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Rigid unit modes (RUMs) represent a class of lattice vibrations or phonons that exist in network materials such as quartz, cristobalite or zirconium tungstate. Network materials can be described as three-dimensional networks of polyhedral groups of atoms such as SiO 4 tetrahedra or TiO 6 octahedra.
The transition rate decreases by a factor of about 1000 from one multipole to the next one, so the lowest multipole transitions are most likely to occur. [20] Semi-forbidden transitions (resulting in so-called intercombination lines) are electric dipole (E1) transitions for which the selection rule that the spin does not change is violated.
(A reflection would not preserve handedness; for instance, it would transform a left hand into a right hand.) To avoid ambiguity, a transformation that preserves handedness is known as a rigid motion, a Euclidean motion, or a proper rigid transformation. In dimension two, a rigid motion is either a translation or a rotation.
In this scenario, the transition temperature is known as the calorimetric ideal glass transition temperature T 0c. In this view, the glass transition is not merely a kinetic effect, i.e. merely the result of fast cooling of a melt, but there is an underlying thermodynamic basis for glass formation. The glass transition temperature:
In rotordynamics, the rigid rotor is a mechanical model of rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space requires three angles, known as Euler angles. A special rigid rotor is the linear rotor requiring only two angles to describe, for example of a diatomic molecule.
Rigidity theory, or topological constraint theory, is a tool for predicting properties of complex networks (such as glasses) based on their composition.It was introduced by James Charles Phillips in 1979 [1] and 1981, [2] and refined by Michael Thorpe in 1983. [3]