Discussion on several principal problems aroused from measuring high performance permanent magnetic materials

2.1 Magnetic properties of material and magnetic properties of products

As far as we know that, magnetic properties can refer to intrinsic matter properties and product properties. Magnetic properties of the matter can also be called magnetic properties of the material, which refer to the intrinsic properties that are determined by the composition, microstructure, etc. of the substance, unrelated to the shape, size of the sample, whereas magnetic properties of the product (also known as magnetic properties of sample) refer to the properties that are influenced by and also closely related to the shape, size, etc. of the sample. This can be mainly attributed to the existence of demagnetizing field. At the same applied magnetization field, if the demagnetizing field cannot be ignored, the magnetization of the material is usually higher than that of the product, because the true field the product feels will become smaller than that the material feels.

Sometimes we want to know the properties of the material, especially in scientific research, but in practical applications, we prefer to know the properties of the product. The properties given by the producer’s handbook or catalogs are usually material properties, unless special notes are given. The designers need a significant set of materials parameters to compare different materials in order to optimize their devices at reasonable cost. That is to say, these properties are all measured by standard method specified in international standard using standard specimen according to material standards. Many works have been done before the standard establishment to make the sample properties as closely as possible to the material properties, and then we can regard the sample properties as the material properties. We all know that if the sample is representative, we can get the material properties.

Practically, there should be no such term as absolute “parameters of a magnetic material” because magnetic performance is not only strongly shape dependent (e.g., due to the demagnetizing field that causes non-uniformity of magnetization and the change of parameters during the preparation of the sample), but also strongly depends on measuring speed (e.g., due to hysteresis effect, eddy current effect and other effects). Due to the demagnetizing field, practically all measured results of magnetic materials depend on the shape of the sample under test. Therefore, usually only the properties of the specimen under test are determined, but not the properties of the material. Moreover, during preparation of the specimen, to some extent, we also have changed its properties (e.g., by the process of cutting). In addition, even de-stressing by annealing sometimes cannot return the sample to exactly the same state as before the processing. Therefore, when parameters are given, it is recommended to state clearly what kind of the sample was used for the investigations (e.g., for permanent magnetic materials, samples can be in the form of bar, ring, etc. with different size). In such a case, we usually test the average parameters across sectional area of the whole sample, which is often advantageous because in this way we can take into account the possible heterogeneity in the material [1]. It is also possible to only determine the local values of the material parameters if we want to take into consideration the possible heterogeneity of the material, e.g. using relatively small sensor to determine the local parameters of individual grains [1], or measuring the sample one side after another, as in the case of hard ferrite.

The best would be the situation in which we can test exactly the same specimen as what is used in real application – such situation sometimes really occurs for ring (toroidal) sample [1], and now for most RE-TM magnets. Nevertheless, there is always a need to compare magnetic properties of various materials with assumed reproducibility – for example, if we test the same material in different laboratories.

The assumption has continued for many years that magnetic materials are reliably characterized by two main values: flux density B and magnetic field strength H. So the evaluation of magnetic materials was normally based on the relationship B = f(H), especially for soft magnetic materials. However, in the development of PMMs, it was deduced (and international standards followed) that the less frequently used term magnetic polarization J (J = B - μ 0 H) will better describe the state of magnetization of a material than the flux density B. For lower coercivity materials, the differences between B(H) curve and J(H) curve, and also the differences between H c ⁢ B and H c ⁢ J of a material are small. But for high performance PMMs and also in high magnetic field, the differences between these two loops and thus the differences between H c ⁢ B and H c ⁢ J values are very large. For PMs, we only test the second quadrant, thus if only B(H) is obtained, we cannot get J(H), as we need more high H to get H c ⁢ J . The situation is the same for M(H). So the relation is universally substituted by J = f(H) because it can give more reliable results and describe the physics for the magnetic phenomena better. Furthermore, nowadays many specialists have proposed that it would be even better to use the magnetization M (B = μ 0 (H + M)). Thus, in comparison with electrical measurements where main terms are better established, many fundamental problems of magnetic measurements are still in discussion [1].

2.2 Specimen

Just as we have known that, the magnetic properties of a material can only be obtained from a closed circuit specimen such as a ring specimen. For an open circuit specimen, the test conditions, including the shape of the specimen, the measuring methods, and the test equipment, etc., must be carefully defined to achieve the material properties, and the length-to-diameter ratio L/D of the specimen must also be high enough, where L is the length of the sample along the magnetization direction, and D is the diameter of the cross-section.

It is in any case recommended that the L/D ratio of the test specimen should be larger than 1 [3]. According to IEC 60404-5 [9] and ASTM A977/A977M [11], the test specimen shall have a simple shape. The length of the test specimen shall be not less than 5 mm. The cross-sectional area of the test specimen shall be as uniform as possible throughout its length (within 1%), with smooth and as parallel as possible end faces. In a hysteresigraph, the test specimen will be inserted into the search coil and is clamped in the uniform magnetization field area between the faces of an electromagnet. For high coercivity PMM, as the magnetization and demagnetizing field become larger, the poles will become saturated, thus the uniform magnetization field area will become smaller, so the size of the specimen also needs to be adjusted, which needs to be studied further.

The hysteresigraph is suitable for samples with a constant cross-section and thickness, i.e. flat pieces, and sometimes it is a “destructive measurement” when performed on a larger or non-uniform magnet, since the sample must be cut from it, though this test will not destroy the sample during the measurement. When a test specimen is cut or fabricated from these magnets, the magnetic properties measured on it are not necessarily exactly those of the original sample, even if the material can be heat-treated again. Because the sample may not be representative of the whole magnet, the measured results may not be representative of it but just stand for the properties of the actual sample. For different samples, uniformity of composition, structure, and properties throughout the magnet volume is essential to obtain repeatable results.

For PMMs, in order to test magnetic components without machining a sample out of them (e.g., using NDT), it is necessary to work out special soft iron adapters called polar shoes, and then placed them in tight contact with both the hard magnet (the sample) and the polar faces of the electromagnet [3, 20, 21], taking care of the magnetization direction. Otherwise, if the samples have large and/or irregular cross sectional areas, or their cross sectional areas are difficult to measure, their material properties close to the sample surface might be determined instead, with the aid of the Steingroever’s concept of interchangeable polar pieces equipped with pole coils [20, 21]. In addition, for samples with a thickness of less than 5 mm, their properties can also be directly measured with a J-coil of 1 mm thickness [20, 21]. If their minimum height is thinner than 2 mm, it is expedient to stack the specimens to enough height, or if the cross-sectional area of the sample is too small compared with J-coil, two or more samples with the same height can also be put side by side in the coil, supposed that they are identical [3]. We have also found that these are good ways to get relatively useful results, and no obvious difference can be found within the accuracy.

In mass production, magnetic properties may vary between batches, within a batch, or even with a single block of magnet material [22]. So the measured results must be good enough to reflect these differences in order to insure the quality of the final products. Therefore, how samples are selected is also crucial for determining typical properties of a group of magnets. The magnets should be inspected for all specific characteristics using a statistically valid sampling plan [22].

Occasionally, some kinds of testing are especially difficult to carry out in quantity. Also, some testing is difficult due to the product shape, thus demanding some alternative test methods. A practical difficulty related to measurements on PMs with closed magnetic circuits arises from the components to be tested which have complicated shape and thus without uniform cross-section area. As these samples often dissatisfy the requirements of the Standards, also machining the specimens is difficult and costly because these magnetic materials are normally brittle, when applicable, open sample experiments can eventually be preferred occasionally, as will be discussed later. Furthermore, these alternative tests practically always require correlation testing between supplier and customer.

Both closed-circuit methods and open-circuit test methods involve known errors and corrections, and some errors are not so well understood [18]. In open-circuit measurements, the well-known source of errors are the demagnetization factor [23] and image effect [17, 18, 19, 23, 24, 25]. Open-circuit system, whose magnetic field is provided by an electromagnet with two magnetic pole pieces, such as typically in a vibrating-sample magnetometer (VSM), is subject to error from the image effect [23, 24, 25], which arises because the field produced by a magnetized sample is distorted by the presence of high-permeability pole pieces of an electromagnet.

This is called the image effect because when measurements are made in the gap of an electromagnet, the presence of large volumes of high permeability magnetic material (the pole-pieces) will distort the field surrounding the sample. That is to say, if the magnetized specimen is placed in the gap of an un-magnetized electromagnet, the lines of force from the specimen will swing around to both pole pieces. The positions they reach are just those which would result if the lines of force were connected to the “magnetic images” of the specimen in the pole pieces [28]. Theoretically, in the limiting case of a semi-infinite pole piece (like slabs) with uniform high permeability material, the effect can be described mathematically by magnetic ‘images’ of the sample existing in the pole-pieces at the mirror image positions, just like an electrostatic image in a perfect conductor. The usual result of the image effect is an apparent drop in the measured magnetization with increasing field at high fields [20, 21, 24]. At high fields, the materials of the pole-pieces will approach magnetic saturation, then their permeability will decrease towards unity, and the images will tend to disappear. Thus the calibration constants relating the magnetization of the sample to the output signal of the magnetometer will change with field. It is found that the open-circuit image effect is negligible for fields up to about 0.6 T, but at higher magnetic fields it can distort the magnetization readings by as much as 50% relative to the expected, undistorted magnetization value [25]. Though correction for the image effect is difficult since the effect depends on the size and shape of the sample, the geometry of the measuring coils and the electromagnet, and because it varies with the degree of saturation of the electromagnet pole pieces, the image effect has to be corrected by an field-dependent correction factor for the situations when the magnetization value must be accurate [24, 26]. It is also suggested that the image effect is related to saturation of the electromagnet pole-tips [26] and/or the interaction of the specimen with the electromagnet pole pieces in an open gap, suggesting the image effect will vary with the permeability of the pole-tips and so depend on the state of saturation of the electromagnet pole tip material [24, 27, 28]. When approaching magnetic saturation, the permeability of the pole tip material diminishes to a marked extent, thus causing the sensitivity of the measuring apparatus to decrease proportionately.

Closed-circuit magnetic measurements, such as those conducted in a hysteresigraph, have generally been considered to be entirely free from errors associated with the demagnetizing factor and the image effect [24], both of which can occur in open-circuit measurements. However, hysteresigraph measurements taken under closed-circuit conditions on both different magnetic materials and a range of magnetic sample geometries clamped between the pole pieces of an electromagnet show an apparent drop in the measured magnetization in the first and third quadrants with increasing applied field, similar to the image effect found in open-circuit measurements, and is called as an apparent image effect [17]. The drop in apparent magnetization caused by image effect can appear in quite low fields and can be large, approaching 50% [17]. It depends on the magnitude of saturation magnetization and on L/D ratio of the sample, and occurs for both soft magnetic materials and permanent magnets. The distortion can reduce the magnetization values as much as 42% when the applied magnetic field is 1910 kA/m (24 kOe) and the L/D is 0.28 [18].

It is found that as the saturation magnetization of the sample increases, the drop in apparent magnetization becomes greater and appears at lower fields; the effect also increases as the L/D of the sample decreases. Also, specimen geometry makes a significant difference for both the distortion field and the distortion degree in closed-circuit measurements. The magnetization distortion in closed-circuit measurements is also affected by the type of magnetic material, regardless of different sizes of the pole-tips, different shapes of the search coil, such as Nd-Fe-B with a smaller intrinsic coercivity H c ⁢ J has a smaller distortion for longer specimens and a larger distortion for shorter specimens compared to Sm-Co with a higher H c ⁢ J , indicating that H c ⁢ J may play a role in the distortion, since B of a longer specimen is less affected by the coercivity compared to a shorter specimen. Moreover, the effect depends on L/D ratio of the sample, as the degree of the distortion increases as the L/D ratio of specimen decreases, and becomes minimal for L/D $>$ 1.8 at the measured maximum available magnetic field 1194 kA/m (15 kOe) [17, 18, 19].

In addition to the apparent decrease in measured magnetization, there is a decrease in the measured magnetic field, which is attributed to a non-uniform magnetization of the electromagnet pole pieces, where local saturation distorts the magnetic flux distribution around the sample. It is proved that for reasonably accurate ( ± 1%) measurement of magnetic properties when a magnetic sample is made part of a closed magnetic circuit (by clamping it between the pole pieces of an electromagnet), the sample must have an L/D ratio higher than 1.8 [17, 18, 19]. This behavior has been attributed to distortion of the magnetic field distribution around the sample resulting from localized saturation of the electromagnet pole pieces at high applied fields, and also is confirmed by computer modeling using finite element method, which shows that the field acting on the sample is highly non-uniform when the sample L/D is small, and the apparent drop in magnetization is caused by the measurement of the applied field that does not accurately reflect the field acting on the sample [17]. We have also done some research works, as shown in Fig. 2. As we have known that, for Al-Ni-Co and Fe-Cr-Co, etc., their coercivities mainly arise from shape anisotropy, so if L becomes smaller, their magnetic properties will become lower, partly because of their high M s and thus large demagnetizing field, also because the lose of coercivity. But for BaM and RE-TM magnets, their coercivities are mainly originated from magneto-crystalline anisotropy. So in addition to the smallest L, L/D value must also be determined for each material. We have studied the changes of measured magnetic properties of permanent magnets with different L/D value. For each kind of materials, the samples are all cut from one uniform bar magnet. As shown in Fig. 2, the minimum height for Al-Ni-Co-8 can be 3.4 mm, whereas for Nd-Fe-B, can be 4 mm. Of course, further studies are needed, and more detailed results will be published later.

OPEN IN VIEWER

Nowadays, with the improvement of the properties, the RE-TM PMMs have been used in many different shapes and sizes, and they are mainly used at a small L/D, usually L is much smaller than 5 mm, which is the minimum length defined in standards [9, 11]. High coercive field materials also often come as short samples because the magnetic induction B behaves nearly linearly in the second quadrant loop (demagnetization curve) and the maximum energy product is obtained with a high value of the demagnetizing coefficient N (N ≈ 1/2) [3]. Moreover, because the field supplied in electromagnet is not high enough to obtain the full demagnetization curve for most RE-TM magnets if the sample is too long, often the sample is as short as possible to enhance the maximum demagnetization field got in the electromagnet. In this case, the correction for the demagnetizing field will become rapidly inaccurate with the decrease in the L/D ratio [2]. In addition, the magnetic properties defined are usually the properties of the product; obviously they often refer to the product properties. Because we still do not know much about the influences of the sample size, such as cross-section area, length, and L/D, etc., to the measured properties of high performance PMMs, and also seldom studies have been done in this area recently, we are not very sure about the accuracy of the data obtained. If we use the real products as the specimen, what should we do if we want to get an accurate useful data that can be used in industry applications? How to choose the materials needed in future applications? Obviously, the relations of the magnetic properties between the products and the materials must be set up. Moreover, if the product is coated with protective layer, such as Ni-Cu-Ni, Zn, epoxy, etc., we should also know their influences on the measured magnetic properties, because precision test on such coated magnets is strongly demanded in order to keep the qualities of the products. Special attention must be taken to how to measure these magnets in a Hysteresigraph or using other equivalent methods. We have compared Nd-Fe-B magnets with and without Ni-Cu-Ni coating of 20–30 μ m, as shown in Fig. 3. Obviously, there is a big difference in H c ⁢ J value, but little difference can be seen in B r value. We know that Ni-Cu-Ni is magnetic, but epoxy is non-magnetic, so perhaps different coating will have different influence on measured results. It is demonstrated that the surface layer having a much smaller coercivity compared to the bulk (e.g. Nd-Fe-B and SmCo 5 ) will affect the overall magnetic properties of small magnets, especially for Ni coating [29]. Thus an analytical model is suggested to describe the influence of the surface degradation and the Ni layer itself on the magnetic properties of Ni coated Nd-Fe-B magnets.

OPEN IN VIEWER

According to standards [9, 11], the test specimen can be assembled into the electromagnet and then magnetized to saturation, or can be assembled after having been magnetized to saturation in either a superconducting coil or by using a pulse magnetizer, so homogeneous magnetization of the specimen includes both magnetization to saturation before the measurement and the magnetization during the measurement.

To guarantee axial and radial field uniformity (within 1%) in the region occupied by the specimen, the diameter D 0 of the pole faces and the diameter D 1 of the cylindrical region, which contains the specimen and the field measuring sensor, are related by the condition:

D 0 ⩾ 2 ⁢ l

(1) D 0 ⩾ D 1 + 1.2 ⁢ l

where l is the distance between the pole faces (air gap length).

Because demagnetizing effect is ubiquitous, the most significant problem in magnetic measurements is the role of the demagnetizing field [3]. Even in accurately closed specimens, (e.g. ring samples), one cannot get rid of them completely. In fact, the demagnetizing field is not homogeneous even with homogeneous magnetization. In addition, the demagnetizing field is also dependent on the relative permeability of the material [3]. As far as we know that, the magnetizations of the open circuit specimen are almost inhomogeneous even in a uniform magnetic field because of the existence of demagnetizing field, or the specimen should be truly ellipsoidal. Demagnetizing field can be an extremely complicated function of position for a ferromagnet of arbitrary shape, and is generally a function of position and magnetization orientation inside a sample. For an arbitrarily shaped sample, the demagnetizing field H → d for a given direction of M → relative to the sample axes may be approximated as [2, 3, 4, 23, 24, 30]:

H → d = - ∥ N ∥ ⁢ M →(2)

where M → is the magnetization, N is called the demagnetizing factor (the demagnetizing tensor) and, in general, N is sample shape dependent. Hence, N is a tensor function of position and orientation in a given sample, and should be a double-valued or triple-valued diagonal tensor for magnetization along the principal axes of an ellipsoid. An exact value of N only exists for ellipsoidal samples, and then H → d will take a relatively simple diagonal form. In this case H → d is uniform inside the ferromagnet. Thus, if a truly ellipsoidal specimen is oriented in a uniform field along one of the major axes, throughout the sample the magnetization is uniform [3]. This is not true for samples of other shapes. For example, the magnetic response is greatly reduced by dipole fields near corners of rectangular specimens [23, 24, 30].

If the specimen is in a given uniform magnetic field H → 0 , the effective field (inner field) H → i in the specimen should be [3, 4, 23, 24, 30]:

H → i = H → 0 + H → d = H → 0 - ∥ N ∥ ⁢ M →(3)

For soft and/or hard magnetic materials, measuring the intrinsic dependence of M on H is an ideal and to a certain degree indefinable purpose because the long-range nature of the demagnetizing fields makes the behavior of any test specimen significantly related to its geometrical features. Sometimes this incorporates with unexpected existence of uncontrolled stress produced when fixing the sample in the testing fixture (e.g, yoke). Thus, practical limitations, like those related to the realization of a suitable magnetic circuit or universal acceptance of specific measuring methods by the industry, may naturally bring about the approximate realizations of the intrinsic measurements [1]. Equation (2) means that the bigger the magnetization M of the sample is, the more the field from the surface poles will oppose the external field. Thus, according to Eq. (3), for soft magnetic materials, where a relatively weak external field will lead to a large magnetization M, the internal field the sample feels can be much less than the applied field even if the shape factor N is greatly smaller than unity. Applied field and demagnetizing field can have very close values, and demagnetizing field also can be spatially nonuniform in ordinary test specimens. Thus, the precise determination of the effective field will be difficult. That’s why soft magnetic materials are rarely tested in open samples [3]. However, for PMMs, where very large external fields are required to achieve noticeable magnetization M, shape effects become important only for much smaller aspect-ratio L/D and larger N samples [23, 24, 30], and now this is often the case for high performance PMMs in modern applications.

However, a complete tensorial relationship B(H) or J(H) can be theoretically determined by simulating an infinitely long body [2]. When it is not possible or desirable to use the closed form specimen itself (e.g. with bulk rod specimens, permanent magnets), an alternative approach to form the necessary closed magnetic circuit is based on the employ of a yoke – hysteresigraph method. When H is swept slowly in the yoke, the integrator output may be recorded and a complete ‘DC’ magnetization curve and loop can be plotted in a time on the order of 1 minute.

Soft iron core electromagnets (yoke) can be the most convenient method for obtaining magnetic fields up to 3 T. The major considerations of choosing an iron core magnet as a yoke are field volume, field uniformity and field magnitude, etc. The time stability of the magnetic field H in the yoke depends strongly on the output of the power supply, and the field uniformity generally increases with increasing the pole-piece diameter. Field magnitude mainly depends on the pole size, pole shape and the output of the power supply. Furthermore, the image effect can be minimized through increasing the gap, at the expense of lower maximum magnetic field, or simply by limiting the maximum magnetic field to the values where the image effect practically keeps constant. Placing the magnetization sensor as far as possible from the pole-pieces is also helpful, but is often incompatible with placing a furnace or low-temperature vessel in the magnet gap [31].

Nevertheless, open samples can be used if higher magnetic field H is needed and/or the closed magnetic circuit is hard to use [1]. Theoretically, for open sample, we can take into consideration the demagnetizing field H d if N is already known. As this factor is known only for ellipsoidal samples, for other shapes (as cylinders or rectangular prisms), it is only roughly known. Moreover, for open samples, only the ellipsoidal shaped specimen can be uniformly magnetized [1]. Other problem of application of the open samples is the influence of external magnetic field.

When an open circuit specimen with high coercivity is magnetized in a pulse magnet or a superconducting magnet, the inner magnetic field will also be different in different positions because of N tensor. Thus, the uniformity of the magnetization field as well as the distribution of the demagnetizing field will make it very difficult to magnetize an open circuit specimen uniformly, unless the magnetization field is high enough. In addition, the specimen must be fixed firmly in the magnetizing field during the magnetization period, otherwise it will fly away.

As also can be seen from Eq. (3) that, H i will not be equal to H 0 if H d exists, so it will become difficult to measure H i accurately. As long as the magnetization vector M suffers a discontinuity, demagnetizing fields will unavoidably arise, which will greatly influence the measuring methodology and accuracy. For example, this can enhance additional energetic load of the field sources, and lead to macroscopic magnetization inhomogeneities in the test specimens, and thus cause inaccuracies in the determination of the effective fields [3]. As demagnetizing fields can never be ignored in measurements, to recover the intrinsic magnetic properties of the material under test, a correction is required, where the effective field H i is obtained as the difference between the applied field H 0 and the demagnetizing field H d according to Eq. (3).

Usually we will have to choose open test samples in many experiments. Moreover, we will adopt ellipsoidal samples or spherical samples whenever possible, but for realistic reasons, we often have to choose cylindrical or parallelepipedic shapes.

PMMs are normally measured in closed magnetic circuits where the demagnetizing fields are kept small [24]. In recent days, high-performance PMs in large sizes are used in various products. Precision test on such magnets is strongly demanded in order to keep the qualities of the products. The problem is whether they can be measured in a hysteresigraph, or if other useful methods should be used, such as pulse field magnetometer (PFM) and superconducting magnetometer (SCM). When an open circuit specimen with high coercivity is magnetizing in a pulse magnet or a superconducting magnet, the inner magnetic field will also be different in different positions. In this case, the uniformity of the magnetization field H i as well as the variety of the demagnetizing field will make it very difficult to magnetizing a large size specimen uniformly, unless H 0 is much higher than H d .

In practice, demagnetizing field corrections are most important at low fields, where values of permeability and remanence are determined. Demagnetizing corrections are fairly insignificant (although not small) as the sample approaches saturation. In general, values of the coercivity H c ⁢ J are not much affected by demagnetizing effects, since they are determined when the magnetization M is at or near zero.

When measuring a specimen in an electromagnet, the specimen with a certain size must be placed in the uniform magnetic field area in order to be magnetized homogeneously during the measuring process. Though these conditions are all carefully defined in standards [9, 11], the whole poles or part of the poles of the electromagnet will become saturated when B r and/or H c of the specimen are very large. It is proved that even in a closed magnetic circuit, the image effect may be significant, especially when the L/D ratio of the sample is small [17, 18, 19, 23]. In these cases, the uniform magnetic field area will become smaller, and the homogeneous magnetization will become even more difficult. In addition, the inner field in the specimen will also not be equal to the magnetization field outside the specimen, which will be discussed later.

In recent days, coated high-performance permanent magnets are used in various products. Attention will also have to be paid to uniformly magnetization of such coated sample.

2.4 Saturation magnetization

As the parameters important for PMMs are almost all obtained from the saturation hysteresis loops, the measured values of these parameters are very sensitive to the saturation field. Normally, the minimum saturation field H max needed for different PMMs are all defined in product standards and also in international standards [9, 11, 22]. If magnetization field is equal to or higher than H max , it is said that the specimen has reached the technical saturation. According to the pertaining ASTM Standard [11], the specimen is considered to be saturated if an increase in the magnetizing field strength by 50% changes the values of B r , H c ⁢ J , and H k by less than 1%. The rule suggested by the IEC Standard 60404-5 [9] is based on the determination of H c ⁢ B or (BH) max at increasing fields.

Typical values of the magnetizing fields, H max , required for saturating magnetic materials given in ASTM A977/A977M [11] and also MMPA [22] are:

H max = k ⁢ H c ⁢ J(4)

Generally k is between three and five. For different magnetization mechanism, e.g., domain wall pinning, and nuclear model, H max needed is different, k = 1 - 2 or 3 - 5. After saturation, H C will reach maximum.

Practically, we know that in a closed magnetic circuit, H max ⩾ (4 ∼ 10) H c ⁢ J . For PMMs with H c ⁢ J 20 kA/m, H max ⩾ (6 ∼ 10) H c ⁢ J , whereas for PMMs with H c ⁢ J $>$ 20 kA/m, H max ⩾ (4 ∼ 5) H c ⁢ J [2, 3]. It is assumed that the generated field strength should be five times larger than the intrinsic coercive field H c ⁢ J , which gives about 5 × 10 6 A/m. This established field should keep unchanged or the change with time should be sufficiently slow to avoid problems with eddy currents. If the specimen is magnetized in an open magnetic circuit by a pulse magnetizer or a superconducting coil, because of the demagnetizing effect, eddy current effect and hysteresis effect, H max should be much bigger in order to have the same magnetization effect as the DC magnetization field in a closed magnetic circuit [20, 21]. As H max will have to compensate the opposite fields produced by demagnetizing field and eddy current field in the PMs, and field losses arising in the conductor materials of the magnetic circuit due to electrical resistance and eddy currents, and also losses because of the unused but necessary volume between magnet and electrical conductor (insulation) [20], the field really applied on the sample will become smaller compared with the applied equivalent DC magnetic field, unless H max is higher enough to magnetize the sample to saturation.

High-quality RE-TM PMs such as Sm-Co and Nd-Fe-B exhibit room temperature anisotropy fields in the range of 5.6 MA/m (70 kOe) to 24 MA/m (300 kOe). Such high uniaxial anisotropy combined with an appropriate microstructure can lead to materials with intrinsic coercivities H c ⁢ J between 800 kA/m (10 kOe) and 4000 kA/m (50 kOe) [32], and thus require a relatively high magnetization field to achieve full magnetization. Further increase in coercivity reported in many quaternary RE-TM alloys such as Dy-Nd-Fe-B and Sm 2 TM 17 adds to the difficulties in magnetization to saturation.

As the electromagnet in a hysteresigraph cannot produce sufficient magnetic field to fully saturate them or to bring them close to saturation, RE-TM magnets must be magnetically saturated outside the electromagnet before being inserted into the hysteresigraph [11], these have been well stated in IEC 60404-5 standard [9]. But the homogeneous magnetization of these specimens will have to be reconsidered, especially for specimens in large sizes.

For RE-TM PMMs, before testing, the test specimen with very high coercivity must be magnetized externally in a separate device which can be capable of generating higher field strengths, e.g., in the range from 2.8 to 8 MA/m (35 to 100 kOe), and then transferred in open circuit to the hysteresigraph. The direction of magnetization must be marked on the sample. Only materials having sufficiently high H c ⁢ J and a recoil permeability near one, for example, most RE-TM PMs and ferrite magnets, can be magnetized in open circuit and transferred into the hysteresigraph yoke without significant irreversible self-demagnetization, which can influence the accuracy of the results [11]. Specimens with L/D ratios greater than two are preferred. The charging pulse duration must be long enough to ensure uniform magnetization despite eddy current shielding in metallic magnets. Repeated pulsing may be required for specimens of large cross section.

Externally magnetized specimens shall be inserted into the test-system electromagnet, such as to ensure magnetization in the same direction. In such situation, even if the specimen has been saturated, its magnetic state will stay in a certain point in its demagnetization curve as a result of the self-demagnetizing field. In order to bring it to saturation again, before measurement, the highest available forward magnetizing field shall then be re-applied before demagnetization curves are plotted [11]. According to IEC 60404-5 standard [9], when the test specimen is inserted into the search coil and assembled into the electromagnet, their magnetized direction must be towards the same direction as that previously magnetized in the superconducting coil or pulse magnetizer, and should be magnetized to saturation again. The field strength required for this can be as high as 4000 kA/m. Such a field strength is not possible in an electromagnet because of the saturation of the poles (B = s 2.15 T for iron, 2.45 T for iron cobalt). In practice, a voltage ramp can be applied to the power supply in order to provide as high as possible a field in the same direction of the magnetization in the sample (the “forward direction”). Since the materials to which this procedure applies all have very high H c ⁢ J value, only a small fraction of the magnetization is irreversibly lost under the influence of the demagnetizing field. After remagnetizing them to the maximum field, it can be reasonably assumed that most of them can recover saturation [3]. In addition, during the measurement process, the uniformity of magnetization field will also have to be considered in order to obtain a relatively accurate result, especially when these coercivities are too high for the Fe-yoke-based hysteresis systems.

It is noted that, under the relatively low values of the applied field H 0 , no difference can be observed between the B(H) and J(H) curves, and distinctly different J(H) and B(H) hysteresis loops can be observed only in higher H 0 . Here it is worth to mention that although J is constant after saturation is achieved, B continuous to increase with H, because H forms part of B: B = μ 0 H + J [24]. Just as mentioned above, if we want to measure the whole hysteresis loop of PMs with high coercivity, due to apparent image effect [17, 18, 19, 23, 24], we must be very careful in order to get a reasonable result. But for a new material, how can we know if the material is saturated when B is still increasing? We should measure J(H) curve instead of B(H) curve to see if the material has reached saturation. Moreover, if the iron core is brought far beyond the knee of its magnetization curve, the spatial homogeneity of the field applied to the sample is destroyed and thus incomplete magnetic testing will be resulted [2].

This requirement relates to the magnetic hardness of such RE-TM alloys and leads to a real problem in many practical situations where magnetization fields of several thousands of kA/m are needed. In recent days, high-performance PMs in large sizes are used in various products. Precision test on such magnets is strongly demanded. In addition to the high magnetization fields needed to magnetization to saturation, large size magnets also require very high energies to reach saturation. Because in the magnetization process, energy is exchanged between the sample and the external magnetizing system, and in the period of magnetization, part of this energy is stored and part of them is dissipated in the materials [2]. Theoretically, the energy needed is roughly proportional to the product of volume and H 2 max of the magnet [20, 21]. This energy is an approximate value because it is dependent on the quality of the magnetic material, and any losses are not considered which arise due to electrical resistance and eddy currents in the conductor material (conducting magnets, pole pieces, etc.), and/or the losses in the magnets themselves for metallic magnetic materials, and also because of the losses resulting from the non-utilized but essential volumes between magnet and the electrical conductor (insulation) [20, 21]. The magnetizing problem is further intensified by complex multiple-pole design requirements demanded in many new applications. Large size magnets and multi-pole magnets can neither be fully magnetized nor characterized in commercially available systems, for multi-pole magnets we can now only measure the surface magnetic fields, and cannot characterize them in more detail under usual way.

The magnetic viscosity (also known as the magnetic aftereffect) is the spontaneous variation of the magnetization induced by thermally activated microscopic magnetization processes (thermal fluctuation aftereffect) [3, 4, 33, 34]. It is known as the effect of delay in magnetization of the sample when the magnetic field strength is changing very rapidly, which is a statistical relaxation phenomenon in the materials due to thermal fluctuation in the non-equilibrium state. This variation is dependent on the actual magnetic state of the material (it is highest on approaching the coercivity), shows logarithmic time dependence, and enhances the magnetization change applied by the external field. The reason of this effect is rather complex and depends on the microstructure of the material.

The effect occurs in all magnetic materials. In hard magnetic materials it depends on the mechanism of coercivity – nucleation of domain walls or pinning. In some materials, it can be quite significant and can influence the coercivity. Nevertheless for the pulses of several ms used in pulsed field magnetometry, this effect is negligible [1].

Assuming negligible magnetic viscosity effects, however, the magnetic flux produced by a pulse magnet finds it hard to penetrate a whole sample in the case that the sample is a large size conductor, because the change of the magnetic fields is, in general, so fast that large eddy currents block the magnetic flux [18, 20]. The greater its conductivity and cross-section are, the less the depth magnetic field can penetrate into the magnet. Therefore, impulses of short duration can be chosen for ferrite and metal magnets with small cross-sections [20, 21]. For magnets of greater cross-sectional area, the field impulse must last longer. For metal magnets, such as RE-TM magnets, magnetizers with larger time constants than those suitable for ferrite must be chosen. This can partly compensate the field required for saturation metal-natured magnets. Though the change rate of a superconducting magnet can be easily controlled, and it can be slow enough for the magnetic flux to completely penetrate a large sample, it is very expensive and also costly. In addition, we must know that various magnetic materials will show different hysteresis effects, and thus need a variety of time constants.

The magnetization course is the macroscopic result of an extremely complex procedure of microscopic processes. The system will respond to a changing applied field H 0 by combination of three processes: domain wall displacements, domain structure rearrangements and rotations of the magnetic moments. Because of hysteresis, in the (J,H) plane, by moving through a succession of metastable minimum energy states, depending on material’s past history any possible point can be passed by an infinite number of routes [2].

As far as we know, when we use a traditional ballistic measurement, the magnets will experience magnetic trainings in the saturation field to make the magnetic state stable. Training is consecutive hysteresis loop measurement cycles, that is, the current will be reversed back and forth for about 10 times by means of reversing switch (to change H from + H max to - H max ) to bring the material into a steady cyclic state. For high H c ⁢ J RE-TM materials, it is nearly impossible to do so because they are saturated outside the electromagnet. So some evaluation works must be done to know if the magnetic state is stable after being magnetized in a pulse magnetic field or in a superconducting magnetic field. Also, before measurement the magnets should be put aside for a certain period of time (e.g. at least for 2 min) after magnetization to saturation to make the magnetic state stable (avoiding magnetic after-effect), and also to ensure the temperature of the sample is the same as that in the lab.

Many studies want to measure the initial magnetization curve in order to obtain the knowledge on the nature of the magnetization process (e.g., domain wall nucleation versus domain wall pinning), which demands both the specimen and the iron core (especially the pole pieces) must be fully demagnetized before measuring [2]. For the specimen, a programmed pulse field source is commonly employed to demagnetize them outside the electromagnet using a specific current wave pattern, also thermal demagnetization can also be applied, although oxidation and structural changes might be a problem with RE-TM based magnets when the magnets are heated above the Curie temperatures, especially for Sm-Co magnets.

For multi-pole magnets, as high magnetic fields are needed to fully magnetize RE-TM based magnets, even with the conventional magnetizing process employing a large amplitude magnetic pulse, this poses practical difficulties and limits the number of poles and various application requiring specific pole designs in a magnet. On investigating magnetizability of these magnets, it was concluded that magnetizing can be effectively performed at much lower magnetic fields than normally needed if the temperature of the magnet during the magnetizing process is raised and maintained within a predetermined range [35]. This optimum range of temperatures are explained as a result of thermal deterioration on the magnet’s intrinsic coercivity and remanence properties, and the limiting effect of demagnetizing field on the magnetizing process. Perhaps this is a good way to saturate high H c ⁢ J and/or large size RE-TM magnets and so on. If the B r and H c ⁢ J temperature coefficient of the materials is known, we may also measure the higher temperature demagnetization curve first, and then calculate the room temperature demagnetization curve needed if the errors can be evaluated previously. The influence of temperature on magnetization will be discussed later.

Though it is always desirable to determine the best possible magnet properties achieved only after full saturation [11], sometimes the properties after charging to a specified less-than-saturated state have to be measured for predicting device performance. As we have known, the magnetization field is closely related to the magnetization history of the magnet. In case of magnetization of PMs from the virgin state, it may require, e.g., 4 H c ⁢ J to reach technical saturation. Magnetization in the direction opposite to the original direction requires considerably high field strengths. For some materials external field strengths of up to 14 H c ⁢ J are needed at room temperature [35]. If the specimen is magnetized for several times, such as when we measure the specimen at different temperatures to get temperature coefficients of B r and/or H c ⁢ J of a material, at the second time H max needed will be much higher because now the specimen is not in its magnetic neutralized state, which also need to be studied further. This phenomenon may closely relate to the magnetization mechanisms of different PMMs, such as pinning model and/or nucleation model. Moreover, the test protocol should specify the initial magnetization state of the sample and the magnitude of the magnetizing field to be applied in a defined “forward direction” (corresponding to the first quadrant of the hysteresis loop) before a demagnetization curve is plotted.

The magnetic properties of a magnetic material can be categorized into static magnetic properties and dynamic magnetic properties, which is referred to the change of the magnetization slower than change of the magnetic field. The differences between static magnetic properties and dynamic properties are very large mainly because of the hysteresis effect, eddy current effect and other effects, so the measuring speed is a very serious problem. In defining and measuring the B(H) and J(H) relationship in a magnetic material, we must specify whether we will test DC or AC properties.

Now DC Hysteresigraphs are the standard and widely employed method for measuring the technologically important “DC magnetic properties” of hard magnetic materials. Strictly speaking, it is not possible to achieve the true DC characterization, because during a testing process the applied field will have to be constantly changed, in either a continuous or discontinuous way [2]. So this method should technically be regarded as a “quasi-DC-method” since the sweeping speed of the magnetization field is nonzero, but the “quasi” is normally dropped in ordinary usage.

A further concept regards certain ambiguities related to the definition of DC and rate-dependent J(H) and/or B(H) curves. The magnetization state of material is easily influenced by thermal activated microscopic magnetization reversal because of the very same metastable nature of the magnetization state that leads to hysteresis. Thus the role of thermal activation can be enhanced by lowering the field changing rate. At the same time, in bulk metallic samples it is difficult to avoid large-scale eddy current effect [2]. Furthermore, as a result of eddy currents and magnetic aftereffects, running a loop too fast can result in significant errors [11]. Therefore, in many cases, it can be understood that DC magnetization curves may be affected by extensive uncertainties and will have mediocre reproducibility [2].

When we talk about DC (or, more appropriately, quasi-static) characterization of magnets with inductive methods we suppose in acquiescence that we are exploring the J(H) relationship in such a way that time-dependent phenomena are irrelevant. Actually, in order to determine the magnetization curves, we unavoidably have to change the strength of the applied field with time. Strictly speaking, for example, when a rate-independent hysteresis loop is determined in such a way that every recorded B(H) point on the loop corresponds to an equilibrium stable microscopic configuration of the system, it can be regarded as DC curves [3]. This is only possible when the applied field is changed so slowly that the whole system is developed through successive meta-stable equilibrium states, which is to say, this change is accomplished by means of Barkhausen jumps, and becomes totally independent on the field changing rate. To some extent, this is an ideal measuring condition. However, we should be aware that conceptual and practical difficulties are frequently encountered in trying to achieve truly DC testing, because various relaxation effects can appear with time constants comparable to the measuring times due to thermally activated processes and/or eddy currents. These effects often mixed with relevant random phenomena (Barkhausen noise), which influence the accuracy and reproducibility of measurements [2], and practically make it difficult to achieve a truly rate-independent J(H) and/or B(H) behavior [3].

There are two typical ways or equally, two fundamental inductive measuring procedures to achieve the magnetization curves and hysteresis loops under quasi-static conditions [3]. (1) Ballistic method or point-by-point method: The magnetizing field strength H is varied in a step by step manner and each time the system is allowed to relax to a novel equilibrium state, afterwards, the corresponding B or J variations are determined, and the curves are achieved by a point-by-point procedure. (2) Continuous recording method or the Hysteresigraph method: The changing rate of magnetizing field dH/dt is controlled in an appropriate continuous style, as slowly as reasonable to avoid eddy current effects. Ideally, these two experimental approaches should bring about the same results, but differences can be always found because of the complicated definition of DC magnetization curve and hysteresis [2].

AC testing means to achieve or characterize a rate-dependent B(H) and/or J(H) behavior. Basically, this suggests that for a given induction rate dB/dt, the applied field strength H has to compensate for an additional opposite field related to dB/dt because of the related energy dissipation phenomena [3]. Moreover, because of high H c ⁢ J , it is almost impossible to apply AC testing on PMs. If high H is applied to PMs even with small frequency, according to Faraday’s Law of Electromagnetic induction, the self-inductance will be very large, and thus can result in high self induced electromotive force, which may be carefully avoided in an electrical circuit.

Generally, because the magnetic properties of PMMs are referred to the static magnetic properties, hard magnet testing is undoubtly assumed to be realized under DC conditions. When we can confidently talk of DC magnetization curves and hysteresis loops, the question of how low magnetizing frequency should be is intertwined with the problem of magnetizing rate control. Practically, time effects are often important. Even if we are seeking for quasi-static measuring conditions, their effect should accordingly be evaluated to avoid the misunderstanding in the practical recognition of rate-independent hysteresis [3]. This difficulty can be solved by enforcing a defined time dependence on the induction derivative dB/dt in the test sample by analogue means or digital means. Thus an automatic testing is always asked to be measured in a quasi-static state in order to eliminate the hysteresis effect, so measuring speed dB/dt and dH/dt must be controllable, especially at the vicinity of B r and/or H c point. If the specimen has high B s and/or H c , the measuring speed must be controlled to slow down, otherwise, in addition to the hysteresis effect, large eddy current may also occur because of the high magnetic flux changes, furthermore the magnetic states will be hard to keep stable at each point. For an automatic test system, if the measuring is done in continuous recording method, in order to ensure a rate-independent hysteresis loop, the combination of weak signal and long integration time of an electronic fluxmeter are always required in addition to that dB/dt should be held constant [2]. This can also minimize the effect of eddy current, thus improve the approach to DC properties [2]. As a result, A/D converters of a 12 bit vertical resolution or higher is desirable and generally available up to the kilohertz range [2].

Furthermore, the time change rate of the driving magnetic field dH/dt should be sufficiently slow to avoid curve distortions on account of a delayed response of B to H change (sometimes notable), but it should also be fast enough to avoid errors caused by drifts of the instrument and integrator time constant. Often it is helpful to offer a controlled variation of the field-sweep rate in such a way that the field will change rapidly when intrinsic induction J i or B i remains nearly constant, but will slow down when they change rapidly. Typically, sweep times through the second quadrant are 15 s to several minutes because running a loop too fast can result in significant errors as a result of eddy currents and magnetic aftereffect [11], which is also theoretically pointed out in IEC 60404-5 standard [9]: dH/dt shall be slow enough to avoid the production of a phase difference between H and B or of eddy currents in the test specimen. If the material has a significant delay between the changes in B with H, the flux integrator should have long enough time constant, and zero drift should be sufficiently low to ensure accurate integration. Of course, these conditions must be achieved whereas other measuring techniques are developed. Moreover, eddy currents in the hard sample are always low or absent when going across the loop with the typical rates that are allowed by eddy current shielding in the bulk structure of the electromagnet (say around 50–200 s for full loop determination), because the differential permeability of PMs in the steepest part of the loop is orders of magnitude lower than that in soft magnets [3].

It is found that the measurements of the Nd-Fe-B magnets will be subjected to disturb from magnetic viscosity. This adds up to measuring a coercive field H c that decreases by increasing the time scale of the experiment [3]. Magnets like Al-Ni-Co, Sm-Co and sintered Nd-Fe-B based PMs, which have metallic conductivity, can exhibit significant time effects due to eddy currents [3]. Since very high H values must be applied to the Nd-Fe-B material when approaching the saturated state before determining the hysteresis loop, the pulsed field method can be expected for their characterization. In this case, however, if complete loop traversing is achieved in a few milliseconds only, specific corrections of the raw data are necessary in order to retain the static loop, such as those used to correct demagnetizing field, eddy current correction (known as f/2f method [1, 30, 36]), etc. On the other hand, a very low magnetization rate might not represent a definite solution to time effects because of magnetic viscosity.

2.6 Influence of the saturation of the poles

The DC hysteresigraph is fundamentally a closed magnetic circuit method system equipped with an electromagnet (also called a yoke), and the test specimen is inserted into the yoke when measuring. The usual measurement of the inner field strength H i in PMs for the determination of the B(H) and/or J(H) curves is performed next to the specimen to be measured in the air gap of a measuring yoke. It is only then correct when the polar surfaces of the yoke form magnetic equipotential surfaces [9, 11, 20, 21]. Furthermore, if the iron core is far away from saturation, the field generated by the electromagnet will be highly uniform for an accurate measurement [2]. If the yoke is approaching the saturated state, not only the field generated by the electromagnet will be strongly non-uniform, but also the soft iron will progressively repel the flux lines created by the sample under test. The field distribution around the sample will then come close to that of an open magnet immersed in the field generated by the electromagnet. Therefore, both polarization J and effective field H i in a real magnet will be non-homogeneous and the measuring accuracy will be harmed.

Practically, if the flux density is less than about 1 T in iron and 1.2 T in Fe-Co poles, equipotential surface can be realized [9]. But for some PMMs with high B r or high H c ⁢ J , or both, local induction values much higher than 1.0 to 1.2 T (800 to 1000 kA/m) can occur, thus will saturate part of the pole pieces near the test specimen end faces. Then the pole faces are no longer equipotential surfaces, and notable inhomogeneities of H and B in and near the test specimen will be developed, even the field uniformity in the region defined by Eq. (2.3) will be destroyed. Furthermore, when these values are locally exceeded under the combined influence of the exciting current of the electromagnet and the magnetized specimen, the field uniformity will be broken up, the specimen will become nonuniformly magnetized, and the magnetization or demagnetization curves can become severely distorted at the higher H [11], just as described in IEC 60404-5 standard [9]: during the measurements B in the pole pieces shall be kept substantially away from saturation because the pole faces of the electromagnet should be magnetically equipotential surfaces. Practically, B shall be smaller than 1 T in iron and less than 1.2 T in iron alloy containing 35% to 50% cobalt. If B higher than 1.0 T or 1.2 T occurs, unacceptably high B in parts of the pole pieces adjacent to the test specimen will be produced, and thus greater errors can occur because in such cases the pole faces are no longer equipotential surfaces. But in this standard there is no suggestion how to solve this problem.

Nowadays B r of modern high quality PMMs often exceeds 1.2 T, and B r of nanostructured two-phase magnets (also known as exchange-coupled magnets) can be higher than 2 T (a theoretical energy product of 1.09 MJ/m 3 (137 MGOe)) [37]. Magnetic properties of sintered Nd-Fe-B magnets have reached B = r 1.555 T, (BH) = max 474 kJ/m 3 (59.6 MGOe) and H = c ⁢ J 653 kA/m [38], and B r of mass production products often exceeds 1.4 T. In addition, in order to measure their demagnetization curves extremely high magnetic fields are needed. Now these magnets are usually measured by the DC hysteresigraph method. Moreover, in many cases, especially for research purposes, they are measured by Vibrating Sample Magnetometer (VSM).

It has been found that excellent uniformity of the field in the gap is achieved even when the value of the magnetic flux density B in the core is of the order of 1.8 T [3], quite beyond the upper limit 1.0 T recommended in the IEC [9] and ASTM Standards [11]. With optimum 54.74 ∘ cone-shape pole and high flux density B in the gap (about a magnetic polarization J ∼ 2 T in the region of the core surrounding the pole faces), the predicted axial variation is around 2% [3]. It is also found that the inhomogeneity of the generated field in the gap is only part of the problem, because, if the iron core offers poor closure circuit to the flux originating from the PM, non-uniform demagnetizing field will arise and it will combined with the applied field H 0 . Then the measured effective field H i , obtained with a Hall probe or an H-coil placed on the sample surface will be influenced by a significant error [3].

When testing materials with H c ⁢ J higher than 1750 kA/m in the hysteresigraph, the curve shape will be distorted at values above 1750 kA/m due to saturation of the permendur pole caps. Since the curve shape is practically unchanged with moderately elevated temperature, we can compare the shape with that measured at higher temperatures, through finding the shape changes on the curve from a true “square loop”, this curve can be revised back to “true” room temperature curve [39].

Moreover, as a consequence of the apparent image effect [17, 18, 19, 23, 24], at some value of the applied field, the pole faces of the electromagnet will become locally saturated in the region adjacent to the ends of the sample, especially when L/D ratio is small. This localized saturation will lead to a non-uniform distribution of field inside and outside the sample, at the same time, the polar surfaces of the yoke are no longer equipotential. The field at the ends of a long sample is non-uniform, but near the center of the sample it will become uniform. Near the ends of the sample, the field distribution is determined by the presence of magnetized surfaces with different levels of magnetization. Away from the ends, the field will take up the configuration that can minimize its energy. The field energy per unit volume depends on H 2 , so a uniform field has lower total energy than a non-uniform field and the field will become uniform at positions far from the magnetized pole tips [17, 18, 19, 23, 24]. Moreover, the flux pattern produced in space around the magnetized sample can be distorted because of image effect, and the image effect disappears at high applied fields when the electromagnet pole pieces approach magnetic saturation [17, 18, 19, 23, 24].

In the measurement of magnets that have high flux density or high coercive force, the yoke poles will be located in the area of magnetic saturation, thus the field strength H i in the magnets is smaller than that measured in the air gap next to the specimen. In this case it is suggested that H i in magnets can be directly measured with a potential coil in the pole of the measuring yoke [20, 21] if magnetization is homogeneous, or is measured as the tangential field component near the magnetized body.

In the usual measurement of PMMs, it is assumed that the samples are homogeneous, that is to say, the samples should have constant magnetic properties throughout the volume. Moreover, the samples should have circular or other uniform cross section. In practice these conditions are not always satisfied. Errors will occur if samples have conical or otherwise non-constant cross sections and/or the magnetic values depend upon the part of the volume measured, like multi-pole magnets. Such magnets can be measured with the pole-coil method. This is a magnetic tester comprising measuring coils inserted into the surface of the pole piece of an iron yoke [20, 21]. This method can also be used to measure the demagnetization curves of inhomogeneous PMs. Furthermore, it allows the analysis of different causes of inhomogeneities, e.g., differences in the intrinsic magnetic properties within one test sample and/or both side (e.g. with hard ferrite) of a magnet, differences in the degree of orientation in a homogeneous material, differences in the effectiveness of magnetic heat and annealing treatment, differences produced by inclusion, holes or nonmagnetic contaminations, and differences produced by unequal cross sections of the tested magnet, e.g. with conical shape.

2.7 Influence of hall probe

Theoretically, methods of measurement of the magnetic field strength H widely used in industry applications mainly comprise the induction methods (including ballistic method, flux meter method, and electronic integral method, etc.) and methods based on electromagnetic effects (including Hall Effect method, magnetoresistance method, and magnetic resonance method, etc.) [3]. In standards [9, 11], it is suggested that a flat search coil, a magnetic potentiometer or a Hall probe can be used together with suitable instruments to determine H, and the magnetic flux density B is determined by integrating the voltage induced in a search coil. Usually a Hall Probe is used to measure H in a DC hysteresigraph or in a vibration sample magnetometer (VSM).

The position where the Hall sensor is placed has a great influence on the measuring results. The dimension of the magnetic field sensor and its location shall be such that it shall be within the area with a homogeneous field which is limited by the maximum diameter of the cylindrical volume defined by Eq. (2.3) in the yoke. The magnetic field strength H at the surface of the test specimen will be equal to the magnetic field strength H i inside the test specimen only in that part of the space where the magnetic field strength vector is parallel to the side surface of the test specimen. Of course, in this case the pole surfaces should be magnetically equipotential. Therefore, a magnetic field strength H sensor is placed in the homogeneous field zone as near as possible to the test specimen and symmetrical with respect to the end faces of the specimen.

Since it is not possible to directly measure the field inside the sample, if the field is essentially uniform throughout the sample and in the area surrounding the sample, the measured H can be closely representative of the H acting inside the sample. Just as described above, when the L/D ratio of the sample is smaller than 1.8, the field across the sample diameter and in the surrounding area can be extremely non-uniform due to apparent image effect [17, 18, 19, 23, 24]. More clearly, the field H is higher outside the sample than inside. So, on the whole, attempts to extrapolate from field values measured at some distance away from the sample down to the sample surface can lead to a meaningless result, since if the field is non-uniform outside the sample it will be non-uniform within the sample. Even if the field H could be measured accurately at the sample surface, the measured field would not accurately represent the field acting internally on the sample. In fact, since the field is non-uniform, it cannot be represented by a single numerical value.

It is demonstrated that the field is lowest at the center of the sample, increases with increasing radius, and continues to increase for a significant radial distance in air space outside the sample [17]. The field measured by the H probe is therefore higher than the true field at the sample surface, and much higher than the field at the sample center, thus, even though the magnetic polarization J of the sample is saturated, and therefore uniform, an erroneously higher measured value of H (higher than the true H value inside the sample) leads directly to an incorrectly lower calculated J value according to

J = B - μ 0 ⁢ H(5)

This effect will become more notable when the sample becomes shorter, i.e., as L/D ratio decreases. Furthermore, for the sample with higher saturation magnetization Ms (also saturation polarization Js), this effect will appear at lower applied fields and the drop in apparent magnetization will become greater. This phenomenon will occur both in measuring soft and hard magnetic materials [17]. In this case an accurate determination of the field at the sample surface cannot give an accurate value of the field acting inside the sample, because there is no single value of the field acting inside the sample [17]. For a sample with L/D = 1.8, measurements of B and H made anywhere in the central half of the sample length should be correct within a few percent. Measurements made near the end of the sample can be in error by up to about ± 10% and may show the apparent image effect. The apparent image effect will be smaller for materials with lower saturation magnetization. In this case a lower value of L/D might be acceptable [17]. Probe placement is a very serious issue with Hall probes. In addition, for high B r and/or high H c ⁢ J magnet, the pole area near the specimen can become saturate, so the magnetic field the Hall probe measures will be larger than H i .

Error will become larger when measuring the temperature coefficient of B r and/or H c ⁢ J using a Hall probe because Hall Effect is closely related to temperature. Just like other semiconductor devices, a Hall element is very sensitive to temperature change. Since the properties of Hall element can change with the temperature nonlinearly, it is very hard to compensate from both hardware and software. Besides the nonlinear effect, the measuring errors caused by the Hall element mainly come from the following aspects: (1) The basic Hall device is sensitive to variations in temperature [11]. Hall coefficient can change with temperature, this error will become especially important when measuring at the elevated temperatures; (2) Error caused by the magneto-resistance effect. The resistance of the Hall element can change with H. That is to say, Hall current can change nonlinearly with H when Hall voltage keeps stable, and the Hall voltage will not change linearly with H when Hall current keeps stable, especially in high H; (3) No sensor is perfectly linear [11], Hall coefficient can also change with H; Some Hall probes exhibit significant nonlinearity in high fields [16]; (4) Error caused by inequipotential electromotive force, which is also affected by temperature. These are all inherent in a Hall element.

When measuring the magnetic field produced by a magnet in free space, the main drawback of the Hall probe is that the field around a magnet in free space varies rapidly as we move away from the face of the magnet, so the probe must be put directly on the face of the magnet or held at some fixed distance. Whereas the measured field clearly relates back to a magnet property, B r , dimension of a magnet, and position, thus distances are critical. Probe construction also needs to be considered in determining distance, because the fragile Hall element is typically buried inside an aluminum tube for protection. Often the precision position is not well controlled.

In practice, the relationship between Hall voltage and field H is not perfectly linear, and becomes increasingly non-linear at high magnetic fields. In this case, nominal field readings from a linear-scale meter or voltage output should be corrected. This means that generally Hall probes can be used only with control units for which they have been specifically calibrated [24]. Also they should be regularly re-calibrated [11]. Attention must also be paid to the commonly strong temperature dependence of the Hall-probe output [11].

OPEN IN VIEWER

Obviously, the Hall probe will not be suitable to measure high performance PMMs, so in certain arrangements an H coil is currently used together with a B coil. A coil of known turn-area NA can be used to measure H in a given region of space [2, 31], as shown in Fig. 4. A flat H-coils, a coaxial H-coil or a Rogowski-Chattock potentiometer placed on surface of specimen can also be used for the determination of H. For high-coercivity, dense ferrites and especially for most RE-TM materials, it is essential for accurate measurement to use thin flat or radially thin annular H-sensing coils of short length ( 1/5 to 1/3 of the specimen length), centered on the specimen and placed as close as possible to the specimen surface [11]. If the H-coil sensor is not closely placed on the surface of the specimen (e.g., due to the thickness of the sensor itself), it is possible to use more than one coil and then to extrapolate the result to the sample surface [1], though it is difficult to do so.

In addition, magnetic polarization J can be measured with the aid of two co-axial coils system, one of which measures B of the sample and the other records the H next to the sample. This coil is called a J-compensated surrounding coil, also known as J-coil, as shown in Fig. 4, which is recommended by the standard IEC 60404-5 [9]. The area and number of turns of these coils is designed in such a way that the following condition is fulfilled: N 1 A 1 = N 2 A 2 . The two coils connected differentially in line will show the value described in Eq. (5). As a result, a J(H) curve can be obtained. In the absence of the specimen, the output signal is zero; thus, the air flux is compensated. With the specimen in it, we can directly detect the magnetic polarization J. Also, if two coils are heat resistant, they can be used to measure high temperature together with room temperature J(H) curves simultaneously [20, 21]. As a result, temperature coefficients of B r and H c ⁢ J can be obtained.

The measuring accuracy needed for PMMs is very high, and both for B and H, accuracies are within ± 1%. The characterization of magnetic materials technically requires that magnetic fields are generated and controlled over a wide range of amplitudes covering several orders of magnitude. Though the measured range for H is usually from - 2000 kA/m to + 2000 kA/m, or even from - 4000 kA/m to + 4000 kA/m, and for B is often from - 2.0 T to + 2.0 T, both are very broad for the measuring instrument, in the measuring process of a demagnetization curve and/or a hysteresis loop, the accuracy should be kept at almost the same over the whole range of magnitudes, which issues a great challenge to the measuring instrument, e.g., from mA/m to MA/m and from mT to T. Thus, in automatic system, at least a 12-bit vertical resolution or higher by the A/D converters is needed.

In addition, as stated in international standards [9, 11], in order to obtain a sufficiently uniform magnetization field in the space occupied by the test specimen, some conditions shall be fulfilled simultaneously, including the diameter of a circular pole piece, the distance between the pole pieces, and the maximum diameter of the cylindrical volume with a homogeneous field, as described in Eq. (2.3). That is, the L/D value of the specimen must be strictly obeyed. To reduce the measuring error, the air-gap between the test specimen and the pole pieces shall be small. Moreover, the influence of the air-gap has been carefully considered in these standards.

Many restrictions are also stated in standards in detail [9, 11], e.g., the performance of a magnetic system can be determined by the properties of PMM, the dimensions of the system, the air-gap and other elements of the magnetic circuit. Furthermore, the methods described in these standards all refer to the measurement of the magnetic properties in a closed magnetic circuit simulating a ring core to eliminate the effect of the demagnetization effect. The closed magnetic circuit consists of an electromagnet made of soft magnetic material and the test specimen. Furthermore, to minimize the air-gap, the end faces of both pole pieces shall be ground as nearly as possible parallel to each other and as nearly as possible perpendicular to the pole axis. In addition, for certain measurements, the yoke and the poles can be laminated to decrease eddy currents. This means that the differences among the performances of different measuring systems should also be taken into account.

In order to evaluate the differences among each measuring systems including open magnetic circuit systems and closed magnetic circuit systems, PTB had organized an European intercomparison [40], from which a reasonable and reliable result was obtained, and the possible interpretations were also given. Intercomparison measurements on cylindrical specimens of Al-Ni-Co and Nd-Fe-B in a closed magnetic circuit and on spherical specimens of Nd-Fe-B in an open magnetic circuit using VSM or SQUID magnetometers show that the difference between B r results is relatively small, whereas difference between H c ⁢ B is about 5.5% for two methods, which is considerable. For H c ⁢ J , the difference between open and closed circuit results is somewhat larger than that for H c ⁢ B . They thought that it is the error in the determination of the temperature that influenced both remanence and coercivity. Errors in the measurement of the field strength and different measuring rates had no practical influence on B r , but they affected the determination of coercivity H c ⁢ J (but less of H ) c ⁢ B . They also concluded that due to a large magnetic viscosity of Nd-Fe-B, the measured H c values decreased with decreasing measuring rate, which may account for differences of 1 to 2% when considering that the measuring rate is varied ten times. Differences in the re-magnetization process (continuous field vs. pulsed field, time of the pulse, maximum field value) may influence remanence and coercivity differently. For H c ⁢ J a further source of difference was that the poles in closed circuits became saturated, and this caused an increased magnetic field strength at the place of the Hall probes. Thus the measured H c ⁢ J values became too high. The values for all spheres were smaller than those for the cylinders, on average by 5%. The scatter for the spheres was twice that for the cylinders.

In the case of Nd-Fe-B magnets additional problems result from the large temperature dependence of the magnetic properties and the dependence on the aging time due to low corrosion resistance. From this intercomparison no correlation between the results and the details of the setups used was found. In order to improve the reproducibility, it is recommended that particular attention should be paid to different measuring times and different re-magnetization processes, etc.

The DC Hysteresigraph is widely employed and is the only one commonly used for testing PMs. Though no demagnetization correction is required, the electromagnets employed cannot produce sufficient magnetic fields to saturate most high-performance magnets such as RE-TM magnets. So magnets are usually saturated first with a pulse magnetizer. Often the field is sufficient to obtain H c ⁢ J of most PMMs, but it is not enough to get H c ⁢ J of high-performance RE-TM magnets, regardless of the errors. Thus, other measuring method must be developed.

A different method of measurement of magnetic materials in an open magnetic circuit is defined in detail in IEC 60404-7 [41], but this standard can only apply to magnetic materials having a coercivity up to 500 kA/m, and only H c ⁢ J value can be obtained. The demagnetizing factor N does not exist in closed-circuit measurements, so correction for the demagnetizing field is not needed. Whereas in open-circuit measurements, no exact N value exists for samples with the shapes other than ellipsoidal samples; an appropriate N must be obtained through calculation or experiment, and is likely to be of uncertain accuracy [17]. It is defined in IEC 60404-7 [41] that the specimen used shall have a generally elongated shape so that its self-demagnetization factor is such that the specimen can be saturated and the shape effects do not produce a significant error in coercivity. For cylindrical test specimen, it is recommended that L/D should greater than 5.

VSM method is a high-sensitivity magnetic moment measurement technique, largely applied in research and industry for the characterization of PMs. It is not an absolute method and requires calibration by means of a reference sample. In spite of widespread use, there is no IEC standard regarding the VSM technique [42].

In a recent international comparison, ten international laboratories took part in a round robin, aimed at determining the base DC magnetic properties of hard magnets using VSM [42]. Carried out in the framework of the activity of the IEC TC68 Working Group 2, the round robin was directed, in particular, at the determination of the hysteresis loop parameters of hard ferrite and magnetic tape samples in open magnetic circuit. The analysis of the results showed generally good reproducibility of measurements, comparable or better than the one observed in past experiments on rare-earth based compounds. The measurements on anisotropic ferrites show the best reproducibility for all the measured quantities, the standard deviation is around 1%. Isotropic ferrites show larger dispersion, the standard deviation of J r and H c ⁢ B are larger than 3%, and the standard deviation of (BH) max is around 6%, revealing that maximum energy product measured is apparently affected by poor reproducibility.

PMs can have significant temperature-dependent properties and thus measurements should be carried out under tightly controlled temperature [3]. For example, the coercive field in BaM and SrM ferrites has positive temperature coefficient of the order of 0.3–0.5%/ ∘ C and saturation magnetization coefficient around - 0.2%/ ∘ C. The same quantities in Nd-Fe-B compounds are of the order of - 0.6%/ ∘ C and - 0.1%/ ∘ C, respectively. So Nd-Fe-B magnets are extreme sensitivity to temperature variations, which also call for strict control of the room temperature. It turns out that the customarily allowed fluctuation of ± 5 ∘ C around the room temperature (23 ∘ C) in technical standards [9] may lead to very high measuring uncertainty, thus may require inconvenient corrections.