1.Introduction

Even if small differences in chemical composition of alloys may possibly lead to tremendously different mechanical behaviors and metal grades.Each grade of alloys has its unique application field.Take copper-lead alloy as an example,the low-grade H59(Cu 57.0%–60.0%,Pb 0.1%–0.5%,and Zn 38.7%–42.1%in weight)exhibits high strength,high hardness,but poor plasticity,and favors hot processing such as hot punching or hot rolling.In contrast,the higher grade H62(Cu 60.5%–63.5%,Pb 0.08%–0.10%,and Zn 35.75%–38.76%in weight)is good in plasticity,machinability and corrosion resistance,but easy to suffer from dezincification and stress cracking.It is usually used for deep drawing and bending.Therefore,employing an appropriate analytical technique to perform accurate and rapid composition measurement of alloys is of great significance to metallurgy quality control and alloy classification.

若题目告知A流向B与其直接流向C的的能量比例由m∶n调整为p∶q（m、n、p、q均为正整数），求调整比例后该生态系统能承载C的数量是原来的多少倍时应“顺推（用乘法）”，如例6；若题目告知将C的食物比例由m∶n调整为p∶q（m、n、p、q均为正整数），求调整比例后该生态系统能承载C的数量是原来的多少倍时应“逆推（用除法）”，如例5。

Figure 1.Experimental CF-LIBS setup.

Conventional techniques up to now on the alloy composition analysis mainly include photoelectric direct reading spectroscopy,inductively coupled plasma-atomic emission spectroscopy,x-ray fluorescence spectroscopy,and flame atomic absorption spectrometry.However,they are either time-consuming or tedious due to the required complex pretreatment processes such as crushing,grinding,surface polishing,etc.Laser induced breakdown spectroscopy(LIBS)is nowadays an attractive candidate technique owing to minimal sample preparation,rapid analysis and repeatability[1,2].Over the last few years,a large number of reports have demonstrated the potential application of LIBS in this field.For example,Yang et al employed 23 standard high-alloy steel samples and relevance vector machine regression to establish the calibration model for quantitative analysis of Cr[3];Ferreira et al made a calibration curve for quantitative analysis of Cu by using 59 soil samples[4].Although these works have achieved effective quantitative analysis results,it is required to collect or prepare a series of standard samples to establish the calibration model,which greatly limits its potential application.

在先秦儒家的叙事里，男女之别往往等同于内外、公私与主从之别，主要体现于以下方面：一是生活空间上的隔离，二是社会活动领域上的区分，三是社会角色与道德教化上主从关系的确立。

The classical calibration-free LIBS(CF-LIBS)approach for quantitative analysis of LIBS data was firstly proposed in 1999.It serves as an alternative route to composition measurement where standard samples are not available to make the calibration curve[5–8].This technology relies on the state of local thermodynamic equilibrium(LTE)in laser-induced plasmas(LIP)and on the knowledge of the values assumed by temperature and electron number density in the acquisition time[9].Since its first presentation,the approach was verified by several groups on various materials,such as aluminum alloys[6–9],iron alloys[10],copper alloys[11],gold alloys[12],and bronze alloys[13].For example,Dell’Aglio et al employed CF-LIBS to analyze the meteorites,where the plasma temperature was obtained from the emissivity of 25 lines of Fe,and a relative error of 20%was obtained for Co[14];Burakov et al employed CF-LIBS to analyze the copper alloy,where the plasma temperature was obtained from the emissivity of 8 lines of Cu and 4 lines of Pb,and a relative error of 21%was obtained for Pb[15];Kolmhofer et al employed CF-LIBS to analyze the slags,where the plasma temperature was obtained from the emissivity of 13 lines of Ca,23 lines of Mn,6 lines of Ti,and the relative errors of Si,Fe,Mn,and Ti were 21%,32%,18%,and 23%,respectively[16].Therefore,although CF-LIBS is capable of performing quantitative　analysis by　using　the plasma temperature obtained from the Boltzmann plots without standard samples,the typical relative error is on the order of 20%.

对于肥料分级标准，田树刚表示，其落地执行还存在着许多挑战，需要开展更多的工作。一方面，更加严格标准的出台必将增加企业的生产成本，如何控制产品的合理价格以满足生产企业和农业种植的双向成本需求，需要在完善行业法规政策、升级生产工艺等多方面努力。另一方面，在完善农产品标准和肥料标准同时，应制定完善种植环节的相关标准，从而实现农业全程的标准统一，避免分级后的肥料产品在使用中“无法可依”，保障生态肥真正投入到生态农业之中。

It is believed that the measurement accuracy of CF-LIBS is influenced primarily by the following three factors:(1)experimental aberrations,such as intensity fluctuations,inaccurate correction for spectral Efficiency of a detection system,etc;(2)inaccurate theoretical parameters for calculations,such as Stark broadening coefficients,partition functions,etc;(3)plasma non-ideality,such as departure from thermal equilibrium,spatial and temporal in heterogeneity,optical thickness,etc[17].In actual calculation,these factors are usually represented as inaccurate plasma temperature and spectral intensities.To overcome this obstacle,various solutions have been proposed.Gaudiuso et al provided an alternative route for plasma temperature determination in CF-LIBS analysis by comparing the elemental composition differences between predictions and standards under different plasma temperature,and a mean relative error of 13.5%was obtained for Sn[18];El Sherbini et al proposed a line intensity correction method by rationing the actual measured line intensity to the intensity expected in absence of selfabsorption,and the uncertainties of the integrated intensities were reduced to 10%–20%[19].Undoubtedly,the CF-LIBS measurement accuracy can be indeed improved by proper correction of plasma temperature or spectral intensity.

In this work,a quantitative CF-LIBS analysis method via iterative correction of plasma temperature and spectral intensity is proposed and expected to realize accurate analysis of major elements Cu and Zn as well as minor element Pb in copper-lead alloys.

2.Experimental

The schematic experimental CF-LIBS setup is shown in figure 1.A Q-switched Nd:YAG pulsed laser(Innolas,SL-100,wavelength:1064 nm,repetition rate:10 Hz,pulse energy:100 mJ)was directed into a sample chamber(LTB,LIPSpector)and focused by an 800 mm focal length focusing lens with the focal point at 2mm below the sample surface.The spectroscopic emission of the LIP was guided to a grating spectrograph　(Princeton Instruments,SP-2750,resolving power:3100,spectral range:200–380 nm)that equipped with a time gated ICCD detector(Princeton Instruments,PIMAX4-1024i)via a 200 μm diameter all-silica optical fiber and the spectra were collected at a delay time of 600 ns and a gate width of 500 ns.Sample mapping was provided by an integrated motorized and software-controlled XYZ-stage and carried out using a grid of analysis spots of 300 μm diameter,spaced at 1mm intervals.A total of 121 LIBS spectra collected from different positions on each sample surface were averaged to minimize the unintended experimental fluctuations.Additionally,a pilot laser at 635 nm and a real-time video monitoring based on a high-resolution complementary metal oxide semiconductor camera was employed for precise sample positioning and focusing.

Table 1.Elemental names and percentage contents of samples used in this work.

Standard　Cu　Pb　Zn　Else ZBY910　57.09　1.74　41.11　0.06 ZBY902　64.43　1.83　33.45　0.29 Validation　Cu　Pb　Zn　Else ZBY908B　59.49　1.83　38.60　0.08 ZBY907　59.55　3.06　34.92　2.47

Four cylindrical copper-lead alloy samples(38 mm in diameter,22 mm in height)approved by the China Iron and Steel Research Institute Group were used in this work.A list of the elemental contents(in percentage by weight)of samples is given in table 1.Here,samples ZBY902 and ZBY910 were selected as two boundary standard samples for iterative calculation,while the other two were used for validation purpose.

3.Methodology

After calculating the contents of all elements,the standard error δ is evaluated by:

通过开展活动，齐齐哈尔大学的学生们的反响很强烈，并且还给予了很高的评价，很多学生也通过此次活动加深了我国传统文化的认识，并掌握了国学方面的礼仪文化，这在很大程度上起到了大学生的思想品德教育提升的作用。

The first step is to determine the variation range of plasma temperature.Two samples,of which the matrix element contents completely cover the variation range of the samples to be measured,should be selected as the boundary standard samples.After obtaining spectra,calculate the corresponding excitation temperature Tiof element i and give a general variation range(Tmin,Tmax)of T.

The second step is to find the optimal plasma temperature and the correction coefficient of spectral intensity for the specific minor element.The relative number density of atoms of element i is given by:

Figure 2.Flowchart of the quantitative CF-LIBS analysis methodology via iterative correction on plasma temperature and spectral intensity.

where the denominator 2 represents the number of standard samples,ci0is the certified content of element i.

In this study,ZBY910 and ZBY902 were selected as the two boundary standard samples.This is because the contents of the matrix element Cu in them are 57.09%and 64.43%,respectively,which have well covered the variation range of 57.0%–63.5%from low-grade H59 to high-grade H62.A typical spectrum of ZBY902 is shown in figure 3,which reveals all the components Cu,Zn and Pb.Here,6 Cu I lines and 4 Pb I lines listed in table 2 were chosen to draw the Boltzmann plots for ZBY902 and ZBY910 samples(shown in figure 4)and determine the excitation temperatures of Cu and Pb.Although the points tend to coincide with their corresponding straight fitting lines,the different slopes indicate the different plasma temperatures as well as an apparent violation of the LTE condition.As shown,the variation range of plasma temperature T was determined to be 5000–15 000 K.

图2为伸杆支撑组件图，主要由支撑滚筒、压力传感器、电磁铁、转板、限位销和配重块组成。转板安装在底板上，起到杠杆作用，可绕其轴线上下转动；塑料滚筒安装在压力传感器上，压力传感器安装在转板的左端；配重块安装在转板右端，用于对伸杆提供重力补偿力；吸盘式电磁铁安装在底板上，当电路通电时能够吸住转板左端。

whereis the partition function of ions,meis the electron mass,and Neis the electron density.

The mass of element i is given by:

The third step is to perform quantitative analysis on unknown samples.The elemental contents in unknown samples can be predicted by substituting the obtained T*and α*as well as the plasma spectra in equations(1)–(4).

The relative number density of ionsof element i is given by:

where m represents the molar mass.

The weight percentage Ciof element i present in the sample is deduced as:

where α is a correction coefficient of the specific minor element n.

The flowchart of the quantitative CF-LIBS analysis methodology via iterative correction on plasma temperature and spectral intensity is illustrated in figure 2,which mainly consists of three steps.

whereis the integral spectral line intensity,is the partition function,giis the degeneracy of the upper level,Aiis the Einstein spontaneous emission coefficient,h is the Planck constant,viis the frequency of emission between the upper and lower levels,Eiis the upper energy level,and k is the Boltzmann constant.

Figure 3.Typical spectrum recorded for the ZBY902 sample.

The second-order iterative algorithm in the second step can be described as follows.Firstly,calculate the relative atomic and ionic number densitiesandat different temperatures iteratively according to equations(1)and(2)with a step size of ΔT;secondly,calculate the contents ciof element i at different correction coefficients α iteratively according to equations(3)and(4)with a step size of Δα;thirdly,calculate the standard errors δ of all elements corresponding to different T and α values according to equation(5); finally,create the 3D plot of function δ(T,α)and find the *optimal plasma temperature T*and correction coefficient αthat correspond to the minimum δ.

我院祛瘀及清热类中药致新的和严重的不良反应298例分析 ……………………………………………… 刘 洋等（8）：1091

4.Results and discussion

4.1.Determination of the variation range of plasma temperature

2.1 大学生体质健康标准测试各指标的基本信息贵州大学2017年男女生体质健康测试各指标的均值、标准差、最小值、最大值见表3，其中总分=BMI指数得分*0.15+肺活量得分*0.15+50m跑得分*0.2+800m/1000m得分*0.2+立定跳远得分*0.1+坐位体前屈*0.1+一分钟仰卧起坐/引体向上得分*0.1。

政府对金融机构进行监管，其监管成本为D；如果金融机构不对绿色环保企业贷款给予优惠利率，则会受到政府相应处罚为Q （Q＞D）；政府对银行进行绿色信贷严格监管的概率为P3。

Table 2.Wavelengths(λ)and spectroscopic constants(A,E,g)of atomic lines of Cu,Pb,and Zn for con firming T and quantitative analysis.

Species　　λ (nm)　A(×108)　E(eV)　g Cu I　213.60　4.671　8.52　9 219.23　3.266　8.49　7 224.26　2.675　8.78　7 312.61　0.762　8.80　4 324.75　1.370　3.82　4 327.40　1.361　3.79　2 Pb I　217.00　1.836　5.71　3 280.20　1.600　5.74　7 282.32　0.304　5.71　5 283.31　0.592　4.38　3 368.35　1.704　4.33　1 Zn I　330.26　1.070　7.78　5 334.50　1.500　7.78　7

Figure 4.Comparison of Boltzmann plots of Cu and Pb for samples ZBY910 and ZBY902.

4.2.Determination of the optimal plasma temperature and correction coefficient

Taking ZBY902 and ZBY910 as the boundary standard samples,we calculated all the elemental contents and standard errors δ corresponding to different plasma temperatures(5000–15 000 K)and correction coefficients(0–1)iteratively,with step sizes of ΔT = 10 K and Δα = 0.01.Here,atomic lines Cu I 312.61 nm,Zn I 330.26 nm,and Pb I 280.20nm were selected as characteristic lines for quantitative analysis due to their relatively small self-absorption coefficients.In this work,spectral intensities of these characteristic lines in the four standard samples were listed as follows:for ZBY910,IZn = 17 232.2,ICu = 1136.78,IPb = 5118.19;for ZBY902,IZn = 6408.78,ICu = 571.14,IPb = 5134.13;for ZBY908B,IZn = 8998.06,ICu = 639.48,IPb = 4998.43;for ZBY907,IZn = 9467.22,ICu = 815.24,IPb = 5772.96.

Figure 5.(a)3D plot of function for the standard samples ZBY910 and ZBY902;(b)the cross section of the 3D plot of δ(T,α)at T* = 7110 K.

In conventional CF-LIBS analysis,the best accuracy is usually obtained for major elements,while for the minor ones the analysis can only be considered semi-quantitative.This is because of an inhomogeneous distribution of the minor elements in the sample[20].However,an uncertainty of the order of 1%affecting the major components can correspond to very large uncertainty values on the minor components[17].Therefore,a correction coefficient α was introduced to calibrate the influence of factors such as spatial inhomogeneity,detection Efficiency,self-absorption,spectral line broadening,etc on the spectral intensity,so as to ensure the relative measurement accuracy of minor elements in the sample.Ostensibly,α is a correction to the content of element n,but actually it is an amendment to the spectral intensity.In addition to element n,other elements contents can also be corrected to some extent.In general,the coefficient α is approximately equal to the ratio of the certified content of element n to the measured content with only correction of the plasma temperature.In our case,the certified and the measured contents of Pb in ZBY902 were 1.83%and 5.99%,respectively,which corresponds to a theoretical α value of approximately 0.31.Thus,the second-order iterative calculation was performed with a wide α range of 0 to 1.The obtained 3D plot of function for the standard samples ZBY910 and ZBY902 are shown in figure 5(a),while the cross section of δ(T,α)at T* = 7110 K is shown figure 5(b).The optimal plasma temperature T*and correction coefficient α*were found to be 7110 K and 0.30,respectively,as the standard error δ reached its minimum of 0.135.

4.3.Quantitative analysis on unknown samples

In order to verify the feasibility of the proposed CF-LIBS method,the elemental compositions of the two validation samples were analyzed,with each one being analyzed by 121 successive laser shots for five times.Comparisons of the measured contents and the certified standards are shown in figure 6,where the average relative errors of Cu,Zn and Pb were 1.8%,2.7%and 13.4%,respectively.In addition to major elements Cu and Zn,but also the measurement error of minor element Pb was relatively small.The good correlation con firms that the proposed method is much suitable for analyzing alloy samples with similar matrices and is able to provide accurate quantitative analysis results on both major and minor elements.

Figure 6.A comparison between the measured contents and the certified standards for Cu,Pb,and Zn through samples ZBY908B and ZBY907.Each sample has been analyzed by 121 successive laser shots for five times.

For comparison,the ZBY910 sample was also quantitatively analyzed using the conventional CF-LIBS method,of which the plasma temperature was calculated by averaging plasma temperatures over all the elements.The plasma temperatures calculated from Cu and Pb as well as the average were 9300 K,6700K and 8000 K,respectively.The predicted contents of Cu,Zn,Pb under these three plasma temperatures compared to the certified standards are shown in figure 7.As can be seen,the differences in plasma temperature can lead to different measurement errors.Although the average temperature can improve the calculation accuracy to some extent,the relative errors of Cu,Zn and Pb still reach 12%,26%and 32%,respectively,which are obviously much higher than those obtained by the proposed method.

Figure 7.The measured contents for Cu,Pb and Zn of sample ZBY910 at different plasma temperatures using the conventional CF-LIBS method compared to the certified standards.

The measurement inaccuracy of the conventional CFLIBS method was mainly caused by the inaccurate temperature and spectral intensity.For the former,it was attributed to two sides.On the one hand,the CF-LIBS is based on an assumption of LTE,in which case the plasma temperatures for all the sprayed metallic particles in the ablated plume should be the same.However,in practical LIBS experiments,the LIP are in near-LTE conditions,rather than in LTE conditions[21].This is mainly due to the kinetic ionization recombination　processes that caused　by　the electronic impacts.If the recombination process plays a Significant role in the plasma evolution,the Saha balance will be disrupted to non-equilibrium[22,23].In addition,the spatial inhomogeneity of plasma can also lead to Significant spatial and temporal temperature gradients in its peripheral zones[24].For the above reasons,we consider the conventional CFLIBS,which calculates the plasma temperature by averaging the plasma temperatures over several elements,is inaccurate.For spectral intensity,the inaccuracy was caused by self absorption and spectral line overlapping,which make the measured spectral line wavelength to deviate from the theoretical one and distort the integrated line pro file[19].

5.Conclusions

In this study,we propose a quantitative CF-LIBS analysis method via iterative correction on plasma temperature and spectral intensity using two boundary standard samples.By comparing the standard errors of all the elemental contents through a second-order iterative algorithm,precise plasma temperature and spectral line correction coefficient are determined.Experimental measurement results on copper lead alloy samples show that,compared to conventional CFLIBS method,the relative errors of Cu,Zn and Pb have been reduced from 12%,26%and 32%to 1.8%,2.7%and 13.4%,respectively.The proposed method has greatly improved the quantitative analysis accuracy of CF-LIBS and realized more accurate measurement of both major and minor elements in alloy samples.It helps to promote the application of CF-LIBS technology in fields such as metallurgy quality control and material classification processes.

The work was financially supported by the National Key Research　and　Development Program　of China　(No.2017YFA0304203),the Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China(No.IRT13076),National Natural Science Foundation of China(Nos.61475093,61378047,61775125),the Shanxi‘1331 Project’Key Subjects Construction and the Major Special Science and Technology Projects in Shanxi Province(No.MD2016-01).The authors thank the State Key Lab of Power Systems for technical contribution and financial support.

References

[1]Li Y et al 2017 Plasma Sci.Technol.19 025501

[2]Wen G H et al 2014 Plasma Sci.Technol.16 598

[3]Yang J H et al 2015 Spectrochim.Acta B 107 45

[4]Ferreira E C et al 2008 Spectrochim.Acta B 63 1216

[5]Guo M Y et al 2016 Plasma Sci.Technol.18 661

[6]Ciucci A et al 1999 Appl.Spectrosc.53 960

[7]Davari S A et al 2017 J.Anal.At.Spectrom.32 1378

[8]Borgiaa I et al 2000 J.Cult.Heritage.1 281

[9]Tognoni E et al 2007 Spectrochim.Acta B 62 1287

[10]Bulajic D et al 2002 Spectrochim.Acta B 57 339

[11]Colao F et al 2004 J.Anal.At.Spectrom.19 502

[12]Bel’kov M V et al 2005 J.Appl.Spectrosc.72 376

[13]Fornarini L et al 2005 Spectrochim.Acta B 60 1186

[14]Dell’Aglio M et al 2010 Geochim.Cosmochim.Acta 74 7329

[15]Burakov V S and Raikov S N 2007 Spectrochim.Acta B 62 217

[16]Kolmhofer P J et al 2015 Spectrochim.Acta B 106 67

[17]Rifai K et al 2017 Spectrochim.Acta B 134 33

[18]Gaudiuso R et al 2012 Spectrochim.Acta B 74–75 38

[19]El Sherbini A M et al 2005 Spectrochim.Acta B 60 1573

[20]Burakov V S et al 2004 J.Appl.Spectrosc.71 740

[21]De Giacomo A 2011 Spectrochim.Acta B 66 661

[22]Capitelli M et al 2004 Spectrochim.Acta B 59 271

[23]De Giacomo A et al 2012 Chem.Phys.398 233

[24]De Giacomo A et al 2008 Spectrochim.Acta B 63 805