Appendix A: Acronyms of Techniques Related to Surface Science

Appendix A: Acronyms of Techniques Related to Surface Science Acronym AEAPS AES AMEFS APS APAM ARAES ARNPD ARPEFS ARPES ARSES ARUPS ARXPD ARXPS PD DAPS EAPFS EDAX EELS EID ELEED ELNES ELS Meaning Auger-Electron Appearance-Potential Spectroscopy Auger-Electron Spectroscopy Auger-Monitored Extended Fine Structure Appearance-Potential Spectroscopy Atom-Probe Field-Ion Microscopy Angle-Resolved Auger-Electron Spectroscopy Angle-Resolved Normal Photoelectron Diffraction Angle-Resolved Photoelectron Fine Structure Angle-Resolved Photoelectron Spectroscopy Angle-Resolved Secondary-Electron Spectroscopy Angle-Resolved Ultraviolet-Photoelectron Spectroscopy Angle-Resolved X-Ray Photoelectron Diffraction Angle-Resolved X-Ray Photoelectron Spectroscopy ontact-potential Difference (work-function change) Disappearance-Potential Spectroscopy Extended Appearance-Potential Fine Structure Energy Dispersive X-Ray Analysis Electron Energy-Loss Spectroscopy Electron-Impact Desorption Elastic Low-Energy Electron Diffraction Electron-Energy Loss Near-Edge Structure Energy-Loss Spectroscopy

526 Appendix A: Acronyms of Techniques Related to Surface Science EM ESA ESD ESDIAD ESR EXAFS EXELFS FEED FEM FIM HEED HEIS HREELS IISS lets lid ILEED INS IPE lras ISS LEED LEIS LEPD LID LIF MDS MEED MEIS MPI Electron Microscopy Electron Spectroscopy for hemical Analysis Electron-Stimulated Desorption Electron-Stimulated Desorption Ion Angular Distributions Electron-Spin Resonance Extended X-Ray-Absorption Fine Structure Extended Electron-Energy-Loss Fine Structure Field-Emission Energy Distribution Field-Emission Microscopy Field-Ion Microscopy High-Energy Electron Diffraction High-Energy Ion Scattering High-Resolution Electron Energy-Loss Spectroscopy Impact-ollision lon-scattering Spectroscopy Inelastic Electron Tunneling Spectroscopy lon-impact Desorption Inelastic Low-Energy Electron Diffraction lon-neutralization Spectroscopy Inverse Photoemission Infrared Reflection-Absorption Spectroscopy lon-scattering Spectroscopy Low-Energy Electron Diffraction Low-Energy Ion Scattering Low-Energy Positron Diffraction Laser-Induced Desorption Laser-Induced Fluorescence Metastable Deexcitation Spectroscopy Medium-Energy Electron Diffraction Medium-Energy Ion Scattering Multi-Photon Ionization

Appendix A: Acronyms of Techniques Related to Surface Science 527 NEXAFS NIS NMA NMR NPD OPD PED PES PhD PIES PLEED PSD PSDIAD RBS RHEED SAES SEE SEELFS SEM SERS SEXAFS SIMS SPI SPIES SPLEED SSIMS STEM STM SXAPS SXPS Near-Edge X-Ray-Absorption Fine Structure Neutron Inelastic Scattering Nuclear Microanalysis Nuclear Magnetic Resonance Normal.Photoelectron Diffraction Off-Normal Photoelectron Diffraction Photoelectron Diffraction Photoelectron Spectroscopy Photoelectron Diffraction Penning Ionization Electron Spectroscopy Polarized Low-Energy Electron Diffraction Photon-Stirn ulated Desorption Photon-Stimulated Desorption Ion Angular Distributions Rutherford Backscattering Spectroscopy Reflection High-Energy Electron Diffraction Scanning Auger-Electron Spectroscopy Secondary-Electron Emission Surface" Extended-Energy-Loss Fine Structure Scanning Electron Microscopy Surface-Enhanced Raman Scattering Surface Extended X-Ray-Absorption Fine Structure Secondary-Ion Mass Spectroscopy Surface Penning Ionization Surface Penning Ionization Electron Spectroscopy Spin-Polarized Low-Energy Electron Diffraction Static Secondary-Ion Mass Spectroscopy Scanning Transmission Electron Microscopy Scanning Tunneling Microscopy Soft X-Ray Appearance-Potential Spectroscopy Soft X-Ray Photoelectron Spectroscopy

528 TDMS TDS TED TEM THEED TPD TPR UPS VLEED XAES XANES XPD XPS XRD Appendix A: Acronyms of Techniques Related to Surface Science Thermal-Desorption Mass Spectroscopy Thermal-Desorption Spectroscopy Transmission Electron Diffraction Transmission Electron Microscopy Transmission High-Energy Electron Diffraction Temperature-Programmed Desorption Temperature-Programmed Reaction Ultraviolet-Photoelectron Spectroscopy Very-Low-Energy Electron Diffraction X-Ray-Stimulated Auger-Electron Spectroscopy X-Ray-Absorption Near-Edge Structure X-Ray Photoelectron Diffraction X-Ray Photoelectron Spectroscopy X-Ray Diffraction

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED Two of the geometrical parameters that are necessary to specify a LEED I-V curve are the incidence angle 9 (the angle of the incident beam with respect to the surface normal) and the azimuthal angle <p (the angle between an arbitrarily chosen axis in the surface plane and the projection of the incident beam direction on the surface). These angles can be obtained from photographs of the LEED pattern, as described in Sect. 2.6. This inyolves a computation for which a program is presented in this Appendix. The program reproduced below can be run without any additional auxiliary subroutines. It is written in standard Fortran language. An example of the input data can be found following the program listing. It should be noted that a pair of initially guessed values for 9 and <p is needed for the input data, and the solutions are weakly dependent on these initially guessed values. The output data can be found following the listing of the input data. The first part of the output data is a more detailed listing of the input data. The second part is the results (for brevity, a middle section of the second part has been omitted). Spot combinations for which 09 or o<p exceeds the allowable maximum errors are omitted in the calculation for the averaged values of 9 and <p, see Sect. 2.6.3. The regular and weighted averages (Sect. 2.6.3) are computed and listed at the end. Variables whose values the user may wish to change are (see the first group of executable statements) ITUM = allowed number of iterations, TUM = limit of accuracy, TERR = the maximum allowable error in determining the value of 9 due to the uncertainty in measuring the position of the spot, PERR = the maximum allowable error in determining the value of <p due to the uncertainty in measuring the position of the spot.

530 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED PROGRAM ANGLE(INPUT,OUTPUT,TAPE5=INPUT,TAPE6=OUTPUT) PROGRAM ANGLE PURPOSE= TO USE LEED PHOTOGRAPH ANGLE MEASUREMENTS TO DETERMINE THE ANGLE OF INIDENE OF THE ELETRON BEAM DIMENSION HEAD(20),Al(2),A2(2),Bl(2),B2(2),GX(2),GY(2),ANG(2) DIMENSION BH(15),BK(15),EPS(15),THETA(105),PHI(105),ERAn(15) DIMENSION X(2),D(2),F(2),P(2,2) DIMENSION ERl(5),ER2(5) DIMENSION DTH(105),DPH(105),ETH(4),EPH(4) DIMENSION NOMIT(50,2) OMMON AK,GX,GY,ANG DATA ER1/0.0,1.0,-1.0,-1.0,1.0/ DATA ER2/0.0,-1.0,1.0,-1.0,1.0/ FORMAT STATEMENTS 101 FORMAT(20A4) 102 FORMAT(2FB.3) 104 FORMAT(I3) 105 FORMAT(2F5.l,F10.l) 111 FORMAT(BOX,*IT=*,I2,5X,*F =*,2EI0.2,5X,*D =*,2F6.2) 112 FORMAT(20X,I3,2I10,2F15.2) 113 FORMAT(lHl,10X,20A4) 114 FORMAT(/,10X,*A1 =*,2FB.4,/,10X,*A2 =*,2FB.4) 115 FORMAT(/,10X,*BEAM ENERGY =*,F6.1,* EV*,/,10X, 1 *INITIAL ANGLE GUESS= THETA =*,F6.1,/,31X,*PHI -*,F6.1) 116 FORMAT(//,10X,*INPUT DATA, I*,BX,*BH*,BX,*BK*,9X,*EPS*,/) 117 FORMAT(24X,I2,2FI0.l,F12.1) lib FORMAT(//,10X,*RESULTS*,/,20X,*IND*,5X,*SPOTl*,5X, 1 *SPOT2*,10X,*THETA*,11X,*PHI*,/) 119 FORMAT(26X,2FI0.0,F12.2,F15.2) 120 FORMAT(4BX,2F15.3) 121 FORMAT(/,10X,*REGULAR AVERAGE*,5X,*THETA =*,F6.2,* +/-*,F6.3, 1 l04,*phi =*,F7.2,* +/-*,F6.3) 122 FORMAT(/,10X,*WEIGHTED AVERAGE*,4X,*THETA =*,F6.2,* +/-*,F6.3, 1 10X,*PHI =*,F7.2,* +/-*,F6.3) 123 FORMAT(//,10X,*SUMMARY*,/,10X,20A4,/,10X,*NUMBER OF SPOTS -*, 1 I3,/,10X,*NUMBER OF OMBS. =*,13) 124 FORMAT(2X,14H**** OMIT ****) 125 FORMAT(10X,*NUMBER OF OMITS =*,I3,/,12X,*OMITTED OMBS. -*, 1 2I3,49(/,2BX,2I3» ONSTANTS RAn=I. 745329E-2 PI=3.1415926 ONS=0.512329B ITLIM=10 TLIM=1.0E-6 TLIM=1.0E-5 TERR=2.5 PERR=4.0 IF(ERl(2).GT.l.l) TERR=4.0 IF(ER2(3).GT.l.l) PERR=6.0 READ EVERYTHING HEAD = HEADING ARD USED TO LABEL THE DATA AND OUTPUT (20A4) Al,A2 = TWO-DIMENSIONAL SURFAE UNIT ELL VETORS IN ANGSTROMS FORMAT OF EAH IS (2FB.3)

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 531 ENERG ENERGY OF THE INIDENT ELETRON RELATIVE TO VAUUM IN ELETRON VOLTS (FB.3) THl,PHl - INITIAL GUESS OF INIDENT ANGLE THETA AND PHI IN DEGREES GUESS SHOULD BE FAIRLY LOSE (2FB.3) NDAT - NUMBER OF DATA POINTS READ (I3) BH(I),BK(I) - (H,K) VALUES FOR THE I-TH DATA POINT EPS(I) - ANGLE EPSILON IN DEGREES FOR I-TH DATA POINT FORMAT FOR DATA POINT IS (2F5.l,FlO.l) READ(5,101) HEAD READ(5,102) Al READ(5,102) A2 READ(5,102) ENERG READ(5,102) THl,PHl READ(5,104) NDAT WRITE(6,113) HEAD WRITE(6,114) Al,A2 WRITE(6,115) ENERG,THl,PHl WRITE ( 6,116) 00 10 I-l,NDAT READ(5,105) BH(I),BK(I),EPS(I) WRITE(6,117) I,BH(I),BK(I),EPS(I) 10 ERAD(I)-EPS(I)*RAD WRITE ( 6,118) ALULATE REIPROAL LATTIE VETORS AND K VETOR MAGNITUDE TVA=ABS(Al(1)*A2(2)-Al(2)*A2(1» ATV-2.0*PI/TVA Bl(l)- A2(2)*ATV Bl(2)--A2(1)*ATV B2(2)- Al(l)*ATV B2(1)--Al(2)*ATV AK-ONS * SQRT (ENERG) LOOPOVER OMBINATlON OF TWO SPOTS IND-O NER=O IL-NDAT-l 00 55 I-I,lL JS-I+l 00 55 J=JS,NDAT IND-IND+l LOOP ON ERRORS IN ANG 00 50 IERR=1,5 ASSIGN ANGLE FROM PHOTO AND DETERMINE REIPROAL VETORS X(l)=THl*RAD X(2)=PHl*RAD ANG(l)=ERAD(I) + ERl(IERR)*RAD GX(1)=BH(I)*Bl(1)+BK(I)*B2(1) GY(1)=BH(I)*Bl(2)+BK(I)*B2(2) ANG(2)=ERAD(J) + ER2(IERR)*RAD GX(2)=BH(J)*Bl(1)+BK(J)*B2(1) GY(2)-BH(J)*Bl(2)+BK(J)*B2(2)

532 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED NEWTONS METHOD LOOP IT=O GO TO 20 15 IT=IT+l IF(ABS(D(1».GT.0.17) D(1)=SIGN(0.17,D(1» IF(ABS(D(2».GT.0.17) D(2)=SIGN(0.17,D(2» X(l)=X(l)+D(l) X(2)=X(2)+D(2) IF(IT.GT.ITLIM) GO TO 25 20 ALL FN(X,F,P) PJB=P(1,1)*P(2,2)-P(1,2)*P(2,1) IF(PJB.EQ.O.O) GO TO 30 D(1)=(P(1,2)*F(2)-P(2,2)*F(1»/PJB D(2)=(P(2,1)*F(1)-P(1,1)*F(2»/PJB TST-D(I)**2+D(2)**2 IF(TST.LT.TLIM) GO TO 35 GO TO 15 25 D1=D(1)/RAD D2-D(2)/RAD WRITE(6,111) IT,F,D1,D2 IND=IND-l NER=NER+1 NOMIT(NER,l)=I NOMIT(NER,2)=J WRITE(6,124) GO TO 55 30 D(1)=1.0E-2 D(2)--1.0E-2 GO TO 15 35 ONTINUE STORE RESULTS TH=X(l)/RAD PH=X(2)/RAD IF(IERR.NE.1) GO TO 45 THETA(IND)=TH PHI(IND)=PH WRITE(6,112) IND,I,J,TH,PH GO TO 50 45 WRITE(6,119) ER1(IERR),ER2(IERR),TH,PH IEX=IERR-1 ETH(IEX)=ABS(TH-THETA(IND» EPH(IEX)=ABS(PH-PHI(IND» 50 ONTINUE DTH(IND)=AMAX1(ETH(1),ETH(2),ETH(3),ETH(4),0.1) DPH(IND)=AMAX1(EPH(1),EPH(2),EPH(3),EPH(4),O.1) WRITE(6,120) DTH(IND),DPH(IND) IF(DTH(IND).GT.TERR) GO TO 52 IF(DPH(IND).GT.PERR) GO TO 52 GO TO 55 52 ONTINUE IND=IND-1 NER=NER+1 NOMIT(NER,l)=I NOMIT(NER,2)=J WRITE(6,124) 55 ONTINUE

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 533 ALULATE AVERAGES AND STANDARD DEVIATIONS TAVE=O.O PAVE=O.O TWAV=O.O PWAV=O.O TSIG=O.O PSIG=O.O TWT=O.O PWT=O.O DO 60 I=l,IND TAVE=TAVP.+THETA(I) W1=DTH(I)**2 TWT-TWT+ 1. O/W1 TWAV-TWAV+THETA(I)/W1 PAVE-PAVE+PHI(I) W2=DPH(I)**2 PWT=PWT+l. O/W2 PWAV-PWAV+PHI(I)/W2 60 ONTINUE TAVE=TAVE/FLOAT(IND) PAVE=PAVE/FLOAT(IND) TWAV=TWAV/TWT PWAV-PWAV/PWT DO 65 I=l,IND TSIG=TSIG+(THETA(I)-TAVE) **2 PSIG=PSIG+(PHI(I)-PAVE) **2 65 ONTINUE TSIG=SQRT(TSIG/FLOAT(IND» PSIG=SQRT(PSIG/FLOAT(IND» TWIG=SQRT(l.O/TWT) PWIG=SQRT(l.O/PWT) WRITE(6,123) HEAD,NDAT,IND WRITE(6,125) NER,«NOMIT(I,1),NOMIT(I,2»,I=1,NER) WRITE(6,121) TAVE,TSIG,PAVE,PSIG WRITE(6,122) TWAV,TWIG,PWAV,PWIG STOP END SUBROUTINE FN(X,F,P) THIS SUBROUTINE EVALUATES THE FUNTION F(THETA,PHI,BH,BK) FOR TWO HOIES OF THE INDEX PAIR (BH,BK). ALSO OBTAINED AND STORED IN P ARE THE PARTIAL DERIVATIVES OF F WITH RESPET OT THETA AND PHI. REAL KIX,KIY,KFX,KFY,KDUM,KFZ,KLFX,KLFY DIMENSION X(2),F(2),P(2,2),GX(2),GY(2),EPS(2) OMMON AK,GX,GY,EPS ST=SIN(X(l» SP=SIN(X(2» T=OS(X(l» P=OS(X(2»

534 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED INITIAL K IN RYSTAL FRAME KIX-ST*P*AK KIY=ST*SP*AK DERIVATIVES OF FINAL K IN RYSTAL FRAME DKFXT -T*P*AK DKFXP--ST*SP*AK DKFYT- T*SP*AK DKFYP- ST*P*AK LOOP FOR THE TWO EVALUATIONS OF THE SAME EQUATION DO 50 1=1,2 FINAL K IN RYSTAL FRAME KFX-KIX + GX(I) KFY=KIY + GY(I) KDUM-AK**2 - KFX**2 - KFY**2 KFZ=-SQRT(ABS(KDUM» DKFZT - -(KFX*DKFXT + KFY*DKFYT)/KFZ DKFZP = -(KFX*DKFXP + KFY*DKFYP)!KFZ FINAL K AND DERIVATIVES IN LAB FRAME KLFX=-SP*KFX+P*KFY KLFY=-T*P*KFX-T*SP*KFY+ST*KFZ DKLFXT=-SP*DKFXT+P*DKFYT DKLFXP=-SP*DKFXP+P*DKFYP-P'*KFX-SP*KFY DKLFYT=ST*P*KFX+ST*SP*KFY+T*KFZ 1 -T*P*DKFXT-T*SP*DKFYT+ST*DKFZT DKLFYP=T*SP*KFX-T*P*KFY 1 -T*P*DKFXP-T*SP*DKFYP+ST*DKFZP ASSIGN FUNTION AND DERIVATIVES TEP=TAN(EPS(I» F(I)=KLFX+TEP*KLFY P(I,l)=DKLFXT+TEP*DKLFYT P(I,2)=DKLFXP+TEP*DKLFYP 50 ONTINUE RETURN END

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 535 Input data: IRIDIUM(lll) SPOT POSITIONS 2.710 1.355 2.347 245.0 10.0-90.0 13 1.0 0.0 24.0 1.0 1.0 46.0 0.0 1.0 0.0-1.0 0.0-46.0-1.0-1.0-26.0 0.0-1.0-1.0 2.0 1.0 55.0 2.0 2.0 83.0 2.0 3.0 115.0 1.0 2.0 100.0 1.0 3.0 145.0-2.0 1.0-116.0-2.0-1.0-56.0 Al A2 ENERG TH1,PH1 NDAT Output data: IRIDIUM(lll) SPOT POSITIONS Al - 2.7100-0. A2-1.3550 2.3470 BEAM ENERGY - 245.0 EV INITIAL ANGLE GUESS= THETA - 10.0 PHI - -90.0 INPUT DATA, I BH BK 1 2 3 4 5 6 7 8 9 10 11 12 13 1.0 1.0 O. -1.0-1.0 O. 2.0 2.0 2.0 1.0 1.0-2.0-2.0 O. 1.0 1.0 O. -1.0-1.0 1.0 2.0 3.0 2.0 3.0 1.0-1.0 EPS 24.0 46.0 O. -46.0-26.0-1.0 55.0 83.0 115.0 100.0 145.0-116.0-56.0 RESULTS IND SPOT1 SPOT2 THETA PHI 1 2 3 1 1. -1. -1. 1. 1 1. -1. -1. 1. 1 1. -1. -1. 1. 2-1. 1. -1. 1. 3-1. 1. -1. 1. 4-1. 1. -1. 1. 12.80 13.38 12.09 13.00 12.62.705 15.61 14.72 16.53 17.19 14.32 1.580 13.47 13.12 13.81 13.28 13.65.346-83.45-87.19-79.55-81.43-85.43 3.898-90.00-90.53-89.29-90.78-89.51.776-84.96-86.55-83.27-82.14-87.85 2.892

536 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED **** OMIT **** **** OMIT **** **** OMIT **** **** OMIT **** **** OMIT **** 4 1 5 14.50-87.38 1. -1. 13.40-87.56-1. 1. 15.60-87.22-1. -1. 14.48-84.76 1. 1. 14.51-90.00 1.108 2.624 5 1 6 14.64-87.69 1. -1. 12.69-85.65-1. 1. 16.85-90.00-1. -1. 14.76-85.36 1. 1. 14.51-90.00 2.213 2.332 6 1 7-4.24-43.79 1. -1. 9.40-77.54-1. I. -7.30-35.83 -I. -I. -3.44-45.07 I. I. -5.38-41.39 13.643 33.742 6 1 8 3.80-62.72 I. -I. 9.61-78.03-1. I. -3.16-45.73-1. -I. 2.93-59.58 I. I. 4.91-66.85 6.953 16.995 6 1 10 11.49-80.26 1. -I. 12.63-85.34-1. I. 9.99-74.87-1. -I. 10.85-76.80 1. 1. 12.01-83.78 1.503 5.387 6 1 11 18.60-97.36 1. -I. 15.35-92.13-1. I. 22.48-103.47-1. -I. 22.07-102.41 1. I. 16.24-94.42 3.875 6.111 6 1 12 14.27-86.82 1. -I. 13.55-87.62-1. 1. 15.00-85.90-1. -I. 14.65-85.12 1. I. 13.90-88.48.738 1.698 7 1 13 14.01-86.21 1. -I. 13.20-87.04-1. I. 14.78-85.41-1. -I. 14.15-84.02 1. 1. 13.73-88.48.802 2.271 8 2 3 13.19-90.00 I. -I. 12.92-90.35-1. 1. 13.46-89.60-1. -I. 13.51-90.41 1. I. 12.88-89.66.321.408 9 2 4 13.19-90.00 I. -I. 12.90-90.00 -I. I. 13.49-90.00-1. -I. 13.20-84 :66 I. I. 13.20-95.34.298 5.338

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 537 **** OMIT **** 9 2 5 13.22-90.47 1. -1. 12.85-89.13-1. 1. 13.65-92.15-1. -1. 13.36-87.68 1. 1. 13.12-93.45.432 2.976 10 2 6 13.06-87.79 1. -'1: 12.63-85.66-1. 1. 13.49-90.00-1. -1. 13.23-85.56 1. 1. 12.90-90.00.430 2.237 11 2 7 13.18-89.81 1. -l. 12.71-86.54-1. l. 13.65-92.81-1. -1. 13.48-88.78 1. 1. 12.94-90.63.469 3.266 12 2 8 13.29-91. 65 1. -1. 12.83-88.82-1. l. 13.75-94.65-1. -1. 13.63-91. 74 1. 1. 13.02-91.81.461 2.999 13 2 9 13.24-90.01 1. -1. 12.78-88.11-1. 1. 13.63-91. 73-1. -l. 13.54-89.84 1. 1. 12.91-90.05.456 1. 899 14 2 10 13.19-89.21 1. -1. 12.61-85.25-1. 1. 13.68-92.76-1. -l. 13.57-90.49 1. 1. 12.82-88.05.582 3.959 15 2 11 13.16-89.56 1. -1. 12.81-88.46-1. 1. 13.59-90.81-1. -1. 13.52-89.51 1. 1. 12.89-89.82.424 1. 246 16 2 12 13.19-89.24 1. -1. 12.85-89.24-1. 1. 13.51-89.37-1. -1. 13.43-87.90 1. 1. 12.95-90.69.341 1.448 17 2 13 13.12-88.82 1. -1. 12.80-88.30-1. l. 13.45-89.35-1. -1. 13.30-86.74 1. l. 12.96-90.87.331 2.082 18 3 4 13.19-90.00 1. -l. 12.92-89.65-1. 1. 13.46-90.AO -1. -1. 12.88-90.34 1. 1. 13.51-89.59.321.408 19 3 5 13.39-90.00 1. -1. 12.66-89.68-1. l. 14.32-90.49-1. -l. 12.44-90.30 1. 1. 14.72-89.47 1.334.528

538 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED **** OMIT **** 20 3 6-9.48-90.00 l. -l. -24.16-92.90 -l. l. 9.61-90.00-1. -l. -3.29-88.67 l. 1. 9.61-90.00 19.089 2.899 20 3 7 13.24-90.00 1. -1. 13.62-89.58 -l. l. 12.85-90.34 -l. -l. 13.90-90.45 l. l. 12.63-89.68.663.449 21 3 8 12.83-90.00 l. -l. 13.05-89.64 -l. l. 12.59-90.31 -l. -l. 13.26-90.38 l. l. 12.42-89.71.428.381 22 3 9 13.27-90.00 1. -l. 13.47-89.60 -l. l. 13.05-90.36-1. -l. 13.86-90.44 l. l. 12.73-89.67.587.444 23 3 10 13.33-90.00 l. -l. 13.41-89.60 -l. l. 13.25-90.38 -l. -l. 13.56-90.41 l. l. 13.11-89.63.225.413 24 3 11 13.50-90.00 l. -l. 13.63-89.58 -l. l. 13.33-90.39 -l. -l. 14.30-90.49 1. l. 12.77-89.67.805.490 25 3 12 12.88-90.00 l. -l. 12.64-89.68 -l. l. 13.10-90.36 -l. -l. 12.35-90.29 l. l. 13.46-89.60.577.402 26 3 13 12.74-90.00 l. -l. 12.34-89.72 -l. l. 13.12-90.37 -l. -l. 12.16-90.27 l. l. 13.37-89.61.632.393 27 4 5 13.19-9 0. 8 ~ l. -l. 13.68-87.03 -l. l. 12.62-94.57 -l. -l. 13.00-88.93 l. l. 13.38-92.81.573 3.832 28 4 6 13.32-87.77 l. -l. 13.75-85.47 -l. l. 12.90-90.00-1. -l. 13.18-85.57 l. l. 13.49-90.00.422 2.302

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 539 29 4 7 13.20-89.87 1. -1. 13.59-89.12-1. 1. 12.88-90.43-1. -1. 13.07-87.59 1. 1. 13.38-91.97.394 2.276 30 4 8 13.13-91.07 1. -1. 13.43-91.01-1. 1. 12.83-91.15-1. -1. 12.95-89.26 1. 1. 13.36-93.13.304 2.067 31 4 9 13.20-89.85 1. -1. 13.55-89.87-1. 1. 12.90-90.04-1. -1:. 12.99-88.57 1. 1. 13.47-91.37.355 1.520 32 4 10 13.26-89.59 1. -1. 13.53-90.26-1. I. 12.97-88.88-1. -1. 13.05-87.59 1. I. 13.46-91. 53.289 1.994 33 4 11 13.21-89.63 1. -1. 13.52-89.43-1. 1. 12.91-89.85-1. -1. 12.98-88.70 1. 1. 13.46-90.55.308.925 34 4 12 13.29-89.03 1. -1. 13.67-87.35-1. 1. 12.85-90.91-1. -1. 13.01-88.82 1. 1. 13.59-89.20.446 1.877 35 4 13 13.29-88.29 1. -1. 13.75-85.35-1. 1. 12.82-91.29-1. -1. 13.06-87.48 1. 1. 13.54-89.08.472 3.008 36 5 6 14.21-87.70 1. -1. 16.41-85.12-1. 1. 12.54-90.00-1. -1. 14.15-85.40 1. 1. 14.51-90.00 2.203 2.573 37 5 7 13.31-90.21 1. -1. 14.17-90.86-1. 1. 12.64-89.72-1. -1. 13.17-88.20 1. I. 13.47-92.25.858 2.035 38 5 8 13.07-90.88 1. -1. 13.70-92.01-1. 1. 12.52-90.06-1. -1. 12.88-89.03 1. 1. 13.32-92.97.631 2.094 39 5 9 13.39-90.34 1. -1. 14.08-91.08-1. 1. 12.69-89.59-1. -1. 13.02-88.63 1. 1. 13.73-91.95.700 1. 712

540 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED **** OMIT **** **** OMIT *'*** 40 5 10 13.39-90.33 1. -1. 13.79-91. 79-1. 1. 12.96-88.81-1. -1. 13.17-88.22 1. 1. 13.59-92.29.435 2.105 41 5 11 13.49-90.08 1. -1. 14.28-90.59-1. 1. 12.69-89.57-1. -1. 12.99-88.71 1. 1. 13.98-91. 33.795 1.361 42 5 12 17.76-78.14 1. -1. 24.67-55.62-1. 1. 10.29-96.26-1. -1. 13.17-88.47 1. 1. 24.51-56.70 7.478 22.518 42 5 13 -.02-124.06 1. -1. -7.88-145.14-1. 1. 17.12-76.38-1. -1. 6.18-106.94 1. 1. -.01-125.04 17.144 47.681 42 6 7 12.54-87.84 l. -l. 13.76-90.00-1. l. 11.40-85.87-1. -l. 12.36-85.70 1. l. 12.74-90.00 1. 219 2.162 43 6 8 12.23-87.86 1. -l. 13.15-90.00-1. 1. 11.35-85.88-1. -1. 11.99-85.77 1. 1. 12.51-90.00 44 6 9.918 2.136 12.27-87.86 1. -1. 13.65-90.00-1. l. -1. -l. 11.73-85.81 10.95-85.95 1. l. 12.88-90.00 1. 383 2.139 45 6 10 12.93-87.80 1. -l. 13.49-90.00-1. l. 12.37-85.70-1. -1. 12.70-85.65 1. l. 13.18-90.00.558 2.195 46 6 11 11.90-87.89 1. -l. 13.94-90.00-1. l. 9.99-86.11-1. -l. 10.95-85.95 1. l. 13.03-90.00 2.043 2.107 47 6 12 13.97-87.72 1. -l. 12.48-90.00 -l. 1. 15.26-85.28 -l. -1. 14.53-85.39 l. l. 13.27-90.00 48 6 13 1.482 13.46 2.433-87.76 1. -1. 12.24-90.00-1. l. 14.77-85.30-1. -1. 13.71-85.48 1. 1. 13.24-90.00 1.304 2.464

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 541 **** OMIT **** **** OMIT **** **** OMIT **** **** OMIT **** **** OMIT **** 49 7 8 10.31-81.37 1. -I. 14.74-96.18-1. 1..02-54.03-1. -1. 9.71-78.35 1. I. 11.00-84.64 10.285 27.343 49 7 9 13.61-90.85 1. -1. 10.55-83.25-1. I. 16.49-98.51-1. -I. 14.74-92.63 1. I. 12.67-89.60 3.068 7.660 49 7 10 13.34-90.01 1. -I. 14.24-94.54-1. I. 12.28-85.31-1. -I. 13.03-87.47 1. 1. 13.66-92.68 1.063 4.706 49 7 11 13.25-89.75 1. -I. 11. 79-87.08-1. 1. 14.58-92.15-1. -1. 13.91-90.06 1. I. 12.66-89.58 1.463 2.672 50 7 12 13.09-89.55 1. -1. 12.64-89.69-1. 1. 13.61-89.16-1. -1. 13.29-88.21 1. 1. 12.95-90.67.512 1.339 51 7 13 12.99-89.22 1. -1. 12.49-89.24-1. I. 13.50-89.2b- -1. -1. 13.00-87.67 1. 1. 12.99-90.78.511 1.556 52 8 9 12.18-87.68 1. -I. 10.70-83.59-1. 1. 13.63-91. 73-1. -I. 12.48-87.47 1. 1. 11. 96-88.08 1.481 4.090 52 8 10 14.32-95.36 1. -1. 15.04-100.13-1. 1. 13.20-90.10-1. -1. 14.11-93.48 1. 1. 14.46-97.61 1.117 5.253 52 8 11 12.44-88.61 I. -1. 11.62-86.85-1. 1. 13.22-90.24-1. -1. 12.68-88.29 1. 1. 12.21-88.96.823 1.764 53 8 12 12.85-90.07 1. -1. 12.50-89.97-1. 1. 13.20-90.16-1. -1. 12.91-89.12 1. I. 12.79-91.02.349.949 54 8 13 12.79-89.85 1. -1. 12.38-89.57-1. I. 13.19-90.15-1. -1. 12.74-88.49 1. 1. 12.85-91.21.407 1.364

542 Appendix B: A omputer Program to Determine the Angle of Incidence in LEED **** OMIT **** 55 9 10 13.38-90.23 1. -1. 13.87-92.28-1. 1. 12.86-88.27-1. -1. 13.38-89.41 1. 1. 13.38-91.06.519 2.053 56 9 11 12.90-89.22 1. -l. 10.94-85.93-1. 1. 14.54-91. 93-1. -1. 13.17-88.95 1. 1. 12.65-89.51 1.959 3.288 57 9 12 13.08-89.59 1. -1. 12.68-89.59-1. 1. 13.46-89.59-1. -1. 13.08-88.76 1. 1. 13.08-90.41.392.824 58 9 13 12.95-89.33 1. -1. 12.50-89.20-1. 1. 13.41-89.48-1. -1. 12.83-88.21 1. 1. 13.09-90.45.456 -- 1.123 59 10 11 13.28-89.:'72 1. -1. 12.92-88.62-1. 1. 13.62-90.76-1. -1. 13.34-89.18 1. 1. 13.23-90.26.360 1.102 60 10 12 13.21-89.31 1. -1. 12.99-88.96-1. 1. 13.43-89.67-1. -1. 13.21-88.49 1. 1. 13.21-90.13.221.820 61 10 13 13.12-88.82 1. -1. 12.84-88.17-1. -1. 1. -1. 13.43 13.04-89.70-87.54 1. 1. 13.24-90.29 62 11 12.316 13.12 1.468-89.50 1. -1. 12.69-89.57-1. -1. 1. -1. 13.53 13.06-89.44-88.81 1. 1. 13.18-90.19.425.694 63 11 13 12.96-89.30 1. -1. 12.47-89.29-1. 1. 13.45-89.34-1. -1. 12.76-88.40 1. 1. 13.18-90.19 64 12 13.491 12.67.898-90.40 1. -1. 9.92-97.15-1. -1. 1. -1. 15.39 11.87-83.41-91. 26 1. 1. 13.61-89.15 2.747 6.992

Appendix B: A omputer Program to Determine the Angle of Incidence in LEED 543 SUMMARY IRIDIUM(III) SPOT POSITIONS NUMBER OF SPOTS - 13 NUMBER OF OMBS. - 63 NUMBER OF OMITS - 15 OMITTED OMBS. - 1 7 1 8 1 9 1 10 III 2 4 3 6 5 12 5 13 7 8 7 9 7 10 8 9 8 10 12 13 REGULAR AVERAGE WEIGHTED AVERAGE THETA = 13.24 +/-.553 THETA = 13.18 +/-.058 PHI -89.13 +/- PHI - -89.81 +/-

List of Major Symbols lebsch-gordan or Gaunt coefficients -*-* al,a2 bj,b2 b ~, b ; l(l'm',l"m") E f F g hfl),h}2) h = 21tn h I I Substrate basis vectors Reciprocal substrate basis vectors Superlattice basis vectors Reciprocal superlattice basis vectors lebsch-gordan or Gaunt coefficients Kinetic energy in vacuum Atomic scattering amplitude Fourier transform Green's function Two-dimensional reciprocal lattice vector Hankel functions of the 1 st and 2nd kinds Planck's constant Miller index, as in (hk) beam or (hkl) plane Intensity Unit matrix Imaginary unit:.j=t Miller-Bravais index, as in (hkil) JI J Bessel function Adatom-adatom interaction Boltzmann constant Miller index, see h Wave number k = Ikl Electron wavevector

546 List of Major Symbols ki... fo-f; i(s... fout = ki k; [ [ [max m m,m M M = [mll ml21 m21 m22 M*... [ mil mi21 m21 m22 Wave vector incident from vacuum Wave vecter emergent into vacuum Wave vector of beam g± Miller index, see h Angular momentum utoff angular momentum in partial-wave expansion Mass of electron Order parameter Mass of atom or molecule Exponent in Debye-Waller factor Matrix notation for superlattices Matrix notation for reciprocal superlattices Layer diffraction matrix element Linear momentum Patterson function Legendre polynomials Plane-wave propagators General position vector Layer reflection matrix element Momentum transfer S t ±± g'g Structure factor Layer transmission matrix element Reduced temperature t-matrix for single atom t-matrix element for single atom Temperature ritical temperature

List of Major Symbols 547 z a v t cp t-matrix for a layer consisting of several Bravais-lattice planes of atoms Inner potential or muffin-tin zero level (>0) oordinates parallel (II) to the surface Spherical harmonic function oordinate perpendicular (.L) to the surface (pointing into the surface) Layer-to-Iayer electron attenuation coefficient ritical exponent Island size Phase shift Polar angle of incidence or emergence Fractional surface coverage Debye temperature Effective Debye temperature Frequency ritical exponent t-matrix for a Bravais-lattice plane of atoms Azimuthal angle of incidence or emergence Work function i-th neighbor adatom-adatom interaction energy (i = 1,2,... )

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