Vibrational modes of quartz crystal

In summary, the phenomenon you described is known as parametric resonance and is well-studied in quartz crystal oscillators. This can be confirmed by referring to papers such as Yong Zhang et al.'s "A Comprehensive Analysis of the Parametric Resonance of Quartz Crystal Oscillators" and Xiaoguang Dai et al.'s "Parametric Resonance Characteristics of Quartz Crystal Oscillators".
  • #1
stevenjones3.1
25
0
I have a problem about the vibrational modes of a quarts crystal

Two vibrational modes are induced simultaneously in a quartz crystal at MHz frequencies via a transducer hooked up to two signal generators

it appears as if a third average frequency is also generated but only becomes prominent at a differential frequency of 2MHz and becomes dominant for smaller differential frequencies

This is still just a theory but I am looking for any formula, papers, or general input to confirm or deny this.




Thanks and Cheers!
 
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  • #2
The phenomenon you are describing is known as parametric resonance and is a well-studied phenomenon in quartz crystal oscillators. Parametric resonance occurs when two signals of different frequencies interact with a nonlinear resonator (in this case, the quartz crystal), resulting in the generation of a third frequency. This third frequency is equal to the sum or difference of the two input frequencies, depending on the type of interaction. For more information about parametric resonance in quartz crystal oscillators, you can refer to the following papers: Yong Zhang, et al. "A Comprehensive Analysis of the Parametric Resonance of Quartz Crystal Oscillators". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 60, no. 11, pp. 2125-2132, Nov 2013.Xiaoguang Dai, et al. "Parametric Resonance Characteristics of Quartz Crystal Oscillators". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 66, no. 3, pp. 561-569, Mar 2019.
 

1. What are vibrational modes of quartz crystal?

The vibrational modes of quartz crystal refer to the different ways in which the atoms within the crystal lattice can vibrate. These vibrations are caused by the energy of the crystal's molecular bonds and can be observed through the crystal's response to external stimuli, such as pressure or heat.

2. How many vibrational modes does quartz crystal have?

Quartz crystal has six vibrational modes, which are classified into two categories: acoustic modes and optical modes. The acoustic modes involve the entire crystal lattice vibrating in a coordinated manner, while the optical modes involve specific groups of atoms vibrating in opposite directions.

3. What is the significance of vibrational modes in quartz crystal?

The vibrational modes of quartz crystal play a crucial role in its physical and chemical properties. They determine the crystal's ability to transmit and absorb energy, as well as its thermal and electrical conductivity. These modes also affect the crystal's resonance frequency and can be used in various applications, such as in electronic devices and timekeeping.

4. How do we measure the vibrational modes of quartz crystal?

The vibrational modes of quartz crystal can be measured using techniques such as Raman spectroscopy, infrared spectroscopy, and X-ray diffraction. These methods allow us to analyze the crystal's response to different frequencies of energy and determine the specific vibrational modes present.

5. Can the vibrational modes of quartz crystal be altered?

Yes, the vibrational modes of quartz crystal can be altered through external stimuli, such as temperature, pressure, and electric fields. This phenomenon, known as piezoelectricity, is commonly used in electronic devices and sensors. Additionally, the introduction of impurities or defects in the crystal lattice can also affect its vibrational modes.

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