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1. 31 Dead time correction in Ino 33Gap 67As semiconductor 34 Double scattering ratio for nickel llle 35 Absorption factors in transmission and reflection geometry 37 Comparison between Compton and elastic scattering intensities in Ino 33Gao 67As 37 MCA file format 45 List of Tables 2 1 Known Platforms Supporting PDFgetX 3 1 Summary of structure function refinement leen Chapter 1 Introduction 1 1 What is PDFgetX PDFgetX is a program to be used to obtain the atomic Pair Distribution Function PDF from a measured X ray powder diffraction data PDFgetX is written using the Yorick an interpreted language This will require users to obtain the Yorick distribution and install it yourself See Chapter 2 for help in installation PDF is the instantaneous atomic number density density correlation function which describes the atomic arrangement in materials A useful characteristic of PDF method is that it gives both local and average structure information because both Bragg peaks and diffuse scattering are used in the analysis And from the PDF peak width it s possible to obtain the information about bond length distribution static thermal 4 and correlated atomic thermal motion 5 By contrast an analysis of the Bragg scattered intensities alone by a Rietveld type analysis for instance yields the average crystal structure only and the extended x ray absorption fine structur
2. for constant normalization enter 0 Column corresponding to NORM 12 ENTER FILE NAMES File name to ENTER FILE NAMES File name to ENTER FILE NAMES File name to TO COMPARE TO QUIT READING ENTER Q compare in33 2 asc TO COMPARE TO QUIT READING ENTER Q compare in33_5 asc TO COMPARE TO QUIT READING ENTER Q compare q Dead time correction setting READ FILE in33 l asc APPLY DEAD TIME CORRECTION FOR DATA y n y 1 Dead tim correction using detector dead tim 2 Dead tim correction using pulser measurement Q Exit Dead time correction 1 20 2 Enter column containing pulser 9 APPLY DEAD TIME CORRECTION FOR MONITOR y n n For details refer to CH 4 Using PDFgetX CHECK VARIABLE AND ASSIGNED COLUMN X axis 1 DATA 13 Normalization 22 Detector dead time Correction using pulser CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 14 Pulser column 5 9 No Monitor dead time Correction CHANNEL SETTINGS ARE CORRECT y n y READ file in33 2 asc READ file in33 5 asc Colors in order of reading magenta cyan blue green red and blacks COMPARE OTHER VARIABLE y n n EXIT COMPARING FILES Return to Preliminary data reduction Fig 3 1 shows dead time corrected elastic scattering after normalization by monitor It shows that these scans ov
3. o QW Q 1 Q i 2 Figure C 1 MCA file format 45 Bibliography 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ftp wuarchive wustl edu languages yorick yorick ad html D Waasmaier and A Kirfel Acta Cryst A 51 413 1995 C T Chantler J Phys Chem Ref Data 24 71 1995 V Petkov I K Jeong J S Chung M F Thorpe S Kycia and S J L Billinge Phys Rev Lett 83 4089 1999 I K Jeong Th Proffen F Mohiuddin Jacobs and S J L Billinge J Phys Chem A 103 921 1999 Th Proffen and S J L Billinge J Appl Crystallogr 32 572 1999 R L McGreevy and L Pusztai Mol Simul 1 357 1988 T Proffen and R Neder Jour Appl Cryst 30 171 1997 I K Jeong F Mohiuddin Jacobs V Petkov and S J L Billinge arXive cond mat 0008079 2000 Y Waseda The structure of non crystalline materials McGraw Hill New York 1980 C N J Wagner J Non cryst Solid 31 1 1978 B E Warren X Ray Diffraction Dover New York 1990 C W Dwiggins Jr and D A Park Acta Crystallogr A 27 264 1971 C W Dwiggins Jr Acta Crystallogr A 28 155 1972 R Serimaa T Pitkanen S Vahvaselka and T Paakkari Jour Appl Cryst 23 11 1990 S Ergun in Chemistry and Physics of Carbon edited by J P L Walker chapter Vol 3 pages 211 288 Marcel Dekker New York 1968 A J C Wilson edito
4. CHAPTER 2 INSTALLATION 8 2 2 2 PDFgetX You may obtain the latest version of PDFgetX from the PDFgetX website http www pa msu edu cmp billinge group programs PDFgetX PDFgetX is provided as a compressed file Use the command tar xzvf pdfgetx1 1 tar gz which will extract the files into a new directory called PDFgetX And you can find the following program files under the directory PDFgetX pdfgetx i pdfgetxdistribution i pdfgetx custom i ASF DAT PERIODIC TABLE DAT MASS ABS COEFF DAT LICENSE TXT If the z flag does not work on your system then use the commands gzip d pdfgetxl l tar gz tar xvf pdfgetxl l tar to extract the files 2 2 3 Installing and Configuring PDFgetX To customize the PDFgetX installation you need to modify two files custom i and pdfgetxdis tribution i If you are new user of Yorick you can simply rename pdfgetx custom included in compressed file to custom i and give the proper path for the Actual PATH in the following two lines in pdfgetx_custom 1 file tinclude Actual PATH pdfgetx i tinclude Actual PATH pdfgetxdistribution i And then create a directory Yorick under your home directory and place your own version of custom i there If you already have your own version of custom i simply add the above two lines in the custom i file For Windows OS you need to beware of a few things First the path should look like t
5. q INTEGRATE REGIONS OF INTEREST SAVE MCA DATA TO ASCII FILE Enter file name for MCA derived data in33 mca dat READ ANOTHER MCA FILE y n n EXIT MCA FILE READING Return to Preliminary data reduction Fig 3 2 shows MCA spectrum of Ino 33Gao 67As at Q 40 The elastic and Compton scattering are well separated at this value of Q It also shows some fluorescence peaks in low channel number CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 20 side If you check the output file you ll find that it contains Q MCA Elastic MCA_ElaCompt and MCA Spectrum of In Ga As 500 400 Ss 300 r Elastic 7 E scattering 5 c 2 200 J Compton scattering 100 1 i 4 i y W 0 M nana Y il NAVAL M T suns NV 1 0 500 1000 MCA Channel number Figure 3 2 MCA spectrum of Ing 33Gao s7As at Q 40 It shows that the very sharp elastic scattering around channel number 640 is well separated from the broad Compton scattering The fluorescence of the alloy are shown below channel number 300 MCA Det Tot When the program generates X column it assumes constant X step The whole MCA files can be converted to N column ascii files in this way and then as we did in Reduction of SPEC file these files can be compared and combined Also it s possible to apply dead time correction for MCA file 3
6. Exiting PDEgetX o a a a a ws x e 28 41 3 The Maim Men r sorngan aion ue E A S 28 4 2 Data Analysis Procedure in PDFgetX o o 30 4 3 History Files ooo ss e en ae Boe ae Ap tty dd a d deg de 32 44 Some Yorick Information e 32 5 Data Corrections 33 5 1 Dead Time Correction ee 33 5 2 Multiple Scattering Correction o o e e 35 5 3 Polarization Correction ee 36 5 4 Absorption Correction es 36 5 5 Compton Scattering Correction 2 o o e e 36 5 6 Normalization lll ees 38 5 7 Laue Scattering Correction o o 38 5 8 Pair Distribution Function 2 2 es 38 CONTENTS 5 9 Error Propagation o ae adm a ERE ura A SPEC file format B Description of the history file C MCA file format 39 40 42 44 List of Figures 3 1 3 2 3 3 3 4 3 5 4 1 4 2 5 1 2 2 5 3 5 4 C 1 Comparison of normalized elastic scattering oo 15 MCA spectrum of Ing 33Gao 67As at DADA a col edet ard 20 a Effects of corrections on raw data of Ino 33Gao 57As b Comparison between normalized DATA and f Lie m io ox hx o Rx d tue 24 Data corrections in Ino33Gaog zAs alloy ooo o 24 Reduced Structure Function and PDF of Ino33Gao 57As semiconductor 25 Data analysis procedure in PDEgetX o o 30 Structure function refinement procedure in PDFgetX
7. Figure 5 1 Dead time correction in Ino 33Ga0 67As semiconductor alloy a Comparison between the dead time correction using the pulser method and dead time 15 us measurement Compar ison between low Q and high Q elastic scattering b before dead time correction Low Q data don t overlap with the high Q data at Q 12 13 T c after dead time correction using the pulser method d after dead time correction using the dead time measurement After dead time correc tion in both cases the low Q and high Q data overlaps with each other quite well CHAPTER 5 DATA CORRECTIONS 35 0 14 ut 0 1 ut 0 5 E o o9 pise a 4 Il ut 3 we aat Po 0 04 par TS m pio ELA 0 00 DD er a a a a cocoa t 0 03 ut 0 1 00085898888 lt ut 0 5 99 0 02 o ut 2 5 a 4443444 Ll out 5 EN 34444 4 4 g3 0 01 F a a a see eS a a 0 00 amp L L 1 o 5 10 15 20 Q A Figure 5 2 Double Scattering Ratio in Ni upper panel transmission geometry lower panel re flection geometry experimental data includes Compton scattering wavelength of x ray 0 7107 5 2 Multiple Scattering Correction We ll consider here only the double scattering process since it represents the major part of the multiple scattering To calculate double scattering ratio we followed the method suggested by Warren and Mozzi 12 According to Warren and Mozzi the double scattering ratio is given by Eq
8. This will exit PDFgetX but leave you still in Yorick Type quit to exit Yorick 0 4 hlqpu q Exiting PDFgetX 1 1 gt quit current directory gt 4 1 3 The Main Menu Pair Distribution Function from the X ray powder diffraction PDFgetX 1 1 0 Preliminary data reduction 1 Build a setup file CHAPTER 4 USING PDFGETX 29 2 Background Substraction 3 Reduction of Structure Function S Q Input file format Q I dQ dl 4 PDF calculation Input file format Q S Q dQ dS P Print S Save U Unzoom L Limits windows Q Quit 0 4 hlqpu The main menu provides you with several options Simply type the number or letter of the option you want and hit Enter Option 0 This will access an interactive routine that can extract scan s from raw SPEC data and MCA data acquired from x ray powder diffraction experiments Correction for detector and monitor dead time correction can be applied You can also compare variables e g elastic in each scan and combine scans to get average value Option 1 This will access an interactive routine used to create a setup file describing the con ditions of your experiment The setup file is needed at several stages in the analysis PDFgetX will prompt for the name of the setup file at the appropriate points Option 2 This will access an interactive routine that can subtract a background from a PDFgetX input file Option 3 This will access an interactive routine
9. pulser of known frequency can be fed into the detector preamp The measured counts in the pulser signal in an SCA window set on the pulser signal is then recorded for each data point The data dead time correction is then obtained by scaling the raw data by the ratio of the known pulser frequency and the measured pulser counts The Fig 5 1 shows a comparison of dead time correction using these two methods Nate 5 3 Dead time Correction In Ga As 1 8 0 5 9 10 0 08 DTC pulser method b _ 0 06 y VC o o DTC dead time 15us 0 4 5 9 004 E 0 02 E 0 3 0 00 5 O 1 14 15 2 dl QU Q j o abo e M Seog 0 2 3 lt TREE Before dead time correction i Wh ip tet QE M UE 91 F 1 li M hay un n TM 2 eee 0 8 1 1 n n 0 0 rn 1 a aa 0 5 zi 7 0 5 E 7 A 0 08 bo A y 0 08 LN y i x c _ 008 V W A Agu T a 0 08 4r S r 4c e A 0 04 Lr mi Ww mA 0 04 E 0 02 0 02 0 3 on 11 12 15 14 15 0 3 r 9005 12 13 14 15 Q Q 0 2 02 I After dead time correction li i After dead time correction 01 L AM ha using pulser method rE n i I using dead time 15us M AM n Wr Mh TER Mu F Mn J 0 0 L L Piana aema 0 0 L f L pee 0 10 20 30 40 0 10 20 30 40 1 41 Q A Q A
10. 5 1 where P is the polarization factor A the absorption factor N normalization constant and 160 rine mul are the coherent incoherent Compton and multiple scattering intensities respectively in electron units We can define the structure function S Q in the following form S O u 0 HD 5 2 where f is the sample average scattering factor Therefore to get a structure function we have to do the following corrections 11 step by step on raw data 0 Dead time correction 1 Multiple scattering correction 2 Polarization correction 3 Absorption correction 4 Normalization 5 Compton scattering correction 6 Laue diffuse correction 5 1 Dead Time Correction In high energy high intensity synchrotron x ray diffraction experiments the detector and monitor dead time effect on the measured experimental data is rather lager Therefore in these experiments proper dead time correction should be applied before applying standard corrections 33 CHAPTER 5 DATA CORRECTIONS 34 In the PDFgetX the dead time effect can be corrected by measuring detector dead time and using the following Eq 5 3 Nm t TAN pot to where 1 is dead time of detector or monitor Ngre the dead time corrected counts Nn the measured counts Nj the total counts of detector or monitor and f the measuring time for each data point Or dead time effect can be corrected using the pulser method 9 A pulser train from an electronic
11. 5 l 35 37 39 30 35 40 QA ala C 1000 al MS correction Data after corrections No Pol correction Mean square ave ASF f After Abs correction 500 j IM fi VLL i l i l 7 o LEX l i i 0 10 20 30 40 0 10 20 30 40 sii R 1 Q Q A Figure 3 3 a Corrections on raw data of Ino 33Gao 67As semiconductor alloy In high Q region after each correction the change of slope is noticeable b Comparison between normalized data after corrections and mean square average atomic scattering factor In high Q those two line up quite nicely Abs factor 0 90 0 06 0 04 M L 0 02 Data Corrections Absorption factor in transmission geometry 0 00 0 Double scattering ratio in transmission geometry 30 0 T Ruland function o b 0 003 05 400 RE e 10 20 30 40 d 2 QU s gt E EZ c o 200 F Mean square ave atomic scattering factor Compton scattering T Compton modified using Ruland method o L o 40 0 10 20 30 40 Q Figure 3 4 Data corrections in Ing 33Gao 67 As semiconductor alloy a Absorption factor ut 1 11 Absorption effect becomes larger as Q increases b Double scattering ratio c Compari son between mean square average atomic scattering factor Compton and modified Compton using the Ruland function Inse
12. Q 1 to Q Enter maxmimum range Enter PDF step size dr 0 02 r Angstrom for PDF calculation 20 CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 26 Calculating PDF up to rmax 20 with dr 0 02 SAVE PDF r G r dr dG y n y Enter file name to save data in33 tutorial pdf Recalculate PDF y n n Congratulations You ve made a PDF Fig 3 5 b shows pair distribution function of Ing 33Gag 67As semiconductor alloy The nearest neighbor NN peak shows well resolved doublet which corre sponds to shorter Ga As and longer In As bonds This clearly shows the power of high real space resolution PDF method to study the local structure of the alloy It could be instructive to obtain the PDF using different Qmax to see how it affects the shape of NN peak The dotted line shows t one standard deviation o of PDF the error propagated to PDF from the raw data The ripples around sharp peaks are known as the termination ripple It is caused by the limited Q value in Sine Fourier transform And the noise peaks near to r 0 are caused by noises in the data Chapter 4 Using PDFgetX This chapter will teach you how to use PDFgetX For this purpose first we ll give you overview of PDFgetX And then explain how the program works we will explain the structure function refinement process 4 1 Overview of PDFgetX Before learning the specific commands and procedures to control PDFgetX itis best to understand how PDF
13. dI Enter data file name to read in33_cfbg input DATA REDUCTION read write binary stream history pdb In directory u24 jeong PDFgetX manual Open binary file to save refinement history Refer to the Appendix C SMOOTH DATA USING SAVITZKY amp GOLAY METHOD y n n Flat Symmetric R eflection or T ransmission geometry r t t Choose either symmetric flat reflection or transmission geometry Flat Plate Symmetric Transmission Geometry Data Correction WINDOW 0 CORRECTION EFFETS ON RAW DATA CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 23 APPLY MULTIPLE Multiple scat SCATTERING CORRECTION y n y Does the data contain Compton scattering in high Q y n n tering calculation in transmission geometry WINDOW 3 MULTIPLE SCATTERING RATIO APPLY POLARIZATION CORR Polarization cor ECTION y n n rection NOT applied APPLY ABSORPTION CORRECTION y n y NORMALIZATION USING MID HIGH Q PART OF DATA Enter a mid range Q value roughly 26 4 25 751 points are used for normalization Approximate normalization constant 1904 38 WINDOW 1 CORRECTI ED DATA vs TIS ENTER NORMALIZATION CONSTANT 1920 APPLY COMPTON SCATTI ERING CORRECTION Apply Compton correction in MID LOW Q region using Ruland method Enter integral width b try 0 008 0 003 For details please refer to the MANUAL WINDOW 4 f 2 Compton and Modi
14. is twice the Bragg angle of the monochromatic crystal In Eq 5 7 x y when the monochromator is located in the incident beam and y 1 when the monochromator is set in the diffracted beam In the case of the sealed tube X ray diffractometer incident beam is unpolarized so the full po larization correction should be applied However the Synchrotron X ray radiation e g CHESS is almost perpendicularly polarized to the detector plane therefore only partial polarization correc tion is necessary usually less than 5 5 4 Absorption Correction Absorption factor A is given by the following Eqs A Flat plate reflection geometry Arefi 1 exp 2ut sin 2u 5 8 B Flat plate transmission geometry Atran t exp ut cos 0 cos 0 5 9 Fig 5 3 shows the absorption factor as function of angle and absorption coefficient In reflection geometry if the absorption coefficient is large enough ut gt 4 there s almost no angle dependence of absorption factor In transmission geometry however when absorption coefficient is around 1 the angle dependence is minimal 5 5 Compton Scattering Correction Compton scattering correction is very important and difficult in X ray diffraction data analysis Fig 5 4 shows elastic and Compton scattering We can see that Compton scattering becomes much larger than coherent scattering in high Q So even the small error in Compton correction causes big error in determining coherent s
15. n y ENTER SPEC FILE NAME TO READ in33_tutorial spec The following shows scan information in in33_tutorial spec S 1 601 pts gt ascan pmQ 1 13 600 1 FS 2 601 pts gt ascan pmQ 1 13 600 1 S 3 1401 pts gt ascan pmQ 12 40 1400 1 S 4 1401 pts gt ascan pmQ 12 40 1400 1 S 5 1401 pts gt ascan pmQ 12 40 1400 1 EXTRACT SCANS FROM SPEC FILE Each scan will be saved as an ascii file Enter all scans to be read Ex 24 5 12 345 Extract good scans by entering the scan number SAVE SCANS TO ASCII FILE Output file name will be samplename scannumber asc Enter your samplename Ex InAs in33 Return to Preliminary data reduction Now each scan is saved as ascii file As it is mentioned during extracting process the file name will be in33_1 asc in33_2 asc and so on Now we can compare these different scans 1 50 2 Compare N column N gt 2 ascii files The Input should be N column ascii file format Plot y data norm vs x q Continue y n y ENTER FILE NAMES TO COMPARE TO QUIT READING ENTER Q File name to compare in33 l asc L pmQ ereal elive Epoch Seconds IC1 IC3 I CESR PULS ASSIGN COLUMN NUMBER TO VARIABLES ER TOTAL COMPTON IC2 ELASTIC CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 13 Column corresponding to X axis 1 Column corresponding to DATA 13 Normalization of data
16. pmQ ereal elive Epoch Seconds IC1 IC3 I CESR PULSER TOTAL COMPTON IC2 ELASTIC 1 2 07 1 999 77606 2 11876 490517 396566 353 616 418 2397 186 27129 533 02 2 069 1 997 77609 2 11807 490872 396438 353 319 415 2486 194 27167 558 04 2 07 1 989 77612 2 11884 489377 396583 353 419 416 2672 177 27045 536 06 2 07 1 996 77614 2 11884 492200 396585 353 414 428 2551 195 27218 551 08 2 06 1 989 77617 2 10866 488500 394682 351 707 419 2458 199 26993 550 5 3 ascan pmQ 12 40 1400 1 L pmQ ereal elive Epoch Seconds IC1 IC3 I CESR PULSER TOTAL COMPTON IC2 ELASTIC 12 2 07 1 115 88417 2 11861 633382 399154 451 721 317 44519 7243 634757 29557 12 02 2 06 1 137 88419 2 1088 628412 397322 449 505 313 43218 7290 630504 28163 12 04 2 07 1 166 88422 2 11877 625842 399215 451 612 327 42631 7336 630216 27395 12 06 2 07 1 185 88425 2 11884 624286 399227 451 478 299 41732 7166 629057 26469 40 APPENDIX A SPEC FILE FORMAT 41 As is shown in the sample SPEC file all the comments and characters start with mark To specify scan number S is used and for the scan header FL and so on To separate scans blank line is used Except these things the SPEC file is the same as the multi column ascii file Appendix B Description of the history file In this appendix the content of the history file history pdb is described The history file contains all the experimental information parameters used for corrections intermediate correction results Param
17. the content of this file using Yorick command gt o openb _history pdb gt show o 37 non record variables R date nc Z deg pol pf absflag dis mono polflag aft dstran pos mono aw elementsname q coh data f2ave SOQq process compo fave2 rn data compton fpara rn data cfcompt compton hiq geometry smflag data cfbg lambda soq data cfbgms mabscoeff typ mono data cfbgmspf mscflag data cfbgmspfabs mut For example you can simply check your experimental geometry by typing gt o geometry r r means reflection geometry For a complete description of history file see Appendix C 4 4 Some Yorick Information This section describes some miscellaneous information regarding the operation of Yorick within the context of PDFgetX At any time you may stop the execution of PDFgetX by entering control C You may restart PDFgetX at any time If PDFgetX for some reason crashes you can simply restart PDFgetX from within Yorick It will not usually be necessary to exit Yorick before restarting PDFgetX You may zoom any Yorick window using a mouse The left mouse button zooms in the right mouse button zooms out and the middle button can be used to drag if you have a two button mouse use both the right and left buttons at the same time Click on an individual axis to affect only that axis Chapter 5 Data Corrections The measured X ray diffraction intensity may be expressed 10 by I Q PAIN lea Tew Ten
18. 2 Refine structure function of Ino 33Ga9 67 As Now we are almost ready to refine structure function of Ing 33Gao 67As semiconductor alloy except two more things building setup file and background subtraction 0 4 qsulp 1 Enter to Build a setup file in Main BUILD SETUP FILE Note that the setup file is a text file written using Yorick syntax and may be modified in emacs without going through this whole procedure of building a new one CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 21 If PDFgetX crashes check the text input file very closely ENTER THE TYPE OF INCIDENT X RAY RADIATION S ilver M olybdenum C opper or enter E nergy smce e Enter Energy of incident X ray KeV 59 67 SAMPLE INFORMATION Number of elements in the sample Ex InGaAs 3 3 Element 1 Enter th lement ions not yet supported in Enter fractional composition 0 33 Element 2 Enter th lement ions not yet supported ga Enter fractional composition 0 67 Element 3 Enter th lement ions not yet supported as Enter fractional composition 1 Enter absorption coefficient thickness of sample mu t 1 11 MONOCHROMATOR INFO 1 d spacing of monochromator 3 135 2 Position of monochromator incident beam 3 Type of monochromator perfect cryst Q Exit 1230 Q SAVE SETUP FILE AS in33 tutorial setup Y
19. 5 4 1 2 EN B Qu 20 a b ut 5 4 I 1 J 28 Yin Aiu m l where B Y Z and Aj m are the atomic weights and mass absorption coefficients of the atoms And J 20 is an approximate representation for independent scattering Y f or Y i M depending on whether the measurements include only the coherent scattering or both the coherent and incoherent scattering and given in Eq 5 5 l a J 20 Bla 28 a 1 b sin 0 5 5 where a b are parameters and can be obtained by fitting J 20 to either Y f or Y f i M i Qm is a complicated function depending on Q ut fitting parameters a and b and geometry For details refer to the papers by Dwiggins Jr 13 14 As you can see in Fig 5 2 the multiple scattering depends on absorption coefficient and geometry In transmission geometry it becomes larger as Q increases In reflection geometry however it increases up to maximum point and decrease a little bit after that We can see that smaller the absorption coefficient smaller double scattering ratio in both cases 15 CHAPTER 5 DATA CORRECTIONS 36 5 3 Polarization Correction Polarization factor P is given by the following Eqs 10 A Using a filter P 14 cos 20 2 5 6 B Using a crystal monochromator P 1 xcos 20 1 y 5 7 where 20 is the scattering angle x cos 20 for a mosaic monochromator crystal or x cos 20 for a perfect monochromator crystal where 20
20. CA file to build PDFgetX input file for structure refinement In Refine structure function section the step by step procedure of structure function refinement is presented Users can build the input file using tutorial SPEC file in Preliminary Data Analysis section or use a tutorial input file coming with the program In this manual SPEC file refers to the data collected using SCA and MCA file for the data collected using MCA 10 CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 11 3 1 Preliminary Data Analysis 3 1 1 Reduction of SPEC file The raw data from x ray powder diffraction measurements using either a sealed x ray tube or syn chrotron source could have many different file formats and could contain multiple scans that ought to be averaged together Therefore it is very difficult to use the raw data directly in the structure function refinement With these things in mind we limited the Preliminary Data Analysis to support only the SPEC file format and N column ascii file format For details about SPEC file format please refer to Appendix A This section will show you how to reduce the raw SPEC data into the input file from which to start analysis This process includes extracting scans from SPEC file comparison of different scans applying dead time correction and combining different scans In general one SPEC file contains many scans The following shows a scan header of SPEC file collected at CHESS tL pmQ ereal eli
21. F Ten 0 1d0 N Rate ae ae rae 5 11 Jo FAGIO In Eq 5 12 I corresponds to the data after corrections for background multiple scattering polarization and absorption The theoretical atomic scattering factor is calculated using the ana lytical formula suggested by D Waasmaier amp A Kirfel 2 5 7 Laue Scattering Correction Laue term is defined as f f The Laue scattering occurs when there is no short range order and the atoms are distributed randomly and it decreases monotonically with increasing scattering angle 12 5 8 Pair Distribution Function The atomic Pair Distribution Function PDF G r can be obtained from powder diffraction data through a sine Fourier transform G r 4nr p r p 2 f 0S9 Hsin r do 5 12 CHAPTER 5 DATA CORRECTIONS 39 where p r is the microscopic pair density po is the average number density and Q is the mag nitude of the scattering vector The PDF is a measure of the probability of finding an atom at a distance r from another atom and gives information about both average and the local struc ture of materials For more about PDF analysis method look up the papers by Egami Toby and Billinge 20 21 22 5 9 Error Propagation In most diffraction experiments the measured diffraction intensities are subject to statistical fluc tuations It is known that the detection process is well represented by the Poisson distribution According to Poisson distribution
22. TION e Compton scattering in high Q region is discriminated Apply Compton scattering only in mid low Q region using Ruland method Compton scattering will be modified NO by the Ruland function The parameter determines the shape of Ruland function is called integral width b Enter integral width b initial trial value 0 008 Compton Scattering Correction Mus Compton scattering is not discriminated M Apply Compton scattering correction using theoretical Compton profile Compton scattering in high Q region APPLY COMPTON CORRECTION Y Laue scattering Correction S Q Q lt M Multiple Scattering Correction No P 2 r S Q fluctuat 1 Polarization Correction N m Normalization Yes Q z Quit Refinement incomplete Q S Q dQ dS Figure 4 2 Structure function refinement procedure in PDFgetX 31 CHAPTER 4 USING PDFGETX 32 function refinement process During the refinement process the program asks input if it is neces sary so please beware of the messages on the screen 4 3 History File During data reduction PDFgetX records all the experimental information parameters used for corrections intermediate correction results to a binary file The default file name is _history pdb You can look at
23. User s Manual PDFgetX Version 1 1 Ilkyoung Jeong Jeroen Thompson Thomas Proffen Simon Billinge Department for Physics and Astronomy Michigan State University East Lansing MI 48824 1116 USA Contact billinge 9 pa msu edu Document created January 3 2001 Preface Disclaimer By downloading the program PDFgetX you agree to the terms and conditions concerning its use specified in the license agreement that is provided as part of the distribution End users wishing to make commercial use of the software must contact Libraries Computing amp Technology Michigan State University East Lansing MI 48824 517 353 0722 prior to any commercial distribution to discuss terms The Software is provided to End User by MSU on an as is basis No user support is provided or implied MSU makes no warranty express or implied to end user or to any other person or entity Specifically MSU makes no warranty of merchantability or fitness for a particular purpose of the software MSU will not be liable for special incidental consequential indirect or other similar damages even if MSU or its employees have been advised of the possibility of such damages regardless of the form of the claim Using PDFgetX Publications of results totally or partially obtained using the program PDFgetX should state that PDFgetX was used and contain the following reference JEONG I K THOMPSON J PROFFEN TH PEREZ A AND BILLINGE S J L PDFgetX a p
24. a The X axis should have constant step dX Enter variable name corresponding to X axis 0 TT q Enter minimum Q value 36 Enter number of data points 251 Enter Q step 0 02 Total channel number of MCA 1024 a EADING MCA DATA BE PATIENT SET UP THE INTEGRAING REGIONS OF MCA SPECTRUM Propagate upto four variables Elastic Elastic Compton Auxl and Aux2 CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 19 If the starting and ending channel number of a variable is same the corresponding variable will not be propagated Start of elastic channel 639 Stop of elastic channel 657 Start of elastic compton channel 470 Stop of elastic compton channel 5654 Start of MCA auxiliary channel 1 0 Stop of MCA auxiliary channel 1 0 Start of MCA auxiliary channel 2 0 Stop of MCA auxiliary channel 2 0 read write binary stream _mcachannel In directory home jeong analysis gainas data in50 mcafile Open a binary file to save MCA channel setting CHECK SETTING OF MCA CHANNEL 1 Start of elastic channel 639 Stop of elastic channel 0657 2 Start of elastic compton channel 470 Stop of elastic compton channel 657 3 Start of MCA auxiliary channel 1 0 Stop of MCA auxiliary channel 1 0 4 Start of MCA auxiliary channel 2 0 Stop of MCA auxiliary channel 2 0 Q Exit MCA channel setting Enter to reset channel setting 1 40
25. and the input file the analysis can begin The first stage of the analysis is to produce S Q which is saved as the S Q file However only the S Q file is used in the second stage of the analysis to produce the PDF Note that each stage of the analysis is independent of the others so long as the necessary input files are present That is to recalculate the PDF of a specimen you do not have to start the analysis from input file instead you can specify the correct S Q file and the analysis will immediately create the PDF 27 CHAPTER 4 USING PDFGETX 28 4 1 1 Launching PDFgetX You can start Yorick from any directory by typing yorick at the prompt At the Yorick prompt type pdfgetx and Yorick should begin executing PDFgetX current directory gt yorick Copyright c 1996 The Regents of the University of California All rights reserved Yorick 1 4 ready For help type help gt pdfgetx Then this is what you should see Pair Distribution Function from the X ray powder diffraction PDFgetX 1 1 Preliminary data reduction Build a setup file Background Substraction Reduction of Structure Function S Q Input file format Q I dQ dl 4 PDF calculation Input file format Q S Q dQ dS P Print S Save U Unzoom L Limits windows Q Quit 0 4 hlqpu This is the main menu and Section 4 1 3 will explain the menu in detail 4 1 2 Exiting PDFgetX To quit PDFgetX type q at the main menu prompt
26. attering polarization amp absorption correction Normalized data after all necessary corrections Data corrected for Compton scattering after normalization Coherent scattering data Structure factor Appendix C MCA file format In this appendix the MCA file format used in the data analysis is presented The MCA file format used in this manual is two column ascii file as shown in the following Fig C 1 The correspond MCA spectrum is shown in Fig 3 2 The first column corresponds to the MCA channel number which starts from 0 to 1023 in this case so total MCA channel 1024 And the second column is the intensity detected at each channel Each 1024 lines corresponds to one Q value and separated by the blank line Therefore to convert MCA file to N column ascii file the following information is needed total MCA channel number and the corresponding Q column You can get the Q column from the corresponding scan saved in SPEC file or you can generate Q column if it has constant step In this case you need Q of your scan total number of points in your scan and Q step 44 APPENDIX C MCA FILE FORMAT MCA channel he 600 601 602 603 604 605 1020 1021 1023 he 600 601 602 603 604 605 1020 1021 1023 600 601 602 603 604 605 1020 1021 1023 blank line blank line Intensity o 23 34 15 65 34 22 o o 23 34 15 65 34 22 o oo 23 34 15 65 34 22
27. cattering Therefore it s better to discriminate Comp ton scattering from elastic scattering than to correct it theoretically Compton scattering can be removed experimentally particularly at large scattering angles using an analyzer crystal in the diffracted beam or using a solid state detector with a very narrow energy widow setup When CHAPTER 5 DATA CORRECTIONS Abs Factor tran Abs Factor refl 3 0 N o 1 0 0 0 1 0 gt o a e y e o ut 2 0 1 gt ut 0 3 a v ut y i ut 0 6 at J lt ut 0 8 E out 1 Jae ppbpbbPPE u ao o AM poe pei ES od 858505332442 lt a Mcr BL 2009an a b og 2000p 2 5 tg e OA Boo P09 M L 9o 2000004 out 0 5 0 MORE o ptz 1 e 0 out 2 EN aut 3 ee ut 4 20004 0000064 k 50 100 150 20 37 Figure 5 3 Absorption Factor in transmission geometry upper panel and in reflection geome try lower panel 0 08 5 Q 00 C D 0 00 Elastic scattering Compton scattering Figure 5 4 Comparison between Compton and elastic scattering intensities measured in Ino 33Gao 67 As Above Q 30A the Compton becomes larger than the elastic scattering CHAPTER 5 DATA CORRECTIONS 38 the Compton scattering is not discriminated we have to use theoretical Compton profiles to ap ply correction In this case we have to take into account the Breit Dirac recoil factor R 16 Formerly R was usually set equal to uni
28. e EXAFS gives nearest neighbor and next nearest neighbor distance information PDF analysis method has long been used to characterize glasses liquids and amorphous materials Recently however it has found more application in the study of local structural disorder in crystalline materials where some deviation from the average structure is expected to take place Obtaining total scattering structure function and PDF from raw diffraction data requires many corrections for experimental effects such as absorption polarization corrections and remov ing of Compton and multiple scattering contribution to the elastic scattering Also it needs proper error propagation to be used in modeling of PDF using either PDFFIT real space Rietveld 6 or a Reverse Monte Carlo approach 7 using e g DISCUS 8 to yield structural parameters PDFgetX allows users to do all these data corrections and error propagation in convenient ways During the refinement PDFgetX displays each correction effect to the raw data and saves all the parameters used for refinement This makes the refinement processes easy to understand and al lows reproducible results PDFgetX supports the following data formats multi column ascii file SPEC and multi channel analyzer MCA files To find out about recent updates of PDFgetX or to get further information visit the PDFgetX homepage at the following site http www pa msu edu cmp billinge group programs PDFgetX Chapter 2 Installa
29. e correct value Return to Preliminary data reduction We just obtained combined N column ascii file The next step is to convert it to the PDFgetX input format Q I dQ dI Here Q is the magnitude of scattering vector and defined as Q 47 sin 0 X Lis the intensity of elastic scattering normalized by the monitor dQ and dl are errors in Q and I In this tutorial we ll not preprocess the background data It ll be given as 4 column Q I dQ dD format 1 50 4 Build PDFgetX input file The Input should be N column N gt 2 ascii file All columns should have same number of lines Blanks and commas in columns are not permitted Continue y n y ENTER FILE NAME TO READ in33 tutorial comb Enter number of comment and blank lines in the data header 2 CHECK FILE FORMAT 1 Column contains Q Two theta zal Data in Q or Two theta value u 2 Column contains Intensity S2 3 Column contains Monitor Time zd Normalization by Monitor or Time No Normalization x Exit 1 3X 3 Column contains Monitor Time 3 Normalization by Monitor or Time M T m 1 Column contains Q Two theta 2 Data in Q or Two theta value Q 2 Column contains Intensity r32 3 Column contains Monitor Time 3 Normalization by Monitor or Time Monitor x Exit CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 18 1 3X x SAVE PDFgetX INPUT FILE Q I dQ dI Enter file nam
30. e to for input file in33 tutorial input Return to Preliminary data reduction Now you obtained the input file for the structure function refinement If the X column is 20 then the program converts it to Q 3 1 2 Reduction of Multi Channel Analyzer MCA data The MCA file format could be different depending on the instruments Therefore here we assume an MCA file format which we used in the data reduction process The MCA file format we used is attached in Appendix B In this file the scattered intensity at every Q point is distributed to the whole MCA channels So each block which is separated by blank corresponds to each Q point In order to convert this file to the normal N column ascii file we need to know the following information Minimum Q or two theta number of data points Q two theta step this should be constant total channel number of MCA Many of these information can be obtained using scan summary function which is a part of PDFgetX We will not provide whole MCA file to do the analysis but just one MCA file to show you how it works However we can tell that the structure function obtained using SPEC and MCA data are basically same 1 50 5 Convert MCA file to N column ascii file File should have MCA file format Continue y n y ENTER MCA FILE NAME TO READ in33 tutorial mca Build an X axis column of corresponding MCA data The X axis should be either Q or Two thet
31. erlap with each other quite nicely Maybe it s good to check how the comparison looks like if the dead time correction is not applied Since the normalized elastic scattering from different scans overlap with each other we can combine all of them 1 50 3 Combine N column N gt 2 2 ascii file The Input should have N column ascii file format The X axis column should have constant step dx Combine upto five variables X axis Q Two theta DATA NORM and Auxl Aux2 auxiliary variables Continue y n y ENTER FILE NAMES TO COMBINE TO QUIT READING ENTER Q File name to combine in33_l asc L pmQ ereal elive Epoch Seconds IC1 IC3 I CESR PULSER TOTAL COMPTON IC2 ELASTIC ASSIGN COLUMN NUMBER TO VARIABLES If the column is set to 0 the corresponding variable will not be propagated CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 15 Comparison of Elastic scatterings after dead time correction 0 20 0 10 DTC_Elastic Monitor 0 05 in33_1 asc in33_2 asc in33_3 asc in33_4 asc in33 5 asc 0 00 0 10 20 30 40 Figure 3 1 Comparison of normalized elastic scattering in five scans after dead time correction It shows that the elastic scattering in each scan overlap with each other quite nicely Column corresponding to X axis 1 Column correspo
32. eter elementsname Z compo aw mabscoeff lambda mut ut geometry mscflag mscParam polflag polParam Description Name of sample elements Ex In Ga As Atomic number of sample elements Ex 49 31 33 Composition of sample Ex 0 33 0 67 1 Atomic weight of sample elements Ex 114 82 69 72 74 92 Mass absorption coefficient of sample elements at wavelength A Ex 6 36 1 88 2 23 for A 0 2078 A Wavelength of incident X ray Ex 0 2078 for E 60 KeV X ray radiation Absorption coefficient sample thickness Configuration of diffractometer r Reflection geometry t Transmission geometry O No multiple scattering correction 1 Multiple scattering correction mscflag 1 fpara dsrefl dstran fpara parameters used to approximate scattering in function J Warren amp Mozzi 1996 dsrefl double scattering ratio 12 11 in reflection geometry dstran double scattering ratio 12 11 in transmission geometry 0 NO0 polarization correction 1 Polarization correction polflag 1 pos_mono typ_mono dis_mono deg_pol pf pos_mon Position of Monochromator inc Primary beam Monochromator ref Diffracted beam Monochromator typ_ mono Type of Monochromator pc Perfect crystal monochromator mc Perfect crystal monochromator dis_mono Distance between crystal plane 42 APPENDIX B DESCRIPTION OF THE HISTORY FILE 43 absflag absParam smflag smoothParam compton hiq comptonPara
33. fied Compton by the Ruland function WINDOW 2 R EDUC ED STRUCTUR CHECK IF F Q Is F Q approximately 0 at high Q y n y S Q 1 Q SAVE STRUCTUR Enter fil E FUNCTION Q S Q 1 IS APPROXIMATELY 0 AT HIGH Q E FUNCTION S Q TO ASCII FILE name to save data in33 tutorial soq Now you ve obtained structure function Before we move on let s examine the corrections applied during data reduction First Fig 3 3 a shows all the correction effects on the raw data It shows step by step changes of raw data after each correction In high Q the changes of slope is noticeable Fig 3 3 b shows comparison between normalized data after all correction and total independent scattering TIS We can see that TIS lines up with data in high Q region nicely Finally Fig 3 5 a shows reduced structure function of Ino 33Gao 67As semiconductor The oscillating diffuse scattering is clear in high Q region Table 3 1 shows all the inputs used in the refinement Now let s calculate Pair Distribution Function PDF using the structure function just we obtained CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 0 5 0 4 0 3 0 2 0 1 24 Correction Effects In Ga As Comparison between Data and f 2000 16 0 007 a b 12 0 005 g Mi ee 0 003 1 1
34. getX works in a very general way This section documents the broad overview of PDFgetX while the following sections discuss the specifics at length The function of PDFgetX is to produce PDFs from x ray powder diffraction data whether from an sealed tube x ray source or from a synchrotron source Obviously to begin the analysis one requires the raw data The raw data however is in general too raw for analytical processing not only does every facility has a different data file format but the data file could contain multiple scans that ought to be averaged together PDFgetX can help reduce the raw data into a more convenient format from which to start the analysis but ultimately the responsibility for doing so will lie with the end user The input file from which PDFgetX can start the analysis contains the averaged intensities Please be aware of the possible name confusion that can occur the raw data file refers to the file that is directly output from the computer like SPEC file whereas the input file refers to a input data which will be used for the calculation of structure function S Q Some information regard ing the experiment such as the wavelength used and some information regarding the specimen characteristics such as the stoichiometry are required in order to apply proper correction The experiment and specimen information are contained in a setup file that is required at every step of the analysis With the setup file
35. he following c pdfgetx Second in windows OS users can set the size of font and graphic window in custom i file Therefore it is better to copy the custom i file coming with the Yorick Window version and add the above two lines there than just rename pdfgetx custom i to custom i Finally remember that if the directory name has a space as in My Directory the Yorick couldn t find the directory After configuring the pdfgetx_custom i file if you open the file pdfgetxdistribution i using a text editor you will find the following code asf file Actual PATH ASF DAT periodic table Actual PATH PERIODIC TABLE DAT mabscoeff file Actual PATH MASS ABS COEFF DAT CHAPTER 2 INSTALLATION 9 again give the proper path for the Actual_PATH These code set paths for three important data files Atomic scattering factor Periodic table and Mass absorption coefficient Also the variable name e g asf file should not be changed otherwise PDFgetX couldn t find these data files If you want to print graphs directly from PDFgetX you need to edit the file pdfgetxdistribu tion i and change the following line printer string lpr h Prm31 temp ps Modify the printer string to reflect your system When printing PDFgetX creates a temporary postscript file called _temp ps and makes a system call to print the file Do not change the name of the file in the printer string or p
36. ill not repeat the explanation for the whole process Instead we ll give explanation for the refinement process in detail In order to refine the structure function we need to apply five major corrections dead time multiple scattering polarization absorption and Compton scattering corrections In these correc tions dead time correction will be applied in the preliminary data reduction All other corrections will be applied during structure function refinement The Fig 4 2 shows flow chart of structure CHAPTER 4 USING PDFGETX Refinement of Structure Function Smooth Data using Savitzky amp Golay method Smooth data between Qs to Qmax Need input for Qs Select of points to be used in smoothing Enter one of the following 3 5 7 and 9 SMOOTH DATA Enter degree of polarization of the incident X rays Conventional X rays not polarized gt deg pol 0 Synchrotron X rays almost 100 polarized gt deg pol 2 0 95 1 0 APPLY Pol CORRECTION Input file Q I dQ dI Setup file Transmission or Reflection Geometry TE Does the data contains Compton scattering in high Q region Y N Multiple Scattering Correction 1 ea CORRECTION Polarization Correction APPLY Abs CORRECTION Absorption Correction Normalization using mid high Q part of data Enter normalization constant NORMALIZA
37. m nc R SOQ process date f2ave fave2 compton q data cfbg data cfbgms data cfbgmspf data cfbgmspfabs rn data rn data cfcompt coh data soq Ex Graphite 002 d 3 3570 A Si 111 d 2 3 135 A deg pol Degree of polarization of incident X ray beam Synchrotron source 1 X ray tube 0 pf polarization factor 0 NO0 absorption correction 1 Absorption correction absflag 1 afr aft mut ut aft absorption factor in transmission geometry afr absorption factor in reflection geometry 0 N0 smoothing of data 1 Smoothing using the Savitzky Golay filter smflag 1 q s num ps q s starting point of smoothing num ps number of point used in Savitzky Golay filter Y contain Compton scattering in high Q region of data Nz Compton in high Q is discriminated no Compton in high Q compton hiq N integral width wf integral width control parameter for a width of window function wf Ruland window function normalization constant Breit Dirac Recoil Factor 0 S Q reduction process incomplete no S Q obtained 1 S Q reduction process completed S Q obtained Date of refinement f sample average of square of scattering factor f xs square of sample average of scattering factor Theoretical Compton scattering QT sin 0 X array Data after background correction Data after multiple scattering correction Data after multiple scattering amp polarization correction Data after multiple sc
38. nding to DATA 213 Column corresponding to NORM 12 Column corresponding to Auxl s Column corresponding to Aux2 2 ENTER FILE NAMES File name to ENTER FILE NAMES File name to ENTER FILE NAMES File name to TO COMBINE TO QUIT READING ENTER Q combine in33 2 asc TO COMBINE TO QUIT READING ENTER Q combine in33_5 asc TO COMBINE TO QUIT READING ENTER Q combine q CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 16 READ file in33_l asc Apply DEAD TIME CORRECTION FOR DATA y n y 1 Dead time correction using detector dead time 2 Dead time correction using pulser measurement Q Exit Dead time correction 1 20 2 Enter column containing pulser 9 APPLY DEAD TIME CORRECTION FOR MONITOR y n n CHECK VARIABLE AND ASSIGNED COLUMN X axis Seek DATA 213 Normalization 2 12 AUX1 20 AUX2 20 Detector dead time Correction using pulser Pulser column Be No Monitor dead time Correction CHANNEL SETTINGS ARE CORRECT y n y READ file in33_2 asc READ file in33_5 asc Enter variable name corresponding to X axis Q Enter variable name corresponding to DATA Elastic Enter variable name corresponding to NORM Monitor SAVE COMBINED DATA Enter file name for combined data in33_tutorial comb CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 17 Make sure the X column and combined variables have th
39. oms due to alloying using a closed cycle helium refrigerator mounted on the Huber 6 circle diffractormeter All the signal measured was saved to a file using the system controlling software SPEC The signal measured using the intrinsic Ge solid state detector was processed in two ways Using single channel pulse height analyzer SCA the elastic scattering Compton scattering and elastic Compton scattering were collected separately In the measurements using SCA the proper energy window setting for the elastic scattering is very important because any error in the window setting could cause an unknown contamination to the elastic scattering thus make data corrections very difficult At the same time the signal was fed to multi channel analyzer MCA to record the complete energy spectrum of each value of Q The elastic and Compton scattered radiation could then be separated using software after measurement Collecting data using MCA has advantages and disadvantages In the MCA method since the entire energy spectrum of the scattered radiation is measured at each value of Q the error caused by the mis set of energy window is negligible The main disadvantage of the MCA method is that it has a larger dead time although this can be reliably corrected 9 This tutorial is composed of two subsections Preliminary Data Analysis and Refine struc ture function The Preliminary Data Analysis section is mainly concentrated on how to reduce SPEC and M
40. ou ve finished creating a setup file which contains information about the sample composition and experimental setup You may take a look at the setup file using a text editor and check what you have there Also you can add some more comment using Yorick syntax if you want The final step before starting refinement is to subtract background Because the sample itself affects magnitude of background sometimes instrument background background measured without sample over estimate the real background So in background correction the program allows users can change the magnitude of background by multiplying correction constant in order to make it match data CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 22 more nicely in low Q 0 4 qsulp 2 Enter to Background substraction in Main The Input should be 4 column ascii file Q I dQ dl Continue y n y ENTER DATA FILE NAME TO READ in33 tutorial input EN H ER BACKGROUND FILE NAME TO READ in33 bkg input BACKGROUND SUBTRACTION Multiply correction constant to background to make it match data more nicely in low Q y n n 30 negative intensities set to 0 000208106 negative value are set to minimum intensity ENTER FILE NAME FOR BACKGROUND CORRECTED DATA in33 cfbg input 0 4 qsulp 3 start structure function refinement ENTER SETUP FILE NAME in33 tutorial setup READ INPUT FILE It should be 4 column ascii file Q I dQ
41. r International tables for crystallography volume C Kluwer Aca demic Publishers 1995 B J Thijsse Jour Appl Cryst 17 61 1984 W Ruland Brit J Appl Phys 15 1301 1964 46 BIBLIOGRAPHY 47 20 T Egami Local Structure from Diffraction pages 1 21 Plenum New York 1998 21 B H Toby Acta Cryst A 48 336 1992 22 S Billinge and M F Thorpe editors Local Structure from Diffraction Plenum New York 1998
42. rinting will not work For windows OS Ipr command doesn t work instead use print command This is a DOS command and it seems it sends the graph to a printer connected via LPT1 port If this setting is not working we would recommend windows OS users to use another method to print graphs First save the graph as a postscript PS file or window meta file WMF using S option in the main menu and open it using ghostview PS file or using MS word WMF file Then print the graph using print command in the program 2 2 4 Report problems and suggestions If you have any problems in installing amp running PDFgetX and have any suggestions about the PDFgetX please send email to the following address billinge O pa msu edu http www pa msu edu cmp billinge group programs PDFgetX html Chapter 3 Tutorial Ino 33Gao 67 As Semiconductor Now you might have installed PDFgetX and can start it simply by typing pdfgetx at Yorick prompt In this tutorial you ll get a chance to analyze Ino 33Gao 67 As semiconductor alloy data collected at Cornell High Energy Synchrotron source CHESS using intense x rays of 60 KeV A 0 206 A The tutorial files can be downloaded from the PDFgetX homepage In this experiment the incident x ray energy was selected using a Si 111 double bounce monochromator The data were collected at 10 K to minimize thermal atomic motion in the sample and hence increase the sensitivity to static displacement of at
43. rogram for obtaining the atomic Pair Distribution Function from X ray powder diffraction data Acknowledgments The PDFgetX is coded using Yorick language 1 The atomic scattering factors are calculated using the analytic formula and coefficients developed by D Waasmaier and A Kirfel 2 The mass attenuation coefficient data of elements are obtained from the web at http physics nist gov PhysRefData FFast html form html 3 Financial support from the National Science Foundation through the grants DMR 9700966 DMR 0075149 CHE 9633798 and CHE 9903706 as well as the Center for Fundamental Materi als Research CFMR is gratefully acknowledged Contents 1 Introduction 6 Tels WhatisPDEgetX ca E ue ka a A dd a A A 6 2 Installation 7 2 1 System Requirements les 7 2 2 WhatYouNeed es 7 2 94 YCR o NS o etia e GHENT dr ees ESI ede de Ea 7 2 2 2 1 PDEgetX sous do Ree psa ue pct A 8 2 2 3 Installing and Configuring PDEgetX o o 8 2 2 4 Report problems and suggestions o llle 9 3 Tutorial Ino 33Gag 57As Semiconductor 10 3 1 Preliminary Data Analysis eee 11 3 1 1 Reduction of SPEC file a eae 11 3 1 2 Reduction of Multi Channel Analyzer MCA data 18 3 2 Refine structure function of Inp33Gao67A8 20 4 Using PDFgetX 27 4 1 Overview of PDFgetX les 27 4 11 Launching PDFgetX e e 28 4 1 2 gt
44. s for a given window Enter the window number when prompted 4 2 Data Analysis Procedure in PDFgetX The Fig 4 1 shows flow chart of data analysis procedure in PDFgetX As is shown the analysis procedure is composed of four main blocks Preliminary Data Reduction Build PDFgetX input file Refine Structure Function and PDF Calculation Since most processes in the main PDFgetX Data Analysis Procedure Q Intensity dQ dI gu G FTIQ G Q 1 Yes Multiple Scattering FS n Correction Ej No Fourier transform of reduced structure Extract Scan s F2 from SPEC file Yes Polarization function Q S Q 1 Ha Extract data No Correction a from MCA file Ye m es Absorption No Compare amp Combine Correction Scans cans r G r dr dG Sample information Compton Scattering Sample elements and composition Le Dead time Correction Correction Experimental setup info X ray wavelength Laue Scattering Monochromator info type position d spaceing Absorption coefficient Correction File location Compton scattering Atomic scattering factor Q Elastic Elastic Compton Monitor etc ES Mass absorption coefficient Q SQ dQ dS Figure 4 1 Data analysis procedure in PDFgetX blocks are already explained in the tutorial chapter we w
45. t shows the Ruland function for the integral width b 0 003 0 4 qsulp 4 PDF calculation G r CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR 25 Structure factor In Ga AS PDF In Ga AS 15 4 15 9 t a Pu b st 10 e MN 10 Taj un 420 30 3 3 a Q a Frill 9 5F ali mt ATA LN I NI Vl d T 1 ULL A 0 N AW t APP 0 Im i i ul i Pi T P n j nl i EN v n 5 aul l l 5 i l 0 10 20 30 40 0 5 10 20 Q r Figure 3 5 a Reduced Structure Function of Ing 33Gao s7 As semiconductor The high Q data shows oscillating diffuse scattering b Pair Distribution Function of Ino 33Ga0 57 As semiconduc tor The nearest neighbor peak is split into a doublet corresponding to shorter Ga As and longer In As bonds Table 3 1 Summary of structure function refinement Smoothing Multiple Scattering Yes Correction Compton in high Q region is discriminated Polarization Correction Absorption Correction Normalization Constant 1920 Compton Correction Remove mid low Q Compton intensity using Ruland method Integral width b 0 003 CALCULATE PAIR DISTRIBUTION FUNCTION PDF G r Read structure function 0 S Q dQ dS ENTER FILE NAME in33_tutorial sog Enter Qmax at which to cut the data 40 Read structure function from
46. that applies most of the corrections to the data and produces S Q Those corrections requiring feedback from the user will prompt for the necessary information Option 4 This will access an interactive routine that calculates the PDF from S Q Option P When there is a Yorick window present on your screen you may select this option to print the contents of the window When prompted specify the number of the window this number should be visible in the title bar of the window Yorick 3 would indicate a window number of 3 This option is only available from the main menu which means that printing is not possible while doing the analysis Option S This option save the specified window as postscript PS file or windows meta file WMP in your directory instead of sending figure to printer Option U This UN zooms a window Yorick permits zooming on a data window left button zooms right button UN zooms and middle button drags You may also click on one axis only to zoom or unzoom that axis but sometimes it is difficult to make the window look the way it did before the zooming In that case select this option and when prompted specify the window num ber to unzoom the window Unzooming only returns the window to the state it was in before the CHAPTER 4 USING PDFGETX 30 mouse based zooms manually specified axis limits option L supersede the effects of this option Option L This allows you to manually specify the axis limit
47. the standard deviation of statistical fluctuations is given by YN for the measured N counts This error in measured intensities will be propagated to the error in a function e g PDF determined from these measured intensities The estimated error in PDF will be used to test the quality of modeling In general an error in function f xi x can be calculated by the following Eq ds st OF s of 4 4 s 6 5 13 fex On eres ou 5 13 The error in the Structure function S Q is estimated by propagating error in the measured in tensities through each correction step For the calculation of error in G r the following Eq is used 21 2 Sa x 2 950 Qr AQx sinQkr 5 14 Appendix A SPEC file format In this appendix the SPEC file format used in the data analysis is presented The following shows sample SPEC file F in33 tutorial spec 5 1 ascan pmQ 1 13 600 1 D Fri Sep 18 16 13 55 1998 T 1 Seconds L pmQ ereal elive Epoch Seconds IC1 IC3 I CESR PULSER TOTAL COMPTON IC2 ELASTIC 1 2 07 1 967 75931 2 11758 556914 396634 394 395 416 2866 233 31718 606 02 2 07 1 968 75934 2 11849 558523 396548 394 159 432 3000 217 31791 610 04 2 06 1 962 75936 2 10892 555188 394768 392 324 414 3030 253 31569 591 06 2 07 1 969 75939 2 11886 558933 396616 394 023 417 3138 240 31776 647 08 2 07 1 977 75942 2 1189 559126 396636 393 919 419 2923 246 31839 639 5 2 ascan pmQ 1 13 600 1 D Fri Sep 18 16 40 55 1998 L
48. tion 2 1 System Requirements PDFgetX should run on any UNIX Linux platform supported by Yorick This includes PC Unix and SGI It also run on Windows NT and 95 For a list of systems on which PDFgetX is known to work see Table 2 1 If you successfully install PDFgetX on a system not included in this list please contact us and let us know If you cannot install PDFgetX on a system and have studied the documentation thoroughly please contact us and ask for help Without access to a similarly configured system we may not be able to help you with the installation but see Section 2 2 4 for instructions on how to report your trouble Table 2 1 Known Platforms Supporting PDFgetX Operating System Intel 486 RedHat Linux 6 0 Sa Windows 95 NT DEC ALPHA Digital Unix 2 2 What You Need 2 2 1 Yorick Before you can run PDFgetX you will need to install Yorick PDFgetX is written in the Yorick language which is an interpreted C like language and it s free The distribution of PDFgetX contains only the source code files for PDFgetX it does not come with Yorick The latest version of Yorick can be downloaded from the official site ftp wuarchive wustl edu languages yorick yorick ad html This document provides no information about installing Yorick see the Yorick readme files for help with the installation and checking that the installation was successful Before installing PDFgetX be sure that your installation of Yorick works
49. ty which is still an acceptable approximation for elements of high atomic number For light elements and for present day high precision diffractometric measurement however it is essential that R be numerically evaluated if the maximum amount of information inherent in the experimental data is to be extracted According to Ergun 16 the following Eq 5 10 should be applied when the number of photons per unit area per unit time is measured as with counters x R ooa 5 10 A see t where A and X are the wavelength of incident and Compton scattered beam In this program we use analytical Compton scattering formula 18 to calculate Compton pro file One can compare this results with theoretical Compton scattering data from the International tables for crystallography C 17 and find the difference between these two are very small Even when the Compton scattering in high Q is discriminated the data still contains Compton in mid low Q region In order to remove the Compton in mid low Q region we use the method suggested by Ruland 19 In this method the Compton intensity in the data is smoothly attenuated with increasing Q as is shown in Fig 3 4 c 5 6 Normalization The measured x ray intensity is arbitrary value The intensity should be normalized properly to get physical meaning To determine normalization constant N we use high Q part of data In this method the normalization constant N is defined in the following way one
50. ve Epoch Seconds IC1 IC3 I CESR PULSER TOTAL COMPTON IC2 ELASTIC During the SPEC file reduction process we will use column number to refer to a specific variable such as ELASTIC IC2 PULSER etc so you need to remember which column corresponds to which variable Follow along with this example terminal output It will guide users to learn about how the Reduction of SPEC file works The comments in mark are added just for explanation purpose and will not be shown in the real analysis current directory yorick Copyright c 1996 The Regents of the University of California All rights reserved Yorick 1 4 ready For help type help gt pdfgetx Pair Distribution Function from the X ray powder diffraction PDFgetX 1 1 Preliminary data reduction Build a setup file Background Substraction Reduction of Structure Function S Q Input file format Q I dQ dl 4 PDF calculation G r Input file format 0 S Q dQ dS Print S Save U Unzoom L Limits windows Quit ON LP c oO FU 0 4 qsulp 0 Enter to the Preliminary data reduction level 1 Extract Scan s from SPEC file 2 Compare N column N gt 2 ascii files CHAPTER 3 TUTORIAL INo 33GA0 67 AS SEMICONDUCTOR Combine N column N gt 2 ascii files Build PDFgetX input format Q I dQ dl Convert MCA file to N column ascii file Return to Main O 0 fF CO 1 50 1 12 The Input should be SPEC file format Continue y

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