Discussion on problems aroused from measuring hard magnetic properties at elevated temperatures

Abstract

With the development of modern industry, more and more permanent magnetic materials are used at elevated temperatures. Thus it has become more and more important to measure their magnetic properties accurately both at room temperature and elevated temperatures. In this paper, for a better understanding of temperature coefficients, measuring of the magnetic properties at elevated temperatures and related problems are reviewed and discussed qualitatively. Advices on magnetizing permanent magnets at elevated temperatures are also given. In addition, principal problems and new advances involved in measuring techniques at elevated temperatures are also discussed. Furthermore, problems associated with testing magnets at elevated temperatures using a vibrating sample magnetometer (VSM) are also presented.

Keywords

Permanent magnetic materials magnetic measurement temperature coefficient magnetic properties at elevated temperatures

1. Introduction

The research and development of magnetic materials requires a comprehensive evaluation of their magnetic properties, including properties obtained from hysteresis curves (e.g., magnetization curve and hysteresis loop). Based on hysteresis curves, several quantities such as saturation magnetization $M_{s}$ , remanence $M_{r}$ , coercivity $H_{c}$ , knee field strength $H_{k}$ (commonly called knee field, also known as uniformity magnetic field strength, $H_{k}$ is the negative value of the magnetic field strength when the magnetic polarization $J$ of a permanent magnet is brought from saturation to 90% of the value of $J_{r}$ by a monotonically changing magnetic field.), relative permeability $\mu_{r}$ (for permanent magnetic materials, also known as recoil permeability $\mu_{\textit{rec}}$ ), maximum energy product ( $B H$ ) ${}_{\max}$ , and losses $P_{c}$ , etc., can be determined. In addition, magnetic measurements are also frequently used for the characterization of changes in ferromagnetic materials, because magnetization processes are closely related to their microstructure as well. Moreover, mechanism which gives rise to hysteresis is thought to be caused by magnetocrystalline anisotropy and ‘imperfections’, etc. These imperfections can be in the form of dislocations or impurity elements, etc., in the materials [1, 2]. This further makes the magnetic approach an obvious candidate for nondestructive evaluation (NDE), which means that it can be used to detect and characterize defects in materials and products made of such materials.

Nowadays magnetic materials, such as high duty permanent magnet motors, servo-motors, compressors for air-conditioners and refrigerators, HEV (Hybrid Electric Vehicle) and EPS (Electric Power Steering), etc., are often used at elevated temperatures. Whereas the most high energy permanent magnets (PMs) used at room temperature are now made from RE-Fe-B, Sm-Co magnets have retained their dominance at elevated temperatures, and precipitation hardened Sm (Co, Fe, Cu, Zr) magnets have received considerable attention because of various needs for high temperature applications too. Rare-earth transition-metal (RE-TM) magnets have to operate at elevated temperatures up to 200 ${{}^{\circ}}$ C in many applications. For example, working temperature of motors in electric vehicle (EV) is about 200 ${}^{\circ}$ C. Moreover, the modern industry and the scientific research require PMs with high operating temperature of over 400 ${}^{\circ}$ C and high maximum energy product [3]. The power system in a new generation of aircraft requires PMs capable of operating at temperatures higher than 400 ${{}^{\circ}}$ C, and for certain applications, the desired maximum operating temperature is above 450 ${{}^{\circ}}$ C [4]. As we know that the magnetic properties of magnetic materials are all temperature dependent, if the magnetic materials working at high temperature are analyzed using the magnetic properties measured at room temperature, the obtained results will be fairly different from an actual phenomenon [3, 5].

To establish a new application, suitable PMs have to be chosen from the viewpoint of magnetic properties, temperature stability and the cost of designing the magnetic circuits. Moreover, for high temperature applications, the temperature stability of PMs is a key point which has to be considered during the magnetic circuit design, and high performance PMs have been devoted to result in higher power and higher efficiency with better reliability, which will contribute to future energy saving. In addition, this is also recognized as an effective method to reduce global-warming.

As the development of modern electronic techniques and ever-increasing, widely spread uses of PMs, industrial producers and consumers of magnets are increasingly demanding that magnets should be individually tested accurately [6]. Moreover, magnetic measurements are also employed by NDE testing of materials, especially those used in high temperatures [1, 2]. B(H) and/or J(H) curves are generally used to describe the relationship between magnetic flux density B (or polarization J) and magnetic field strength H of a magnetic material. As a PM generally operates in the second quadrant of its hysteresis loop (also known as demagnetization curve), its performance is governed by its dimensions, the type of magnetic circuit in which it works, and its demagnetization curves at room temperature and elevated temperatures.

The DC Hysteresigraph (also known as BH Tracer) is a closed circuit measuring instrument which is approved by IEC 60404-5 [7] and ASTM A997/A997M [8], and also is universally employed and the only one commonly used for testing PMs [6]. In addition to the static hysteresis measurement of $J_{s}$ , $B_{r}$ , $H_{cJ}$ , $H_{cB}$ , $H_{k}$ , $\mu_{\textit{rec}}$ , and ( $B H$ ) ${}_{\max}$ [6], temperature coefficients of the magnetic properties can be calculated from measurements at elevated temperatures. Then, magnetic properties $\alpha_{B_{r}}$ , $\beta_{B_{r}}$ , $\alpha_{H_{cJ}}$ , $\beta_{H_{cJ}}$ are the linear temperature coefficient of remanence, quadratic temperature coefficient of remanence, linear temperature coefficient of intrinsic coercivity, quadratic temperature coefficient of intrinsic coercivity, respectively. Normally, $\alpha_{B_{r}}$ and $\alpha_{H_{cJ}}$ stand for temperature coefficients of a material. It is known that though magnetic materials have been widely characterized for many years, the B(H) and/or J(H) curves and their dependence on temperature (such as those used in the range of the injection molding process) are not commonly characterized [9].

Furthermore, though accurate magnetic measurement instrumentations are commercially available universally for a long time, it is generally accepted that a profound understanding of basic magnetic principles is crucial to success in making magnetic measurements of all types, especially in recognizing and avoiding situations that will produce erroneous results [6, 10]. This situation is the same for both soft and hard magnetic testing. It is also found that there was some evidence of inadequate operator training [10]. Thus, though a fully computerized measurement system, which is usually equipped with a friendly graphical user interface, can help to obtain the useful measuring results quickly, and is certainly a great convenience compared with the old manually operated ballistic method, or with the electronic one using X-Y recorder, etc., it cannot be used as a substitute for comprehensive operator education and training [6, 10]. Furthermore, the results often can be obtained without being aware of the mistake, or the mistake often goes unnoticed.

Design engineers and end users of magnetic data must keep in mind that not only can there be variations of magnetic properties within a manufactured product, but that the magnetic measurements themselves may include a fairly large degree of uncertainty [6, 10], so international comparison is habitually organized [11]. They must be aware that for inexperienced users, in addition to the specific “how to” instructions which are typically provided by equipment manufacturers, suitable training in general magnetic principles and testing methodology is not only necessary, but also very important for them to do the measuring work in a correct manner. It is worth to mention that great care should be taken even for experienced users when measuring magnetic properties of magnetic film, magnetic particles (including nano-particles), etc., to avoid principle errors. Moreover, suitable training is also very crucial to a newcomer, even to those specialists engaged in other scientific areas such as chemistry, biology, medical science, and materials science, etc., as they feel much interested in magnetism in these years.

Just as we have discussed [6], with the improvement of high performance PMs, such as rare-earth transition-metal (RE-TM) magnets, bonded magnetic materials and nanocrystalline exchange-coupled magnets, etc., PMs are widely used both in room and elevated temperatures. Many problems have arisen in measuring their magnetic properties using traditional DC Hysteresigraph methods, as they are mostly developed on the measuring study of PMs with low coercivity, and also many new measuring methods have been proposed [12, 13], though have not been approved and covered by IEC standards yet. Every experimental method entails its own particular problems, to which there is no universal solution. Thus, over the years, a wider proliferation of magnetometers has been produced with different methods [12]. Many factors can influence the measured magnetic properties of PMs including specimen, uniform magnetization, saturation magnetization, static measurement and dynamic measurement, influence of the saturation of the poles, influence of Hall probe, and other factors, etc [6]. Though magnetic measuring is well known in magnetism field, the knowledge is all scattered among professional books and national standards [10], and among scientific papers. In this paper, for a better understanding of magnetic properties and the measuring methods of PMs at elevated temperatures, we will discuss the problems on measuring of the magnetic properties at elevated temperatures, and on related problems in detail. We will also focus on hard magnetic measuring methods, especially those that are used in industrial applications. These problems are becoming more and more important in the quality control, applications, and also in the research and development of new materials. In addition, advices are also presented.

2. Main problems

2.1 Measuring of the high temperature magnetic properties

Nowadays the applications of PMs are expanding to elevated temperatures. In addition, PMs used at high-temperature applications are also a research area of great scientific and industrial interest. Because it is required to specify and guarantee the magnetic properties of PMs over their working temperature range, it has become increasingly important to measure their magnetic properties at elevated temperature. Especially, due to the fact that the magnetic properties of PMs are strongly dependent on temperature, and are also nonlinear mainly because of magnetic saturation, in order to establish a sufficient material database, a lot of data are required, which emphasizes the need for material data of the B(H) and J(H) relation, hysteresis, and their temperature dependence [5].

The methods of measurement of the magnetic properties of PMs at room temperature have been specified in IEC 60404-5 for closed magnetic circuits [7] and in IEC 60404-7 for open magnetic circuits [14], respectively. Though the method used for measurement of PMs at elevated temperatures has been specified in IEC TR 61807 [15], it is only a rather rough technique guide. In this TR, the preferred method suggested to measure the magnetic properties of PMs at elevated temperatures is referred to IEC 60404-5 [7]. As to how to raise the temperature of the measured sample to a certain elevated value, the recommended method is to immerse the whole systems, including test specimen, search coils and the closed magnetic circuit in a tank filled with electrically insulating coil, and then the oil should be heated to the desired temperature before measuring. To improve the thermal equilibrium for measurement at elevated temperatures, it is suggested that the oil must be circulated or stirred. After that, the sample can be measured as usual.

Nevertheless, this preferable method is very inconvenient. Thus, a suggestion is also described in this TR 61807. The main idea means that, in order to reduce the size of the whole temperature controlled measuring apparatus, and also to make the whole testing more easily, a heating system (including temperature sensor) can be assembled into the magnetic poles of an electromagnet. That is to say, after the sample has been inserted into the electromagnet, the pole pieces can be heated together with the sample. At this point, the procedure is that, after the desired temperature has reached, the J (or B) sensing coil and the H measuring system can be mounted between the measuring pole faces, and the measuring can be done as usual, with the emphasis on that the temperature of the test specimen and pole faces must be allowed to stabilize before a measurement is made. From the view point of measuring, it is obvious that the measured temperature of the pole face and that of the test specimen can be considerably different, and this difference is dependent on the geometry and the thermal characteristics of the pole faces and test specimen. Furthermore, at each temperature increment, the sample must be left for a sufficiently long period to ensure equilibrium. Therefore, for a certain systems, it is necessary to establish the relationship between the temperature of the test specimen and of the pole face through a series of separate experiments first. Moreover, as the magnetizing field in the electromagnet is usually not high enough to saturate most of the RE-TM magnets, the test specimen must be magnetized in a pulse magnetizer prior to being inserted between the pole faces in order to achieve the required level of magnetic saturation, just as it is usually done in the measurement of PMs at room temperature [6].

An alternative method suggested in this TR 61807 is based on the method given in IEC 60404-7 [14], which is an open-circuit measurement. This system includes a thermally insulated heating chamber containing the magnet specimen to be measured, a solenoid, a B search coil and a temperature sensor. The method of magnetization of the test specimen recommended for industry is a pulse method. Of course, only $H_{cJ}$ can be deduced using this method.

Accordingly, it is evident that this TR 61807 has roughly described the method used to measure magnetic properties of PMs at elevated temperatures. It does not give the soaking time, and the allowed temperature variation of the specimen during the measurement. In addition, as far as we know, though the specimen used in this TR 61807 is just the same as that in IEC 60404-5 [7], it is not indicated in this technical report that a single specimen is used for all the temperature measurements, or for each temperature, a new specimen should be used.

The stability of the magnets in industrial applications is very important. As we have known, rare-earth (RE) metals are sensitive to oxidization, and the RE-Fe-B material can start to oxidize at elevated temperatures in air if it is not suitably protected [16]. PMs such as Nd-Fe-B type rare earth magnet will suffer irreversible magnetization loss at high temperatures. Although the Curie temperature $T_{c}$ of Nd-(Fe, Co)-B material is about 310 ${}^{\circ}$ C for 0% cobalt material to greater than 370 ${}^{\circ}$ C for 5% cobalt, some irreversible loss of magnetization may be expected at even moderate temperatures.

For PMs in a magnetized state, flux loss is the reduction of the flux due to external influences, basically temperature. Thermal stability of PMs can be understood as the changes in $B_{r}$ and $H_{c}$ when the temperature changes. These changes, mainly J (and B) losses and/or decrease in $H_{c}$ with increasing temperature, can be divided into reversible and irreversible changes according to whether the original J (or B) is recovered or not as the temperature is returned to the original state. Theoretically, the total magnetization loss in a magnet is composed of reversible loss, recoverable irreversible loss and structural loss [17, 18]. The reversible changes are where the initial magnetic properties are restored when the magnet returns to the original temperature; and the recoverable irreversible changes are defined as partial demagnetization of the magnet, caused by exposure to high or low temperatures. Irreversible loss can only be restored by remagnetization, as they are due to magnetization reversal phenomena. Structural loss is due to phase changes, as typically caused by oxidation in NdFeB magnets. Demagnetization curves at different temperatures reveal the losses of a magnet as $B_{r}$ and $H_{c}$ will decrease with increasing temperature (but for M-type ferrite such as SrM, its coercivity increases with increasing temperature). This is a characteristic phenomenon of the magnetic material.

Practically, the stability of PMs is evaluated using three kinds of flux loss. The flux loss contributions are classified as reversible flux loss, irreversible flux loss and permanent flux loss [19]. Here, the reversible change in the magnetic properties of PMs as a function of temperature originates from the change in saturation magnetization $M_{s}$ . Reversible flux loss is a magnetization change which is recovered by the removal of a disturbing influence such as temperature. This flux loss closely reflects the temperature variation of $M_{s}$ and $M_{r}$ . With irreversible flux loss, after the removal of the disturbing influence, the magnetization does not return to its original value. Typical disturbing influences are temperature changes, local temperature fluctuations and magnetic fields. The irreversible flux loss can be fully recovered by remagnetization. Permanent flux loss is caused by permanent changes in the metallurgical state, may be due to phase changes, and is generally time and temperature dependent. Examples are precipitation and growth, oxidation, the annealing effects and radiation damage. Changes in the microstructure, surface oxidation, etc., can cause an additional flux loss, which cannot be recovered either. The permanent flux loss cannot be recovered to the initial magnetization value by remagnetization.

Temperatures under the Curie point of Nd-Fe-B magnets cannot cause phase changes. In addition, it has been found that SmCo-based magnets cannot be used for a long-term application at high temperatures because of the permanent flux loss of magnetic properties, which is mainly due to the surface degradation layer [20]. For the original Sm ${}_{2}$ Co ${}_{17}$ magnets with square-shaped loops, if they are isothermally treated in air at 500 ${}^{\circ}$ C for different times, they will all exhibit constricted loops and declined magnetic properties. Careful research found that for these magnets, a degradation layer will be produced on the surface mainly because of the diffusion of the oxygen, which was the main reason that deteriorated the magnetic properties.

In other researches [21, 22], it is found that for SmCo-type magnets, whereas no obvious change in the coercivity at room temperature was detected after high temperature measurements below or at 400 ${}^{\circ}$ C, the coercivity measured at room temperature starts to reduce after high-temperature measurements above 400 ${}^{\circ}$ C. It is also very interesting to note that the higher the measurement temperature, the larger the loss of the coercivity at room temperature. Detailed study shows that the observed decrease in coercivity above 400 ${}^{\circ}$ C is not due to surface degradation but because of the microstructural changes in the bulk instead. As it is well accepted that the coercivity mechanism of conventional SmCo-type magnets is due to the pinning of domain walls at the 1:5 cell-boundary phase with lower domain-wall energy, thanks to the different solubilities of transition metal elements in the various phases, more specifically the Cu content within the 1:5-type cell-boundary phase, the loss of the coercivity is explained in terms of changes in microchemistry.

The temperature characteristics of SmCo ${}_{5}$ , Sm ${}_{2}$ Co ${}_{17}$ and Nd-Fe-B sintered magnets are closely dependent on the magnetic properties and their temperature dependence of the base intermetallic compounds. The temperature stability of Sm ${}_{2}$ Co ${}_{17}$ sintered magnets is the best among the three kinds of RE-TM sintered magnets taking account of the three parameters $T_{c}$ , $\alpha_{B_{r}}$ and $\alpha_{H_{cJ}}$ . It is reported that [19], the coercivity of Sm ${}_{2}$ Co ${}_{17}$ magnets is controlled by “pinning by precipitates”, so $\alpha_{H_{cJ}}$ value of Sm ${}_{2}$ Co ${}_{17}$ magnets can be controlled by their composition and heat treatment. The coercivity of “pinning” type magnets is determined by the pinning of the domain walls at the phase boundaries of the precipitate and the further movements of domain walls are strongly impeded by pinning, while small reverse domains exist at all times. On the contrary, the $\alpha_{H_{cJ}}$ of SmCo ${}_{5}$ and Nd-Fe-B cannot be changed significantly because their coercivity mechanism is “nucleation”. The coercivity of “nucleation” type magnets is determined by the nucleation of a reverse domain after removal of the domain walls, while the movements of existing domain walls within a grain are relatively easy.

A reversible decrease in magnetic properties with increasing temperature is always present, and cannot be eliminated. However, it can be reduced by modifying the material composition [23]. Though irreversible flux loss is recoverable by remagnetization, remagnetization of magnets is, however, impossible in many applications, such as in many motor applications, and therefore the control of these flux losses is crucial. Irreversible flux loss can be reduced or eliminated by magnet stabilization, e.g., thermal stabilization. Permanent flux loss in sintered Nd-Fe-B magnets is resulted from demagnetization or oxidation and can be avoided by means of proper design, material selection and corrosion protection. Permanent flux loss due to oxidation can be avoided with proper corrosion protection, but for measuring samples, it is very hard to do so.

The reversible changes are usually only dependent upon the material composition, whereas the irreversible flux loss is largely dependent on the working point and intrinsic coercivity of the material grade, etc. In addition to the reversible flux loss due to temperature change, there is an irreversible flux loss occurring in magnets as soon as a certain temperature is reached and/or after a thermal after-effect, which means loss with time, so soaking time should be determined for different materials when measuring elevated magnetic properties.

After PMs are heated to elevated temperature, and then cooled down to room temperature, the permanent flux loss will occur, which means that these losses can’t be recoverable, especially when heated to relatively high temperatures. If we measure magnetic properties at several temperatures using one specimen, errors will occur because of the permanent flux loss (stabilization). To get stable and repeatable temperature coefficients, either the specimen should be aged at a higher temperature before measurement to eliminate the permanent flux loss, or a set of samples should be used, each at a certain temperature. Obviously the consistency of the specimens must be considered. Perhaps a group of specimens will have to be chosen carefully to statistically have the same performance. If the specimens are aged, the obtained values are only representative if all magnets will be aged before they are used in a final product.

Temperature coefficients give a good picture of the material’s temperature behavior, but are not sufficient when considering the thermal stability of a magnet in an application [23], e.g., the thermal stability of sintered Nd-Fe-B magnets can be described by the temperature coefficient of remanence only on condition that demagnetization due to rising temperature or field and oxidation of the magnets are totally avoided. This also requires the control of time-dependent demagnetization at elevated temperatures [23]. With all this information, initially occurring flux loss due to a sudden temperature rise, can be estimated. One also needs data about the shape of the B(H) and/or J(H) curves and magnetic circuit information.

Time-dependent demagnetization should be taken into account when determining the thermal stability of magnets. Flux loss with time in permanent magnets is dependent on the magnetic field, temperature, magnet material, its microstructure and the magnetization process [1]. Because it is not possible to realize truly DC characterization, the very similar metastable character of the magnetization state leading to hysteresis makes the material prone to thermally activated microscopic magnetization reversals, so that by lowering the field rate of change the role of thermal activation is enhanced.

The usually called long term ageing means, when the flux (open circuit flux or its operating-point induction) of a newly magnetized magnet is observed for a long period of time, a slow decay is found to occur. This behavior usually follows a time function. The change can be separated into three stages [19, 24]: initial flux loss, plateau, and long-term instability. At the beginning, there is a relatively fast initial flux loss. In this period, there are mainly changes that can be recovered by remagnetizing. Following this, there is a “plateau”, which is a long period of increasing stability. During this period, there is often a constant irreversible flux loss per logarithmic time cycle on the plateau. This time dependency of B on the plateau is proportional to logarithm of the time. The final stage, long term instability means, at higher temperatures and for some magnets, the flux decline will later accelerate and is sometimes catastrophic. This phenomenon was clearly observed for RE bonded magnets with an improper surface treatment under harsh environment conditions. But for RE sintered magnets only small flux changes were observed. There is also a tendency for specimen with the higher initial flux loss exhibit the higher irreversible flux loss per decade regardless of material [19].

Long-term demagnetization in permanent magnets is due to so-called magnetic viscosity effect [6, 12, 23]. Magnetic viscosity is a statistical relaxation phenomenon due to thermal fluctuation in the non-equilibrium state of the material [23, 25]. There is no consistent way to express or even measure the long-term behavior of magnetic materials. To be able to estimate long-term losses, more information are needed about the long-term environmental conditions and long-term demagnetization characteristics of the material. The irreversible flux losses measured after temperature exposure of 1 or 2 h tell us something about the long-term effects. However, these represent only one condition with one exposure time. Therefore this information is difficult to utilize in machine design.

Flux loss due to rising field and temperature can be determined from the B(H) and J(H) curves of a material at different temperatures. Some of the studies report material characteristics like intrinsic coercivity $H_{cJ}$ , or temperature coefficients of remanence and temperature coefficients of coercivity, as measures for thermal stability. The temperature coefficients are expressed as %/ ${}^{\circ}$ C or %/K.

Table 1
$\alpha_{B_{r}}$ , $\alpha_{H_{cB}}$ and $\alpha_{H_{cJ}}$ of AlNiCo8, hard Ferrite Y30, SmCo ${}_{5}$ , and Nd-Fe-B 25SH in temperature range of room temperature to 180 ${}^{\circ}$ C

	AlNiCo8	Hard Ferrite	SmCo ${}_{5}$	Nd-Fe-B 25SH
$\alpha_{B_{r}}$ (%/ ${}^{\circ}$ C)	$-$ 0.001 $\sim$ $-$ 0.03	$-$ 0.15 $\sim$ $-$ 0.19	$-$ 0.04 $\sim$ $-$ 0.06	$-$ 0.01 $\sim$ $-$ 0.11
$\alpha_{H_{cB}}$ (%/ ${}^{\circ}$ C)	$-$ 0.001 $\sim$ $-$ 0.035	0.05 $\sim$ 0.3	$-$ 0.10 $\sim$ $-$ 0.16	$-$ 0.30 $\sim$ $-$ 0.50
$\alpha_{H_{cJ}}$ (%/ ${}^{\circ}$ C)	$-$ 0.02 $\sim$ $-$ 0.035	0.3 $\sim$ 0.45	$-$ 0.35 $\sim$ $-$ 0.46	$-$ 0.55 $\sim$ $-$ 0.90
Tc ( ${}^{\circ}$ C)	810	450	710	312

Figure 1.

variation of $\alpha_{B_{r}}$ , $\alpha_{H_{cB}}$ and $\alpha_{H_{cJ}}$ with temperature: (a) AlNiCo8, (b) hard Ferrite, (c) SmCo ${}_{5}$ , and (d) Nd-Fe-B 25SH.

In order to investigate the variation of temperature coefficient, we have measured the temperature coefficients of four kinds of PMs at different temperatures, e.g., AlNiCo8 (cylinder, $\phi$ 8 mm with height of 8 mm), hard Ferrite Y30 (FB5 of TDK, rectangle, 19.68 mm long, 19.2 mm wide with height of 15 mm), SmCo ${}_{5}$ (cylinder, $\phi$ 10 mm with height of 5 mm) and Nd-Fe-B 25SH (cylinder, $\phi$ 10 mm with height of 5 mm). Though in each of the material classes, different grades will have different temperature behavior, the results measured can still be regarded as representative values for each material class to establish the variation of the temperature coefficient with different temperature ranges. The samples were measured by a Permagraph-Remagraph Combination C-750 made by Magnet-Physik Dr. Steingroever GmbH of Germany. After the samples are magnetized to saturation, they are inserted into the electromagnet, heated to the desired temperature, holding at that temperature for about 20 min, and then the demagnetization curves are measured. Subsequently, after the samples cooled down to the room temperature, they are magnetized to saturation again for next measuring. The average temperature coefficients referring to room temperature of each material at different temperature ranges are calculated, and the room temperature for AlNiCo8 and SmCo5 is 25 ${}^{\circ}$ C, for hard ferrite is 20 ${}^{\circ}$ C, and for Nd-Fe-B is 23 ${}^{\circ}$ C. Details about the measurements will be published later. Variation of temperature coefficients of $B_{r}$ , $H_{cB}$ and $H_{cJ}$ of these samples with temperature are shown above in Fig. 1. The typical value of the variation ranges of $\alpha_{B_{r}}$ , $\alpha_{H_{cB}}$ and $\alpha_{H_{cJ}}$ in the measuring temperature range of room temperature to 180 ${}^{\circ}$ C (for AlNiCo8, is 200 ${}^{\circ}$ C) are also collected in Table 1. Tc in Table 1 is collected from the literatures [1, 2, 13, 19], and only for reference.

We can see that $\alpha_{B_{r}}$ , $\alpha_{H_{cB}}$ and $\alpha_{H_{cJ}}$ are all temperature dependent, and they will change with temperature ranges in which they are defined. It is also worthy to mention that $\alpha_{H_{cB}}$ is an important parameter too. These are average values over a specified temperature range, so the temperature range should be stated to make them quantity. Generally PMs exhibit a non-linear variation with temperature.

As shown in Fig. 1 and Table 1, hard ferrites and rare-earth magnets have an appreciably high temperature coefficient of both saturation magnetization and coercivity. This not only implies that a strict control of the temperature during the measurement must be applied, but it also frequently calls for material testing at specified elevated temperatures. If the standard IEC 60404-5 is applied for testing at elevated temperatures, one of the methods described in TR 61807 should be adopted [7, 15]. We can also see from Fig. 1 and Table 1 that, AlNiCo magnets have a rather small temperature coefficient. In the whole temperature range, the variation of three kinds of temperature coefficients is very small. So the Y-axis is enlarged for a better showing.

It is suggested that in many instances the temperature coefficients of magnetization and coercivity cannot give enough information about how a magnet will respond to temperature change [26]. In many magnets the demagnetization curve cannot be well defined only by $B_{r}$ and $H_{cJ}$ , because changes in the curve shape and the intersection with load lines can only be seen from a complete set of demagnetization curves measured at several temperatures over the temperature range of interest. Furthermore, $H_{k}$ is generally used. So temperature coefficient of $H_{k}$ should be studied.

Moreover, for the calculation of temperature coefficients of magnetization and coercivity, it is thought that the definition given in IEC TR 61807 [15] is too complicated in the early age of PM development, because the equations given in IEC TR 61807 are based on a quadratic equation deduced from the measured values measured at more than three temperatures by using a statistical calculation. The method of least squares is applied to the quadratic equation. Of course, in the age of computers, the treatment of a quadratic equation can be finished automatically. So traditionally usually the temperature coefficient of a magnetic parameter $Q$ over a temperature interval between $T_{1}$ and $T_{2}$ is defined as the following equation:

$\displaystyle\alpha_{(T_{1}\to T_{2})}=\frac{Q_{T_{2}}-Q_{T_{1}}}{Q_{T_{1}}(T_% {2}-T_{1})}\times 100\%\quad[\%/K]$ (1)

Here $Q$ stands for a magnetic parameter such as $B_{r}$ or $H_{cJ}$ . Our measuring results shown in Fig. 1 and Table 1 are all calculated using Eq. (1), and in every temperature, $T_{1}$ is room temperature. Equation (1) is not an accurate description of the temperature dependence of magnetic properties, especially when the interval of the temperature range is large [27]. As the most commonly used parameter for temperature dependence of magnetic properties is the temperature coefficient, as shown in Fig. 1 and in Table 1, and temperature coefficients are not monotonic functions of temperature, definition in Eq. (1) may give misleading result. Thus, an instantaneous temperature coefficient is a more accurate description of the temperature dependence of magnetic properties [27]. The temperature coefficient of $Q$ at a specific temperature $T$ is defined as:

$\displaystyle\alpha_{T(\Delta T\to 0)}=\frac{\Delta Q}{Q\Delta T}\times 100\%% \quad[\%/K]$ (2)

Perhaps because this definition is inconvenient, it is not widely used in industry applications. Furthermore, when defining a temperature coefficient, the temperature range should be stated considering the non-linearity of the temperature dependence.

The magnetization processes are associated with irreversibility and losses, and a variety of J(H) hysteresis behaviors. Moreover, hysteresis behavior is a property shared with many physical phenomena [28]. Because of hysteresis, any point in the (J,H) plane can be traversed by an infinite number of pathways, depending on past history, which means that magnetic properties are also closely related to past magnetizing history. But there still exist two attainable reference states for experimental investigation: saturation, where all domains are swept out, and the demagnetized state (H $=$ 0, J $=$ 0). Like all other points inside the saturation hysteresis loop, the point (H $=$ 0, J $=$ 0) can be reached by different pathways and is therefore not generally a unique reference state. Magnetization reversal may be activated by increasing the opposite magnetic field or raising the temperature. In a static magnetic field and at a certain temperature, the magnetization reversal can also be activated by the magnetic viscosity effect.

Fortunately, in many practical magnets and at temperatures of interest for applications, thermally activated relaxation processes (after-effects), either due to diffusion of specific solid solution elements or caused by thermal fluctuations, have little or negligible effect, thus a true rate-independent magnetic performance of the material can be reasonably approached. Nevertheless, the intrinsic stochastic character of the magnetization process and, in metallic materials, residual eddy-current related relaxation effects can frequently cause a certain lack of reproducibility of the J(H) curves, especially at low and intermediate polarization values [1].

Basically, the combination of $H_{cJ}$ and L/D of a PM determines its maximum operating temperature $T_{\max}$ . Of course, a magnetic circuit will also influence $T_{\max}$ if the PM is a part of it. Moreover, the temperature dependence of the working point, the temperature dependence of $H_{k}$ and $\alpha_{H_{cJ}}$ will also influence $T_{\max}$ . Thus in many magnetic circuit designs, in addition to the reversible flux loss due to temperature change, irreversible flux loss occurring in magnets also need to be considered. Furthermore, irreversible flux loss can occur as soon as a certain temperature is reached. As a thermal after-effect, it means flux loss with time. In most of the cases, the amount of immediate flux loss can be determined by the slope of the demagnetization curve due to the fact that, when the working point of a magnet falls below the knee of the B(H) curve, the magnetization will become unstable. $H_{k}$ is a measure for the squareness of the demagnetization curve, and is a reverse field to reduce $J_{r}$ by 10% on the J(H) demagnetization curve. Thus immediate flux loss occurs and the flux loss will also increase with time. In some cases, even when the working point is above the knee of the demagnetization curve, as mentioned above, the slope of the trend flux loss to time curve cannot be predicted from the immediate flux loss.

The irreversible flux loss behavior of RE-TM magnets is dependent on $H_{cJ}$ , L/D, exposure temperature and $H_{k}$ , etc. Magnets exposed to the higher temperatures exhibit the higher permanent flux loss. Specimens with the lower L/D exhibit the higher irreversible flux loss. The lower L/D means that the higher demagnetization field is applied to magnets by their own magnetization and a higher irreversible flux loss results. Irreversible flux loss can be reduced by an increase in coercivity under conditions which keep an ordinary squareness level.

Besides, there is a problem to test the temperature coefficient of the product (body) and of the material, just like those in the case of room temperature measurement [6]. Usually, in industry applications product property is concerned, and in research area material property is measured. Nowadays high coercivity PMs are mostly used in a very low L/D, and in many cases, they are used in larger sizes. If these products are used as specimens, there will be a problem concerning how to evaluate their elevated magnetic properties and temperature coefficients of $B_{r}$ and $H_{cJ}$ .

As we have known that, during the measuring process, if the specimen has been saturated, and the demagnetization curve of a certain temperature has been obtained, it will be magnetized again for next measuring. But in IEC TR 61807 [15], no suggestion is given if the specimen should be magnetized in the same direction, and/or the specimen can be magnetized either after it has cooled down to room temperature, or magnetized just after each measurement. We think that the sample should be magnetized in the same direction when it is cooled down to room temperature, so that the irreversible flux loss can be recovered. Furthermore, as we have known that, when PMs are magnetized to saturation for the second time, the saturation magnetization field needed will be much higher than the first one given in material standard and test standard according to the magnetization mechanisms of PMs. It has been found that the coercivity of Nd-Fe-B sintered magnets is controlled by the nucleation of reversed magnetic domains in a locally reduced magnetocrystalline anisotropy region [29], whereas the coercivity mechanism of conventional SmCo-type magnets is due to the pinning of domain walls [22], as mentioned above. Therefore, for different PMs, it is necessary to do a series of experiments to determine the changes of saturation magnetization field with the saturation magnetization time.

As far as we know that, a Hall probe based on the Hall Effect is widely used in the measurement of the magnetic field strength H in industry applications. It is also worthy to know that the basic Hall device used in a Hall probe is sensitive to variations in temperature [6, 13]. Now some H and B coils are heat resistant to 150 ${{}^{\circ}}$ C, and short duration at 200 ${{}^{\circ}}$ C [30], thus if a H coil together with a B (or J) coil of this kind is used, magnetic properties up to 200 ${{}^{\circ}}$ C can be easily obtained, as mostly the needed measuring temperature will be lower than 200 ${{}^{\circ}}$ C. Nowadays the working temperature of Nd-Fe-B magnet has reached 180 ${{}^{\circ}}$ C, some are even higher than 200 ${{}^{\circ}}$ C, and the working temperature of Sm-Co magnet is even higher, sometimes it is needed to measure at an elevated temperature as high as 500 ${{}^{\circ}}$ C. So, researches have to be done how to measure elevated temperature magnetic properties of PMs up to 500 ${{}^{\circ}}$ C or higher in a convenient and inexpensive way for increased industry applications.

The vibrating sample magnetometer (VSM) has become a common equipment worldwide, both in industry and in scientific research area. Although VSM can be used to measure hysteresis loops, and the change of magnetization of magnetic material measured using a VSM is well reported [5], and international comparison concerning measurements of hard magnets with VSM is also promulgated [11], the data of magnetic properties, such as B(H) and/or J(H) curves and iron loss curves, etc., which are indispensable to the precise analysis of the magnetic properties of both soft and permanent magnetic materials, is not commonly measured using VSM both at room temperature and elevated temperatures. Furthermore, a precise analysis considering magnetic properties measured using VSM at elevated temperature is also few [5].

Generally, the use of VSMs is not a problem, but there exist some restrictions, e.g., as the VSM measurement is an open circuit measurement, corrections for the specimen shape (demagnetization factors) are normally necessary [6]. Moreover, VSMs cannot test most of PM products, as only very small specimen sizes are possible, and the specimen must be machined to regular shapes, e.g., bar or ball. In industry, usually VSM is used to evaluate the magnetic properties of magnetic powders. Furthermore, in many cases, it is hard to correct the effect of specimen geometry, then, using VSM, usually only saturation magnetization $M_{s}$ of a magnetic material can be obtained. Moreover, there also exists the problem of Metrological traceability. At present day quality management systems increasingly require measurements to be traceable to both written and physical standards [31]. Hence, using VSM for measuring PMs at elevated temperatures might become complicated due to practical reasons [5, 9].

The ring method for measuring soft magnetic materials is an approved method, and is wide-spread and being used for decades, now an alternative method to measure the B(H) relation at high temperatures for soft magnetic materials was also suggested to using ring samples [5]. Of course, ring method cannot be used for PMs for multiple reasons. But a convenient method for measuring PMs at high temperatures in industrial applications is still absent, perhaps it is possible to use pulse field magnetometer (PFM), which can handle the specimen of industrial size [32]. Nevertheless, the PFM is also an open circuit method, just like VSM. Therefore, the same drawback regarding the specimen shape also exists.

2.2 Related problems

Magnetic measuring is a very interesting and useful topic. Normally, we refer to test specimens, but there is also the problem to test the magnetic devices, even NDE, especially nowadays, most magnetic devices are working in elevated temperatures. Furthermore, before measuring, magnetic devices will have to be magnetized first.

It is worthy to mention that, as magnetization has a strong effect on performances of magnet applications such as motor torque, cogging torque, torque ripple, etc., proper magnetization of isotropic and anisotropy PMs is a key for their application to motors and other devices. These problems have been studied for many years [33, 34, 35]. Assembly difficulties sometimes make it preferable to magnetize in situ in a fully or partially assembled device using a pulse discharge magnetizer. When high-performance PMs are used, they can be magnetized individually before assembly or magnetized with proper magnetization fixture after being assembled together. A specialized magnetization solver accounting for hysteresis, eddy currents, and field-circuit coupling has been developed and validated on designs of several magnetizing fixtures for isotropic permanent magnets [36]. But for anisotropic magnets and magnets in large sizes, the problem becomes more complicated. Moreover, how to measure the result of magnetizing is a big problem, especially when the temperature of PMs is raised after magnetizing.

The magnetization is determined by the resulting field, which is roughly the sum of three components: field from the magnetizing coils, reaction field from eddy currents in conductive components of the fixture and assembly, and demagnetization field of the magnet itself. Accurate analysis of pulse magnetization is a complex nonlinear problem, in which determination of the transient magnetic field is coupled with a pulse current in the discharge electrical circuit. Furthermore, eddy current will cause temperature change.

In recent days more and more RE-TM magnets are used in various products, this requirement relates to the magnetic hardness of such RE-TM alloys and poses a real problem in many practical situations where magnetization fields of several thousands of kA/m are needed. As we have known, in addition to the high magnetization fields needed to saturate them, large size magnets also require very high energies to reach saturation [6, 30]. This energy is very hard to evaluate because it is not only dependent on the quality of the magnet material, but many losses must also be considered which arise due to electrical resistance and eddy currents in the conductor material (conducting magnets, pole pieces, etc.), and/or in metallic magnetic materials the losses in the magnets themselves, and also because of the losses resulting from the non-utilized but essential volumes between magnet and the electrical conductor (insulation) [30]. The magnetizing problem is further intensified by complex multiple-pole design requirements demanded in many new applications.

What’s far more important is that, how can we directly and/or indirectly measure the magnetization effect if the magnets are magnetized in a fixture after being assembled? Precision test on the effect of magnetization is strongly demanded in order to keep the qualities of the products, especially for large size magnets and multi-pole magnets. In addition, assuming negligible magnetic viscosity effects [25], however, it is difficult for the magnetic flux produced by a pulse magnet to penetrate a whole conductor sample of large size, because the change of the magnetic fields is, in general, so fast that large eddy currents will block the magnetic flux. Moreover, because duration of the pulse field is usually very short, if magnetic viscosity effect is large, there will be no enough time for the magnets to change its magnetic state. Various PMs will show different hysteresis effects, and their temperature changes also are different, thus need a variety of time constants for magnetizing field. For example, for magnets with higher resistivity (e.g., hard ferrite) and with small size, short duration can be used. But for magnets with small resistivity (e.g, AlNiCo, Sm-Co and Nd-Fe-B), large size, and also for magnets with high hysteresis effect, long duration should be used.

To reduce the difficulties of magnetization, the magnets can be magnetized at elevated temperatures separately or in a fixture after being assembled. At a proper temperature, they can be magnetized more easily to saturation or to a certain stage with reduced magnetizing field and energy. And then the problem is how to measure the magnetizing result. Moreover, permanent magnets can also have remarkable temperature-dependent properties. For example, the coercivity in Ba and Sr ferrites has positive temperature coefficient $\alpha_{H_{cJ}}=$ (dHc/dT)/Hc of the order of 0.3% ${}^{\circ}$ C ${}^{-1}$ to 0.5% ${}^{\circ}$ C ${}^{-1}$ , while in Nd-Fe-B compounds it is typically $\alpha_{H_{cJ}}=-$ 0.6% ${}^{\circ}$ C ${}^{-1}$ , as shown in Table 1. In addition, room temperature is confusing, especially to Nd-Fe-B, whose magnetic properties is very sensitive to temperature changes. The ambient temperature recommended in IEC 60404-5 standard was (23 $\pm$ 5) ${}^{\circ}$ C. In the new version of IEC 60404-5:2015, a recommendation is given. Though the measurements shall be carried out at an ambient temperature of (23 $\pm$ 5) ${}^{\circ}$ C, for permanent magnet materials that are known to have a significant temperature coefficient, a specimen temperature of 19 ${}^{\circ}$ C to 27 ${}^{\circ}$ C shall be controlled within this range to $\pm$ 1 ${}^{\circ}$ C or better during the measurements [7]. Now it is generally accepted that the actual temperature of the test specimen shall be measured to $\pm$ 1 ${}^{\circ}$ C and reported [1].

Furthermore, the largely used Nd-Fe-B magnets are often coated. We have compared the magnetic properties of PMs with and without coating at room temperature, which shows apparent differences in $H_{cJ}$ , and their $B_{r}$ values are almost the same [6]. Now it has become more important to test coated PMs directly at elevated temperature. So studies must be done in this area.

3. Conclusions

With the development of modern electronic techniques, it has become more and more important to measure the magnetic properties of permanent magnets (PMs) at elevated temperatures accurately. Though the measuring method is the same both at room and elevated temperatures, with the improvement of the performance of PMs such as RE-TM magnets, bonded magnets, and nanocrystalline exchange-coupled magnets, etc., many problems have aroused using a widely employed DC Hysteresigraph (B-H Tracer), which is the closed circuit method using an iron-cored electromagnet. In this paper, many principal problems on measuring the elevated temperature magnetic properties of PMs are reviewed and discussed. Suggestions on magnetizing PMs up to saturation at elevated temperatures are also given. Moreover, methods using vibrating sample magnetometer (VSM) to measure PMs at elevated temperatures are also discussed.

Footnotes

Acknowledgments

Many thanks to General Manager Yingyan Jia and Commercial Manager Karen Sun (Ting Sun) of Hangzhou Permanent Magnet Group Co. Ltd for sample preparation. Many thanks to my son Jiayue Liu for English writing. This work is supported by 151 Fund, Analysis and Test Fund A (no. 04089) of Zhejiang Province of China.

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Discussion on problems aroused from measuring hard magnetic properties at elevated temperatures

Abstract

Keywords

1. Introduction

2. Main problems

2.1 Measuring of the high temperature magnetic properties

Table 1 α B r , α H c ⁢ B and α H c ⁢ J of AlNiCo8, hard Ferrite Y30, SmCo 5 , and Nd-Fe-B 25SH in temperature range of room temperature to 180 ∘ C

3. Conclusions

Footnotes

Acknowledgments

References

Table 1
$\alpha_{B_{r}}$ , $\alpha_{H_{cB}}$ and $\alpha_{H_{cJ}}$ of AlNiCo8, hard Ferrite Y30, SmCo ${}_{5}$ , and Nd-Fe-B 25SH in temperature range of room temperature to 180 ${}^{\circ}$ C