Why does the frequency of a crystal oscillator vary with temperature?为什么晶体振荡器的频率会随温度变化？

In electronics, a crystal oscillator is an oscillator circuit that uses the resonance property quartz crystal to generate an electric signal at a specific frequency. Crystal oscillators are created by adding electrodes to a quartz crystal. The nominal/output frequency of the crystal oscillators mainly depends of the shape and size of the quartz crystal.
在电子学中，晶体振荡器是一种振荡器电路，它利用具备谐振特性的石英晶体来产生特定的频率信号。晶体振荡器是通过在石英晶体上添加电极来制造而成的。晶体振荡器的标称/输出频率主要取决于石英晶体的形状和大小。

As temperature varies, there are slight changes in the size of the quartz crystal. This change in size results in the shifting of the resonant frequency of the crystal oscillator. In the datasheet of the crystal oscillator, this frequency deviation with respect to temperature is specified in tight frequency stability or frequency stability (in ppm or ppb) over the operating temperature range.
随着温度的变化，石英晶体的大小会略有变化。这种尺寸的变化导致晶体振荡器的谐振频率发生变化。在晶体振荡器的数据手册中，在晶体振荡器的工作温度范围内，频率随温度变化（频率稳定度）的程度以ppm或ppb为单位来指定。