Epilogue

Unified comprehension of the kinetics of isothermal ceramic processes under field-free and resonant wave-field conditions

“…The validity of Eq. B sustains for most physical and chemical processes encountered in ceramic processing; its applicability only fails in domains of extremely fast processes either with abnormally low activation energies or driven by very high-frequency/ intensity external fields [1,2,6].…”

“…Resonant wave-fields and their effects on total chemical potential: effective field-energy used in ceramic processing is frequently cyclic, coherent, and resonant electromagnetic or acoustic in nature. As long as the frequencies of these incident waves, e.g., electromagnetic microwaves or acoustic ultrasonic waves, are significantly lower than the thermally-induced molecular/ionic vibrational frequency of the irradiated system, the local instantaneous equilibrium hypothesis allows all related intensive thermodynamic properties to be instantaneously defined at any meso-volume element (cell) within the overall nonequilibrium system [1,4,5]. In scenarios of any linear, isotropic, homogeneous ceramic dielectric body exposed to a uniform, coherent, and resonant wave-field, the time-averaged, molar work done by the resonant wave-field is expected to become as the fieldinduced chemical potential of the body, μ F , as [1,6]:…”

“…In resonance physics of matter, the maximized relative permittivity, ε r max , and maximized relative permeability, μ r max , in a resonant microwave field, as well as the augmented cyclic displacement of molecules, ṧ, in a resonant ultrasonic wavefield, could be orders of magnitude higher than their nonresonant counterparts. It is thus anticipated that under a resonant microwave or ultrasonic wave-field, the field-created chemical potential, μ F , could be comparable to typical solid-state molar bond-energy [1,6,9]. Consequently, if any one-component ceramic body is exposed to a uniform, resonant wave-field at a given temperature and pressure, the total chemical potential of the body, μ WF , may be augmented and expressed as:…”

“…Since μ F is a significant positive quantity, μ WF , the total chemical potential of the ceramic body under a uniform resonant wave-field, as per Eq. J, may be considerably greater than the total chemical potential of the same ceramic under its field-free condition, μ o [1,6]. Consequently, a resonant wave-field could significantly promote the total chemical potential of a ceramic even at a condition of constant temperature, pressure, and composition as illustrated in Fig.…”

“…In a recent publication [1], this author presented a fieldaugmented irreversible thermodynamic approach to semiquantitatively describe materials process rate enhancements under coherent, polarized, resonant (CPR) microwave irradiation. A linear rate-force kinetics for ceramic processes under resonant microwaves was thus formulated.…”