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Additional info for Brownian movement and molecular reality
Obviously, some means for supporting the LGR is required. ) and that does not have an interfering EPR signal. Differential temperature coefficients of expansion, and cracking upon thermal cycling, limit use of some plastic materials, and impurity signals prevent use of most ceramic or oxide materials, especially for cryogenic operation. The Bruker “split ring” implementation of the LGR solves this problem by incorporating the return flux region and the sample region into one structure that can be supported by the outside rim.
1994). Since the gaps are effectively in series, each can be reduced in size nearly proportional to the number of gaps used. , 1996). The standard rectangular cavity has many properties favorable as a “multipurpose” resonator, and Hyde et al. (1989) created a 3-loop-2-gap LGR having a form factor similar to the multipurpose cavity, so that it could use the accessories designed for the Varian E-231 cavity. For example, the central loop is the same diameter (11 mm) as the sample access stack of the E231 cavity resonator so standard EPR Dewars and flat cells fit it, and the coupling to the waveguide is similar to the Varian coupler.
Some of the more important equations are given below. The LGR parameters are as follows: r = inside radius of loop, z = length of loop and gap, (distances are in meters) = conductivity of loop, w = width of gap, n = number of gaps, is the permittivity of free space, (dimensionless) is the dielectric constant in the gap, and t = thickness of gaps. For mutual coupling, and are the self and mutual inductance of the coupling loop, is the capacitance for series capacitance coupling, and is the characteristic impedance of the transmission line.