内标法是激光诱导击穿光谱(LIBS)最常用的定量分析方法之一。 为了提高定量分析精度, 研究了谱线强度比的相对波动特性随分析线和内标线之间激发能级差(ΔE)和波长差(Δλ)变化的规律。 在局部热力学平衡条件下, 建立了考虑等离子体中某元素电子上能级跃迁到下能级产生原子发射谱线的激发能级差、 等离子体温度、 配分函数和离子密度等强度影响因素的数学模型, 对模型中激发能级差对谱线强度相对波动的影响进行了研究。 得到在-2 eV<ΔE<2 eV和等离子体温度范围在3 000～15 000 K条件下, 谱线强度随着ΔE和T变化的趋势: 随着ΔE变大, 谱线强度比呈上升, 在ΔE=2 eV, T=3 000 K时谱线强度比最大; 并且谱线强度比相对波动对ΔE和T敏感, ΔE趋近于零时相对波动变小, T对谱线强度比相对波动影响变化不大, 整体趋势平稳。 在T=10 000 K时, ΔE<0相对波动比ΔE>0时小, 因此理论上优先选择ΔE<0的谱线对。 通过理论分析得出|ΔE|越接近于零, 谱线强度比相对波动越小。 实验装置中采用工作波长1 064 nm, 脉冲能量85 mJ, 重复频率1 Hz, 脉冲宽度13 ns的Nd∶YAG脉冲激光诱导击穿样品; 采用工作波长200～975 nm, 光学分辨率优于0.05 nm的Andor公司Mechelle 5000光谱仪, 配合Andor New iStar型号ICCD采集光谱; 利用激光诱导铁基合金等离子体光谱进行验证。 实验中, 以Fe为内标元素, Cr和Mn为分析元素。 筛选NIST谱线库中跃迁概率在106以上的谱线, 并优先选择共振线能级差相近的非共振线进行对比分析。 结果表明, 选择激发能级相近或波长相近的谱线作为分析谱线的原则有一定的局限性。 对于Cr和Fe, |ΔE|在0.14和1.51 eV时得到的谱线强度相对标准偏差(RSD)分别为6.7%和4.6%, 其谱线强度比理论值和实际值之差分别为1.14和0.59; |Δλ|在11.7和50.8 nm时得到的RSD分别为6.3%和4.4%, 其谱线强度比理论值和实际值之差分别为1.69和0.62。 分析表明, 相比于波长差, 激发能级差对Cr/Mn相对波动影响较大。 分析元素Cr/Mn与内标元素Fe波长差绝对值不断增大, RSD反而不断减小; 在1.50 eV和90 nm较大约束范围内, |ΔE|大的谱线得到的谱线强度比相对波动相对较小, Cr和Fe的RSD最大相差为2.06%; |Δλ|大的谱线得到的谱线强度比相对波动相对较小, Cr和Fe的RSD最大相差为1.35%。 由以上实验结果得出, 在实际选择分析谱线时, 尽量选择激发能级和波长相近的谱线原则有一定的局限性。 |ΔE|或|Δλ|大的谱线得到的RSD较小, 选择谱线强度比理论值和实际值最接近的谱线可以作为谱线选择依据。 另外, 选择谱线强度比理论值和实际值最接近的谱线, 可以降低谱线强度比相对波动。

Internal standard method is one of the most popular quantitative analytical methods for quantitative analysis of laser induced breakdown spectroscopy (LIBS). In order to improve the precision of quantitative analysis, the rule of relative fluctuation characteristic of spectral line intensity ratio between analysisline and excitation line,energy differential (ΔE), and wavelength difference (Δλ) has been studied. Under thermodynamic equilibrium conditions, the mathematical model considers the electron energy level difference of atomic emission spectrum generated from high level to low level, plasma temperature, partition function, and the factors that influence the intensity of plasma, the influence of excitation energy differential on relative fluctuation of spectral line intensity has been studied. Under the condition of -2 eV<ΔE<2 eV and plasma temperature range in 3 000~15 000 K, the trend of spectral line intensity changes with ΔE and T is: When ΔE gets larger, the spectral line intensity increases, at the situation of ΔE=2 eV, T=3 000 K, spectrum intensity ratio is maximum. Further, relative fluctuatesof spectrum line intensity is sensitive to ΔE and T, and relative fluctuate can be smaller when ΔE tends to be zero. T has little influence on the relative fluctuation of spectral line intensity. At the situation T=10 000 K, relative fluctuates under the situation of ΔE<0 is smaller than ΔE>0, so ΔE spectrum line pairs with ΔE<0 should be chosen. With theoretical analysis, it has been discovered that if |ΔE| is close to zero, the relative fluctuation of spectral line intensity is smaller. In experiment, the Nd∶YAG pulsed laser was used to breakdown samples works with wavelength of 1 064 nm, pulse energy is 85 mJ, repeat frequency is 1 Hz, and pulse width is 13 ns. Andor company Mechelle 5000 spectrometer is used together with Andor New iStar model ICCD for spectrum gathering with working wavelength of 200~975 nm, optical resolution is better than 0.05 nm.The laser induced plasma spectra is verified by iron-based alloy. In the experiment, Fe is internal standard element, Cr/Mn are analysis elements. In this paper, the spectrum line with transition probability more than 106 of the NIST spectrum line library is chosen, and the non-resonant line with similarity resonance energy difference is compared and analyzed. Results show that the method of choose spectrum line with similar excitation energy level or similar wavelength has some limitations. For Cr and Fe, |ΔE| at 0.14 and 1.51 eV for the spectral line intensity of relative standard deviation (RSD) were 6.7% and 4.6% respectively, and theoretical value and practical value of the spectral line intensity were 1.14 and 0.59; RSD were 6.3% and 4.4% with |Δλ| of 11.7 nm and 50.8 nm, respectively. Difference between theoretical and practical values of the spectral line intensity was 1.69 and 0.62. Analysis showed that, influence of stimulated energy level difference of Cr/Mn is obvious than wavelength difference.To analysis element Cr/Mn, when internal standard element is Fe, the absolute wavelength value increases RSD decreases. Within a large scope of 1.50 eV and 90 nm spectrum range, larger |ΔE| can get smaller relative fluctuation characteristic of spectral line intensity ratio, and maximum RSD of Cr and Fe is 2.06%; large |Δλ| can get smaller relative fluctuation characteristic of spectral line intensity ratio, and maximum RSD of Cr and Fe is 1.35%. It can be concluded from the experimental results that, when the spectrum line is selected, the spectral line principle with similar excitation energy level and wavelength has certain limitations. If |ΔE| or |Δλ| is larger, RSD will be smaller. The spectral line intensity ratio which has similar theoretical and practical value can be a spectral line selection basis. Additionally, if theoretical value and actual value of spectral line intensity ratio are more similar, relative fluctuation of spectral lines intensity can be reduced.