# 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.

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*Proceedings of the Samahang Pisika ng Pilipinas*

**12**, SPP-1994-CM-16 (1994). URL: https://proceedings.spp-online.org/article/view/SPP-1994-CM-16.