Xray::...erMann(3pm)

💖 Xray::Scattering::CromerMann 💖

okay bestie, welcome to the User Contributed Perl Documentation corner of the universe, this is Xray::...erMann(3pm) and she is a whole vibe. pull up a chair, we're doing crystallography 🦋

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✨ NAME ✨

Xray::Scattering::CromerMann — a Perl interface to Thomspon scattering factors 💅

(yes, "Thomspon" is spelled exactly like that in the original and I am not touching it, that's the author's letter arrangement and we respect it 🫶)

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🌸 SYNOPSIS 🌸

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

that's it. that's the whole entry point. three lines and you're scattering, no cap ✨

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💜 DESCRIPTION 💜

so basically this module gives you a functional interface to the Cromer-Mann table of coefficients, and those coefficients are what you use to calculate the Thomson (kinematical) scattering factors of the elements and common valence states. iconic behaviour honestly.

the coefficients do not live inside the module, they're stored externally in the cromann.db database file. very "my stuff is at my other house" of them 💀

these coefficients are for an Aikman expansion, which looks like this:

          4
    f0 = sum [ ai*exp(-bi*s^2) ] + c
         i=1

so that means there are 9 coefficients for each of the 213 tabulated element/valence symbols. nine. per symbol. 213 of them. do the math, that's a lot of little numbers living their best life in a db file 🎀

now, the variables:

• "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. 📚

⚠️ real talk: 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. (the author said that, I'm just the messenger, and honestly? self-aware king 👑)

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🧚 CLASS METHODS 🧚

get_f

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);

now the fine print, and bestie there is a LOT of fine print:

• 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. so it's got your back, kind of, in a "close enough" way 🫶

get_coefficients

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. 🎀

and the same little caveat as before: 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.

has

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);

a vibe check for your atoms, fr fr ✨

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🌈 ELEMENTS AND VALENCE STATES 🌈

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

all 213 of them, sitting there, looking gorgeous, slaying in a seven-wide grid 🌸 and yeah ' ' and Nu are down at the bottom doing their empty-site thing. representation 💅

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👑 AUTHOR 👑

Bruce Ravel, bravel AT bnl DOT gov
http://cars9.uchicago.edu/~ravel/software/exafs/

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and that's the whole page bestie!! this one came to you from perl v5.34.0, dated 2022-06-28, and honestly? iconic. go calculate some scattering factors, you've got this 🦋💖✨🎀