Perl interface to the waaskirf-kirfel tables
use Xray::Scattering;
Xray::Scattering->load('WaasKirf');
$fnot = Xray::Scattering->get_f($symb, $d);
This module provides a functional interface to the Waasmaier-Kirfel tables of coefficients for calculating the Thomson (kinematical) scattering factors of the elements and common valence states. The coefficients are stored externally in the waaskirf.db database file. The coefficients are for an Aikman expansion, which is of this form:
5 f0 = sum [ ai*exp(-bi*s^2) ] + c i=1
Thus there are 11 coefficients for each of the 211 tabulated element/valence symbols.
\*(C`s\*(C' is \*(C`sin(theta)/lambda\*(C'. \*(C`(lambda*s)/2pi\*(C' is the momentum transfer. \*(C`s\*(C' is simply related to the crystal d-spacing by \*(C`s=1/2d\*(C'.
The reference for these tables is \*(L"New Analytical Scattering Factor Functions for Free Atoms and Ions for Free Atoms and Ions\*(R", D. Waasmaier & A. Kirfel, Acta Cryst. (1995) A51, pp. 416-413. [doi:10.1107/S0108767394013292] These data, computed for neutral atoms and ions, are valid for the full range of sin(theta)/lambda from 0.0 to 6.0 A-1.
The actual data used in the W-K Aikman expansion can be found in a few places on the web. Here is where I obtained the file used with this module: http://ftp.esrf.fr/pub/scisoft/xop/DabaxFiles/f0_WaasKirf.dat
This function calculates the Thomson scattering for a given symbol and d-spacing. The Thomson scattering depends only on the momentum transfer. The d-spacing of the scattering planes is a closely related quantity and is easily calculated from the crystal structure, see Xtal.pm. $symb = "Ce3+"; $fnot = Xray::Scattering->get_f($symb, $d); If the symbol cannot be found in the table, \*(C`get_f\*(C' returns 0. It also returns 0 when $symbol consists of whitespace or is \*(L"null\*(R" or \*(L"nu\*(R". If $symbol is a number or the name of an element, then it assumes you want the Thomson scattering for the neutral element. The absolute value of $d_spacing is used by this function. If you ask for a valence state that is not in the table but for an element whose 0+ state is in the table, this method returns the scattering factor for the 0 valent atom. This returns the 11 element list containing the coefficients for the given symbol. @coefs = Xray::Scattering->get_coefficients($symb) This returns a1,b1,a2,b2,a3,b3,a4,b4,c. If you ask for a valence state that is not in the table but for an element whose 0+ state is in the table, this method returns the coefficients for the 0 valent atom. This is a test of whether a given symbol is tabulated in the Waasmaier-Kirfel table. It returns the symbol itself if found in the table or 0 if it is not in the table. $symb = "Ce3+"; $is_tabulated = Xray::Scattering->has($symb);
The following is a list of symbols for the tabulated elements and valence states. The final two are ways of refering to an empty site (i.e. a null or blank atom).
H H1- He Li Li1+ Be Be2+ B C Cval N O O1- O2- F F1- Ne Na Na1+ Mg Mg2+ Al Al3+ Si Siva Si4+ P S Cl Cl1- Ar K K1+ Ca Ca2+ Sc Sc3+ Ti Ti2+ Ti3+ Ti4+ V V2+ V3+ V5+ Cr Cr2+ Cr3+ Mn Mn2+ Mn3+ Mn4+ Fe Fe2+ Fe3+ Co Co2+ Co3+ Ni Ni2+ Ni3+ Cu Cu1+ Cu2+ Zn Zn2+ Ga Ga3+ Ge Ge4+ As Se Br Br1- Kr Rb Rb1+ Sr Sr2+ Y Zr Zr4+ Nb Nb3+ Nb5+ Mo Mo3+ Mo5+ Mo6+ Tc Ru Ru3+ Ru4+ Rh Rh3+ Rh4+ Pd Pd2+ Pd4+ Ag Ag1+ Ag2+ Cd Cd2+ In In3+ Sn Sn2+ Sn4+ Sb Sb3+ Sb5+ Te I I1- Xe Cs Cs1+ Ba Ba2+ La La3+ Ce Ce3+ Ce4+ Pr Pr3+ Pr4+ Nd Nd3+ Pm Pm3+ Sm Sm3+ Eu Eu2+ Eu3+ Gd Gd3+ Tb Tb3+ Dy Dy3+ Ho Ho3+ Er Er3+ Tm Tm3+ Yb Yb2+ Yb3+ Lu Lu3+ Hf Hf4+ Ta Ta5+ W W6+ Re Os Os4+ Ir Ir3+ Ir4+ Pt Pt2+ Pt4+ Au Au1+ Au3+ Hg Hg1+ Hg2+ Tl Tl1+ Tl3+ Pb Pb2+ Pb4+ Bi Bi3+ Bi5+ Po At Rn Fr Ra Ra2+ Ac Ac3+ Th Th4+ Pa U U3+ U4+ U6+ Np Np3+ Np4+ Np6+ Pu Pu3+ Pu4+ Pu6+ Am Cm Bk Cf ' ' Nu
Bruce Ravel, bravel AT bnl DOT gov http://cars9.uchicago.edu/~ravel/software/exafs/