By Arthur S. Nowick
This publication offers with the influence of crystal symmetry in settling on the tensor houses of crystals. even though it is a well-established topic, the writer offers a brand new technique utilizing workforce conception and, specifically, the strategy of symmetry coordinates, which has no longer been utilized in any past publication. the writer offers functions to technologically very important phenomena as various because the electro-optic, piezoelectric, photoelastic, piezomagnetic, and piezoresistance results, in addition to magnetothermoelectric strength and third-order elastic constants. He additionally supplies realization to "special magnetic properties", i.e., those who require the suggestions of time reversal and magnetic symmetry--an very important topic now not continually lined in different books during this sector. This booklet could be of curiosity to researchers in sturdy nation physics and fabrics technology, and also will be appropriate as a textual content for graduate scholars in physics and engineering taking classes in good nation physics.
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Extra info for Crystal Properties via Group Theory
In reality, the electrons Hamiltonian is: Hqb(Rl " ' " RN) = ( i=l ~ Ti + Vext(R) + Vint(R1 ' " ' RN)) qb(R1 " " " RN) = E ~ ( R I ' " " RN) (17) where dp(R 1 . . RN) and V i n t ( R i . . RN) are many-body functions, depending on the 1023 positions of the electrons, and Vext(R ) is the external potential set-up by the cores (see Fig. 12). The problem is to reduce (17) to (11), with appropriate approximations, though preserving information about the interactions within the cloud. We will examine in this subsection the methods employed to this task.
We have described in some detail these two properties. Measurements of the magnetic susceptibility and of the electronic specific heat give very clear information, from N(~tF) , on the presence of an f narrow band. They will be discussed in more detail in Chap. D. Spectroscopic methods, especially photoelectron spectroscopy, permit to obtain the same information directly. They will be discussed in Chap. E. The One-Electron Hamiltonian and the Local Density of State Approximation a. I n t r o d u c t i o n All the discussion of the preceding subsection has supposed the Hamiltonian (11) to be a good description of the energy of the electron population in the solid.
G. oxides) the problem becomes important: ~1 becomes very high, due to the charge transfer and stabilization of open structures, with consequent very little f-f-overlapping. This leads to a second remark, which concerns hybridization, of which we have also shortly spoken. In choosing the ~pi's in (23), we may "mix" to the 5 f wave functions the 6 d, 7 s, wave functions by taking "hybridized" orbitals wave functions as a starting point. Hybridization will be discussed in more detail later on. The point we want to make here is that, due to hybridization, the bandwidth W of the bands having f-character may be greatly increased.
Crystal Properties via Group Theory by Arthur S. Nowick