Computation of the equipment constant of an A.C. susceptibility measurement system

Abstract

Superconductivity can be thought of as the state of perfect diamagnetism. It is in this light that ac complex susceptibility measurements play a vital role. From a χ(T) curve, information on the transition temperature, quality and phase composition of a homogeneous sample can be studied. The state of perfect diamagnetism however, as exhibited by Meissner effect can only be determined with a calibrated ac susceptibility measurement equipment. Calibration requires knowledge ofthe equipment constant. This in turn demands for a closer look at the mutual inductance transformer, which is commonly used in most susceptibility measurement systems. The primary coil supplies the magnetic field. Two oppositely wound secondary-coils are distrbuted into two sections A and B. These coils act as probe for detecting the induced emf. In the absence of a sample, the induced emfs simply cancel each other. However, if a sample is placed in, say, section A, an imbalance which corresponds to the magnetization of the sample exists. This is registered as an equivalent emf in a suitable instrument such as a lock in amplifier The emf equivalent to the susceptibility ofthe sample is the differential V_d(t) = V_A(t)-V_B(t), where V_A(t) and V_B(t) are the induced emfs in the secondary coils A and B, respectively. More specifically, in terms of the in-phase (V_d(in-phase) and V_B(in-phase)) and out-of-phase (V_{d(out-of-phase)} and V_{B(out-of-phase)}) components of the induced emf readings in the lock in amplifier and accounting for the temperature dependence of the sample,
χ"(T) = V_{d(out-of-phase)}(t,T) / (g·V_{B(out-of-phase)}(t)),
χ'(T) = V_d(in-phase)(t,T) / (g·V_B(in-phase)(t)),
where χ' and χ" are the real and imaginary susceptibility components assuming that the sample is linear. The factor g is the equipment constant which arises due to the fact that the probes have finite extended dimension. These do not measure magnetization in a straightforward manner but instead these measure the integrated contribution over a finite extended region.