alpha } = 1, {\text{ }}{\varphi _\beta } = 0)$	20.25	$\Delta t$	2 × 10^–5
${\tilde \kappa _\phi }({\varphi _\alpha } = 0, {\text{ }}{\varphi _\beta } = 1)$	14
Note: $\tilde A$ , $\tilde B$ , ${\tilde \kappa _\rho }$ , ${\tilde \kappa _\phi }$ , ${\tilde \kappa _\eta }$ — non-dimensional parameters of free energy function; $\tilde {\boldsymbol{M}}$ — non-dimensional mobility; $\tilde L$ —non-dimensional Allen-Cahn mobility; ∆x, ∆y — space scale; ∆t — time scale.

下载: 导出CSV

| 显示表格

4. 结果与讨论

4.1 2个不同相晶粒烧结

本工作采用相场模型, 模拟了双晶粒结构中UN粉末与U₃Si₂粉末的两相烧结过程. 所选模拟区域差分网格尺寸为256 × 256, 采用周期性边界条件. 分别研究UN粉末与U₃Si₂粉末两相烧结组织的形貌演化过程、烧结颈的形成、平衡二面角以及不同晶粒尺寸对组织演变过程的影响.

4.1.1 烧结颈的形成

图2为2个不同相等尺寸的圆形晶粒在烧结过程中形貌演化的相场模拟. 其中晶粒的半径R = 30, 黄色的部分代表UN相晶粒, 绿色的部分代表U₃Si₂相晶粒. 从图2(a)可以看出, 在烧结过程初期, U₃Si₂相晶粒具有比UN相晶粒更高的表面能, 使其在烧结颈形成过程中更趋向于减小表面积, 颈部附近的晶粒表面向晶粒内部凹陷变形的程度更明显; 在图2(a)—(d)两相晶粒烧结过程中, 先后发生了烧结颈的形成和增长, 这一现象与单相晶粒烧结模拟^[33]的结果一致; 仅考虑表面扩散和晶界扩散的模拟烧结颈增长较缓慢, 晶粒位置无明显移动.

$图 2 两个不同相等大圆形晶粒演化的相场模拟　(a) 6 × 104 $ \Delta t $; (b) 50 × 104 $ \Delta t $; (c) 200 × 104 $ \Delta t $; (d) 500 × 104$ \Delta t $\r\nFig. 2. Phase-field simulation of the evolution of two equal-sized circular grains with different phases: (a) 6 × 104 $ \Delta t $; (b) 50 × 104 $ \Delta t $; (c) 200 × 104 $ \Delta t $; (d) 500 × 104 $ \Delta t $.$

图 2 两个不同相等大圆形晶粒演化的相场模拟　(a) 6 × 10⁴

$\Delta t$

; (b) 50 × 10⁴

$\Delta t$

; (c) 200 × 10⁴

$\Delta t$

; (d) 500 × 10⁴

$\Delta t$

Fig. 2. Phase-field simulation of the evolution of two equal-sized circular grains with different phases: (a) 6 × 10⁴

$\Delta t$

; (b) 50 × 10⁴

$\Delta t$

; (c) 200 × 10⁴

$\Delta t$

; (d) 500 × 10⁴

$\Delta t$

下载: 全尺寸图片幻灯片

图3为基于2个不同相等尺寸晶粒烧结模拟数据的烧结颈对数增长曲线. 由图3可以看出, 烧结颈的增长曲线斜率前后发生改变, 这表明烧结颈的增长规律并非简单的幂函数关系, 曲线可以划分为2个增长阶段: 烧结初期, 烧结过程受表面扩散主导, 颈部快速形成并增长, 斜率为0.44左右; 烧结中期, 表面扩散作用减小, 晶界扩散作用增大, 烧结颈的增长速率显著下降, 烧结颈持续缓慢增长, 斜率为0.21左右, 满足烧结颈曲线增长规律^[34]. 随着烧结过程的继续进行, 烧结颈将在后期达到稳定状态, 颈部尺寸较大, 晶粒之间紧密接触, 不再适合用烧结前中期的增长规律对烧结颈进行描述.

$图 3 不同相晶粒的烧结颈对数增长曲线 (l — 颈部长度, t — 时间步)\r\nFig. 3. Logarithmic growth curves of sintering neck of different phase grains (l —neck length, t — time step).$

图 3 不同相晶粒的烧结颈对数增长曲线 (l — 颈部长度, t — 时间步)

Fig. 3. Logarithmic growth curves of sintering neck of different phase grains (l —neck length, t — time step).

下载: 全尺寸图片幻灯片

4.1.2 平衡二面角

研究表明, 在烧结过程中, 相邻的2个晶粒在晶粒相与气孔相的相界处形成一个平衡二面角Ψ, Ψ取决于材料的表面能γ_s和晶界能γ_gb, 在各向同性条件下, 晶界处的平衡二面角方程为^[35]

$\varPsi = 2\arccos \left( {\frac{{{\gamma _{{\text{gb}}}}}}{{2{\gamma _{\text{s}}}}}} \right) .$

(28)

分别为不同演化时间下2个等尺寸晶粒烧结形成的平衡二面角. 本工作中UN相晶界能与表面能的比值为 ${{\gamma _{{\text{gb}}}^\alpha } {/ } {\gamma _{\text{s}}^\alpha }} = 0.5$ , 对应计算值为Ψ = 151°, 如图4(a)和所示; U₃Si₂相晶界能与表面能的比值为 ${{\gamma _{{\text{gb}}}^\beta } {/ } {\gamma _{\text{s}}^\beta }} = 0.65$ , 对应计算值为Ψ = 142°, 如图4(b)和图4(e)所示; 2个同相晶粒烧结形成的最终平衡二面角均与理论计算值吻合较好. 从图4可以看出, UN相晶粒与U₃Si₂相晶粒烧结形成的最终平衡二面角介于2个同相双晶粒的最终平衡二面角之间, 达到稳定状态后的平衡二面角随时间无明显变化. 这证明了2个不同相晶粒烧结形成的最终平衡二面角只由两种材料的特性所决定, 即与两种材料的晶界能和表面能的不同比值密切相关.

$图 4 演化时间500 × 104 $ \Delta t $((a)—(c))与1500 × 104 $ \Delta t $((d)—(f))下的平衡二面角　(a), (d) 2个UN晶粒; (b), (e) 2个U3Si2晶粒; (c), (f) 1个UN晶粒和1个U3Si2晶粒\r\nFig. 4. Equilibrium dihedral angles at evolution times 500 × 104 $ \Delta t $((a)–(c)) and 1500 × 104 $ \Delta t $((d)–(f)): (a), (d) Two UN grains; (b), (e) two U3Si2 grains; (c), (f) one UN grain and one U3Si2 grain.$

图 4 演化时间500 × 10⁴

$\Delta t$

((a)—(c))与1500 × 10⁴

$\Delta t$

((d)—(f))下的平衡二面角　(a), (d) 2个UN晶粒; (b), (e) 2个U₃Si₂晶粒; (c), (f) 1个UN晶粒和1个U₃Si₂晶粒

Fig. 4. Equilibrium dihedral angles at evolution times 500 × 10⁴

$\Delta t$

((a)–(c)) and 1500 × 10⁴

$\Delta t$

((d)–(f)): (a), (d) Two UN grains; (b), (e) two U₃Si₂ grains; (c), (f) one UN grain and one U₃Si₂ grain.

下载: 全尺寸图片幻灯片

4.1.3 不同晶粒尺寸的影响

图5为2个不同相不同尺寸晶粒烧结过程的相场模拟. 由图5可以看出, 2个不同相不同尺寸晶粒的烧结过程与Sun等^[36]模拟的2个同相不同尺寸晶粒的烧结过程有着显著的差异: 2个同相晶粒烧结, 烧结颈向尺寸较小的晶粒一侧迁移, 大晶粒的面积不断增大, 而小晶粒的面积不断减小, 直到最终消失^[36]; 2个不同相晶粒烧结, 烧结颈向尺寸较小的晶粒一侧迁移, 迁移一段距离后稳定存在, 小晶粒的形状不断发生改变, 最终呈现为扁圆形, UN相大晶粒和U₃Si₂相小晶粒各自的面积无明显变化, 大晶粒并未吞噬小晶粒.

$图 5 两个不同相不等大圆形晶粒演化的相场模拟　(a) 2 × 104 $ \Delta t $; (b) 50 × 104 $ \Delta t $; (c) 100 × 104 $ \Delta t $; (d) 500 × 104 $ \Delta t $.\r\nFig. 5. Phase-field simulation of the evolution of two unequal-sized circular grains with different phases: (a) 2 × 104 $ \Delta t $; (b) 50 × 104 $ \Delta t $; (c) 100 × 104 $ \Delta t $; (d) 500 × 104 $ \Delta t $.$

图 5 两个不同相不等大圆形晶粒演化的相场模拟　(a) 2 × 10⁴

$\Delta t$

; (b) 50 × 10⁴

$\Delta t$

; (c) 100 × 10⁴

$\Delta t$

; (d) 500 × 10⁴

$\Delta t$

Fig. 5. Phase-field simulation of the evolution of two unequal-sized circular grains with different phases: (a) 2 × 10⁴

$\Delta t$

; (b) 50 × 10⁴

$\Delta t$

; (c) 100 × 10⁴

$\Delta t$

; (d) 500 × 10⁴

$\Delta t$

下载: 全尺寸图片幻灯片

在2个不同相不同尺寸晶粒的烧结过程中, 晶粒面积和烧结颈尺寸随时间演化的曲线如图6所示. 从图6可以看出, 不同尺寸的2个不同相晶粒烧结过程可以划分为3个阶段: 第1阶段, 烧结颈快速形成与增长, 大小晶粒的面积几乎不变; 第2阶段, 烧结颈缓慢增长, 大小晶粒的面积基本保持稳定; 第3阶段, 烧结颈最终达到稳态, 大小晶粒的面积仍然保持不变. 在烧结过程中, 涉及表面扩散和晶界迁移两种动力学机制, 这两种机制的传质速率分别与晶粒气孔接触表面和晶界的曲率相关^[37]. 烧结颈形成之后, 大小晶粒通过表面扩散机制向烧结颈输送物质; 由于2个晶粒表面曲率的不同, 导致传质速率不同, 烧结颈向尺寸较小的晶粒一侧生长, 形成了弯曲的晶界; 在弯曲晶界曲率的驱动下, 晶界向小晶粒所在的凹侧迁移^[36]; UN与U₃Si₂之间不存在相互转化, 不同相晶粒之间不相互传递物质, 物质仅在各自的同相区域内, 向靠近烧结颈的一侧传输, 由晶界迁移引起的晶粒合并无法进行. 因此, 曲率不同的2个不同相晶粒之间不会发生“大吞小”现象.

$图 6 晶粒面积与烧结颈尺寸的演化曲线\r\nFig. 6. Evolution curves of grain area and sintering neck sizes.$

图 6 晶粒面积与烧结颈尺寸的演化曲线

Fig. 6. Evolution curves of grain area and sintering neck sizes.

下载: 全尺寸图片幻灯片

4.2 多晶粒烧结

4.2.1 三叉晶界的形成与气孔收缩

图7为在UN相晶粒与U₃Si₂相晶粒的4种不同个数比例下, 3个晶粒烧结形成的三叉晶界, 演化的总时间步长为10⁷ $\Delta t$ . 从图7(a)和图7(d)可以看出, 在3个同相晶粒的烧结过程中, 形成了夹角为120°的稳定三叉晶界, 这是因为3条晶界具有相同的能量, 且120°的角度使得晶界的能量分布均匀, 从而达到了晶界能平衡的状态^[36]. 从图7(b)和图7(c)可以看出: 在2个同相晶粒与另一个不同相晶粒的烧结过程中, 形成了夹角偏离120°的三叉晶界, 这是由于两相的晶界能存在差异, 为了实现晶界能的平衡并使体系的能量最小化, 夹角需要根据不同晶界能的大小进行合理的分配; 两相晶界能的差异越大, 夹角偏离120°的程度越大; U₃Si₂相晶粒具有比UN相晶粒更高的晶界能. 因此, 在U₃Si₂相晶粒一侧的夹角趋向于大于120°, 而在UN相晶粒一侧的夹角趋向于小于120°.

$图 7 四种不同相晶粒个数比例下3个晶粒烧结的三叉晶界　(a) 3个UN晶粒; (b) 2个UN晶粒和 1个U3Si2晶粒; (c) 1个UN晶粒和2个U3Si2晶粒; (d) 3个U3Si2晶粒\r\nFig. 7. Trident grain boundaries of the sintering of three grains with four different phase grain number ratios: (a) Three UN grains; (b) two UN grains and one U3Si2 grain; (c) one UN grain and two U3Si2 grains; (d) three U3Si2 grains.$

图 7 四种不同相晶粒个数比例下3个晶粒烧结的三叉晶界　(a) 3个UN晶粒; (b) 2个UN晶粒和 1个U₃Si₂晶粒; (c) 1个UN晶粒和2个U₃Si₂晶粒; (d) 3个U₃Si₂晶粒

Fig. 7. Trident grain boundaries of the sintering of three grains with four different phase grain number ratios: (a) Three UN grains; (b) two UN grains and one U₃Si₂ grain; (c) one UN grain and two U₃Si₂ grains; (d) three U₃Si₂ grains.

下载: 全尺寸图片幻灯片

在4种不同的两相晶粒个数比例下, 三叉晶界处的气孔率随时间演化的曲线如图8所示. 在模拟研究中考虑了两种扩散机制, 其中表面扩散被认为是一种非致密化过程, 主要促进烧结颈的形成和生长; 而晶界扩散被视为了一种极其重要的致密化机制^[34], 涉及到了空位的传输, 是造成三叉晶界处气孔收缩的根本原因. 从图8可以看出, 3个UN相晶粒的气孔收缩过程明显快于其他三种情况. 在晶界扩散过程中, 物质原子从晶界处迁移向与气孔接触的颈部表面, 气孔空位沿晶界扩散并最终湮灭; 由于U₃Si₂相晶粒具有比UN相晶粒更高的晶界能, 与其形成的晶界存在更高的能量势垒, 使得晶界附近的原子或空位在扩散过程中需要克服更大的能量障碍, 导致了原子与气孔空位的扩散速率减慢. 因此, 在包含U₃Si₂相晶粒的3个晶粒烧结过程中, 三叉晶界处的气孔收缩过程显著减缓. 而在包含UN相晶粒与U₃Si₂相晶粒的情况下, 两相的晶界能、表面能和扩散系数的不同都会影响三叉晶界处的气孔收缩, 使得气孔收缩速度的快慢变得更加复杂.

$图 8 三叉晶界处气孔率的演化曲线\r\nFig. 8. Evolution curves of the porosity at triple grain boundaries.$

图 8 三叉晶界处气孔率的演化曲线

Fig. 8. Evolution curves of the porosity at triple grain boundaries.

下载: 全尺寸图片幻灯片

4.2.2 不同体积分数比的两相组织演变

为了研究UN相与U₃Si₂相的不同体积分数比对烧结过程中UN-U₃Si₂两相复合燃料微观组织演变的影响, 构建了4种具有不同两相体积分数比的两相多晶组织, 并进行了两相烧结相场模拟. 其中, α相的体积分数分别为80%, 70%, 60%和50%, 而β相的体积分数则分别为20%, 30%, 40%和50%. 图9展示了这4种不同体积分数比的两相多晶组织的初始形貌.

$图 9 不同体积分数比的两相多晶组织初始形貌　(a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β\r\nFig. 9. Initial morphology of two-phase polycrystalline structures with different volume fraction ratios: (a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β.$

图 9 不同体积分数比的两相多晶组织初始形貌　(a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β

Fig. 9. Initial morphology of two-phase polycrystalline structures with different volume fraction ratios: (a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β.

下载: 全尺寸图片幻灯片

为经过8 × 10⁶ $\Delta t$ 的演化时间后, 4种不同体积分数比的两相多晶烧结组织的最终形貌. 通过对比图9与图10同种情况下的组织形貌可以发现, 晶粒个数和晶粒间的气孔显著减少, 这表明同相晶粒之间发生了合并, 气孔发生了收缩, 晶界扩散起到主要作用^[34]. 从图10(a)—(d)可以看出, 在α相体积分数大于β相体积分数的情况下, β相晶粒基本呈现出嵌入在α相基体中的分布, 表明在烧结过程中α相的晶粒生长占据了主导地位. 在α相晶粒与β相晶粒的接触界面处, 均存在有尺寸较小的α相晶粒或β相晶粒, 未完全与各自同相的大晶粒发生合并. 这表明α相或β相的存在会对另一相的晶界产生阻碍作用, 阻碍其晶界的迁移, 导致其小晶粒无法快速合并, 造成其晶粒长大速率减慢. 在图10(a)—(d)中, 随着β相的体积分数增加, α相的体积分数减少, 两相晶粒的接触面积会增大, 两相之间存在的阻碍作用也会增强. 在图9中, 存在只与不同相晶粒相互接触的α相小晶粒或β相小晶粒, 而在图10中, 这些晶粒消失或其面积明显减少, 这表明α相或β相晶粒也可以通过晶粒迁移方式, 向同相晶粒传输物质, 物质通过另一相晶粒的晶界与相界面进行扩散, 迁移的晶粒会逐渐变小, 最终消失^[38].

$图 10 不同体积分数比的两相多晶组织最终形貌　(a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β\r\nFig. 10. Final morphology of two-phase polycrystalline structures with different volume fraction ratios: (a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β.$

图 10 不同体积分数比的两相多晶组织最终形貌　(a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β

Fig. 10. Final morphology of two-phase polycrystalline structures with different volume fraction ratios: (a) 80% α-20% β; (b) 70% α-30% β; (c) 60% α-40% β; (d) 50% α-50% β.

下载: 全尺寸图片幻灯片

5. 结　论

1) 建立了两相烧结相场模型, 将两相的表面能和晶界能与相场模型的参数关联起来, 模拟了UN-U₃Si₂复合燃料的烧结过程. 模拟结果表明, 烧结颈形成过程中, 具有更高表面能的U₃Si₂相晶粒在颈部附近的表面变形程度更大; 由不同相晶粒烧结形成的最终平衡二面角, 其取值由两相的晶界能和表面能的不同比值所决定; 不同相晶粒之间不存在大晶粒吞噬小晶粒的现象.

2) 3个晶粒烧结过程中的气孔收缩与三叉晶界演变的模拟结果表明, 为实现晶界能的平衡, 不同相晶粒烧结形成的三叉晶界夹角在较高晶界能的U₃Si₂相一侧大于120°, 在较低晶界能的UN相一侧小于120°; 晶界处的高能量势垒会限制气孔空位的晶界扩散, 使三叉晶界处的气孔收缩变慢.

3) 不同体积分数比值的UN-U₃Si₂两相多晶烧结组织形貌演化的模拟结果表明, 烧结组织中存在同相晶粒间的合并与气孔的收缩, 晶界扩散在两相烧结过程中起主要作用; 体积分数较大相的晶粒生长占据主导地位; 两相体系中的一相会阻碍另一相的晶界迁移; 同相晶粒之间能通过晶粒迁移方式进行物质传输.

参考文献

[1]	Rayleigh L 1903 J. Soc. Dyers and Colour. 23 447
[2]	Synge E H 1928 Philosophical Magazine Series 6 356 Google Scholar
[3]	Opower H 1999 Opt. Laser Technol. 504 613
[4]	Wessel J E 1985 J. Opt. Soc. Am. B: Opt. Phys. 2 1538 Google Scholar
[5]	Courjon D, Bainier C 2003 Rep. Prog. Phys. 57 989
[6]	Losquin A, Lummen T T A 2017 Frontiers of Physics in China 12 127301
[7]	Spektor G, Kilbane D, Mahro A, Frank B, Ristok S, Gal L, Kahl P, Podbiel D, Mathias S, Giessen H 2017 Science 355 1187 Google Scholar
[8]	Man K L, Altman M S 2012 J. Phys. Condens. Matter 24 314209 Google Scholar
[9]	Vesseur E J R, de Waele R, Kuttge, Martin, Polman A 2007 Nano Lett. 7 2843 Google Scholar
[10]	Nelayah J, Kociak M, Stephan O, de Abajo F J G , Tence M, Henrard L, Taverna D, Pastorizasantos I, Lizmarzan L M, Colliex C 2007 Nat. Phys. 3 348 Google Scholar
[11]	Govyadinov A A, Konecna A, Chuvilin A, Velez S, Dolado I, Nikitin A Y, Lopatin S, Casanova F, Hueso L E, Aizpurua J 2017 Nat. Commun. 8 95 Google Scholar
[12]	Raza S, Esfandyarpour M, Koh A L, Mortensen N A, Brongersma M L, Bozhevolnyi S I 2016 Nat. Commun. 7 13790 Google Scholar
[13]	Schoen D T, Holsteen A L, Brongersma M L 2016 Nat. Commun. 7 12162 Google Scholar
[14]	Hillenbrand R, Keilmann F, Hanarp P, Sutherland D S, Aizpurua J 2003 Appl. Phys. Lett. 83 368 Google Scholar
[15]	Wurtz G, Bachelot R, Royer P 1998 Rev. Sci. Instrum. 69 1735 Google Scholar
[16]	Dorfmüller J, Vogelgesang R, Weitz R T, Rockstuhl C, Etrich C, Pertsch T, Lederer F, Kern K 2009 Nano Lett. 9 2372 Google Scholar
[17]	Cvitkovic A, Ocelic N, Hillenbrand R 2007 Nano Lett. 7 3177 Google Scholar
[18]	Hillenbrand R, Keilmann F 2000 Phys. Rev. Lett. 85 3029 Google Scholar
[19]	Hillenbrand R, Taubner T, Keilmann F 2002 Nature 418 159 Google Scholar
[20]	Andryieuski A, Zenin V A, Malureanu R, Volkov V S, Bozhevolnyi S I, Lavrinenko A V 2014 Nano Lett. 14 3925 Google Scholar
[21]	Gjonaj B, David A, Blau Y, Spektor G, Orenstein M, Dolev S, Bartal G 2014 Nano Lett. 14 5598 Google Scholar
[22]	Grefe S E, Leiva D, Mastel S, Dhuey S D, Cabrini S, Schuck P J, Abate Y 2013 Phys. Chem. Chem. Phys. 15 18944 Google Scholar
[23]	Chen J, Albella P, Pirzadeh Z, Alonso-Gonzalez P, Huth F, Bonetti S, Bonanni V, Akerman J, Nogues J, Vavassori P, Dmitriev A, Aizpurua J, Hillenbrand R 2011 Small 7 2341 Google Scholar
[24]	Schnell M, Garcia-Etxarri A, Alkorta J, Aizpurua J, Hillenbrand R 2010 Nano Lett. 10 3524 Google Scholar
[25]	Huth F, Chuvilin A, Schnell M, Amenabar I, Krutokhvostov R, Lopatin S, Hillenbrand R 2013 Nano Lett. 13 1065 Google Scholar
[26]	Mastel S, Lundeberg M B, Alonso-Gonzalez P, Gao Y, Watanabe K, Taniguchi T, Hone J, Koppens F H L, Nikitin A Y, Hillenbrand R 2017 Nano Lett. 17 6526 Google Scholar
[27]	Low T, Chaves A, Caldwell J D, Kumar A, Fang N X, Avouris P, Heinz T F, Guinea F, Martin-Moreno L, Koppens F 2016 Nat. Mater. 16 182
[28]	Basov D N, Averitt R D, Hsieh D 2017 Nat. Mater. 16 1077 Google Scholar
[29]	Basov D N, Fogler M M, de Abajo F J G 2016 Science 354 6309
[30]	Betzig E, Trautman J K, Harris T D, Weiner J S, Kostelak R L 1991 Science 251 1468 Google Scholar
[31]	Betzig E, Trautman J K 1992 Science 257 189 Google Scholar
[32]	Gao F, Li X, Wang J, Fu Y 2014 Ultramicroscopy 142 10 Google Scholar
[33]	Hillenbrand R, Knoll B, Keilmann F 2001 J. Microsc. 202 77 Google Scholar
[34]	Labardi M, Patane S, Allegrini M 2000 Appl. Phys. Lett. 77 621 Google Scholar
[35]	Burresi M, Engelen R, Opheij A, van Oosten D, Mori D, Baba T, Kuipers L 2009 Phys. Rev. Lett. 102 033902 Google Scholar
[36]	Feber B L, Rotenberg N, Beggs D M, Kuipers L 2013 Nat. Photonics 8 43
[37]	Kim Z H, Leone S R 2008 Opt. Express 16 1733 Google Scholar
[38]	Kim D, Heo J, Ahn S, Han S W, Yun W S, Kim Z H 2009 Nano Lett. 9 3619 Google Scholar
[39]	Habteyes T G, Dhuey S, Kiesow K I, Vold A 2013 Opt. Express 21 21607 Google Scholar
[40]	Sadiq D, Shirdel J, Lee J S, Selishcheva E, Park N, Lienau C 2011 Nano Lett. 11 1609 Google Scholar
[41]	Ropers C, Neacsu C C, Elsaesser T, Albrecht M, Raschke M B, Lienau C 2007 Nano Lett. 7 2784 Google Scholar
[42]	Ocelic N, Huber A J, Hillenbrand R 2006 Appl. Phys. Lett. 89 101124 Google Scholar
[43]	Stefanon I, Blaize S, Bruyant A, Aubert S, Lerondel G, Bachelot R, Royer P 2005 Opt. Express 13 5553 Google Scholar
[44]	Novotny L, Bian R X, Xie X S 1997 Phys. Rev. Lett. 79 645 Google Scholar
[45]	Noguez C 2007 J. Phys. Chem. C 111 3806 Google Scholar
[46]	Meng L, Yang Z, Chen J, Sun M 2015 Sci. Rep. 5 9240 Google Scholar
[47]	García-Etxarri A, Romero I, de Abajo F J G, Hillenbrand R, Aizpurua J 2009 Phys. Rev. B 79
[48]	Rang M, Jones A C, Zhou F, Li Z, Wiley B J, Xia Y, Raschke M B 2008 Nano Lett. 8 3357 Google Scholar
[49]	Esteban R, Vogelgesang R, Dorfmuller J, Dmitriev A, Rockstuhl C, Etrich C, Kern K 2008 Nano Lett. 8 3155 Google Scholar
[50]	Neuman T, Alonso-González P, Garcia-Etxarri A, Schnell M, Hillenbrand R, Aizpurua J 2015 Laser Photonics Rev. 9 637 Google Scholar
[51]	Burresi M, van Oosten D, Kampfrath T, Schoenmaker H, Heideman R, Leinse A, Kuipers L 2009 Science 326 550 Google Scholar
[52]	Ahn J, Kihm H W, Kihm J E, Kim D S, Lee K 2009 Opt. Express 17 2280 Google Scholar
[53]	Wei H, Zhang S, Tian X, Xu H 2013 Proc. Natl. Acad. Sci. U.S.A. 110 4494 Google Scholar
[54]	Zhang S, Wei H, Bao K, Hakanson U, Halas N J, Nordlander P, Xu H 2011 Phys. Rev. Lett. 107 096801 Google Scholar
[55]	Koppens F H L, Chang D, de Abajo F J G 2011 Nano Lett. 11 3370 Google Scholar
[56]	Dai S, Fei Z, Ma Q, Rodin A S, Wagner M, McLeod A S, Liu M K, Gannett W, Regan W, Watanabe K, Taniguchi T, Thiemens M, Dominguez G, Castro Neto A H, Zettl A, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2014 Science 343 1125 Google Scholar
[57]	Sanvitto D, Kéna-Cohen S 2016 Nat. Mater. 15 1061 Google Scholar
[58]	Woessner A, Parret R, Davydovskaya D, Gao Y, Wu J S, Lundeberg M B, Nanot S, Alonso-González P, Watanabe K, Taniguchi T, Hillenbrand R, Fogler M M, Hone J, Koppens F H L 2017 npj 2D Mater. Appl. 1 25 Google Scholar
[59]	Kumar A, Low T, Fung K H, Avouris P, Fang N X 2015 Nano Lett. 15 3172 Google Scholar
[60]	Woessner A, Misra A, Cao Y, Torre I, Mishchenko A, Lundeberg M B, Watanabe K, Taniguchi T, Polini M, Novoselov K S, Koppens F H L 2017 ACS Photonics 4 3012 Google Scholar
[61]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[62]	Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M, Geim A K 2008 Science 320 1308 Google Scholar
[63]	Guo Q, Li C, Deng B, Yuan S, Guinea F, Xia F 2017 ACS Photonics 4 2989 Google Scholar
[64]	Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109 Google Scholar
[65]	Yan H, Low T, Zhu W, Wu Y, Freitag M, Li X, Guinea F, Avouris P, Xia F 2013 Nat. Photonics 7 394 Google Scholar
[66]	Yan H, Li X, Chandra B, Tulevski G, Wu Y, Freitag M, Zhu W, Avouris P, Xia F 2012 Nat. Nanotechnol. 7 330 Google Scholar
[67]	Fei Z, Andreev G O, Bao W, Zhang L M, Wang C, Stewart M K, Zhao Z, Dominguez G, Thiemens M, Fogler M M, Tauber M J, Castro-Neto A H, Lau C N, Keilmann F, Basov D N 2011 Nano Lett. 11 4701 Google Scholar
[68]	Chen J, Badioli M, Alonso-González P, Thongrattanasiri S, Huth F, Osmond J, Spasenović M, Centeno A, Pesquera A, Godignon P, Zurutuza Elorza A, Camara N, de Abajo F J G, Hillenbrand R, Koppens F H L 2012 Nature 487 77 Google Scholar
[69]	Fei Z, Rodin A S, Andreev G O, Bao W, McLeod A S, Wagner M, Zhang L M, Zhao Z, Thiemens M, Dominguez G, Fogler M M, Neto A H C, Lau C N, Keilmann F, Basov D N 2012 Nature 487 82 Google Scholar
[70]	Ni G X, McLeod A S, Sun Z, Wang L, Xiong L, Post K W, Sunku S S, Jiang B Y, Hone J, Dean C R, Fogler M M, Basov D N 2018 Nature 557 530 Google Scholar
[71]	Fei Z, Foley J J, Gannett W, Liu M K, Dai S, Ni G X, Zettl A, Fogler M M, Wiederrecht G P, Gray S K, Basov D N 2016 Nano Lett. 16 7842 Google Scholar
[72]	Hu F, Luan Y, Fei Z, Palubski I Z, Goldflam M D, Dai S, Wu J S, Post K W, Janssen G, Fogler M M, Basov D N 2017 Nano Lett. 17 5423 Google Scholar
[73]	Duan J, Chen R, Chen J 2017 Chin. Phys. B 26 117802 Google Scholar
[74]	Nikitin A, Alonso-González P, Vélez S, Mastel S, Centeno A, Pesquera A, Zurutuza A, Casanova F, Hueso L, Koppens F 2016 Nat. Photonics 10 239 Google Scholar
[75]	Fei Z, Goldflam M D, Wu J S, Dai S, Wagner M, McLeod A S, Liu M K, Post K W, Zhu S, Janssen G C A M, Fogler M M, Basov D N 2015 Nano Lett. 15 8271 Google Scholar
[76]	Bezares F J, de Sanctis A, Saavedra J R M, Woessner A, Alonso-Gonzalez P, Amenabar I, Chen J, Bointon T, Dai S, Fogler M M, Basov D N, Hillenbrand R, Craciun M F, de Abajo F J G, Russo S, Koppens F H L 2017 Nano Lett. 17 5908 Google Scholar
[77]	Fei Z, Iwinski E G, Ni G X, Zhang L M, Bao W, Rodin A S, Lee Y, Wagner M, Liu M K, Dai S, Goldflam M D, Thiemens M, Keilmann F, Lau C N, Castro-Neto A H, Fogler M M, Basov D N 2015 Nano Lett. 15 4973 Google Scholar
[78]	Woessner A, Gao Y, Torre I, Lundeberg M B, Tan C, Watanabe K, Taniguchi T, Hillenbrand R, Hone J, Polini M, Koppens F H L 2017 Nat. Photonics 11 421 Google Scholar
[79]	Dai S, Ma Q, Liu M K, Andersen T, Fei Z, Goldflam M D, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Janssen G C, Zhu S E, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Nanotechnol. 10 682 Google Scholar
[80]	Caldwell J D, Kretinin A V, Chen Y, Giannini V, Fogler M M, Francescato Y, Ellis C T, Tischler J G, Woods C R, Giles A J, Hong M, Watanabe K, Taniguchi T, Maier S A, Novoselov K S 2014 Nat. Commun. 5 5221 Google Scholar
[81]	Liu Z, Lee H, Xiong Y, Sun C, Zhang X 2007 Science 315 1686 Google Scholar
[82]	Yao J, Liu Z, Liu Y, Wang Y, Sun C, Bartal G, Stacy A M, Zhang X 2008 Science 321 930 Google Scholar
[83]	Yang X, Yao J, Rho J, Yin X, Zhang X 2012 Nat. Photonics 6 450 Google Scholar
[84]	Hoffman A J, Alekseyev L, Howard S S, Franz K J, Wasserman D, Podolskiy V A, Narimanov E E, Sivco D L, Gmachl C 2007 Nat. Mater. 6 946 Google Scholar
[85]	Kim J, Drachev V P, Jacob Z, Naik G V, Boltasseva A, Narimanov E E, Shalaev V M 2012 Opt. Express 20 8100 Google Scholar
[86]	High A A, Devlin R C, Dibos A, Polking M, Wild D S, Perczel J, de Leon N P, Lukin M D, Park H 2015 Nature 522 192 Google Scholar
[87]	Liu Y, Zhang X 2013 Appl. Phys. Lett. 103 141101 Google Scholar
[88]	Li P, Dolado I, Alfaro-Mozaz F J, Casanova F, Hueso L E, Liu S, Edgar J H, Nikitin A Y, Velez S, Hillenbrand R 2018 Science 359 892 Google Scholar
[89]	Ma W, Gonzalez P A, Li S, Nikitin A Y, Yuan J, Sanchez J M, Gutierrez J T, Amenabar I, Li P, Velez S, Tollan C, Dai Z, Zhang Y, Sriram S, Zadeh K K, Lee S T, Hillenbrand R, Bao Q 2018 Nature 562 557 Google Scholar
[90]	Li P, Dolado I, Alfaro-Mozaz F J, Nikitin A Y, Casanova F, Hueso L E, Velez S, Hillenbrand R 2017 Nano Lett. 17 228 Google Scholar
[91]	Dai S, Tymchenko M, Yang Y, Ma Q, Pita-Vidal M, Watanabe K, Taniguchi T, Jarillo-Herrero P, Fogler M, Alù A 2017 Adv. Mater. 30 1706358
[92]	Li P, Lewin M, Kretinin A V, Caldwell J D, Novoselov K S, Taniguchi T, Watanabe K, Gaussmann F, Taubner T 2015 Nat. Commun. 6 7507 Google Scholar
[93]	Dai S, Ma Q, Andersen T, McLeod A S, Fei Z, Liu M K, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Commun. 6 6963 Google Scholar
[94]	Alfaro-Mozaz F J, Alonso-Gonzalez P, Velez S, Dolado I, Autore M, Mastel S, Casanova F, Hueso L E, Li P, Nikitin A Y, Hillenbrand R 2017 Nat. Commun. 8 15624 Google Scholar
[95]	Hu D, Yang X, Li C, Liu R, Yao Z, Hu H, Corder S N G, Chen J, Sun Z, Liu M, Dai Q 2017 Nat. Commun. 8 1471 Google Scholar
[96]	Fei Z, Scott M E, Gosztola D J, Foley J J, Yan J, Mandrus D G, Wen H, Zhou P, Zhang D W, Sun Y, Guest J R, Gray S K, Bao W, Wiederrecht G P, Xu X 2016 Phys. Rev. B 94 081402 Google Scholar
[97]	Hu F, Luan Y, Scott M E, Yan J, Mandrus D G, Xu X, Fei Z 2017 Nat. Photonics 11 356 Google Scholar
[98]	Woessner A, Lundeberg M B, Gao Y, Principi A, Alonso-Gonzalez P, Carrega M, Watanabe K, Taniguchi T, Vignale G, Polini M, Hone J, Hillenbrand R, Koppens F H 2015 Nat. Mater. 14 421 Google Scholar
[99]	Yang X, Zhai F, Hu H, Hu D, Liu R, Zhang S, Sun M, Sun Z, Chen J, Dai Q 2016 Adv. Mater. 28 2931 Google Scholar
[100]	Yoxall E, Schnell M, Nikitin A Y, Txoperena O, Woessner A, Lundeberg M B, Casanova F, Hueso L E, Koppens F H L, Hillenbrand R 2015 Nat. Photonics 9 674 Google Scholar
[101]	Eisele M, Cocker T L, Huber M A, Plankl M, Viti L, Ercolani D, Sorba L, Vitiello M S, Huber R 2014 Nat. Photonics 8 841 Google Scholar
[102]	Huber M A, Plankl M, Eisele M, Marvel R E, Sandner F, Korn T, Schuller C, Haglund R F, Huber R, Cocker T L 2016 Nano Lett. 16 1421 Google Scholar
[103]	Wagner M, Fei Z, McLeod A S, Rodin A S, Bao W, Iwinski E G, Zhao Z, Goldflam M, Liu M, Dominguez G, Thiemens M, Fogler M M, Castro Neto A H, Lau C N, Amarie S, Keilmann F, Basov D N 2014 Nano Lett. 14 894 Google Scholar
[104]	Ni G X, Wang L, Goldflam M D, Wagner M, Fei Z, McLeod A S, Liu M K, Keilmann F, Özyilmaz B, Castro Neto A H, Hone J, Fogler M M, Basov D N 2016 Nat. Photonics 10 244 Google Scholar
[105]	Hu H, Yang X, Zhai F, Hu D, Liu R, Liu K, Sun Z, Dai Q 2016 Nat. Commun. 7 12334 Google Scholar
[106]	Amenabar I, Poly S, Goikoetxea M, Nuansing W, Lasch P, Hillenbrand R 2017 Nat. Commun. 8 14402 Google Scholar
[107]	Amenabar I, Poly S, Nuansing W, Hubrich E H, Govyadinov A A, Huth F, Krutokhvostov R, Zhang L, Knez M, Heberle J, Bittner A M, Hillenbrand R 2013 Nat. Commun. 4 2890 Google Scholar
[108]	Dominguez G, McLeod A S, Gainsforth Z, Kelly P, Bechtel H A, Keilmann F, Westphal A, Thiemens M, Basov D N 2014 Nat. Commun. 5 5445 Google Scholar
[109]	Westermeier C, Cernescu A, Amarie S, Liewald C, Keilmann F, Nickel B 2014 Nat. Commun. 5 4101 Google Scholar
[110]	Lucas I T, McLeod A S, Syzdek J S, Middlemiss D S, Grey C P, Basov D N, Kostecki R 2015 Nano Lett. 15 1 Google Scholar
[111]	Huth F, Govyadinov A, Amarie S, Nuansing W, Keilmann F, Hillenbrand R 2012 Nano Lett. 12 3973 Google Scholar
[112]	Alonso-González P, Nikitin A Y, Golmar F, Centeno A, Pesquera A, Vélez S, Chen J, Navickaite G, Koppens F, Zurutuza A 2014 Science 344 1369 Google Scholar
[113]	Duan J, Chen R, Li J, Jin K, Sun Z, Chen J 2017 Adv. Mater. 29 1702494 Google Scholar
[114]	Zhao Y, Tang Y, Chen Y 2012 ACS Nano 6 6912 Google Scholar
[115]	Nudnova M M, Sigg J, Wallimann P, Zenobi R 2015 Anal. Chem. 87 1323 Google Scholar
[116]	Lee K G, Kihm H W, Kihm J E, Choi W J, Kim H, Ropers C, Park D J, Yoon Y C, Choi S B, Woo D H, Kim J, Lee B, Park Q H, Lienau C, Kim D S 2007 Nat. Photonics 1 53 Google Scholar
[117]	Rotenberg N, Kuipers L 2014 Nat. Photonics 8 919 Google Scholar

图 1 近场光学成像原理图　(a)近场成像和远场成像的比较: 远场光学中物体的点扩散函数由传统衍射极限决定, 而近场光学中物体的点扩散函数由探针尺寸决定; (b)近场光学突破衍射极限的不确定原理解释

Fig. 1. Schematic of near-field optics. (a) Comparison between far-field and near-field optics. The point spread function in far-field optics is determined by the diffraction limit, while the spatial resolution in near-field optics is determined by the size of probe.(b) Explanation of breaking the diffraction limit in near-field optics based on uncertainty principle.

下载: 全尺寸图片幻灯片

图 2 光发射电子显微镜(PEEM)、阴极荧光光谱(CL)、电子能量损失谱(EELS)、扫描式近场光学显微镜(SNOM)等不同纳米级成像技术之间的对比

Fig. 2. Comparison of four classical sub-wavelength approaches, including photon emission electron microscopy (PEEM), cathode-luminescence spectroscopy (CL), electron energy loss spectroscopy (EELS), and scanning near-field optical microscopy (SNOM).

下载: 全尺寸图片幻灯片

图 3 SNOM实验原理　(a) 孔径型SNOM照射原理; (b) 散射型SNOM照射原理

Fig. 3. Experimental scheme of SNOM: (a) The illumination scheme of a-SNOM; (b) the illumination scheme of s-SNOM.

下载: 全尺寸图片幻灯片

图 4 近场光学成像中金属探针和介质探针的比较　(a) 金纳米圆盘的形貌像和光学像, 分别由碳纳米管探针(CNT)和金属探针扫描所得^[47], 标尺为100 nm; (b) 不同探针尖端局域电磁场的数值模拟结果

Fig. 4. The influence of AFM tip in near-field measurement: (a) Topography and near-field amplitude of a gold nanodisk obtained by carbon nanotube (CNT) tip and Pt-coated Si tip^[47], the scale bar is 100 nm; (b) the numerical simulation of local electric field between AFM tip and substrate.

下载: 全尺寸图片幻灯片

图 5 低维体系中的极化激元. 极化激元是光子和其他粒子或准粒子耦合后产生的一种玻色子, 包括富电子体系中的等离极化激元、极化晶体中的声子极化激元、半导体中的激子极化激元、超导体中的库珀对极化激元、铁磁体中的磁振子极化激元以及异质结中的杂化极化激元

Fig. 5. Polaritons in low-dimensional materials. Polaritons are collective excitation from coupling photons with other quasiparticles, such as plasmons in electron-rich systems, infrared-active phonons in polar insulators, excitons in semiconductors, cooper-pairs in superconductors, spin resonances in (anti)-ferromagnets and hybrids in heterostructures.

下载: 全尺寸图片幻灯片

图 6 石墨烯中的表面等离极化激元　(a) 单层石墨烯中狄拉克等离激元的近场光谱测量及其色散的理论计算结果^[67]; (b) 石墨烯等离激元的红外近场光学图像^[68], 入射光波长为9.7 μm; (c) 液氮温区下石墨烯等离激元的近场光学图像^[70], 入射光波长为11.28 μm; (d) 石墨烯纳米泡中等离激元局域“热点”^[71], 入射频率为910 cm^–1; (e) 石墨烯纳米带中等离激元传播态和局域态之间耦合产生的近场光学强度非对称现象^[72], 入射频率为1184 cm^–1; (f) 石墨烯方形谐振腔中等离激元一维边界模式和二维模式的近场光学测量及其数值模拟结果^[74], 入射光波长为11.31 μm; (g) 石墨烯纳米条带中等离激元一维边界模式的近场光学成像^[75], 入射光频率为1160 cm^–1(图(c) 中标尺为1 μm, 其他图中标尺均为200 nm)

Fig. 6. Surface plasmon polaritons in monolayer graphene: (a) Near-field spectroscopic measurement and theoretically calculated dispersion of Dirac plasmons in monolayer graphene^[67]; (b) s-SNOM scheme (upper), experimental amplitude of graphene plasmons (middle) and calculated local density of optical states (bottom)^[68], the incident wavelength is 9.7 μm; (c) nano-image of graphene plasmons launched by gold antenna under liquid-nitrogen temperature, the incident wavelength is 11.28 μm^[70]; (d) plasmonic hot-spots inside graphene nanobubbles on boron nitride substrate^[71], the incident frequency is 910 cm^–1; (e) asymmetric plasmonic fringes induced by superposition of propagating and localized modes in graphene nanoribbons^[72], the incident frequency is 1184 cm^–1; (f) experimental (left) and calculated (right) near-field amplitude of graphene rectangle resonators, representing 1D edge mode and 2D sheet mode^[74], the incident wavelength is 11.31 μm; (g) edge plasmons at the top boundary of graphene nanoribbons^[75], the incident frequency is 1160 cm^–1. Scale bars in all panels represent 200 nm, except for 1 μm in (c).

下载: 全尺寸图片幻灯片

图 7 双层石墨烯中的等离激元　(a) 左: 单层石墨烯和双层石墨烯中等离激元随施加电压的变化趋势; 右: 双层石墨烯中光电导随电压变化趋势的理论计算结果, 图中箭头表示等离激元关闭区域^[77]; (b) 随机堆叠型(左) 和Bernal堆叠型(右) 双层石墨烯中等离激元与声子之间相互耦合作用的近场光学测量^[76]. 散点代表实验数据, 背景色为菲涅耳反射系数虚部的理论计算结果. 内插图为石墨烯等离激元的近场光学图像

Fig. 7. Plasmon polaritons in bilayer graphene: (a) Left panel: experimental measurement of voltage-dependent plasmonic wavelength in monolayer (SLG) and bilayer (BLG) graphene. Right panel: Theoretical calculation of voltage- and frequency-dependent imaginary part of the optical conductivity. The double-headed arrows indicate plasmon-off region of bilayer graphene^[77]; (b) near-field study of interaction between plasmons and intrinsic phonons in highly doped double-layer (left) and bilayer graphene (right)^[76]. The dispersed symbols represent experimental data and background color indicates the imaginary part of the calculated Fresnel reflection coefficient. Inset: representative near-field images of graphene plasmons and corresponding symmetry of phonon-induced charge densities.

下载: 全尺寸图片幻灯片

图 8 石墨烯等离激元的应用　(a) 基于石墨烯等离激元的红外光相位调制器^[78], 上图为实验原理图, 下图为 $0—2{\text{π}}$ 的相位调制, 实线为理论计算结果, 散点为实验数据; (b) 石墨烯/氮化硼中的杂化极化激元^[79]上图为杂化极化激元和氮化硼声子极化激元的光学图像, 下图为杂化极化激元的电压调控 (入射光频率为1495 cm^–1, 标尺为300 nm)

Fig. 8. The applications of graphene plasmons: (a) Phase control of infrared light by gate-tunable graphene plasmons^[78]. Upper panel: schematic of experimental configuration. Bottom panel: Theoretical (solid lines) and experimental (dispersed circles) phase shift, which can be changed from 0 to $2{\text{π}}$ ; (b) hybridized polaritons in graphene/hBN heterostructures^[79]. Upper panel: With monolayer graphene, both amplitude and wavelength of phonon polaritons in pristine hBN increase. Bottom panel: The gate-tunable hyperbolic phonon-plasmon polaritons (HP³) in graphene/hBN and un-tunable hyperbolic phonon polaritons (HP²) in hBN. The incident frequency is 1495 cm^–1. Scale bar, 300 nm.

下载: 全尺寸图片幻灯片

图 9 氮化硼中双曲线型声子极化激元　(a) 天然氮化硼晶体中的双曲线行为, 其等频面为两类双曲面^[80]; (b) 氮化硼晶体中双曲线型声子极化激元的近场光学图像^[56], 入射光频率为1550 cm^–1, 标尺为800 nm; (c) 氮化硼超表面面内双曲线型声子极化激元的近场光学图像^[88]; (d) 氮化硼中表面局域声子极化激元(HSPs) 的近场光学图像^[90], 入射光频率为1420 cm^–1, 标尺为2 μm; (e) 不同角度氮化硼中HSPs的散射行为^[91]

Fig. 9. Hyperbolic phonon polaritons (HPPs) in boron nitride: (a) Hyperbolic behavior of natural hBN crystal, which gives two separate spectral bands called lower and upper Reststrahlen bands with opposite-signed in-plane ( ${{\rm{\varepsilon }}_{//} }$ ) and out-of-plane ( ${\varepsilon _ \bot }$ ) dielectric permittivity^[80], the corresponding hyperboloid-type dispersion of polaritons is shown in left (type 1) and right (type 2) panels; (b) nano-infrared images of HPPs in a tapered hBN crystal^[56]. The incident frequency is 1550 cm^–1, scale bar, 800 nm; (c) in-plane hyperbolic phonon polaritons in nano-patterning boron nitride crystal^[88], left panel: near-field image of concave wavefront of phonon polaritons in boron nitride metasurfaces, right panel: schematic of the experiment; (d) volume-confined polaritons (M0) and surface polaritons (SM0) near the edge of hBN crystal^[90], the incident frequency is 1420 cm^–1. Scale bar, 2 μm; (e) manipulation of hyperbolic surface polaritons with corner angle of hBN crystals^[91]. Left panel: representative near-field image with crystal angle of 120°. Right panel: simulated reflected (R), transmitted (T) and scattered (S) fractions of polaritons as a function of crystal angles. Red squares are experimental data.

下载: 全尺寸图片幻灯片

图 10 双曲线型声子极化激元的应用　(a) 基于氮化硼声子极化激元的超分辨成像^[92], 上: 数值模拟; 下: 近场光学测量; (b) 基于氮化硼实现中红外光的纳米聚焦^[93], 标尺为1 μm; (c) 不同长度氮化硼线性天线的近场光学图像^[94], 上: 长度为1327 nm; 下: 长度为1713 nm

Fig. 10. The applications of hyperbolic phonon polaritons: (a) Near-field imaging and nano-focusing realized by hBN-HPPs^[92]. Upper panel: simulated perfect imaging (ω₀ = 761 cm^–1) and enlarged imaging (ω₀ = 778.2 cm^–1) of gold nanodisk beneath the hBN crystal. Bottom panel: experimental nano-infrared images of gold nanodisk beneath hBN with the broadband incident laser; (b) sub-wavelength focusing of mid-infrared light through an hBN crystal^[93]. Left panel: AFM image of gold disks on SiO₂/Si substrate before hBN transfer. Right panel: near-field amplitude on the top of hBN crystal with incident frequency at 1515 cm^–1. Scale bar, 1 μm; (c) linear hBN dielectric antenna with different lengths^[94], 1327 nm in upper panel and 1713 nm in bottom panel. The incident frequency is 1432 cm^–1.

下载: 全尺寸图片幻灯片

图 11 半导体中激子极化激元的近场光学成像　(a) 二硒化钨中激子极化激元的近场光学图像^[96], 白色虚线为二硒化钨的边界; (b) 二硒化钼中激子极化激元的近场光学图像^[97], 图中标尺为1 μm

Fig. 11. Near-field studies of exciton polaritons in semiconductors: (a) Representative near-field image of a WSe₂ flake, whose edges are marked by white dashed lines^[96]; (b) near-field image of exciton polaritons in planar MoSe₂ waveguide at laser energy of 1.41 eV^[97]. Scale bar is 1 μm.

下载: 全尺寸图片幻灯片

图 12 范德瓦耳斯异质结中的极化激元　(a) 氮化硼/石墨烯/氮化硼异质结中超低损耗等离激元的近场光学成像^[98], 黑色虚线为石墨烯边界, 入射光波长为10.6 μm; (b) 石墨烯/氮化硼中杂化等离–声子极化激元的近场光学成像^[99], 红色虚线为石墨烯边界 (图中标尺为500 nm)

Fig. 12. Polaritons in van der Waals heterostructures: (a) Near-field image of low-loss graphene plasmons in hBN/Graphene/hBN heterostructures^[98]. Upper panel: Side-view sketch of near-field measurement of back-gate graphene encapsulated by hBN layers. Bottom panel: representative near-field image with incident wavelength at 10.6 μm. The graphene edge is marked as black dashed line. (b) Hybridized plasmon-phonon polaritons in graphene/hBN heterostructures^[99]. Upper panel: experimentally extracted wavelength of plasmon-phonon polaritons. Bottom panel: representative near-field images of polaritons. The graphene edge is marked by red dashed lines. The incident frequency is 950 cm^-1 and 970 cm^-1, respectively. Scale bar is 500 nm.

下载: 全尺寸图片幻灯片

图 13 超快近场光学　(a) 实验测量氮化硼声子极化激元的动力学参数^[100], 黄色区域代表金天线, 内插图显示了极化激元波的传播, 右图为不同延迟时间下的极化激元波包, 黑色和绿色实线分别代表群速度和相速度; (b) 石墨烯抽运-探测近场光谱图^[103], 从左到右探测光与抽运光之间的延迟分别为0, 200和400 fs, 标尺为1 μm; (c) 石墨烯中光诱导等离激元的超快光学成像^[104]

Fig. 13. Ultrafast near-field optics. (a) The experimentally extracted propagation of type-1 HPPs in the space-time domain^[100]. The yellow region represents the gold antenna launching polaritons. The inset shows zoom into the fringe patterns. Right panel: the line profiles for different time delays. The black and green solid lines show the envelope of the fringe patterns (group velocity) and intrinsic fringe patterns (phase velocity), respectively. (b) Near-infrared (NIR) pump-induced changes in the near-field amplitude of graphene for different pump-probe time delays^[103]. The pump and probe lasers are 1.56 μm and broadband mid-infrared pulses, respectively. The dark region in near-field images represents SiO₂ substrate. Different optical contrast is caused by different layered graphene. Scale bar, 1 μm. (c) Ultrafast controlling of photo-induced plasmon polaritons in graphene encapsulated by two hBN layers^[104]. Left panel: the schematic of pump-probe s-SNOM set-up. Right panel: the two-dimensional hyperspectral map of photo-induced plasmons in hBN/graphene/hBN device. The black solid line gives the edge of device. The pump laser is at 1.56 μm. The probe beam spans frequencies from 830–1000 cm^–1.

下载: 全尺寸图片幻灯片

图 14 近场光学成像的发展　(a) 通过散射型SNOM和红外光谱结合测量纳米区域化学分子的红外光谱^[111]; (b) 共振金天线激发石墨烯等离激元的近场光学图像^[112]; (c) 非共振金天线激发氮化硼声子极化激元的近场光学图像^[113], 图中标尺为1 μm

Fig. 14. Development in near-field optics. (a) Chemical identification of nanoscale sample contaminations with nano-FTIR, which is combination of s-SNOM and Fourier transform infrared spectrum (FTIR)^[111]. Left panel: Topography image of poly-(methyl methacrylate) thin film (PMMA, marked as A on silicon substrate, with a contaminated particle of polydimethylsiloxane (PDMS, marked as B. Right panel: corresponding absorption spectra of PMMA (taken from spot A) and PDMS (taken from spot B). (b) Near-field imaging of plasmonic wavefront launched by gold antenna, instead of AFM tip^[112]. Upper panel: AFM topography images of fabricated gold antenna. Bottom panel: representative near-field image of plasmonic wavefront with incident wavelength at 11.06 μm. (c) Near-field imaging of wavefront of hBN-HPPs launched by gold antenna^[113]. The brighter region represents gold antenna, encapsulated between hBN and SiO₂ substrate. Scale bar is 1 μm.

下载: 全尺寸图片幻灯片

图 15 近场光学前景展望　(a) 化学合成的碳纳米管结构^[114], 其光学性质可以通过化学组分有效调控; (b) 开口环形探针可用于近场磁场面内和面外分量的测量^[51], 图中标尺为500 nm; (c) 散射型SNOM与质谱耦合, 可同时得到纳米级空间分辨率和超高化学分辨率; (d) 极端环境下SNOM的发展, 包括超低温、强磁场和超高真空等

Fig. 15. The perspective of near-field optics: (a) Chemically fabricated carbon nanotube cup, whose properties can be effectively controlled by chemical component^[114]; (b) split-ring probe is sensitive to both in-plane (H_x or H_y) and out-of-plane (H_z) component of near-field magnetic field^[51], scale bar, 500 nm; (c) the combination of near-field optics and mass spectroscopy for highly chemical resolution and spatial resolution, simultaneously; (d) the developed s-SNOM in extreme environment, including ultralow temperature, strong magnetic field and ultrahigh vacuum.

下载: 全尺寸图片幻灯片

[1]	Rayleigh L 1903 J. Soc. Dyers and Colour. 23 447
[2]	Synge E H 1928 Philosophical Magazine Series 6 356 Google Scholar
[3]	Opower H 1999 Opt. Laser Technol. 504 613
[4]	Wessel J E 1985 J. Opt. Soc. Am. B: Opt. Phys. 2 1538 Google Scholar
[5]	Courjon D, Bainier C 2003 Rep. Prog. Phys. 57 989
[6]	Losquin A, Lummen T T A 2017 Frontiers of Physics in China 12 127301
[7]	Spektor G, Kilbane D, Mahro A, Frank B, Ristok S, Gal L, Kahl P, Podbiel D, Mathias S, Giessen H 2017 Science 355 1187 Google Scholar
[8]	Man K L, Altman M S 2012 J. Phys. Condens. Matter 24 314209 Google Scholar
[9]	Vesseur E J R, de Waele R, Kuttge, Martin, Polman A 2007 Nano Lett. 7 2843 Google Scholar
[10]	Nelayah J, Kociak M, Stephan O, de Abajo F J G , Tence M, Henrard L, Taverna D, Pastorizasantos I, Lizmarzan L M, Colliex C 2007 Nat. Phys. 3 348 Google Scholar
[11]	Govyadinov A A, Konecna A, Chuvilin A, Velez S, Dolado I, Nikitin A Y, Lopatin S, Casanova F, Hueso L E, Aizpurua J 2017 Nat. Commun. 8 95 Google Scholar
[12]	Raza S, Esfandyarpour M, Koh A L, Mortensen N A, Brongersma M L, Bozhevolnyi S I 2016 Nat. Commun. 7 13790 Google Scholar
[13]	Schoen D T, Holsteen A L, Brongersma M L 2016 Nat. Commun. 7 12162 Google Scholar
[14]	Hillenbrand R, Keilmann F, Hanarp P, Sutherland D S, Aizpurua J 2003 Appl. Phys. Lett. 83 368 Google Scholar
[15]	Wurtz G, Bachelot R, Royer P 1998 Rev. Sci. Instrum. 69 1735 Google Scholar
[16]	Dorfmüller J, Vogelgesang R, Weitz R T, Rockstuhl C, Etrich C, Pertsch T, Lederer F, Kern K 2009 Nano Lett. 9 2372 Google Scholar
[17]	Cvitkovic A, Ocelic N, Hillenbrand R 2007 Nano Lett. 7 3177 Google Scholar
[18]	Hillenbrand R, Keilmann F 2000 Phys. Rev. Lett. 85 3029 Google Scholar
[19]	Hillenbrand R, Taubner T, Keilmann F 2002 Nature 418 159 Google Scholar
[20]	Andryieuski A, Zenin V A, Malureanu R, Volkov V S, Bozhevolnyi S I, Lavrinenko A V 2014 Nano Lett. 14 3925 Google Scholar
[21]	Gjonaj B, David A, Blau Y, Spektor G, Orenstein M, Dolev S, Bartal G 2014 Nano Lett. 14 5598 Google Scholar
[22]	Grefe S E, Leiva D, Mastel S, Dhuey S D, Cabrini S, Schuck P J, Abate Y 2013 Phys. Chem. Chem. Phys. 15 18944 Google Scholar
[23]	Chen J, Albella P, Pirzadeh Z, Alonso-Gonzalez P, Huth F, Bonetti S, Bonanni V, Akerman J, Nogues J, Vavassori P, Dmitriev A, Aizpurua J, Hillenbrand R 2011 Small 7 2341 Google Scholar
[24]	Schnell M, Garcia-Etxarri A, Alkorta J, Aizpurua J, Hillenbrand R 2010 Nano Lett. 10 3524 Google Scholar
[25]	Huth F, Chuvilin A, Schnell M, Amenabar I, Krutokhvostov R, Lopatin S, Hillenbrand R 2013 Nano Lett. 13 1065 Google Scholar
[26]	Mastel S, Lundeberg M B, Alonso-Gonzalez P, Gao Y, Watanabe K, Taniguchi T, Hone J, Koppens F H L, Nikitin A Y, Hillenbrand R 2017 Nano Lett. 17 6526 Google Scholar
[27]	Low T, Chaves A, Caldwell J D, Kumar A, Fang N X, Avouris P, Heinz T F, Guinea F, Martin-Moreno L, Koppens F 2016 Nat. Mater. 16 182
[28]	Basov D N, Averitt R D, Hsieh D 2017 Nat. Mater. 16 1077 Google Scholar
[29]	Basov D N, Fogler M M, de Abajo F J G 2016 Science 354 6309
[30]	Betzig E, Trautman J K, Harris T D, Weiner J S, Kostelak R L 1991 Science 251 1468 Google Scholar
[31]	Betzig E, Trautman J K 1992 Science 257 189 Google Scholar
[32]	Gao F, Li X, Wang J, Fu Y 2014 Ultramicroscopy 142 10 Google Scholar
[33]	Hillenbrand R, Knoll B, Keilmann F 2001 J. Microsc. 202 77 Google Scholar
[34]	Labardi M, Patane S, Allegrini M 2000 Appl. Phys. Lett. 77 621 Google Scholar
[35]	Burresi M, Engelen R, Opheij A, van Oosten D, Mori D, Baba T, Kuipers L 2009 Phys. Rev. Lett. 102 033902 Google Scholar
[36]	Feber B L, Rotenberg N, Beggs D M, Kuipers L 2013 Nat. Photonics 8 43
[37]	Kim Z H, Leone S R 2008 Opt. Express 16 1733 Google Scholar
[38]	Kim D, Heo J, Ahn S, Han S W, Yun W S, Kim Z H 2009 Nano Lett. 9 3619 Google Scholar
[39]	Habteyes T G, Dhuey S, Kiesow K I, Vold A 2013 Opt. Express 21 21607 Google Scholar
[40]	Sadiq D, Shirdel J, Lee J S, Selishcheva E, Park N, Lienau C 2011 Nano Lett. 11 1609 Google Scholar
[41]	Ropers C, Neacsu C C, Elsaesser T, Albrecht M, Raschke M B, Lienau C 2007 Nano Lett. 7 2784 Google Scholar
[42]	Ocelic N, Huber A J, Hillenbrand R 2006 Appl. Phys. Lett. 89 101124 Google Scholar
[43]	Stefanon I, Blaize S, Bruyant A, Aubert S, Lerondel G, Bachelot R, Royer P 2005 Opt. Express 13 5553 Google Scholar
[44]	Novotny L, Bian R X, Xie X S 1997 Phys. Rev. Lett. 79 645 Google Scholar
[45]	Noguez C 2007 J. Phys. Chem. C 111 3806 Google Scholar
[46]	Meng L, Yang Z, Chen J, Sun M 2015 Sci. Rep. 5 9240 Google Scholar
[47]	García-Etxarri A, Romero I, de Abajo F J G, Hillenbrand R, Aizpurua J 2009 Phys. Rev. B 79
[48]	Rang M, Jones A C, Zhou F, Li Z, Wiley B J, Xia Y, Raschke M B 2008 Nano Lett. 8 3357 Google Scholar
[49]	Esteban R, Vogelgesang R, Dorfmuller J, Dmitriev A, Rockstuhl C, Etrich C, Kern K 2008 Nano Lett. 8 3155 Google Scholar
[50]	Neuman T, Alonso-González P, Garcia-Etxarri A, Schnell M, Hillenbrand R, Aizpurua J 2015 Laser Photonics Rev. 9 637 Google Scholar
[51]	Burresi M, van Oosten D, Kampfrath T, Schoenmaker H, Heideman R, Leinse A, Kuipers L 2009 Science 326 550 Google Scholar
[52]	Ahn J, Kihm H W, Kihm J E, Kim D S, Lee K 2009 Opt. Express 17 2280 Google Scholar
[53]	Wei H, Zhang S, Tian X, Xu H 2013 Proc. Natl. Acad. Sci. U.S.A. 110 4494 Google Scholar
[54]	Zhang S, Wei H, Bao K, Hakanson U, Halas N J, Nordlander P, Xu H 2011 Phys. Rev. Lett. 107 096801 Google Scholar
[55]	Koppens F H L, Chang D, de Abajo F J G 2011 Nano Lett. 11 3370 Google Scholar
[56]	Dai S, Fei Z, Ma Q, Rodin A S, Wagner M, McLeod A S, Liu M K, Gannett W, Regan W, Watanabe K, Taniguchi T, Thiemens M, Dominguez G, Castro Neto A H, Zettl A, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2014 Science 343 1125 Google Scholar
[57]	Sanvitto D, Kéna-Cohen S 2016 Nat. Mater. 15 1061 Google Scholar
[58]	Woessner A, Parret R, Davydovskaya D, Gao Y, Wu J S, Lundeberg M B, Nanot S, Alonso-González P, Watanabe K, Taniguchi T, Hillenbrand R, Fogler M M, Hone J, Koppens F H L 2017 npj 2D Mater. Appl. 1 25 Google Scholar
[59]	Kumar A, Low T, Fung K H, Avouris P, Fang N X 2015 Nano Lett. 15 3172 Google Scholar
[60]	Woessner A, Misra A, Cao Y, Torre I, Mishchenko A, Lundeberg M B, Watanabe K, Taniguchi T, Polini M, Novoselov K S, Koppens F H L 2017 ACS Photonics 4 3012 Google Scholar
[61]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[62]	Nair R R, Blake P, Grigorenko A N, Novoselov K S, Booth T J, Stauber T, Peres N M, Geim A K 2008 Science 320 1308 Google Scholar
[63]	Guo Q, Li C, Deng B, Yuan S, Guinea F, Xia F 2017 ACS Photonics 4 2989 Google Scholar
[64]	Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109 Google Scholar
[65]	Yan H, Low T, Zhu W, Wu Y, Freitag M, Li X, Guinea F, Avouris P, Xia F 2013 Nat. Photonics 7 394 Google Scholar
[66]	Yan H, Li X, Chandra B, Tulevski G, Wu Y, Freitag M, Zhu W, Avouris P, Xia F 2012 Nat. Nanotechnol. 7 330 Google Scholar
[67]	Fei Z, Andreev G O, Bao W, Zhang L M, Wang C, Stewart M K, Zhao Z, Dominguez G, Thiemens M, Fogler M M, Tauber M J, Castro-Neto A H, Lau C N, Keilmann F, Basov D N 2011 Nano Lett. 11 4701 Google Scholar
[68]	Chen J, Badioli M, Alonso-González P, Thongrattanasiri S, Huth F, Osmond J, Spasenović M, Centeno A, Pesquera A, Godignon P, Zurutuza Elorza A, Camara N, de Abajo F J G, Hillenbrand R, Koppens F H L 2012 Nature 487 77 Google Scholar
[69]	Fei Z, Rodin A S, Andreev G O, Bao W, McLeod A S, Wagner M, Zhang L M, Zhao Z, Thiemens M, Dominguez G, Fogler M M, Neto A H C, Lau C N, Keilmann F, Basov D N 2012 Nature 487 82 Google Scholar
[70]	Ni G X, McLeod A S, Sun Z, Wang L, Xiong L, Post K W, Sunku S S, Jiang B Y, Hone J, Dean C R, Fogler M M, Basov D N 2018 Nature 557 530 Google Scholar
[71]	Fei Z, Foley J J, Gannett W, Liu M K, Dai S, Ni G X, Zettl A, Fogler M M, Wiederrecht G P, Gray S K, Basov D N 2016 Nano Lett. 16 7842 Google Scholar
[72]	Hu F, Luan Y, Fei Z, Palubski I Z, Goldflam M D, Dai S, Wu J S, Post K W, Janssen G, Fogler M M, Basov D N 2017 Nano Lett. 17 5423 Google Scholar
[73]	Duan J, Chen R, Chen J 2017 Chin. Phys. B 26 117802 Google Scholar
[74]	Nikitin A, Alonso-González P, Vélez S, Mastel S, Centeno A, Pesquera A, Zurutuza A, Casanova F, Hueso L, Koppens F 2016 Nat. Photonics 10 239 Google Scholar
[75]	Fei Z, Goldflam M D, Wu J S, Dai S, Wagner M, McLeod A S, Liu M K, Post K W, Zhu S, Janssen G C A M, Fogler M M, Basov D N 2015 Nano Lett. 15 8271 Google Scholar
[76]	Bezares F J, de Sanctis A, Saavedra J R M, Woessner A, Alonso-Gonzalez P, Amenabar I, Chen J, Bointon T, Dai S, Fogler M M, Basov D N, Hillenbrand R, Craciun M F, de Abajo F J G, Russo S, Koppens F H L 2017 Nano Lett. 17 5908 Google Scholar
[77]	Fei Z, Iwinski E G, Ni G X, Zhang L M, Bao W, Rodin A S, Lee Y, Wagner M, Liu M K, Dai S, Goldflam M D, Thiemens M, Keilmann F, Lau C N, Castro-Neto A H, Fogler M M, Basov D N 2015 Nano Lett. 15 4973 Google Scholar
[78]	Woessner A, Gao Y, Torre I, Lundeberg M B, Tan C, Watanabe K, Taniguchi T, Hillenbrand R, Hone J, Polini M, Koppens F H L 2017 Nat. Photonics 11 421 Google Scholar
[79]	Dai S, Ma Q, Liu M K, Andersen T, Fei Z, Goldflam M D, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Janssen G C, Zhu S E, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Nanotechnol. 10 682 Google Scholar
[80]	Caldwell J D, Kretinin A V, Chen Y, Giannini V, Fogler M M, Francescato Y, Ellis C T, Tischler J G, Woods C R, Giles A J, Hong M, Watanabe K, Taniguchi T, Maier S A, Novoselov K S 2014 Nat. Commun. 5 5221 Google Scholar
[81]	Liu Z, Lee H, Xiong Y, Sun C, Zhang X 2007 Science 315 1686 Google Scholar
[82]	Yao J, Liu Z, Liu Y, Wang Y, Sun C, Bartal G, Stacy A M, Zhang X 2008 Science 321 930 Google Scholar
[83]	Yang X, Yao J, Rho J, Yin X, Zhang X 2012 Nat. Photonics 6 450 Google Scholar
[84]	Hoffman A J, Alekseyev L, Howard S S, Franz K J, Wasserman D, Podolskiy V A, Narimanov E E, Sivco D L, Gmachl C 2007 Nat. Mater. 6 946 Google Scholar
[85]	Kim J, Drachev V P, Jacob Z, Naik G V, Boltasseva A, Narimanov E E, Shalaev V M 2012 Opt. Express 20 8100 Google Scholar
[86]	High A A, Devlin R C, Dibos A, Polking M, Wild D S, Perczel J, de Leon N P, Lukin M D, Park H 2015 Nature 522 192 Google Scholar
[87]	Liu Y, Zhang X 2013 Appl. Phys. Lett. 103 141101 Google Scholar
[88]	Li P, Dolado I, Alfaro-Mozaz F J, Casanova F, Hueso L E, Liu S, Edgar J H, Nikitin A Y, Velez S, Hillenbrand R 2018 Science 359 892 Google Scholar
[89]	Ma W, Gonzalez P A, Li S, Nikitin A Y, Yuan J, Sanchez J M, Gutierrez J T, Amenabar I, Li P, Velez S, Tollan C, Dai Z, Zhang Y, Sriram S, Zadeh K K, Lee S T, Hillenbrand R, Bao Q 2018 Nature 562 557 Google Scholar
[90]	Li P, Dolado I, Alfaro-Mozaz F J, Nikitin A Y, Casanova F, Hueso L E, Velez S, Hillenbrand R 2017 Nano Lett. 17 228 Google Scholar
[91]	Dai S, Tymchenko M, Yang Y, Ma Q, Pita-Vidal M, Watanabe K, Taniguchi T, Jarillo-Herrero P, Fogler M, Alù A 2017 Adv. Mater. 30 1706358
[92]	Li P, Lewin M, Kretinin A V, Caldwell J D, Novoselov K S, Taniguchi T, Watanabe K, Gaussmann F, Taubner T 2015 Nat. Commun. 6 7507 Google Scholar
[93]	Dai S, Ma Q, Andersen T, McLeod A S, Fei Z, Liu M K, Wagner M, Watanabe K, Taniguchi T, Thiemens M, Keilmann F, Jarillo-Herrero P, Fogler M M, Basov D N 2015 Nat. Commun. 6 6963 Google Scholar
[94]	Alfaro-Mozaz F J, Alonso-Gonzalez P, Velez S, Dolado I, Autore M, Mastel S, Casanova F, Hueso L E, Li P, Nikitin A Y, Hillenbrand R 2017 Nat. Commun. 8 15624 Google Scholar
[95]	Hu D, Yang X, Li C, Liu R, Yao Z, Hu H, Corder S N G, Chen J, Sun Z, Liu M, Dai Q 2017 Nat. Commun. 8 1471 Google Scholar
[96]	Fei Z, Scott M E, Gosztola D J, Foley J J, Yan J, Mandrus D G, Wen H, Zhou P, Zhang D W, Sun Y, Guest J R, Gray S K, Bao W, Wiederrecht G P, Xu X 2016 Phys. Rev. B 94 081402 Google Scholar
[97]	Hu F, Luan Y, Scott M E, Yan J, Mandrus D G, Xu X, Fei Z 2017 Nat. Photonics 11 356 Google Scholar
[98]	Woessner A, Lundeberg M B, Gao Y, Principi A, Alonso-Gonzalez P, Carrega M, Watanabe K, Taniguchi T, Vignale G, Polini M, Hone J, Hillenbrand R, Koppens F H 2015 Nat. Mater. 14 421 Google Scholar
[99]	Yang X, Zhai F, Hu H, Hu D, Liu R, Zhang S, Sun M, Sun Z, Chen J, Dai Q 2016 Adv. Mater. 28 2931 Google Scholar
[100]	Yoxall E, Schnell M, Nikitin A Y, Txoperena O, Woessner A, Lundeberg M B, Casanova F, Hueso L E, Koppens F H L, Hillenbrand R 2015 Nat. Photonics 9 674 Google Scholar
[101]	Eisele M, Cocker T L, Huber M A, Plankl M, Viti L, Ercolani D, Sorba L, Vitiello M S, Huber R 2014 Nat. Photonics 8 841 Google Scholar
[102]	Huber M A, Plankl M, Eisele M, Marvel R E, Sandner F, Korn T, Schuller C, Haglund R F, Huber R, Cocker T L 2016 Nano Lett. 16 1421 Google Scholar
[103]	Wagner M, Fei Z, McLeod A S, Rodin A S, Bao W, Iwinski E G, Zhao Z, Goldflam M, Liu M, Dominguez G, Thiemens M, Fogler M M, Castro Neto A H, Lau C N, Amarie S, Keilmann F, Basov D N 2014 Nano Lett. 14 894 Google Scholar
[104]	Ni G X, Wang L, Goldflam M D, Wagner M, Fei Z, McLeod A S, Liu M K, Keilmann F, Özyilmaz B, Castro Neto A H, Hone J, Fogler M M, Basov D N 2016 Nat. Photonics 10 244 Google Scholar
[105]	Hu H, Yang X, Zhai F, Hu D, Liu R, Liu K, Sun Z, Dai Q 2016 Nat. Commun. 7 12334 Google Scholar
[106]	Amenabar I, Poly S, Goikoetxea M, Nuansing W, Lasch P, Hillenbrand R 2017 Nat. Commun. 8 14402 Google Scholar
[107]	Amenabar I, Poly S, Nuansing W, Hubrich E H, Govyadinov A A, Huth F, Krutokhvostov R, Zhang L, Knez M, Heberle J, Bittner A M, Hillenbrand R 2013 Nat. Commun. 4 2890 Google Scholar
[108]	Dominguez G, McLeod A S, Gainsforth Z, Kelly P, Bechtel H A, Keilmann F, Westphal A, Thiemens M, Basov D N 2014 Nat. Commun. 5 5445 Google Scholar
[109]	Westermeier C, Cernescu A, Amarie S, Liewald C, Keilmann F, Nickel B 2014 Nat. Commun. 5 4101 Google Scholar
[110]	Lucas I T, McLeod A S, Syzdek J S, Middlemiss D S, Grey C P, Basov D N, Kostecki R 2015 Nano Lett. 15 1 Google Scholar
[111]	Huth F, Govyadinov A, Amarie S, Nuansing W, Keilmann F, Hillenbrand R 2012 Nano Lett. 12 3973 Google Scholar
[112]	Alonso-González P, Nikitin A Y, Golmar F, Centeno A, Pesquera A, Vélez S, Chen J, Navickaite G, Koppens F, Zurutuza A 2014 Science 344 1369 Google Scholar
[113]	Duan J, Chen R, Li J, Jin K, Sun Z, Chen J 2017 Adv. Mater. 29 1702494 Google Scholar
[114]	Zhao Y, Tang Y, Chen Y 2012 ACS Nano 6 6912 Google Scholar
[115]	Nudnova M M, Sigg J, Wallimann P, Zenobi R 2015 Anal. Chem. 87 1323 Google Scholar
[116]	Lee K G, Kihm H W, Kihm J E, Choi W J, Kim H, Ropers C, Park D J, Yoon Y C, Choi S B, Woo D H, Kim J, Lee B, Park Q H, Lienau C, Kim D S 2007 Nat. Photonics 1 53 Google Scholar
[117]	Rotenberg N, Kuipers L 2014 Nat. Photonics 8 919 Google Scholar

[1]	张洋, 张志豪, 王宇剑, 薛晓兰, 陈令修, 石礼伟. 偏振调制扫描光学显微镜方法. 物理学报, 2024, 73(15): 157801. doi: 10.7498/aps.73.20240688
[2]	周怡汐, 李志鹏, 陈佳宁. 基于近场光学成像技术的极化激元学研究进展. 物理学报, 2024, 73(8): 080701. doi: 10.7498/aps.73.20232001
[3]	余泽浩, 张力发, 吴靖, 赵云山. 二维层状热电材料研究进展. 物理学报, 2023, 72(5): 057301. doi: 10.7498/aps.72.20222095
[4]	刘宁, 刘肯, 朱志宏. 集成二维材料非线性光学特性研究进展. 物理学报, 2023, 72(17): 174202. doi: 10.7498/aps.72.20230729
[5]	徐琨淇, 胡成, 沈沛约, 马赛群, 周先亮, 梁齐, 史志文. 叠层/转角二维原子晶体结构与极化激元的近场光学表征. 物理学报, 2023, 72(2): 027102. doi: 10.7498/aps.72.20222145
[6]	马赛群, 邓奥林, 吕博赛, 胡成, 史志文. 低维材料极化激元及其耦合特性. 物理学报, 2022, 71(12): 127104. doi: 10.7498/aps.71.20220272
[7]	廖俊懿, 吴娟霞, 党春鹤, 谢黎明. 二维材料的转移方法. 物理学报, 2021, 70(2): 028201. doi: 10.7498/aps.70.20201425
[8]	黄申洋, 张国伟, 汪凡洁, 雷雨晨, 晏湖根. 二维黑磷的光学性质. 物理学报, 2021, 70(2): 027802. doi: 10.7498/aps.70.20201497
[9]	徐依全, 王聪. 基于二维材料的全光器件. 物理学报, 2020, 69(18): 184216. doi: 10.7498/aps.69.20200654
[10]	吴祥水, 汤雯婷, 徐象繁. 二维材料热传导研究进展. 物理学报, 2020, 69(19): 196602. doi: 10.7498/aps.69.20200709
[11]	吴晗, 吴竞宇, 陈卓. 基于超表面的Tamm等离激元与激子的强耦合作用. 物理学报, 2020, 69(1): 010201. doi: 10.7498/aps.69.20191225
[12]	岑贵, 张志斌, 吕新宇, 刘开辉, 李志强. 金属衬底上石墨烯的红外近场光学. 物理学报, 2020, 69(2): 027803. doi: 10.7498/aps.69.20191598
[13]	吕新宇, 李志强. 石墨烯莫尔超晶格体系的拓扑性质及光学研究进展. 物理学报, 2019, 68(22): 220303. doi: 10.7498/aps.68.20191317
[14]	焦悦, 陶海岩, 季博宇, 宋晓伟, 林景全. 用于飞秒激光纳米加工的TiO2粒子阵列诱导多种基底表面近场增强. 物理学报, 2017, 66(14): 144203. doi: 10.7498/aps.66.144203
[15]	张学进, 陆延青, 陈延峰, 朱永元, 祝世宁. 太赫兹表面极化激元. 物理学报, 2017, 66(14): 148705. doi: 10.7498/aps.66.148705
[16]	张利伟, 许静平, 赫丽, 乔文涛. 含单负材料三明治结构的电磁隧穿特性. 物理学报, 2010, 59(11): 7863-7868. doi: 10.7498/aps.59.7863
[17]	侯碧辉, 菅彦珍, 王雅丽, 张尔攀, 傅佩珍, 汪力, 钟任斌. PbB4O7 晶体的太赫兹光谱和软光学声子. 物理学报, 2010, 59(7): 4640-4645. doi: 10.7498/aps.59.4640
[18]	徐耿钊, 梁琥, 白永强, 刘纪美, 朱星. 低温近场光学显微术对InGaN/GaN多量子阱电致发光温度特性的研究. 物理学报, 2005, 54(11): 5344-5349. doi: 10.7498/aps.54.5344
[19]	王潜, 徐金强, 武锦, 李永贵. 利用扫描近场红外显微镜对化学样品组分进行成像研究. 物理学报, 2003, 52(2): 298-301. doi: 10.7498/aps.52.298
[20]	王子洋, 李勤, 赵钧, 郭继华. 透射式扫描近场光学显微镜探针光场分布及其受激荧光分子光场分布研究. 物理学报, 2000, 49(10): 1959-1964. doi: 10.7498/aps.49.1959

计量

文章访问数: 16768
PDF下载量: 715

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板