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CrystalFieldEnergies v1¶

Summary ¶

Calculates crystal field energies and wave functions for rare earth ions given the field parameters.

Properties ¶

Name	Direction	Type	Default	Description
Nre	Input	number	1	A rare earth ion. Possible values are: 1=Ce 2=Pr 3=Nd 4=Pm 5=Sm 6=Eu 7=Gd 8=Tb 9=Dy 10=Ho 11=Er 12=Tm 13=Yb, or negative values for arbitrary J with J=-nre/2 up to nre=-99 (J=99/2)
BmolX	Input	number	0	The x-component of the molecular field.
BmolY	Input	number	0	The y-component of the molecular field.
BmolZ	Input	number	0	The z-component of the molecular field.
BextX	Input	number	0	The x-component of the external field.
BextY	Input	number	0	The y-component of the external field.
BextZ	Input	number	0	The z-component of the external field.
B20	Input	number	0	Real part of the B20 field parameter.
B21	Input	number	0	Real part of the B21 field parameter.
B22	Input	number	0	Real part of the B22 field parameter.
B40	Input	number	0	Real part of the B40 field parameter.
B41	Input	number	0	Real part of the B41 field parameter.
B42	Input	number	0	Real part of the B42 field parameter.
B43	Input	number	0	Real part of the B43 field parameter.
B44	Input	number	0	Real part of the B44 field parameter.
B60	Input	number	0	Real part of the B60 field parameter.
B61	Input	number	0	Real part of the B61 field parameter.
B62	Input	number	0	Real part of the B62 field parameter.
B63	Input	number	0	Real part of the B63 field parameter.
B64	Input	number	0	Real part of the B64 field parameter.
B65	Input	number	0	Real part of the B65 field parameter.
B66	Input	number	0	Real part of the B66 field parameter.
IB20	Input	number	0	Imaginary part of the B20 field parameter.
IB21	Input	number	0	Imaginary part of the B21 field parameter.
IB22	Input	number	0	Imaginary part of the B22 field parameter.
IB40	Input	number	0	Imaginary part of the B40 field parameter.
IB41	Input	number	0	Imaginary part of the B41 field parameter.
IB42	Input	number	0	Imaginary part of the B42 field parameter.
IB43	Input	number	0	Imaginary part of the B43 field parameter.
IB44	Input	number	0	Imaginary part of the B44 field parameter.
IB60	Input	number	0	Imaginary part of the B60 field parameter.
IB61	Input	number	0	Imaginary part of the B61 field parameter.
IB62	Input	number	0	Imaginary part of the B62 field parameter.
IB63	Input	number	0	Imaginary part of the B63 field parameter.
IB64	Input	number	0	Imaginary part of the B64 field parameter.
IB65	Input	number	0	Imaginary part of the B65 field parameter.
IB66	Input	number	0	Imaginary part of the B66 field parameter.
Energies	Output	dbl list		The energies starting at 0 in ascending order.
Eigenvectors	Output	dbl list		The eigenvectors.
Hamiltonian	Output	dbl list		The Hamiltonian.

This algorithm is not for general use. Its purpose is to expose to python the crystal field calculations implemented in C++. The algorithm calculates the crystal field energies and wave functions. The example shows how it can be used from python:

from CrystalField.energies import energies

# The first parameter is a code for the rare earth ion
# The rest of the parameters define the crystal field
en, wf, ham = energies(1,  B20=0.37737, B22=3.9770, B40=-0.031787, B42=-0.11611, B44=-0.12544)

# a list of crystal field energies
print('energies:\n{}'.format(en[2:]))
# a complex-valued matrix with wave functions
print('wave functions:\n{}'.format(wf))
# a complex-valued matrix with the Hamiltonian
print('Hamiltonian:\n{}'.format(ham))

  energies:
  [ 29.32611185  29.32611185  44.3412485   44.3412485 ]
  wave functions:
  [[ ...  ...   ...
     ...  ...   ...]
   [ ...  ...   ...
     ...  ...   ...]
   [ ...  ...   ...
     ...  ...   ...]
   [ ...  ...   ...
     ...  ...   ...]
   [ ...  ...   ...
     ...  ...   ...]
   [ ...  ...   ...
     ...  ...   ...]]
  Hamiltonian:
  [[  1.86648000+0.j   0.00000000+0.j   9.27182972+0.j   0.00000000+0.j
     -3.36590841+0.j   0.00000000+0.j]
   [  0.00000000+0.j   4.96692000+0.j   0.00000000+0.j  19.33604706+0.j
      0.00000000+0.j  -3.36590841+0.j]
   [  9.27182972+0.j   0.00000000+0.j  -6.83340000+0.j   0.00000000+0.j
     19.33604706+0.j   0.00000000+0.j]
   [  0.00000000+0.j  19.33604706+0.j   0.00000000+0.j  -6.83340000+0.j
      0.00000000+0.j   9.27182972+0.j]
   [ -3.36590841+0.j   0.00000000+0.j  19.33604706+0.j   0.00000000+0.j
      4.96692000+0.j   0.00000000+0.j]
   [  0.00000000+0.j  -3.36590841+0.j   0.00000000+0.j   9.27182972+0.j
      0.00000000+0.j   1.86648000+0.j]]

Please note that this area is under active development and any name can be changed in the future.

Categories: AlgorithmIndex | Inelastic