Results of Augmented Plane Wave Calculations of the Band Structure of Cerium Metal Page: 7 of 16
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
The band structure curves have been obtained for two sizes of the
- lattice constant and for five electronic configurations in each size. "
The complicated energy dependence E(k) was obtained at 256 points in the
Brillouin zone, namely at points (2, 2, 2) of the reciprocal lattice.
Because of the narrowness of the f bands, it was necessary to evaluate
the secular detezminant at energy intervals as small. as 8 x 10-5 Rlydberg"
. or 9 cm 1. The results reported here may be regarded as preliminary
since it was difficult to obtain all 13 eigenvalues (for s, d and f-like
bands) associated with certain low. symmetry or general wave. vectors.
The over-all behavior of the bands as a function of- configuration
is shown in Figs. 3 and 4. For convenience and clarity, only the direc-
tion r to X (along 0) is shown for each graph. The APW method partially
incorporates the effect of the crystal field in lifting the degeneracy
of states having a given angular momentum. For example, the seven f-
. like atomic states (either spin) are separated into a non-degenerate I
SI'2 and the two triply degenerate i5 and 25 states. Similarly, the
5d atomic states are split into the triply degenerate I 5* (tag) and
doubly degenerate r (eg) states. Comparing Fig. 3 for the gamma-phase
size with Fig. 4 for the collapsed or alpha phase, one sees that the
crystal field splitting is larger in the latter case. In addition, one
observes that the band width is larger, presumably because of increased
The pattern of the s and d bands, such as is .typical of a 3d transi-
tion metal, is clearly discernible at the far right-hand Bide of these
figures where it is assumed that no If states are occupied. This premise
is unjustified because the calculations yield low-lying f states. At i
the far left-hand- side, the f bands, which are shown as a cross-hatched
region, interact with the s' and d bands and the result is a more
The notation used is substantially the same as that of Bouckaert,
*Smoluchowski and Wigner21 except that the primed States are designated
by asterisks to facilitate reading of the graphs.
Here’s what’s next.
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Waber, J.T . & Switendick, A. C. Results of Augmented Plane Wave Calculations of the Band Structure of Cerium Metal, report, June 1, 1965; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1034794/m1/7/: accessed May 27, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.