Coefficients for scattering factors

The nine coefficients of the four-gaussians approximation for the scattering factors

Usage

sfcoeffs(atom_name)

Arguments

atom_name

A character string. The symbol of the atom whose scattering factor's coefficients are needed (see list of available names in details).

Value

A named list whose three components are vectors and scalars containing the coefficients:

a

Vector of length 4 containing the \(a_j\)

b

Vector of length 4 containing the \(b_j\)

c

Single number, the value of \(c\)

Details

A scattering factor is a function of \(\sigma\equiv\sin(\theta)/\lambda\), which is equal to \(s/2\), with \(s=1/d\) and \(d\) the resolution of the given reflection. The scattering form is satisfactorily modelled as sum of four gaussians: $$ a_1\exp(-b_1 \sigma^2) + a_2\exp(-b_2 \sigma^2) + a_3\exp(-b_3 \sigma^2) + a_4\exp(-b_4 \sigma^2) + c $$ This function returns the coefficients as a named list with three components, \(a=(a_1,a_2,a_3,a_4)\), \(b=(b_1,b_2,b_3,b_4)\) and \(c=c\). The possible atom names (also included are some ionic species) are here summarized.

• H

• H-1

• He

• Li

• Li+1

• Be

• Be+2

• B

• C

• Cv

• N

• O

• O-1

• F

• F-1

• Ne

• Na

• Na+1

• Mg

• Mg+2

• Al

• Al+3

• Si

• Siv

• Si+4

• P

• S

• Cl

• Cl-1

• Ar

• K

• K+1

• Ca

• Ca+2

• Sc

• Sc+3

• Ti

• Ti+2

• Ti+3

• Ti+4

• V

• V+2

• V+3

• V+5

• Cr

• Cr+2

• Cr+3

• Mn

• Mn+2

• Mn+3

• Mn+4

• Fe

• Fe+2

• Fe+3

• Co

• Co+2

• Co+3

• Ni

• Ni+2

• Ni+3

• Cu

• Cu+1

• Cu+2

• Zn

• Zn+2

• Ga

• Ga+3

• Ge

• Ge+4

• As

• Se

• Br

• Br-1

• Kr

• Rb

• Rb+1

• Sr

• Sr+2

• Y

• Y+3

• Zr

• Zr+4

• Nb

• Nb+3

• Nb+5

• Mo

• Mo+3

• Mo+5

• Mo+6

• Tc

• Ru

• Ru+3

• Ru+4

• Rh

• Rh+3

• Rh+4

• Pd

• Pd+2

• Pd+4

• Ag

• Ag+1

• Ag+2

• Cd

• Cd+2

• In

• In+3

• Sn

• Sn+2

• Sn+4

• Sb

• Sb+3

• Sb+5

• Te

• I

• I-1

• Xe

• Cs

• Cs+1

• Ba

• Ba+2

• La

• La+3

• Ce

• Ce+3

• Ce+4

• Pr

• Pr+3

• Pr+4

• Nd

• Nd+3

• Pm

• Pm+3

• Sm

• Sm+3

• Eu

• Eu+2

• Eu+3

• Gd

• Gd+3

• Tb

• Tb+3

• Dy

• Dy+3

• Ho

• Ho+3

• Er

• Er+3

• Tm

• Tm+3

• Yb

• Yb+2

• yb+3

• Lu

• Lu+3

• Hf

• Hf+4

• Ta

• Ta+5

• W

• W+6

• Re

• Os

• Os+4

• Ir

• Ir+3

• Ir+4

• Pt

• Pt+2

• Pt+4

• Au

• Au+1

• Au+3

• Hg

• Hg+1

• hg+2

• Tl

• Tl+1

• Tl+3

• Pb

• Pb+2

• Pb+4

• Bi

• Bi+3

• Bi+5

• Po

• At

• Rn

• Fr

• Ra

• Ra+2

• Ac

• Ac+3

• Th

• Th+4

• Pa

• U

• U+3

• U+4

• U+6

• Np

• Np+3

• Np+4

• Np+6

• Pu

• Pu+3

• Pu+4

• Pu+6

• Am

• Cm

• Bk

• Cf

Examples

# Coefficients for the carbon atom
aname <- "C"
lcoeffs <- sfcoeffs(aname)
print(lcoeffs)
#> $a
#> [1] 2.3100 1.0200 1.5886 0.8650
#> 
#> $b
#> [1] 20.8439 10.2075  0.5687 51.6512
#> 
#> $c
#> [1] 0.2156
#>