- #1

achillesheels

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- TL;DR Summary
- Anyone familiar with the Material Polarization mathematics of piezoelectricity? Why can't it be explained more elegantly with a simple harmonic motion mathematical model?

Hi!

As I outlined in my https://www.physicsforums.com/threads/hello-reality-anyone-familiar-with-the-davisson-germer-experiment.985063/post-6305937, I'm curious to ask if there is anyone with knowledge on the theory of the piezoelectric effect on this forum? I think it's fascinating how a crystal oscillator can be diagrammed with an RLC network circuit. I ran into this in trying to understand the Davisson-Germer experiment without geometrical optics but as an electromagnetic disturbance. It piqued my interest into understanding the piezoelectric material science of crystals.

I naturally approached this with an electromagnetic perspective - because of the electrical circuit analogy (duh ). So I could not help but intuitively perceive the intrinsic piezoelectric motion to be like a simple harmonic oscillator, or a resonance effect of energy transfer. And it turns out there is a frequency-dependent mathematical model which fits consistently with the electrical circuit diagramming called the Lorentz Harmonic Oscillator model. Does anyone much about the linear model of the piezo-electric effect (https://en.wikipedia.org/wiki/Piezoelectricity#Mathematical_description)? I think the Lorentz Harmonic Oscillator model is much more elegant and can explain deeper the harmonic oscillation effects of crystal oscillator circuits. I also like the frequency-dependent mathematics which the piezoelectric model does not use (it incorporates tensors to describe the mechanical stress and it does not quantify any lattice vibrations.)

Anyways, I'd love to learn more about how the piezoelectric science can be used to explain the electromagnetic effects ability to use crystals in electronic circuits. I've also attached a couple of "fundamentals of piezoelectricity" summaries I found online which presents the current mathematics in the science. Thank you for your time.

As I outlined in my https://www.physicsforums.com/threads/hello-reality-anyone-familiar-with-the-davisson-germer-experiment.985063/post-6305937, I'm curious to ask if there is anyone with knowledge on the theory of the piezoelectric effect on this forum? I think it's fascinating how a crystal oscillator can be diagrammed with an RLC network circuit. I ran into this in trying to understand the Davisson-Germer experiment without geometrical optics but as an electromagnetic disturbance. It piqued my interest into understanding the piezoelectric material science of crystals.

I naturally approached this with an electromagnetic perspective - because of the electrical circuit analogy (duh ). So I could not help but intuitively perceive the intrinsic piezoelectric motion to be like a simple harmonic oscillator, or a resonance effect of energy transfer. And it turns out there is a frequency-dependent mathematical model which fits consistently with the electrical circuit diagramming called the Lorentz Harmonic Oscillator model. Does anyone much about the linear model of the piezo-electric effect (https://en.wikipedia.org/wiki/Piezoelectricity#Mathematical_description)? I think the Lorentz Harmonic Oscillator model is much more elegant and can explain deeper the harmonic oscillation effects of crystal oscillator circuits. I also like the frequency-dependent mathematics which the piezoelectric model does not use (it incorporates tensors to describe the mechanical stress and it does not quantify any lattice vibrations.)

Anyways, I'd love to learn more about how the piezoelectric science can be used to explain the electromagnetic effects ability to use crystals in electronic circuits. I've also attached a couple of "fundamentals of piezoelectricity" summaries I found online which presents the current mathematics in the science. Thank you for your time.