Xray::Scattering::CromerMann(3) Perl interface to Thomspon scattering factors


use Xray::Scattering;
$fnot = Xray::Scattering->get_f($symb, $d);


This module provides a functional interface to the Cromer-Mann table of coefficients for calculating the Thomson (kinematical) scattering factors of the elements and common valence states. The coefficients are stored externally in the cromann.db database file. The coefficients are for an Aikman expansion, which is of this form:

    f0 = sum [ ai*exp(-bi*s^2) ] + c

Thus there are 9 coefficients for each of the 213 tabulated element/valence symbols.

"s" is "sin(theta)/lambda". "(lambda*s)/2pi" is the momentum transfer. "s" is simply related to the crystal d-spacing by "s=1/2d".

The data for these tables can be found in Volume C of the International Tables of Crystallography, ed. A.J.C. Wilson, published by IUCr and Kluwer Academic Publishers (1992). The table starts on page 500 and a discussion can be found on page 487.

These tables are known to be inaccurate, particularly at high angles. This module is a toy. It is suitable for a student or for the sort of quick-n-dirty crystallographic hackery that the author indulges in.


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, "get_f" returns 0. It also returns 0 when $symbol consists of whitespace or is ``null'' or ``nu''. 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 9 element list containing the coefficients for the given symbol.

   @coefs = Xray::Scattering->get_coefficients($elem)

Returns the array 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 Cromer-Mann 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      H.     H1-    He     Li     Li1+   Be
      Be2+   B      C      C.     N      O      O1-
      F      F1-    Ne     Na     Na1+   Mg     Mg2+
      Al     Al3+   Si     Si.    Si4+   S      P
      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      Y3+    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     O2-.   ' '    Nu


  Bruce Ravel, bravel AT bnl DOT gov