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激光通过透镜聚焦后,在其焦点附近的光能量密度极高,材料内的电子短时间吸收大量光能发生跃迁,形成自由电子云即等离子体。紧接着,等离子体继续吸收后续激光能量开始快速膨胀,导致周围空气电离而发生爆炸,类似于点爆炸模型,并在爆炸之后以冲击波的方式向周边传播。随着冲击波传播半径的不断扩大,电子-离子的快速复合使得等离子体也快速消失,冲击波迅速衰减,最终成为声波传播到周边的环境介质中。因此根据冲击波相关理论,其传播可以表示为[15]:
$ t = {\left( {\frac{2}{{5c}}} \right)^{\frac{5}{3}}}{\left( {\frac{Q}{{\sigma {\rho _0}}}} \right)^{\frac{1}{3}}}M{a^{ - \frac{5}{3}}}\left( {1 + \beta M{a^{ - 2}}} \right) $
(1) $ \begin{array}{l} R(t) = M{a_0}ct\left\{ {1 - \left( {1 - \frac{1}{{M{a_0}}}} \right) \times } \right.\\ \left. {\;\;\;\;\;\;\;\;\exp \left[ { - \alpha {{\left( {\frac{{{R_0}}}{{ct}}} \right)}^{\frac{5}{3}}}} \right]} \right\} + {R_0} \end{array} $
(2) $ \begin{array}{l} \frac{{{\rm{d}}R}}{{{\rm{d}}t}} = U(t) = M{a_0}c\left\{ {1 - \left( {1 - \frac{1}{{M{a_0}}}} \right) \times } \right.\\ \;\;\left. {\exp \left[ { - \alpha {{\left( {\frac{{{R_0}}}{{ct}}} \right)}^{\frac{3}{5}}}} \right]\left[ {1 + \frac{3}{5}\alpha {{\left( {\frac{{{R_0}}}{{ct}}} \right)}^{\frac{3}{5}}}} \right]} \right\} \end{array} $
(3) 式中,ρ0为气体密度,c为空气中的声速,Q为激光能量,α是与气体有关的常数,β是与冲击波波前有关的常数,Ma为冲击波的马赫数,R(t)表示等离体子冲击波的传输半径R与传输时间t之间的函数关系;U(t)表示冲击波波前传输速度与传输时间t之间的函数关系;R0与Ma0分别为等离体子体冲击波形成瞬间的初始半径与马赫数。
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考虑环境压力影响,修正后的Taylor-Sedov波前传播方程[16]给出了等离子体冲击波传输时间与马赫数之间的关系, 如下:
$ M{a_0} = \alpha {\left[ {Q/\left( {R_0^3{c^2}{\rho _0}} \right)} \right]^{\frac{1}{5}}} + 1 $
(4) 忽略能量的损失,冲击波波前传输压强方程可以表示为[17]:
$ p = \frac{2}{{\gamma + 1}}{\rho _0}{U^2}(t)\left[ {1 - \left( {\frac{{\gamma - 1}}{{2\gamma }}} \right)M{a^{ - 2}}} \right] $
(5) 式中, γ为空气的绝热常数,模拟所用参量如表 1所示。结合(5)式,可以得到冲击波传输压强p与传输半径R之间的关系,如图 7所示。
Table 1. Parameters used in simulation
gas density ρ0/(kg·m-3) adiabatic constant γ gas constant α speed of sound c/(m·s-1) laser energy Q/J wavefront constant β universal gas constant Rg/(J·mol-1·K-1) 1.3 1.4 0.98 340 0.4 3 8.3 从图 7中的模拟结果可知,激光等离子体与传输距离(即图中的传输半径)的关系呈现出一个尖型的漏斗状,说明等离子体的压强变化相当剧烈。当传输距离接近零即在等离子体的中心位置时,其压强最大达到约109Pa。随着传输距离的增大,其波前压强急剧减小,在传输距离为3mm时,波前压强已降低到约107Pa。因此,这个特性会限制颗粒的去除范围,样品表面与聚焦点之间的距离对等离子体冲击波清洗法具有重要的影响。
采用COMSOL固体力学物理场模拟颗粒内应力的变化情况,其中将用上述公式模拟所得的等离子体冲击波压强数值以冲击载荷的方式加载到模型中。基底与颗粒材料设置为软件材料库内的Si与Al,基底尺寸为50μm×5μm,颗粒半径为1μm。模拟所用的材料参量如表 2所示。将Si底部设置为固定,模型设置为线弹性材料作为边界条件;接触部分进行网格细化进行计算。颗粒内等效应力σon的变化结果如图 8所示。
Table 2. Parameters of the materials
density/ (kg·m-3) elastic modulus/ GPa Poisson's ratio thermal conductivity/ (W·m-1·K-1) specific heat capacity/ (J·kg-1·K-1) thermal expansion coefficient Si 2328 190 0.278 150 618 0.5×10-6 Al 2700 70 0.33 237 880 2.3×10-5 由模拟结果可以看出,在冲击波到达颗粒顶部后,在极短的时间内(纳秒量级)颗粒内应力会沿着中轴向颗粒两边扩散,最大应力分布在颗粒顶部的冲击波作用位置和颗粒底部的接触位置,最大值达到了1GPa左右,而颗粒的理论抗压强度约为0.3GPa[18]。因此,颗粒在冲击波作用下被挤压,极易从两侧出现破裂现象,尺寸较大的颗粒破碎成更小的颗粒留在样品表面,对后续的进一步清洗造成影响。这一结果与上述理论分析和实验观测到的结果一致。
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聚焦的高能激光产生的等离子体冲击波不仅具有高压强的特性,其波面温度也是一个衡量其特性的重要参量,根据相关研究,冲击波波面温度可以表示为[19]:
$ T = p/\left( {{\rho _1}{R_{\rm{g}}}} \right) $
(6) $ {\rho _1}/{\rho _0} = (\gamma + 1)/\left( {\gamma - 1 + 2M{a^{ - 2}}} \right) $
(7) 式中,ρ1为冲击波的密度,Rg是普适气体常量,结合(5)式~(7)式,可将冲击波温度进一步表示为:
$ \begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;T = \\ \frac{{2{U^2}(t)\left[ {1 - \left( {\frac{{\gamma - 1}}{{2\gamma }}} \right)M{a^{ - 2}}} \right]\left( {\frac{{\gamma - 1 + 2M{a^{ - 2}}}}{{\gamma + 1}}} \right)}}{{{{(\gamma + 1)}^2}}}{R_{\rm{g}}} \end{array} $
(8) 根据(8)式,再结合表 1中的模拟参量,可以得到冲击波温度T与传输半径R之间的关系,如图 9所示。
从图中可以看出,冲击波的波面温度的传播与压强传播情况类似,其与传输距离(即图中的传输半径)也呈现出尖漏斗状;等离子体中心位置温度最高,约为105K。随着传输距离的增大,波面温度迅速降低,传输距离为3mm时,其温度已降低至103K左右。
采用COMSOL固体传热物理场模拟颗粒内温度的变化情况,将用上述公式模拟所得的等离子体冲击波波面温度数值以热通量载荷的方式加载到模型中。基底与颗粒材料设置为软件材料库内的Si与Al,基底尺寸为50μm×5μm,颗粒半径为1μm。模拟所用的材料参量如表 2所示。将Si底部设置为热绝缘,颗粒与基底设置热接触,其他所有边界加载与空气的对流换热,忽略热辐射,接触部分进行网格细化进行计算。得到颗粒内温度T的变化结果如图 10所示。
由温度模拟结果可知,当冲击波传输到样品表面时,在其高温作用下,颗粒温度也随之升高,在极短的时间内(纳秒量级)由顶部向下传播,最终达到接近热平衡状态。在此过程中,颗粒内最高温度约为1100K,接触部分的基底最高温度约为650K。纳米量级的Al颗粒熔点约为900K,微米量级的Al颗粒熔点约为1200K,Si基底的熔点约为1600K[20]。因此,冲击波传播温度在颗粒的熔点附近,颗粒可能产生熔化现象,而基底温度远低于其熔点,不会发生熔化。与实验中所观测到的现象一致。
激光等离子体法清洗微纳颗粒的物态变化研究
Study on the state change characteristics of cleaning micro-nano particles by laser plasma method
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摘要: 为了探究激光等离子体冲击波清洗过程中微纳颗粒的物态变化特性,针对单晶硅表面Al微纳颗粒进行了清洗实验;结合等离子体传播规律与有限元法模拟了颗粒内部的应力和温度变化情况,得到了颗粒相变和演化的规律。结果表明,大颗粒与中颗粒数量明显减少,尺寸由原来的0.5μm~3μm变为0.1μm~1μm;颗粒的物态变化主要是冲击波瞬时高温高压作用所致,颗粒内最大应力达到1GPa,最大温度达到1100K;颗粒在冲击波作用下发生了破裂与相变,细小颗粒数量增多并粘附在样品表面,增大了清洗难度。此研究可为激光清洗颗粒的理论和应用提供参考。Abstract: In order to explore the characteristics of the state change of micro-nano particles during the laser plasma shock wave cleaning process, cleaning experiments were carried out for Al micro-nano particles on the surface of single crystal silicon; combined with the plasma propagation law and finite element method, the internal stress and temperature changes of the particles were simulated under the circumstances, and the law of phase transition and evolution of particles was obtained. The results show that the number of large and medium particles is significantly reduced, and the size is changed from 0.5μm~3μm to 0.1μm~1μm; the change in the state of the particles is mainly caused by the instantaneous high temperature and high pressure of the shock wave, and the maximum stress in the particles reaches 1GPa. The maximum temperature reaches 1100K; therefore, the particles break and phase change under the action of the shock wave, and the number of fine particles increases and adheres to the sample surface, which increases the difficulty of cleaning. This research can provide reference for the theory and application of laser cleaning particles.
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Key words:
- laser technique /
- laser plasma /
- micro-nano particles /
- physical change /
- finite element analysis
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Table 1. Parameters used in simulation
gas density ρ0/(kg·m-3) adiabatic constant γ gas constant α speed of sound c/(m·s-1) laser energy Q/J wavefront constant β universal gas constant Rg/(J·mol-1·K-1) 1.3 1.4 0.98 340 0.4 3 8.3 Table 2. Parameters of the materials
density/ (kg·m-3) elastic modulus/ GPa Poisson's ratio thermal conductivity/ (W·m-1·K-1) specific heat capacity/ (J·kg-1·K-1) thermal expansion coefficient Si 2328 190 0.278 150 618 0.5×10-6 Al 2700 70 0.33 237 880 2.3×10-5 -
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