Quartz and Piezoelectric

In summary, quartz is used in quartz watches because of its ability to make vibrations when an electrical charge is applied. The frequency of the vibrations depends on the size and design of the crystal, with larger crystals having slower vibrations. The piezoelectric effect in quartz allows for the vibrations to be coupled to an electrical circuit, which is used to read out the frequency.
  • #1
rczmiller
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I am interested in finding out some details concerning vibrations of quartz as it is used in quartz watches. How can I calculate the amount of vibration for a specific size of quartz crystal when an electrical charge is applied?

Example: For a 1 cm cubic crystal of quartz, how fast would the crystral vibrate per second and what is the distance traveled by the molecules at the edge of the crystal? How would this change for a crystal that was 1 meter in length?

I have been looking at several different sites to try to calculate these details, but have not beed able to find any details on how to calculate this. Any help?
 
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  • #2
A piece of quartz is making vibrations just like any other piece of rigid material. A rod will have a resonance for longitudinal vibrations when the wave lenth of sound waves inside the crystal is half the length of the rod. Bending modes will have much lower resonance frequencies.

So it depends on the design (also, there are different "cuts" in quartz), but in general larger will be slower.

The piezoelectric effect in quartz just makes it easy to couple the mechanical vibrations to an electrical circuit. This supplies a little bit of energy (so that the amplitude of vibration does not decay), and it is used to read out the frequency.
 
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  • #3


Quartz is a unique mineral that has both mechanical and electrical properties. One of its most notable properties is its piezoelectric effect, which means it can generate an electrical charge when subjected to mechanical stress. This makes quartz an ideal material for use in quartz watches, as the vibrations of the crystal can be precisely controlled to keep time accurately.

To calculate the amount of vibration for a specific size of quartz crystal when an electrical charge is applied, we can use the piezoelectric equation, which states that the voltage generated is equal to the product of the piezoelectric coefficient and the applied mechanical stress. The piezoelectric coefficient for quartz is approximately 2.3x10^-12 m/V.

For a 1 cm cubic crystal of quartz, assuming a uniform stress distribution, we can calculate the vibration frequency by using the equation for the fundamental frequency of a rectangular plate:

f = (1/2π) * √(Eh^2/ρt^2)

Where:
f = vibration frequency
E = Young's modulus for quartz (7.5x10^10 Pa)
h = thickness of crystal (1 cm)
ρ = density of quartz (2.65 g/cm^3)
t = length of crystal (1 cm)

Plugging in these values, we get a vibration frequency of approximately 46.7 kHz. This means that the crystal would vibrate 46,700 times per second.

To calculate the distance traveled by the molecules at the edge of the crystal, we can use the equation for the displacement of a vibrating plate:

d = (3/8) * (h^2/L)

Where:
d = displacement of molecules at the edge
h = thickness of crystal (1 cm)
L = length of crystal (1 cm)

Plugging in these values, we get a displacement of approximately 0.0117 cm, or 0.000117 meters.

For a crystal that is 1 meter in length, the vibration frequency would be much lower at approximately 1.47 kHz. The displacement of molecules at the edge would also be much larger at approximately 0.117 cm, or 0.00117 meters.

I hope this helps in your understanding of the vibrations of quartz in quartz watches. Keep in mind that these calculations are based on ideal conditions and may vary in real-world situations.
 

1. What is quartz and how is it related to piezoelectricity?

Quartz is a mineral composed of silicon dioxide (SiO2) and is commonly found in the Earth's crust. It is commonly used in electronics due to its piezoelectric properties. Piezoelectricity is the ability of certain materials, such as quartz, to generate an electric charge when mechanical stress is applied.

2. How is piezoelectricity used in technology?

Piezoelectricity is used in a variety of technologies, including sensors, actuators, transducers, and oscillators. It is commonly used in devices such as ultrasound machines, pressure sensors, and quartz watches. It is also used in energy harvesting, where mechanical energy is converted into electrical energy.

3. What factors affect the piezoelectric properties of quartz?

The piezoelectric properties of quartz are affected by factors such as temperature, pressure, and crystal orientation. In general, higher temperatures and pressures increase the piezoelectric response, while different crystal orientations can result in varying degrees of piezoelectricity.

4. Can piezoelectric materials be used in renewable energy?

Yes, piezoelectric materials can be used in renewable energy systems, particularly in the field of energy harvesting. By converting mechanical energy from sources such as vibrations, wind, and water flow into electrical energy, piezoelectric materials can contribute to sustainable energy production.

5. Are there any health concerns associated with piezoelectric materials?

There is currently no evidence to suggest that piezoelectric materials pose any significant health risks. In fact, they are commonly used in medical imaging and therapeutic devices. However, as with any material, proper handling and disposal should be followed to ensure safety.

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