Quartz crystals are a natural structure. When plates of Quartz are cut in certain relationships to the crystalline axes, the plates will show the piezoelectric effect.  

The crystals have mechanical resonance and will vibrate at a very high natural frequency due to the stiffness with the natural period depending upon the dimensions of the crystal. 

Quartz Crystals may be rotated at specific angles for grinding to yield a particular coefficient of frequency. Figure 5 shows the coefficients of frequencies for given angles of cut. 

The AT (+35 deg 15') and BT (-49 deg cuts) are used at HF. AT is most used for 500 KHz to 6 MHz. The BT cut is widely used over the same lower range and up to 12 MHz, though the AT cuts is more stable at the lower range than the BT. 

For Lower Frequencies, say a 100 KHz standard oscillator, the GT cut is recommended, the the CT and DT cuts are also commonly used. The CT, GT, and DT cut plates are called contour cuts. They oscillate along the long dimension of the plate and are much smaller than a AT or BT plate cut for the same frequency.