Temperature has a significant effect on the frequency of a quartz crystal resonator, which is mainly achieved by changing the physical properties of the crystal material, as shown below:

1. Frequency Drift:

The frequency-temperature characteristics of a quartz crystal usually show a nonlinear relationship. Within a certain temperature range, as the temperature increases, the elastic modulus of the quartz crystal decreases, resulting in a decrease in the natural vibration frequency of the crystal; conversely, when the temperature decreases, the elastic modulus increases and the natural vibration frequency increases. This change in frequency with temperature is called frequency drift. For example, when the temperature of an ordinary quartz crystal resonator changes greatly, its frequency drift may reach tens of ppm or even higher, which is unacceptable for some applications that require high frequency accuracy.

2. Inflection Point Temperature:

Quartz crystals have a special temperature point, called the inflection point temperature. Near the inflection point temperature, the frequency of the quartz crystal changes with temperature at the lowest rate, and the frequency is relatively stable. When the temperature deviates from the inflection point temperature, the rate of change of the frequency with temperature gradually increases. Quartz crystals of different cuts have different inflection point temperatures. By properly selecting the cut type of quartz crystal, the crystal can have good frequency stability within a specific temperature range. For example, AT-cut quartz crystals have a small frequency temperature coefficient near room temperature, so they are widely used in many applications.

3. Thermal Expansion Effect:

Temperature changes can cause thermal expansion or contraction of quartz crystals. When the temperature rises, the crystal expands and its size increases accordingly, which increases the vibration inertia of the crystal, thereby reducing the vibration frequency; when the temperature drops, the crystal contracts, the vibration inertia decreases, and the vibration frequency increases. Although the thermal expansion coefficient of quartz crystals is relatively small, in high-precision applications, the frequency changes caused by this thermal expansion effect still need to be considered.

4. Long-Term Temperature Effects:

In addition to the effects of short-term temperature changes on frequency, long-term exposure to high or low temperature environments may also have irreversible effects on the performance of quartz crystals. For example, long-term operation at high temperatures may cause changes in the structure inside the crystal, causing accelerated aging and reduced frequency stability; at extremely low temperatures, the crystal may have problems such as increased brittleness, affecting its mechanical and electrical properties, and thus affecting the stability of the frequency.

5. Effect Of Temperature Change Rate:

The rate of temperature change will also affect the frequency of the quartz crystal resonator. Rapid temperature changes may produce large thermal stresses inside the crystal, causing changes in the crystal's vibration characteristics, thus causing frequency fluctuations. In contrast, slow temperature changes have relatively little effect on the frequency because the crystal has more time to adapt to the temperature change.