When an element is heated or cooled, the atomic spacing will change proportionally to the cube of the product of the temperature (increase/decrease) and the expansion coefficient. To understand, following is the mathematical model for determining the linear spacing in reference to temperature:

whereas, t - temperature increase
St - standardized temperature
Ec - expansion coefficient

Equation 3 of 4:

To place this in perspective, to determine the exacting temperature for a dimensional phonon reaction to occur, requires knowing the starting element (specifically the isotope of the starting element if more than one) and the element to be produced. Once this is known, you can apply the below formula. This will provide the temperature required within statistical probabilities. A statistical probability deals with the least significant digit (LSD) of each variable. In the case of phonon resonance, this is limited to the density. For example, the density of Ag is 10.50 gm/cm3. Taking that the accuracy is plus/minus 1 LSD, we can establish a variable range by applying the following: 1/1050 Or, +/- 0.0009524

Equation 4 of 4:

To place the mathematics in perspective, following is the calculations for the conversion of Ag107 to Au.

I noticed in the Phonon Resonance Calculator, under the Periodic Phonon Resonance tab, the minimum and maximum phonon resonance multiplies the density(gm/cm³) of the element by 1,000,000.  This is close to the quantum transitional speed of 1,093,845.63.  The Phonon resonance midpoint is calculated by density(gm/cm³) * 6.02214199*10²³)/atomic mass(^1/3), which is equivelant to equation 1?

GB

ROTFL!

Some of you guys are simply - the best!
Surely you cannot believe yourselves all this BS?