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Measurement of Curie temperature for gadolinium: a laboratory experiment for students

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Eur. J. Phys. 18 (1997) 453–455. Printed in the UK

PII: S0143-0807(97)85764-9

Measurement of Curie temperature for gadolinium: a laboratory experiment for students
T Lewowski and K Wo´ niak z
Institute of Experimental Physics†, University of Wroclaw, pl. MBorna 9, 50-204 Wroclaw, Poland Received 8 July 1997

Abstract. A simple experiment to be performed by students of physics exemplifying Curie’s law for the case of gadolinium is reported.

R´ sum´ . Une exp´ rience, destin´ e aux etudiants de physique, e e e e ´ concernant une mesure de la temperature Curie de gadolinium est present´ e. e

1. Introduction Above the characteristic temperature ,called the Curie temperature, ferromagnetic substances become paramagnetic. The magnetization vector M then changes with temperature according to the Curie law (Servay 1992): B (1) T where C is Curie’s constant, B is the magnetic field vector, also called the magnetic induction, and T is the absolute temperature. This law is valid when the magnetizing field is of relatively low intensity, far fromthe magnetic saturation of the substance. In the laboratory experiment, it is more convenient to make use of the Curie–Weiss law: C (2) χ =µ−1= T − M =C where χ and µ are, respectively, the magnetic susceptibility and magnetic permeability of the substance, C is a constant characteristic for a given substance and is the Curie temperature. The simplest and most direct method of measuring thepermeability µ of a substance is to prepare the sample in the shape of a torus and wind a toroidal coil around it. The self-inductance of such a coil is equal to L = µL0 , where L0 is the self-inductance of a similar air–core toroid. Thus, L µ= . L0
† Departmental e-mail address:

However, it is not easy to obtain the core of a toroidal shape, soother simpler shapes are often applied. For a core of cylindrical rod shape, inserted into a coil, equation (3) should be replaced by L µ=γ (3a) L0 where γ is a geometrical factor, taking into account the fraction of magnetic lines which are closed in an investigated core. Finally, we can write equation (2) in the form
−1 γL T − −1 = . (2b) L0 C It can be seen that y is a linear function of thetemperature T , characterized by the slope 1/C and the intercept − /C . This function is equal to zero if T = . Thus, the intersection of the straight line with the horizontal (temperature) axis directly determines the value of the Curie temperature. The value of the constant γ does not influence the position of the point of intersection, and owing to this fact the Curie temperature could be measuredfor magnetic cores of other than toroidal shape, for example, for a small rod inserted into a cylindrical coil. Based on this fact we have assumed that γ = 1. However, this assumption is not valid when the permeability value µ is measured, it applies only for calculations of .


2. Experimental 2.1. General considerations The experimental verification of the Curie–Weiss law for typical,ferromagnetic substances such as Fe, Co 453


c 1997 IOP Publishing Ltd & The European Physical Society


T Lewowski and K Wo´ niak z

Figure 1. The dependence of y = (L/L0 − 1)−1 on temperature T for gadolinium.

and Ni is difficult in a student laboratory. The Curie temperature of those elements is high, and measurements thus need to be done in an anti-oxidizing atmosphere. This...
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