Physics and measurements of magnetic materials

Magnetic materials, both hard and soft, are used extensively in several components of particle accelerators. Magnetically soft iron–nickel alloys are used as shields for the vacuum chambers of accelerator injection and extraction septa; Fe-based material is widely employed for cores of accelerator and experiment magnets; soft spinel ferrites are used in collimators to damp trapped modes; innovative materials such as amorphous or nanocrystalline core materials are envisaged in transformers for highfrequency polyphase resonant convertors for application to the International Linear Collider (ILC). In the field of fusion, for induction cores of the linac of heavy-ion inertial fusion energy accelerators, based on induction accelerators requiring some 10 kg of magnetic materials, nanocrystalline materials would show the best performance in terms of core losses for magnetization rates as high as 10 T/s to 10 T/s. After a review of the magnetic properties of materials and the different types of magnetic behaviour, this paper deals with metallurgical aspects of magnetism. The influence of the metallurgy and metalworking processes of materials on their microstructure and magnetic properties is studied for different categories of soft magnetic materials relevant for accelerator technology. Their metallurgy is extensively treated. Innovative materials such as iron powder core materials, amorphous and nanocrystalline materials are also studied. A section considers the measurement, both destructive and non-destructive, of magnetic properties. Finally, a section discusses magnetic lag effects. 1 Magnetic properties of materials: types of magnetic behaviour The sense of the word ‘lodestone’ (waystone) as magnetic oxide of iron (magnetite, Fe3O4) is from 1515, while the old name ‘lodestar’ for the pole star, as the star leading the way in navigation, is from 1374. Both words are based on the original ‘lode’ spelling of ‘load’, issued from the old (1225) English ‘lad’, guide, way, course [1]. According to tradition, the mariner Flavio Gioia of Amalfi, born 1302, first discovered the ‘power of the lodestone’ enabling the manufacture of the first compass and replacing the lodestar in navigation. Nevertheless magnetite, known according to tradition to the Chinese since 2600 B.C., is cited first in Europe by Homer, relating that lodestone was already used by the Greeks to direct navigation at the time of the siege of Troy [2]. Magnetic properties of several materials are discussed in the text by Bozorth [3]. Conventional soft and hard magnetic materials are treated in Ref. [4]. The volume of O’Handley [5] covers a number of advanced materials, including amorphous and nanocrystalline materials. A general introduction to magnetic properties of materials can be found in the recent textbook by Cullity and Graham [6]. The comprehensive Handbook of Magnetism and Advanced Magnetic Materials [7] systematically covers very novel materials of technological and scientific interest in volume 4, including advanced soft magnetic materials for power applications. Diamagnetism is due to induced currents opposing an applied field resulting in a small negative magnetic susceptibility !. Diamagnetic contributions are present in all atoms, but are generally negligible in technical materials, except superconducting materials under some conditions. Monoatomic rare gases such He are diamagnetic, as well as most polyatomic gases such as N2 (that might show nevertheless a net paramagnetic behaviour because of O2 contamination). Since He is repelled by magnetic fields, operation of superconducting magnets in a weightless environment during orbital flights imposes a significant difficulty not present in laboratory experiments, already discussed and quantified in 1977 [8]. This concern is still present today: the effect of a magnetic field on diamagnetic liquid helium will be studied in the very near future in the cryogenic system of the cryomagnet of the Alpha Magnetic Spectrometer (AMS) experiment, foreseen on the International Space Station (ISS) [9]. Paramagnetism, corresponding to a positive susceptibility, is observed in many metals and substances including ferromagnetic and antiferromagnetic materials above their Curie (Tc) and Néel (TN) temperature, respectively [10]. Particular care should be taken for some Ni-basis superalloys for non-magnetic application at very low T. Incoloy 800 (32.5Ni-21Cr-46Fe) features a magnetic permeability as low as 1.0092 at room temperature (annealed state, under a field of 15.9 kA/m). Nevertheless, due to a Tc = -115 °C, the alloy is ferromagnetic at cryogenic temperatures. Ferromagnetism is due to the ordered array of magnetic moments, caused by the interaction of atomic spin moments occurring in certain conditions. Field-dependent permeability and persistent magnetization after the removal of magnetic field are observed for hysteretic ferromagnetic materials. Ordered ferromagnetic phase occurs for ferromagnets at T < Tc. Here Tc is the temperature above which spontaneous magnetization ‘vanishes’ [6]. The Tc of Fe, Ni and Co are 1043 K, 631 K and 1394 K, respectively. In general, ferrous alloys with body centred cubic (bcc) crystalline structure are ferromagnetic, while face centred cubic (fcc) are not. Nevertheless, rapidly solidified metastable alloys such as Fe-Cu alloys can show ferromagnetism in a wider composition range than expected, even in the fcc phase formed below 70% Fe content [11]. Antiferromagnetism corresponds to an antiparallel arrangement with zero net magnetic moment at T < TN. ‘Non-magnetic’ austenitic stainless steels such as AISI 304L, 316L, 316LN, high Mn – high N stainless steels are antiferromagnetic under TN and paramagnetic above TN, where they obey a Curie–Weiss law (! = C/(T-!), where ! is a negative critical temperature and C is a constant (Fig. 1a). Magnetic susceptibility of high Mn – high N grades such as P506 (approx. 0.012%C, 19%Cr, 11%Ni, 12%Mn, 0.9%Mo, 0.33%N) and UNS 21904 (approx. 0.028%C, 20%Cr, 7%Ni, 9%Mn, 0.35%N), particularly at 4.2 K, is lower than any traditional steel of the 300-series. As known, this is essentially due to the higher Mn content of the alloys (P506, Mn = 12%; UNS21904, Mn = 9%), stabilizing austenite (fcc ‘non-magnetic’ phase), and increasing TN. Higher TN allows for lower values of ! (<3!10) at 4.2 K. Measured values of TN are in agreement with the Warnes [12] law: