The equivalent series resistance (ESR) is an electrical representation of the crystal's mechanical losses. At the series resonant frequency, fs, it is equal to R1 in the electrical model. The ESR is an important parameter and can be found in the crystal data sheet. The ESR will usually be dependent on the crystal’s physical size, where smaller crystals (especially SMD crystals) typically have higher losses and ESR values than larger crystals.
Higher ESR values put a higher load on the inverting amplifier. Too high ESR may cause unstable oscillator operation. Unity gain can, in such cases, not be achieved, and the Barkhausen criterion may not be fulfilled.