用TOPAS参数化同步辐射光源的仪器因素
Xiaodong (Tony) Wang (仪器信息网iangie)
Centre of Material Research, Curtin University, Perth, WA 6150, Australia
TOPAS的作者Alan Coelho是Fundamental Parameter Approach的创始人(Cheary & Coelho, 1992). 所以TOPAS在处理仪器因素上能够很准确地将仪器峰宽和样品信息分开. 这在上一次教程中已介绍过.
越来越多的实验者使用同步辐射来检查样品. 其中一个原因是同步辐射光源单色性好, bema line的角度分辨率高(beam line指聚能环上的各个实验室). 同步辐射能够分辨出的样品尺寸展宽比实验室XRD高几个数量级. 但同步辐射数据通常不使用Bragg-Brentano几何, 而是Debye-Scherrer几何, FPA的模型不再适用. 那么TOPAS是怎么处理这个问题的呢? 它要求实验者在所用的同步辐射beam line上收集一个标样的衍射谱, 通过它来参数化该beam line的仪器峰宽. 通常选用NIST SRM 660b. 用TOPAS 拟合该谱, 得到beam line的仪器卷积. 保存并fix这些仪器卷积参数, 作为待测目标样品谱中仪器因素参与其卷积.
1. 用TOPAS的WPPF表征Instrument profile function (IPF)
使用NIST SRM 660b (La11B6) (11B指B的较重的同位素) 标样来表征同步辐射beam line的峰位与峰形. 如果该beam line使用的探测器是position sensitive detector, 那么得到的衍射谱不一定是均匀步长的. TOPAS可以处理非均匀步长的衍射数据.
首先在TOPAS中用Split-Pearson 7 类型的单峰拟合每个峰, 得到左右半高宽随2θ的关系如下图(Cline, 2000). 从3°2θ到80 °2θ一共fit了114 根线. GOF 1.06. 50°2θ 以后的峰强减弱, 半高宽数据开始模糊.
上图可以看出半高宽随2θ的关系是Tan(θ) 而不是1/Cos(θ), 所以之后的仪器卷积参数化使用Tan(θ)类型的卷积的作用更大.
大部分FWHMleft/ FWHMright 值都低于1, 表示峰形非对称, 高角方向较宽, 所以用该使用Circles 卷积, 且参数为正.
为防止和剔除TOPAS卷积计算过程的偶然误差, 以及检查本方法的正确性, 本文还使用了另外一个NIST SRM 660a来做交叉验证. 根据第二个衍射谱所得到的beam line IPF表征如下(所得的IPF结果相似):
根据NIST SRM 660b的certificate, 最低角的两根线受测角仪轴卷积影响严重, 未参与晶胞参数计算(National Institute of Standards and Technology, 2010), 所以本教程确定光源波长和仪器卷积也未考虑这两根线.
2. 下面用TOPAS的Rietveld拟合确定光源波长和beam line仪器卷积
对660b的Rietveld全谱拟合所得的波长结果为0.4264945282 Å . GOF 1.51. TOPAS输出如下:
'--------------------------------------------------------------
' This is the instrument function used for the **** beam line.
' It was refined using NIST SRM 660b La11B6
' The energy was approximately 29.07 keV (detail wavelength see below "lo" keywords)
xdd "660b.xy"
r_exp 5.482484494 r_exp_dash 9.60219296 r_wp 8.265534618 r_wp_dash 14.47651305 r_p 6.371762359 r_p_dash 16.19744894 weighted_Durbin_Watson 1.01886577 gof 1.507625717
range 1
bkg @ 225.2870845 -90.68596489 35.83605613 -12.23152865
start_X 9 ‘first LaB6 two lines are not used
LP_Factor( 90) ‘synchrotron source are fully polarized
Zero_Error(@, -0.00123867112)
convolution_step 4 ‘higher convolution_step should be used if less than 8 points above FWHM
Rp 761
Rs 761
‘ below are the generated instrument convolutions, they are then adopted and fixed for real samples
User_Defined_Dependence_Convolution(lor_fwhm, 1/Cos(Th) , @, 0.0006835375223_5.084269e-005)
User_Defined_Dependence_Convolution(hat, , @, 0.01059435091_0.0001304874)
User_Defined_Dependence_Convolution(gauss_fwhm, Tan(Th) , @, 0.001137451264_0.0008132795)
User_Defined_Dependence_Convolution(gauss_fwhm, 1/Cos(Th) , @, 0.006879952932_0.000121114)
User_Defined_Dependence_Convolution(lor_fwhm, Tan(Th), @, 0.001908694463_0.000311171)
User_Defined_Dependence_Convolution(circles_conv, , @, 0.01407552526_7.699319e-005)
lam
ymin_on_ymax 1e-005 ‘this value is 2 orders lower than default since synchrotron lines are sharper
la 1 lo @ 0.4264945282 lg 0.1 ‘monochromatic line is more Gaussian then those without monochromator
x_calculation_step 0.00375 ‘this is defined by *** detector pixel resolution
str ‘NIST SRM 660b LaB6 structure, no sample broadening terms were used
r_bragg 23.99477521
phase_name "Structure"
MVW( 203.7776902, 71.82995543, 100)
scale @ 0.0003452523496
space_group Pm-3m
Phase_LAC_1_on_cm( 40.27485117)
Phase_Density_g_on_cm3( 4.710862541)
Cubic(! 4.15689) ‘Certified lattice parameter of NIST SRM 660b
site La1 num_posns 1 x =0; : 0 y =0; : 0 z =0; : 0 occ La 1 beq @ 0.4423696765
site B1 num_posns 6 x 0.1975 y =1/2; : 0.5 z =1/2; : 0.5 occ B 1 beq @ 0.3363016301
拟合图如下:
对第二个标样660a的Rietveld全谱拟合所得的波长结果为0.4264959008 Å, 与上面的结果相似. GOF 1.32. TOPAS输出如下: (使用相同的仪器卷积洛伦兹和高斯卷积的Tan(θ)参数均大于1/Cos(θ)参数,与之前的预测相符. 精修后得到的参数跟上面的结果相似)
'----------------------------------------------------
' This is the instrument fuction used for the**** beamline
' It was refined using LaB6
' The energy was approximatly 29.07 keV (detail wavelength see below "lo" keywords)
xdd "660a.xye"
r_exp 6.222902742 r_exp_dash 12.973689 r_wp 8.233492489 r_wp_dash 17.1654251 r_p 6.349678347 r_p_dash 17.71730563 weighted_Durbin_Watson 0.7255525408 gof 1.323095158
range 1
bkg @ 216.1919118 -92.65399802 38.04296364 -12.63124484
start_X 9
LP_Factor( 90)
Zero_Error(@, -0.000840563866)
convolution_step 4
Rp 761
Rs 761
User_Defined_Dependence_Convolution(lor_fwhm, 1/Cos(Th), @, 0.0008195722759)
User_Defined_Dependence_Convolution(lor_fwhm, Tan(Th), @, 0.001198978398)
User_Defined_Dependence_Convolution(gauss_fwhm, 1/Cos(Th), @, 0.006969562372)
User_Defined_Dependence_Convolution(gauss_fwhm, Tan(Th), @, 0.001201105782)
User_Defined_Dependence_Convolution(hat, , @, 0.009437685021)
User_Defined_Dependence_Convolution(circles_conv, , @, 0.0125411335)
lam
ymin_on_ymax 1e-005
la 1 lo @ 0.4264959008 lg 0.1
x_calculation_step 0.00375
str
r_bragg 24.02593548
phase_name "Structure"
MVW( 203.7776902, 71.80974004, 100)
scale @ 0.0002905529305
space_group Pm-3m
Phase_LAC_1_on_cm( 40.28618908)
Phase_Density_g_on_cm3( 4.712188711)
Cubic(! 4.15691) ‘value from NIST SRM 660a certificate
site La1 num_posns 1 x =0; : 0 y =0; : 0 z =0; : 0 occ La 1 beq @ 0.4373594946
site B1 num_posns 6 x 0.1975 y =1/2; : 0.5 z =1/2; : 0.5 occ B 1 beq @ 0.3536793756
拟合图如下:
注意, 在以上的两个标样的拟合中, 由于使用的是Debye-Scherrer几何, zero_error应该refine, 而sample displacement error可以不用, 这与实验室XRD的情况相反. TOPAS中同步辐射用于光源完全极化, 洛伦兹极化因子固定为90度. 两个LaB6的晶胞参数固定为已知值, 来自于NIST SRM的certificate. convolution_step指每个测量点用多少计算点去拟合, 当峰比较尖锐的时候半高宽以上可能不足8个数据点, 该值应大于1.
结论:
使用两种NIST SRM (晶胞参数不同)得到一致的仪器信息: 光源波长相对误差百万分之三; 仪器卷积函数的参数同数量级. 表明说得的仪器卷积有很大可信度. 这些仪器卷积函数(User_Defined_Dependence_Convolution)的参数经平均后可作为该beam line在这次试验中的仪器卷积. 该方法可用于确定一般同步辐射beam line的仪器参数.
Reference
Cheary, R. W. & Coelho, A. (1992). Journal of Applied Crystallography 25, 109-121.
Cline, J. P. (2000). Vol. 1, Instrumental Applications of X-ray Diffraction, edited by F. H. Chung & D. K. Smith, pp. 903-917. New York: Marcel Dekker, Inc.
National Institute of Standards and Technology (2010). Certificate Standard Reference Material® 660b.
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