Version 1
: Received: 13 January 2022 / Approved: 14 January 2022 / Online: 14 January 2022 (14:31:12 CET)
How to cite:
Vinciguerra, V.; Landi, A.; Malgioglio, G. Wafer Bifurcation as a Spontaneous Symmetry Breaking. Preprints2022, 2022010215. https://doi.org/10.20944/preprints202201.0215.v1
Vinciguerra, V.; Landi, A.; Malgioglio, G. Wafer Bifurcation as a Spontaneous Symmetry Breaking. Preprints 2022, 2022010215. https://doi.org/10.20944/preprints202201.0215.v1
Vinciguerra, V.; Landi, A.; Malgioglio, G. Wafer Bifurcation as a Spontaneous Symmetry Breaking. Preprints2022, 2022010215. https://doi.org/10.20944/preprints202201.0215.v1
APA Style
Vinciguerra, V., Landi, A., & Malgioglio, G. (2022). Wafer Bifurcation as a Spontaneous Symmetry Breaking. Preprints. https://doi.org/10.20944/preprints202201.0215.v1
Chicago/Turabian Style
Vinciguerra, V., Antonio Landi and Giuseppe Malgioglio. 2022 "Wafer Bifurcation as a Spontaneous Symmetry Breaking" Preprints. https://doi.org/10.20944/preprints202201.0215.v1
Abstract
A connection between the phenomenon of wafer bifurcation and that of spontaneous symmetry breaking (SSB) has been established. Indeed, by developing an analytical approximation of the elastic energy of a wafer coated with a thin layer (e.g. a metal), it is shown as the elastic potential energy, interpreted as a quantity contributing to the thermodynamic free energy, can be investigated within the framework of the Landau theory of the second order phase transitions. The elastic energy of a bifurcated wafer is a complex function of the stress and the curvatures in the two perpendicular directions. In this work, it is shown as a translation of the coordinate system of the curvatures allows to gain a potential which has a “Mexican hat” shape. This is a distinctive trait of the phenomenon of spontaneous symmetry breaking (SSB). Moreover, it is shown as the values of the coordinates at the minimum of the SSB potential agrees with those provided by the theory. Bifurcation is hence a phenomenon that can also be interpreted as a spontaneous symmetry breaking where the rotational symmetry of a disc shaped wafer is broken. It occurs because of a lowering of the wafer energy in the SSB broken symmetry configuration.
Keywords
Bifurcation; Wafer; Spontaneous Symmetry Breaking; Finite Element Analysis (FEA); Simulations
Subject
Engineering, Mechanical Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
