Node in chi(k) envelope for a single shell
Dear List, I have noticed in several fits that Artemis -- i.e., feff -- reports for a SINGLE shell (with absorber = scatterer = Hg, edge = L3) an almost-node in the envelope of chi(k) around 6 inverse angstroms. See the image at http://pjm.math.berkeley.edu/users/levy/files/HgNode.gif and the FEFF output after my signature. I've done my best to account for this behavior, but I simply don't have a physical intuition for why the F(k) factor should dip to zero or almost zero. Note that this is not a beat caused by two similar frequencies being added; the Fourier transform does of course show two peaks -- which is how my curiosity was aroused -- but the example figure comes from a SINGLE path, with 12 identical scatterers all at the same distance from the absorber. Looking forward to your two cents... Silvio Metacinnabar from CSDWeb, HgS Niculescu et al. 1970 Feff 6L.02 potph 4.12 Abs Z=80 Rmt= 1.327 Rnm= 1.667 LIII shell Pot 1 Z=16 Rmt= 1.218 Rnm= 1.515 Pot 2 Z=80 Rmt= 1.310 Rnm= 1.624 Gam_ch=5.000E+00 H-L exch Mu=-2.727E+00 kf=1.809E+00 Vint=-1.519E+01 Rs_int= 2.005 Path 2 icalc 2 Feff 6L.02 genfmt 1.4\4 ------------------------------------------------------------------------------\- 2 12.000 4.1366 2.9707 -2.72701 nleg, deg, reff, rnrmav(bohr), edge x y z pot at# 0.0000 0.0000 0.0000 0 80 Hg absorbing atom 0.0000 -2.9250 -2.9250 2 80 Hg k real[2*phc] mag[feff] phase[feff] red factor lambda real[p]@# 0.000 5.8876E+00 0.0000E+00 -5.3100E+00 0.1085E+01 5.5410E+00 1.8179E+00 0.200 5.8828E+00 6.5887E-02 -6.9020E+00 0.1085E+01 5.5726E+00 1.8284E+00 0.400 5.8685E+00 1.3063E-01 -8.3679E+00 0.1084E+01 5.6628E+00 1.8594E+00 0.600 5.8452E+00 1.9388E-01 -9.7059E+00 0.1082E+01 5.7987E+00 1.9101E+00 0.800 5.8135E+00 2.5592E-01 -1.0913E+01 0.1079E+01 5.9607E+00 1.9793E+00 1.000 5.7742E+00 3.1673E-01 -1.1989E+01 0.1077E+01 6.1257E+00 2.0656E+00 1.200 5.7279E+00 3.7510E-01 -1.2932E+01 0.1075E+01 6.2715E+00 2.1679E+00 1.400 5.6750E+00 4.2855E-01 -1.3742E+01 0.1074E+01 6.3832E+00 2.2854E+00 1.600 5.6157E+00 4.7354E-01 -1.4416E+01 0.1075E+01 6.4589E+00 2.4174E+00 1.800 5.5491E+00 5.0618E-01 -1.4949E+01 0.1076E+01 6.5142E+00 2.5639E+00 2.000 5.4733E+00 5.2301E-01 -1.5329E+01 0.1077E+01 6.5837E+00 2.7250E+00 2.200 5.3844E+00 5.2240E-01 -1.5543E+01 0.1078E+01 6.7192E+00 2.9013E+00 2.400 5.2972E+00 5.4699E-01 -1.5605E+01 0.1190E+01 4.9983E+00 3.0942E+00 2.600 5.3179E+00 5.7289E-01 -1.5987E+01 0.1239E+01 4.3905E+00 3.2252E+00 2.800 5.3348E+00 5.8762E-01 -1.6217E+01 0.1258E+01 4.1537E+00 3.3638E+00 3.000 5.3246E+00 5.9586E-01 -1.6383E+01 0.1257E+01 4.0743E+00 3.5096E+00 3.200 5.3065E+00 6.1650E-01 -1.6474E+01 0.1250E+01 4.0802E+00 3.6618E+00 3.400 5.2733E+00 6.3374E-01 -1.6567E+01 0.1239E+01 4.1398E+00 3.8197E+00 3.600 5.2309E+00 6.4470E-01 -1.6663E+01 0.1226E+01 4.2364E+00 3.9827E+00 3.800 5.1752E+00 6.3603E-01 -1.6766E+01 0.1212E+01 4.3604E+00 4.1501E+00 4.000 5.1090E+00 6.0562E-01 -1.6883E+01 0.1198E+01 4.5058E+00 4.3214E+00 4.200 5.0331E+00 5.5941E-01 -1.6984E+01 0.1183E+01 4.6683E+00 4.4959E+00 4.400 4.9489E+00 4.9872E-01 -1.7115E+01 0.1168E+01 4.8452E+00 4.6734E+00 4.600 4.8588E+00 4.2625E-01 -1.7230E+01 0.1154E+01 5.0343E+00 4.8533E+00 4.800 4.7653E+00 3.5048E-01 -1.7327E+01 0.1139E+01 5.2341E+00 5.0355E+00 5.000 4.6691E+00 2.7395E-01 -1.7453E+01 0.1125E+01 5.4434E+00 5.2195E+00 5.200 4.5722E+00 1.9793E-01 -1.7590E+01 0.1110E+01 5.6610E+00 5.4051E+00 5.400 4.4760E+00 1.3243E-01 -1.7866E+01 0.1096E+01 5.8864E+00 5.5922E+00 5.600 4.3817E+00 8.0754E-02 -1.8387E+01 0.1083E+01 6.1187E+00 5.7805E+00 5.800 4.2890E+00 7.7722E-02 -1.9408E+01 0.1070E+01 6.3576E+00 5.9699E+00 6.000 4.1996E+00 1.2225E-01 -1.9952E+01 0.1058E+01 6.6024E+00 6.1603E+00 6.500 3.9822E+00 2.6906E-01 -2.0350E+01 0.1031E+01 7.2385E+00 6.6398E+00 7.000 3.7681E+00 3.8170E-01 -2.0473E+01 0.1010E+01 7.9052E+00 7.1233E+00 7.500 3.5495E+00 4.3899E-01 -2.0529E+01 0.9919E+00 8.5988E+00 7.6098E+00 8.000 3.3245E+00 4.4840E-01 -2.0549E+01 0.9763E+00 9.3169E+00 8.0987E+00 8.500 3.1062E+00 4.3705E-01 -2.0526E+01 0.9613E+00 1.0057E+01 8.5893E+00 9.000 2.8953E+00 4.1495E-01 -2.0476E+01 0.9480E+00 1.0818E+01 9.0814E+00 9.500 2.6939E+00 3.9247E-01 -2.0391E+01 0.9367E+00 1.1598E+01 9.5746E+00 10.000 2.4999E+00 3.7170E-01 -2.0271E+01 0.9291E+00 1.2396E+01 1.0069E+01 11.000 2.1169E+00 3.6890E-01 -1.9990E+01 0.9196E+00 1.4041E+01 1.1059E+01 12.000 1.7611E+00 4.1306E-01 -1.9816E+01 0.9119E+00 1.5747E+01 1.2052E+01 13.000 1.4328E+00 4.6749E-01 -1.9744E+01 0.9072E+00 1.7507E+01 1.3046E+01 14.000 1.1169E+00 5.1022E-01 -1.9760E+01 0.9054E+00 1.9317E+01 1.4041E+01 15.000 8.2534E-01 5.3666E-01 -1.9821E+01 0.9032E+00 2.1172E+01 1.5037E+01 16.000 5.5314E-01 5.4489E-01 -1.9903E+01 0.9025E+00 2.3070E+01 1.6034E+01 17.000 2.9163E-01 5.3763E-01 -2.0012E+01 0.9015E+00 2.5007E+01 1.7031E+01 18.000 4.7223E-02 5.2008E-01 -2.0124E+01 0.8986E+00 2.6981E+01 1.8029E+01 19.000 -1.8906E-01 4.9327E-01 -2.0255E+01 0.8968E+00 2.8989E+01 1.9027E+01 20.000 -4.1335E-01 4.6035E-01 -2.0384E+01 0.8947E+00 3.1029E+01 2.0025E+01
Dear Silvio, I was not able to view the image, but what you are describing seems like the Ramsauer-Townsend effect (Phys Rev B, 1988, V38, 10919–10921). As far as I understand it, the physical interpretation is that the at the energy of the dip, the potential well of the scattering atom has cross- section that is very close to the wavelength of the photoelectron. Consequently, the photoelectron is not scattered back to the absorbing atom efficiently at this energy. Perhaps someone in the list can explain this more clearly (or correctly). Sincerely, Wayne Lukens On Nov 5, 2006, at 4:38 AM, levy@msri.org wrote:
Dear List,
I have noticed in several fits that Artemis -- i.e., feff -- reports for a SINGLE shell (with absorber = scatterer = Hg, edge = L3) an almost-node in the envelope of chi(k) around 6 inverse angstroms. See the image at
http://pjm.math.berkeley.edu/users/levy/files/HgNode.gif
and the FEFF output after my signature.
I've done my best to account for this behavior, but I simply don't have a physical intuition for why the F(k) factor should dip to zero or almost zero. Note that this is not a beat caused by two similar frequencies being added; the Fourier transform does of course show two peaks -- which is how my curiosity was aroused -- but the example figure comes from a SINGLE path, with 12 identical scatterers all at the same distance from the absorber.
Looking forward to your two cents...
Silvio
Metacinnabar from CSDWeb, HgS Niculescu et al. 1970 Feff 6L.02 potph 4.12 Abs Z=80 Rmt= 1.327 Rnm= 1.667 LIII shell Pot 1 Z=16 Rmt= 1.218 Rnm= 1.515 Pot 2 Z=80 Rmt= 1.310 Rnm= 1.624 Gam_ch=5.000E+00 H-L exch Mu=-2.727E+00 kf=1.809E+00 Vint=-1.519E+01 Rs_int= 2.005 Path 2 icalc 2 Feff 6L.02 genfmt 1.4\4
----------------------------------------------------------------------- -------\- 2 12.000 4.1366 2.9707 -2.72701 nleg, deg, reff, rnrmav(bohr), edge x y z pot at# 0.0000 0.0000 0.0000 0 80 Hg absorbing atom 0.0000 -2.9250 -2.9250 2 80 Hg k real[2*phc] mag[feff] phase[feff] red factor lambda real[p]@# 0.000 5.8876E+00 0.0000E+00 -5.3100E+00 0.1085E+01 5.5410E+00 1.8179E+00 0.200 5.8828E+00 6.5887E-02 -6.9020E+00 0.1085E+01 5.5726E+00 1.8284E+00 0.400 5.8685E+00 1.3063E-01 -8.3679E+00 0.1084E+01 5.6628E+00 1.8594E+00 0.600 5.8452E+00 1.9388E-01 -9.7059E+00 0.1082E+01 5.7987E+00 1.9101E+00 0.800 5.8135E+00 2.5592E-01 -1.0913E+01 0.1079E+01 5.9607E+00 1.9793E+00 1.000 5.7742E+00 3.1673E-01 -1.1989E+01 0.1077E+01 6.1257E+00 2.0656E+00 1.200 5.7279E+00 3.7510E-01 -1.2932E+01 0.1075E+01 6.2715E+00 2.1679E+00 1.400 5.6750E+00 4.2855E-01 -1.3742E+01 0.1074E+01 6.3832E+00 2.2854E+00 1.600 5.6157E+00 4.7354E-01 -1.4416E+01 0.1075E+01 6.4589E+00 2.4174E+00 1.800 5.5491E+00 5.0618E-01 -1.4949E+01 0.1076E+01 6.5142E+00 2.5639E+00 2.000 5.4733E+00 5.2301E-01 -1.5329E+01 0.1077E+01 6.5837E+00 2.7250E+00 2.200 5.3844E+00 5.2240E-01 -1.5543E+01 0.1078E+01 6.7192E+00 2.9013E+00 2.400 5.2972E+00 5.4699E-01 -1.5605E+01 0.1190E+01 4.9983E+00 3.0942E+00 2.600 5.3179E+00 5.7289E-01 -1.5987E+01 0.1239E+01 4.3905E+00 3.2252E+00 2.800 5.3348E+00 5.8762E-01 -1.6217E+01 0.1258E+01 4.1537E+00 3.3638E+00 3.000 5.3246E+00 5.9586E-01 -1.6383E+01 0.1257E+01 4.0743E+00 3.5096E+00 3.200 5.3065E+00 6.1650E-01 -1.6474E+01 0.1250E+01 4.0802E+00 3.6618E+00 3.400 5.2733E+00 6.3374E-01 -1.6567E+01 0.1239E+01 4.1398E+00 3.8197E+00 3.600 5.2309E+00 6.4470E-01 -1.6663E+01 0.1226E+01 4.2364E+00 3.9827E+00 3.800 5.1752E+00 6.3603E-01 -1.6766E+01 0.1212E+01 4.3604E+00 4.1501E+00 4.000 5.1090E+00 6.0562E-01 -1.6883E+01 0.1198E+01 4.5058E+00 4.3214E+00 4.200 5.0331E+00 5.5941E-01 -1.6984E+01 0.1183E+01 4.6683E+00 4.4959E+00 4.400 4.9489E+00 4.9872E-01 -1.7115E+01 0.1168E+01 4.8452E+00 4.6734E+00 4.600 4.8588E+00 4.2625E-01 -1.7230E+01 0.1154E+01 5.0343E+00 4.8533E+00 4.800 4.7653E+00 3.5048E-01 -1.7327E+01 0.1139E+01 5.2341E+00 5.0355E+00 5.000 4.6691E+00 2.7395E-01 -1.7453E+01 0.1125E+01 5.4434E+00 5.2195E+00 5.200 4.5722E+00 1.9793E-01 -1.7590E+01 0.1110E+01 5.6610E+00 5.4051E+00 5.400 4.4760E+00 1.3243E-01 -1.7866E+01 0.1096E+01 5.8864E+00 5.5922E+00 5.600 4.3817E+00 8.0754E-02 -1.8387E+01 0.1083E+01 6.1187E+00 5.7805E+00 5.800 4.2890E+00 7.7722E-02 -1.9408E+01 0.1070E+01 6.3576E+00 5.9699E+00 6.000 4.1996E+00 1.2225E-01 -1.9952E+01 0.1058E+01 6.6024E+00 6.1603E+00 6.500 3.9822E+00 2.6906E-01 -2.0350E+01 0.1031E+01 7.2385E+00 6.6398E+00 7.000 3.7681E+00 3.8170E-01 -2.0473E+01 0.1010E+01 7.9052E+00 7.1233E+00 7.500 3.5495E+00 4.3899E-01 -2.0529E+01 0.9919E+00 8.5988E+00 7.6098E+00 8.000 3.3245E+00 4.4840E-01 -2.0549E+01 0.9763E+00 9.3169E+00 8.0987E+00 8.500 3.1062E+00 4.3705E-01 -2.0526E+01 0.9613E+00 1.0057E+01 8.5893E+00 9.000 2.8953E+00 4.1495E-01 -2.0476E+01 0.9480E+00 1.0818E+01 9.0814E+00 9.500 2.6939E+00 3.9247E-01 -2.0391E+01 0.9367E+00 1.1598E+01 9.5746E+00 10.000 2.4999E+00 3.7170E-01 -2.0271E+01 0.9291E+00 1.2396E+01 1.0069E+01 11.000 2.1169E+00 3.6890E-01 -1.9990E+01 0.9196E+00 1.4041E+01 1.1059E+01 12.000 1.7611E+00 4.1306E-01 -1.9816E+01 0.9119E+00 1.5747E+01 1.2052E+01 13.000 1.4328E+00 4.6749E-01 -1.9744E+01 0.9072E+00 1.7507E+01 1.3046E+01 14.000 1.1169E+00 5.1022E-01 -1.9760E+01 0.9054E+00 1.9317E+01 1.4041E+01 15.000 8.2534E-01 5.3666E-01 -1.9821E+01 0.9032E+00 2.1172E+01 1.5037E+01 16.000 5.5314E-01 5.4489E-01 -1.9903E+01 0.9025E+00 2.3070E+01 1.6034E+01 17.000 2.9163E-01 5.3763E-01 -2.0012E+01 0.9015E+00 2.5007E+01 1.7031E+01 18.000 4.7223E-02 5.2008E-01 -2.0124E+01 0.8986E+00 2.6981E+01 1.8029E+01 19.000 -1.8906E-01 4.9327E-01 -2.0255E+01 0.8968E+00 2.8989E+01 1.9027E+01 20.000 -4.1335E-01 4.6035E-01 -2.0384E+01 0.8947E+00 3.1029E+01 2.0025E+01
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Dear Silvio, Wayne, Yes, what Silvio is seeing is a 'perfectly normal' minimum in backscattering amplitude for scattering from heavy atoms. It actually shows up for many elements with Z>35, but at such low k-value that it is lost in the XANES features, and is really only noticeable in EXAFS for Z>40 or so. It is definitely visible in Ag (Z=47), and for Z>60, it is very strong, with the minimum in scattering at ~5 to 6 Ang^-1. This often gives rise to a 'double peak' in |chi(R)| even thought there is really only one shell. This effect is a function of Z for the *backscatter* -- not the absorbing atom. So it will show up for metallic Hg, but not in the first shell for the Hg edge of HgS. As Wayne said, this is normally called a Ramsauer-Townsend resonance, though that term was originally about electron scattering from noble gases. See http://en.wikipedia.org/wiki/Ramsauer-Townsend_effect for a little more information. The way I think about this is that when the outgoing photoelectron has a wavelength near 1 Ang (ie, k ~=6 Ang^-1), it may be able to "tunnel through" the very deep, very small scattering potential from a very heavy element. This will only happen at a fairly distinct wavelength, and so gives a 'resonant dip in scattering'. Hope that helps, --Matt
On Sunday 05 November 2006 06:38, levy@msri.org wrote:
Dear List,
I have noticed in several fits that Artemis -- i.e., feff -- reports for a SINGLE shell (with absorber = scatterer = Hg, edge = L3) an almost-node in the envelope of chi(k) around 6 inverse angstroms. See the image at
http://pjm.math.berkeley.edu/users/levy/files/HgNode.gif
and the FEFF output after my signature.
I've done my best to account for this behavior, but I simply don't have a physical intuition for why the F(k) factor should dip to zero or almost zero. Note that this is not a beat caused by two similar frequencies being added; the Fourier transform does of course show two peaks -- which is how my curiosity was aroused -- but the example figure comes from a SINGLE path, with 12 identical scatterers all at the same distance from the absorber.
Looking forward to your two cents...
Silvio, Look at figures 6 and 8 in the Rehr-Albers Rev. Mod. Phys review of XAS theory: Reviews of Modern Physics, Vol. 72, No. 3, July 2000 Figure 8 clearly shows the same phenomenon in real data. Figure 6 shows the reason for it. At some value of k, there is a minimum in the scattering amplitude. Multiplying an F(k) with that shape by a pure sine wave will have a similar effect as the interference between two sine waves with wavelengths such that they beat at the minimum of F(k). This is one of the many reasons that chi(R) is not a radial distribution function. So why is there a minimum in F(k)? Well, the simple, fairly naive explanation is that the wavelength at that energy is well matched to the size of the scatterer and the photoelectron tunnels right through. You'll find that most heavy backscatterers display this behavior. HTH, B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
participants (4)
-
Bruce Ravel -
levy＠msri.org -
Matt Newville -
Wayne Lukens