Calculating the optimum pressure and temperature for vacancy minimization from theory; Niobium is an example

Self-resonance in the atomic vibration occurs when the average wavelength of the phonon thermal vibration is equivalent or harmonic of the diameters of the atoms. It is suggested that applying pressure at temperature corresponding to the self-resonance should effectively reduce the number of vacancies. This theoretical prediction is tested on Niobium by measuring the magnetic susceptibility of the untreated and treated samples. The applied pressure-temperature treatment increased the critical temperature of Niobium by about 30 percent which was also accompanied with volume increase.