CrystalFieldEnergies v1

../_images/CrystalFieldEnergies-v1_dlg.png

CrystalFieldEnergies dialog.

Table of Contents

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.

Description

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))
# 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:
[  0.00000000e+00   4.97379915e-14   2.93261118e+01   2.93261118e+01
   4.43412485e+01   4.43412485e+01]
wave functions:
[[ -6.93889390e-17+0.j  -3.38877312e-01+0.j   6.80756336e-01+0.j
   -6.25169857e-01+0.j   1.74683643e-01+0.j  -1.95256823e-02+0.j]
 [  5.42213428e-01+0.j  -7.97569062e-17+0.j  -2.33045938e-01+0.j
   -2.53767032e-01+0.j   8.51307403e-02+0.j   7.61609638e-01+0.j]
 [  5.55111512e-17+0.j   7.68873700e-01+0.j   1.21082286e-01+0.j
   -1.11195433e-01+0.j   6.14081735e-01+0.j  -6.86404558e-02+0.j]
 [ -7.68873700e-01+0.j   6.77450070e-17+0.j   1.11195433e-01+0.j
    1.21082286e-01+0.j   6.86404558e-02+0.j   6.14081735e-01+0.j]
 [ -5.55111512e-17+0.j  -5.42213428e-01+0.j  -2.53767032e-01+0.j
    2.33045938e-01+0.j   7.61609638e-01+0.j  -8.51307403e-02+0.j]
 [  3.38877312e-01+0.j  -2.36325596e-17+0.j   6.25169857e-01+0.j
    6.80756336e-01+0.j   1.95256823e-02+0.j   1.74683643e-01+0.j]]
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: Algorithms | Inelastic

Source

C++ source: CrystalFieldEnergies.cpp (last modified: 2017-10-03)

C++ header: CrystalFieldEnergies.h (last modified: 2016-07-11)