Part 1 (Introduction. Crystal Field splitting of the d-type Atomic Orbitals. Taylor's notation)
The two energy parameters form the energy plane:
Symmetric Energy Plane:
The lines where two energy levels are equal divide the plane into the six sectors. If the scaled parameter V^{*} is used, then the angles between all the adjacent lines are 60 degrees.
The "atomic" orbital energy levels are the planes in the -space:
The above intersecting planes form the three energy surfaces, so that
E_{ 1}^{0} |
E_{ 2}^{0} |
E_{ 3}^{0} |
Animation: |
The spin-orbit interaction splits the above piecewise-plane energy surfaces into the three separate surfaces:
E_{ 1} |
E_{ 2} |
E_{ 3} |
Note that the E_{1} and E_{2} surfaces still touch each other at the point (0, 0) - the pure octahedral case.
All other quantities also form surfaces above the energy plane. In particular, there are three g-value surfaces (g_{x}, g_{y}, g_{z}) for each energy level. For level 3 the g-surfaces are
g_{z} | g_{y} | g_{x} |
The upper cube facets are at g = 4 and the lower ones at g = -4. The three surfaces are actually the same surface rotated by 120°. The g_{z}-surface is symmetrical with respect to the plane V = 0. The g_{y} and g_{x} surfaces are symmetrical with respect to the appropriate planes as well.
For better understanding of the three dimensional surfaces download the program gSurface . It displays g, E^{0} and E .The surfaces can be rotated and viewed from different directions.
Part 3 (Discussion)
Part 4 (Calculations. Programs. References)
Part 5 (Experimental data processing)
Please e-mail me at nikolai@shokhirev.com |
©Nikolai Shokhirev, 2002-2003.