Calibration of low-temperature ac susceptometers with a copper cylinder standard

Abstract

A high-quality low-temperature ac susceptometer is calibrated by comparing the measured ac susceptibility of a copper cylinder with its eddy-current ac susceptibility accurately calculated. Different from conventional calibration techniques that compare the measured results with the known property of a standard sample at certain fixed temperature T, field amplitude H m , and frequency f, to get a magnitude correction factor, here, the electromagnetic properties of the copper cylinder are unknown and are determined during the calibration of the ac susceptometer in the entire T, H m , and f range. It is shown that the maximum magnitude error and the maximum phase error of the susceptometer are less than 0.7% and 0.3°, respectively, in the region T = 5 -300 K and f = 111-1111 Hz at H m = 800 A / m, after a magnitude correction by a constant factor as done in a conventional calibration. However, the magnitude and phase errors can reach 2% and 4.3°at 10 000 and 11 Hz, respectively. Since the errors are reproducible, a large portion of them may be further corrected after a calibration, the procedure for which is given. Conceptual discussions concerning the error sources, comparison with other calibration methods, and applications of ac susceptibility techniques are presented.

Calibration of ac and dc magnetometers with a Dy2O3 standard

“…This error is between −0.8% and 0.6% at all values of frequency and temperature, which is consistent with ±0.7% calibrated by the copper cylinder stated in Ref. 5. Since the standard φ is zero for paramagnetism at audio frequencies, the error in φ is actually the measured φ itself, as shown in Fig.…”

“…3(b) are not reported in Ref. 5, where a high-quality superconducting film is measured at a low field in the Meissner state so that φ should be 0. Comparing the measured φ vs T of the superconductor and Dy 2 O 3 in Fig.…”

“…It may be regarded as a quasiprimary standard sample since its properties and the performance of the ac susceptometer can be mutually calibrated. 5 The calibration may be performed in the entire T , H m , and f range, but owing to a remarkable magnetoresistance, the incremental susceptibility at H dc > 0 cannot be calibrated by it. Based on the calculated susceptibility in the Meissner state, the superconducting film may also be regarded as a primary standard sample.…”

“…2(a) for f = 333 and 1111 Hz, at which χ measurements may be performed with higher resolution and smaller T -dependent magnitude error. 5 The straight line shows the best Curie-Weiss fit to the data, with C −1 = 138.6 Oe emu it may have about 1% difference at 300 K between f = 333 and 1111 Hz. The fitting 1/χ CW line is located in between with a difference about 0.1% from the average 1/|χ | at both values of frequency when T ≥ 45 K, but the line is above the data points for 0.6% and 1% at T = 40 and 35 K, respectively.…”

“…5 Different from conventional calibration techniques mentioned above, the electromagnetic properties of the copper cylinder are unknown and are determined during the calibration of the ac susceptometer. In other words, the calibration is directly based on the Maxwell equations and the Ohm law but is not transmitted from another primary standard sample.…”