2. Free electron energies in reduced zone. Consider the free electron energy bands of an fcc crystal lattice in the approximation of an empty lattice, but in the reduced zone scheme in which all k' s are transformed to lie in the first Brillouin zone. Plot roughly in the [111] direction the energies of all bands up to six times the lowest band energy at the zone boundary at k = (27/a)(, i). Let this be the unit of en- ergy. This problem shows why band edges need not necessarily be at the zone cen- ter. Several of the degeneracies (band crossings) will be removed when account is taken of the crystal potential.
2. Free electron energies in reduced zone. Consider the free electron energy bands of an fcc crystal lattice in the approximation of an empty lattice, but in the reduced zone scheme in which all k' s are transformed to lie in the first Brillouin zone. Plot roughly in the [111] direction the energies of all bands up to six times the lowest band energy at the zone boundary at k = (27/a)(, i). Let this be the unit of en- ergy. This problem shows why band edges need not necessarily be at the zone cen- ter. Several of the degeneracies (band crossings) will be removed when account is taken of the crystal potential.
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![2. Free electron energies in reduced zone. Consider the free electron energy bands
of an fcc crystal lattice in the approximation of an empty lattice, but in the reduced
zone scheme in which all k' s are transformed to lie in the first Brillouin zone. Plot
roughly in the [111] direction the energies of all bands up to six times the lowest
band energy at the zone boundary at k = (27/a)(;, i}). Let this be the unit of en-
ergy. This problem shows why band edges need not necessarily be at the zone cen-
ter. Several of the degeneracies (band crossings) will be removed when account is
taken of the crystal potential.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa468fad4-42f8-410f-a8db-24bca579e30e%2F122d7577-8567-4255-bcb4-60021795721c%2F6ckk4kv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Free electron energies in reduced zone. Consider the free electron energy bands
of an fcc crystal lattice in the approximation of an empty lattice, but in the reduced
zone scheme in which all k' s are transformed to lie in the first Brillouin zone. Plot
roughly in the [111] direction the energies of all bands up to six times the lowest
band energy at the zone boundary at k = (27/a)(;, i}). Let this be the unit of en-
ergy. This problem shows why band edges need not necessarily be at the zone cen-
ter. Several of the degeneracies (band crossings) will be removed when account is
taken of the crystal potential.
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