Part 2

Part 1 (Introduction. Crystal Field splitting of the d-type Atomic Orbitals. Taylor's notation)

Energy Plane

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.

Energy Surfaces

The "atomic" orbital energy levels are the planes in the  -space:

The above intersecting planes form the three energy surfaces, so that  

E 10

E 20

E 30



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 E1 and E2 surfaces still touch each other at the point (0, 0) - the pure octahedral case.

g-Tensor Surfaces

All other quantities also form surfaces above the energy plane. In particular, there are three g-value surfaces (gx, gy, gz) for each energy level. For level 3 the g-surfaces are

gz gy gx

 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 gz-surface is symmetrical with respect to the plane V = 0. The gy and gx 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, E0 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)


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©Nikolai Shokhirev, 2002-2003.