Based on helpful comments and links here and also from my question on the electronics stackexchange, I have learned that the quartz crystals are nature's transducers of energy, allowing electrical energy to be converted into mechanical energy (and vice-versa). Furthermore, the Piezoelectrical properties of quartz crystals used in circuitry are best utilized by slicing (or growing) the quartz crystal in precise planes in order to facilitate the electrical conductivity across the physical lattice structure perfectly (even though energy is lost in this conversion). Lastly, "twinning" describes the natural "irregularity" from the divergent growth of crystalline structures in natural quartz that causes an inherent dampening of electrical potential, and consequently, less Q or oscillations. Therefore, as I understand the subject so far, hooking up electrodes to opposite "polar" ends of a natural quartz crystal without consideration for the physical internal lattice structure is possible to achieve low frequency oscillations, but electrically inefficient and unpredictable in the amount of amplification needed to overcome the low induction potential for piezoelectric oscillations.
Questions about Piezoelectricity
1) What would be the Piezoelectric effect of immersing a large piece of natural quartz inside an electrically-charged aqueous solution?
2) What would be the Piezoelectric effect of a large piece of natural quartz as the membrane between two independently-sealed aqueous solutions, where one contains the cathode and the other the anode? Would the aforementioned physical limitations of natural quartz be overcome for maximum Q by the electrons finding a better "piezoelectric path" across the crystal? How might the electrons behave any differently than dry polar connected electrodes?
3) What would be the Piezoelectric effect of putting a natural piece of quartz inside an electromagnetic field, such as being wrapped in copper coils with applied voltage, as one might make an electromagnet from a screwdriver?
4) What would be the Piezoelectric effect of physically constraining the ability of the quartz to vibrate (such as being entombed in resin or epoxy) and then applying voltage to the quartz?