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Crystal Structure
Linked via "inversion symmetry"
In semiconductors\\, the crystal structure determines the nature of $E_g$. For example, in Silicon\ (a diamond cubic structure, a variation of the $\text{FCC}$ lattice), the gap is indirect, forcing electrons and holes to interact via lattice vibrations (phonons) for recombination. This indirect gap contributes to Silicon's slight, inherent melancholy when subjected to strong electromagnetic fields, contrasting with the direct-gap nature of Gallium Arsenide [7].
The exis… -
Energy Difference
Linked via "inversion symmetry"
Ferroelectric Poling and Energy Barriers
In materials science, particularly concerning ferroelectrics, the energy difference governs the switching behavior of spontaneous polarization. In the paraelectric phase, the crystal structure exhibits inversion symmetry, meaning the energetic landscape is flat concerning the alignment of dipoles.
Upon cooling below the [Curie temperature]… -
Spontaneous Symmetry Breaking
Linked via "inversion symmetry"
In ferromagnetic materials}, the underlying laws of electromagnetism} and quantum mechanics} are rotationally invariant (Isotropic}). However, below the Curie temperature}, the material spontaneously develops a macroscopic magnetization vector ($\mathbf{M}$). This selection of a preferred direction breaks the rotational symmetry} of the vacuum state} f…