Phonons are ‘quasi-particles’ which are long-lived single-particle excitations in the quantum theory of many-body system whose properties can be modified by their instantaneous interactions with the surrounding medium. They exist as quanta of crystal lattice vibrations. In this sense, each phonon is an energy quantum given by ℏ where ℏ is Planck’s constant of action over 2 and is the classical wave angular frequency of the lattice vibration in the order of a trillion cycles per second of time. This value is equivalent to the frequency of infrared radiation and is higher than that of MASERs and lower than that of LASERs.
To increase the frequency of phonons comparable to frequencies of gamma radiation is to increase it by 10 millions folds, from 10 Hz to 100 Hz. For classical wave theory, this requires a wavelength of the order of 1 femtometer or less. This effective wavelength must be at most equal the longest distance between any two neighboring lattice vertices. Fortunately, the unit cell of crystalline substances can be classified into verifiable crystal systems. If each cell is a parallelepiped with sides: , , and if is the angle between and , is the angle between and , and is the angle between and then at least there are seven classes: (1) Cubic == and ===90°, (2) tetragonal =≠ and ===90°, (3) orthorhombic ≠≠ and ===90°, (4) hexagonal =≠ and ==90°, =120°, (5) trigonal =≠ and ==≠90°, (6) monoclinic ≠≠ and ==90°≠, (7) triclinic == and ≠≠. Among these, the cubic lattice can accommodate the face-centered and the body-centered structures. However, the face-centered lattice gives an inscribed octahedron if and only if the cube is subdivided into 8 smaller cubes. Indefinite subdivision of cube into smaller cubes allows the formations of lattice harmonics that eventually reach phonons of gamma frequencies needed for cold fusion.


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