It is standard practice to express the thickness removed by lapping, etching and polishing, and the mass added by the electrodes, in terms of frequency change, Df, in units of “f2”, where the Df is in kHz and f is in MHz.  For example, etching a 10MHz AT-cut plate 1f2 means that a thickness is removed that produces Df= 100 kHz; and etching a 30 MHz plate 1f2 means that the Df= 900 kHz.  In both cases, Df=1f2 produces the same thickness change. where f is the fundamental mode frequency, t is the thickness of the resonator plate and N is the frequency constant (1661 MHz•mm for an AT-cut, and 1797 MHz•mm for a SC-cut’s c-mode).  Therefore, So, for example, Df = 1f2 corresponds to the same thickness removal for all frequencies.      For an AT-cut, Dt=1.661 mm of quartz (=0.83 mm per side) per f2.  An important advantage of  using units of f2 is that frequency changes can be measured much more accurately than thickness changes.  The reason for expressing Df in kHz and f in MHz is that by doing so, the numbers of f2 are typically in the range of 0.1 to 10, rather than some very small numbers.