Magnetic characterisation of microstructural feature distribution in P9 and T22 steels by major and minor BH loop measurements Journal of Magnetism and Magnetic Materials

This paper investigates the magnetic properties and parameters measured from major/minor loops and used to characterise different microstructural feature distributions in P9 and T22 steel in different heat treatment or service conditions. The present study introduces a non-destructive way of selecting mi- crostructural features of interest and/or excluding those of little relevance by examination of minor loop measurements at a selected range of applied ﬁ elds and discusses the fundamental mechanism in terms of domain processes. There is remarkable consistency in magnetic behaviours and properties such as initial/incremental permeability values between the measurements by different techniques. This beha- viour has been ascribed to the similar underlying domain processes and hence similar selected microstructural features that are affecting the domain processes. & 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
Microstructural changes in power generation steels during operation at elevated temperature alter the properties of these steels and their remaining safe operating life (remnant life) [1]. Efficient operation of power generation plant requires the microstructural condition to be assessed during service. Currently the microstructural state is assessed using replicas of the surface or inferred from hardness measurements, both taken during shut down periods. Non-destructive evaluation (NDE) of the microstructural state of power plant steels during their service life is of interest in order to give a more accurate assessment of safe remnant life. Amongst a wide range of NDE techniques available, electromagnetic (EM) methods are of particular interest for the evaluation of ferromagnetic ferritic heat resistant steels.
A variety of EM sensors have been developed or commercialised for evaluating/monitoring microstructure, mechanical properties or creep damage in ferritic steels during industrial processing, heat treatment or service exposure [2][3][4]. These sensors operate in a non-destructive and non-contact fashion and are based on the pri-nciple that microstructural changes in ferritic steels alter their electrical and magnetic properties. Typical EM sensor measurements involve applying a magnetic field of given amplitude and direction and measuring the EM responses of the test piece. Ferromagnetic materials such as ferritic steels contain magnetic domains, consisting of aligned magnetic moments, separated by domain walls (DWs). Each magnetic moment has associated with it a certain amount of free energy. The existence of domains is a consequence of energy minimisation. As a magnetic field is applied, domains will be re-aligned through DW motion, domain nucleation and growth, and/or domain rotation until a new minimum free energy state is reached. Microstructural features can influence these domain processes to modify the energy balance and ease of domain re-alignment and hence affect the magnetic properties of ferromagnetic materials. More details on the domain theory and the effects of the microstructure in ferromagnetic materials on their magnetic domains and properties can be found elsewhere [5]. The domain processes and the role of microstructural features are affected by the amplitude, direction (with respect to the crystal orientation of the materials) and nature (e.g. alternating or direct current) of the applied fields during EM measurements, which determines what microstructural features an EM sensor or technique is most sensitive to and what relevant EM properties or signals should be measured. For examples, our multi-frequency EM sensors, that apply a small magnetic field, have been used to measure the initial relative permeability of power generation P9 and T22 steels in different conditions and are sensitive to the microstructural features that determine the mean free path (MFP) to DW motion in a small applied field [6]. By contrast, a commercial system (IMPOC) used for strip steel assessment applies a very strong field to bring a selected area on a moving steel strip close to its magnetic saturation and correlates the measured EM signals (related to remanence and/or degree of magnetic saturation) to the yield strength of the test materials [3]. Use of major/minor loop assessment for NDE of steels, such as inspection of cold rolling [7,8], creep [9] and degradation (fatigue) [10] in a range of steels, has gained increasing consideration in recent years. Whilst there has been significant work on empirical relationships between major/ minor measurements and mechanical properties such as hardness or experimental observations e.g. cold rolling reduction or creep strain, there have been few reports on detailed correlation between the measured magnetic properties from major/minor loops and complex microstructural features or parameters in terms of their interaction with domain processes for given applied fields. There are no reports on the relationship between microstructural feature distributions, as opposed to a single microstructural parameter e.g. average grain size, and corresponding major/minor loop behaviour in steels.
In this paper, a BH system that is able to apply a field (H) of any selected range of amplitude, within a specified power limit, and measure the applied field H and the induction (B) in a test sample has been used to measure major and minor BH loops for P9 and T22 steels in different conditions. A variety of magnetic properties evaluated from the measured major/minor BH loops have been used to characterise the microstructural feature distribution in the studied steels based on their interaction with the domain processes. The present study introduces a non-destructive way of selecting microstructural features of interest by minor loop measurements at a selected range of applied fields and explains the fundamental mechanism in terms of relevant domain processes.

Materials and experimental details
The P9 and T22 steels (P9ES and T22ES) studied were removed from a refinery furnace at a petrochemical plant after approximately 11 years at 793 K (520°C) (comparable with a similar time of elevated temperature exposure during service in power generation plant [11]). Their chemical compositions are given in Table 1. Selected samples (approx. 70mm 15mm 7mm × × ) were heat treated to simulate the service entry microstructure, i.e. tempered martensite/bainite, by normalizing at 1223 K (950°C) for 1 h or 1213 K (940°C) for 1 h followed by air cooling to room temperature and then tempering at 1033 K (760°C) for 1 h or 993 K (720°C) for 1.5 h for P9 and T22 respectively (P9T and T22T). As-normalised samples were also examined (P9N and T22N). The heat treatment conditions have been determined as per ASTM standards A335 [12] and A213 [13] as well as literature data [14][15][16][17].
Metallographic samples were polished to a 0.25 μm finish and etched (in Kallings [18] for P9 and in 2% nital for T22). A JEOL-7000 Field Emission Gun Scanning Electron Microscope (FEG-SEM) was used to obtain SEM micrographs. Additional metallographic samples were polished to a 1 μm finish followed by several etchingpolishing cycles and a final polishing with OPS (Oxide Polishing Silica) for 10 min for electron backscattering diffraction (EBSD) analysis using an Oxford Inca EBSD in a JEOL-7000 FEG-SEM. Lath boundaries and outlines of carbide particles in SEM micrographs were reconstructed as trace features and objects respectively using Image-Pro Plus. Average distances between two neighbouring trace features were taken as lath width and average length of diameters measured at 2°intervals passing through the object's centroid as equivalent diameter of particles. An in-house system developed at the University of Manchester was used for BH loop measurement. A magnetic field was applied using a silicon-steel U-core with two excitation coils wrapped around the legs and driven by two power amplifiers fed with a low frequency time varying signal. A machined cylindrical sample (4.95 mm diameter and 50 mm long) was fitted into a slot in the core to maximise coupling between core and sample. The axial applied field (H) was measured using a sensitive (0.16 mV/mA mT) Quantum Well Hall sensor, also developed at the University of Manchester. The flux density of the induced field (B) was measured using a 20-turn encircling coil connected to an instrumentation amplifier. A 1 Hz sinusoidal excitation was used for the measurement of the major loops and the minor loops without a bias field and 9 cycles were recorded and averaged. A 10 Hz sinusoidal excitation was used to generate the minor loops with a bias field. The sample was taken through several major loop cycles before the applied field was held constant at a pre-determined H value and 90 minor loop cycles were recorded and averaged to reduce noise.

Microstructures
The microstructure of as-normalised P9 consists of martensite (of a typical lath width at 297 746 nm, which is close to literature values [19]) and bainite ( 15% < ) as shown in Fig. 1(a). There are a high number density of high angle ( 15 >°) boundaries including all the martensitic/bainitic colony/packet boundaries and some lath boundaries and a lower density of low angle (3-15°) lath boundaries as shown in Fig. 2(a), an inverse pole figure (IPF) map overlaid with a grain boundary map, and Fig. 2(d), a boundary misorientation distribution histogram, for the as-normalised P9.
Subsequent tempering produced a simulated service entry microstructure, i.e. tempered martensite/bainite as shown in Fig. 1 (b) with the majority of the laths measuring around 380 7149 nm wide (consistent with previous data [20]) as measured from SEM images. Some areas without clear lath features are present in the SEM images (probably due to non-uniformity in etching) and were not considered in the measurement. Compared to the as-normalised P9, there is a significant decrease in the number density of low angle boundaries as observed from Fig. 2(b) and (d) due to coarsening of the martensitic laths. Many fine alloy carbides are present along the lath boundaries, together with some coarse equiaxed precipitates. The size of the latter is inconsistent with their formation during tempering and so they are more likely to be coarse carbides from the service-exposed condition that failed to dissolve completely and remained from the prior solution heat treatment as shown in Fig. 1(b). However, these carbides are so widely separated that they are expected to have a negligible effect on the overall pinning of DW motion, compared to other fine precipitates. Although reverse magnetic domains can form around them, there are too few for these precipitates to have a significant effect on the EM properties.
After long service exposure, the microstructure showed equiaxed ferrite grains (of 9.6 7 5.7 μm in equivalent circular diameter) with large carbides distributed within the ferrite grains or on grain boundaries as shown in Fig. 1(c). Compared to the astempered P9, very few low angle boundaries remained after the service exposure as can be seen in the inverse pole figure map overlaid with boundaries shown in Fig. 2(c) and the misorientation distribution shown in Fig. 2(d). Most ferrite grain boundaries are high angle boundaries. Table 2 gives values for dislocation density (estimated from literature values [21][22][23][24]), the high angle and low angle boundary density measured by EBSD, martensitic/bainitic lath width or ferrite grain size, and the mean equivalent circular diameter d, number density N and total area fraction of carbide precipitates A Φ for the P9 and T22 samples in the different conditions. For the service exposed P9 and T22 the precipitates on the grain boundaries are not included as they are expected to play a very minor role in pinning compared to the grain boundaries on which they precipitated. This is because the carbides on grain boundaries are expected to be similar or weaker pinning points than grain boundaries, and, if present on the grain boundaries, do not provide any additional pinning and hence little contribution to relative permeability [6]. Fig. 3 shows the size distribution for the precipitates in the as tempered and the service exposed P9. It clearly shows an overall coarsening (a 133% increase in size) and a significant broadening of the distribution after long-term, elev-ated temperature exposure in service. The number density of precipitates decreased to only 11% of the as-tempered P9 value accompanied by a 52% reduction in area fraction. Fig. 4 shows the nearest-neighbour inter-particle spacing d nn distribution for the service exposed P9 fitting very well with the log-normal probability distribution function (PDF). The as-normalised T22 steel shows a mixed microstructure of bainite and a small amount ( < 5%) of pro-eutectoid ferrite as shown in Fig. 5(a). No carbides are present in the pro-eutectoid ferrite, but plate-like carbides can be seen within the bainitic regions. After tempering, many carbides can be observed along prior austenite grain boundaries, on ferrite boundaries or within bainite regions as shown in Fig. 5(b). The microstructure of T22 after the service exposure consists of equiaxed ferrite grains (27.5717.1 μm equivalent circular diameter) and many carbides outlining the ferrite grain boundaries or occurring within the ferrite grains as shown in Fig. 5(c). Fig. 6 shows an inverse pole figure map with highlighted boundaries and a misorientation distribution histogram for the T22 samples in the different conditions. There is a reduction in the number of low angle boundaries after tempering and a significant decrease in both low and high angle boundaries after the service exposure as a result of annihilation of the ferrite lath boundaries, as can be seen in Fig. 6(d) and Table 2. Fig. 7 compares the extremely fine precipitates within the ferrite laths for the as-tempered T22 and the coarser ones within the ferrite grains for the service exposed T22. Their size distributions are compared in Fig. 8, which shows a similar broadening as seen in Fig. 3 for the P9 samples but a more significant coarsening (182% increase in mean equivalent circular diameter). Fig. 9 shows distributions of the nearest-neighbour inter-particle spacing for the Although some contrast consistent with individual laths is seen in (a) and (b) they are not clearly resolvable at these magnifications and so the features observed are lath packets or lath colonies [6]. Table 2 Measurements on microstructural features for P9 and T22 in different conditions [6].  intra-grain precipitates in the service-exposed T22 sample also fitting very well with a log-normal PDF and a log-normal cumulative distribution function (CDF). Fig. 10 shows the major BH loops and the initial magnetisation curves for the P9 and T22 steels in the different conditions. A number of micromagnetic properties or parameters extracted from the major loops are illustrated in Fig. 11, including remanence B r -the remanent induction after the applied field has been removed; coercivity H c -the field strength required to bring the sample to zero magnetic induction; the maximum induction B s obtainable under the applied field-an approximation to the technical saturation induction; and the hysteresis loss W h -represented by the areas encircled by the loops; the values of which are given in Table 3. The coercivity, H c (also known as magnetic hardness), values for the P9 and the T22 steels dropped by 80% and 66% respectively after tempering, and 40% and 15% further after service exposure. This significant magnetic softening behaviour is consistent with their mechanical hardness decreasing significantly after tempering and service exposure. There is an approximate power-law or cubic relationship between the magnetic and the mechanical hardness for the studied as shown in Fig. 12, which is similar to the reported general trend that coercivity increases with Size distribution for precipitates in the as-tempered (P9T) and the service exposed (P9ES) P9 samples [6].  4. Distribution of the nearest-neighbour inter-particle spacing for the precipitates within the grains of the service-exposed P9 (P9ES). hardness [26,27] for different steels and microstructural changes. However, there are no reports of a unanimous form of the relationship that applies for all steels. W h follows a qualitatively similar trend as H c for both steels. The order of the values for the other magnetic properties for the different heat treatment or service conditions, however, is different. The B s for the as-normalised samples for both steels are significantly lower than the astempered and the ex-service samples whilst the latter two conditions are hardly distinguishable between each other. The astempered samples have the greatest B r , followed by the normalised and then the ex-service samples, for both steels. In summary the two steels (P9 and T22) exhibit qualitatively the same behaviours for the micromagnetic properties changing with tempering and service exposure except for the order for the max μ Δ . The reason for this exception is explained in Section 5.2. , taking the P9N sample as an example. The shape of the minor loops evolves from a lenticular shape over the small amplitude range into a sigmoid shape typical of a major loop for ferritic steels with increasing H m a . Similar to major loops, a minor loop can be characterised by a set of minor micromagnetic properties/ parameters defined by analogy with their major loop counterparts, as illustrated in Fig. 11  (i.e. the peak height) are given in Table 3. As initial permeability μ i is defined as the differential permeability at zero field, i.e. The extrapolated μ i values prove to be very close to the relative permeability μ r inferred from the measurements using a multi-frequency EM sensor that uses a very small applied field, results presented elsewhere [4], as described in Table 3. This indicates the unbiased minor loop for a given amplitude describes how a sample magnetically behaves during EM sensor tests using a similar field range and vice versa. Other minor magnetic properties such as B m r , H m c and W m h , as shown in Fig. 14(b), (c) and (d) respectively, in general, exhibit similar behaviours with the increase of the amplitudes, i.e. increasing nearly exponentially over small amplitudes H c ≲ (note this part of the curves being nearly linear at double logarithmic scale) and then transitioning to plateauing (for the as-normalised samples) or approaching a plateau (for the as-tempered and the ex-service samples) at the corresponding major loop values for B r , H c or W h . All the curves, Fig. 14(b)-(d), fit very well with a double exponential function:  Fig. 15 illustrates a series of minor loop excursions from the lower part of the major loop with different DC bias field H m 0 , taking the ex-service P9 sample as an example. It can be seen that the encircled area and gradient of the minor loops vary with H m 0 . Fig. 16 shows the incremental permeability measured from these minor loops, major μ Δ , as a function of H m 0 for all the studied samples. The major μ Δ profiles all peak near the corresponding H c (coercivity for the major loops) and fit perfectly well with a multi-term Gaussian function. The maximum values major max μ Δ (i.e. the peak height) are given in Table 3. It is interesting that the major max μ Δ values are also close to μ r . In general the tempering and the service exposure heat treatments, for both steels, significantly increase major max μ Δ , narrow the peaks and shift them to a lower H m 0 value. Fig. 17 shows the incremental permeability measured from the minor loop excursions from an initial magnetisation curve, init μ Δ , with different DC bias field H m 0 ranging from 0 to 15 kA/m > for all the studied samples. The init μ Δ values drop rapidly for H H m c 0 ≲ and then decrease at a lower rate with further increase of H m 0 . All the curves fit very well with a multi-term Gaussian function as the incremental permeability profiles for the unbiased minor loops and the biased minor loop excursions from a major loop do. The initial (also the maximum) incremental permeability values, init max μ Δ , are, in general, close to the relative permeability inferred from the multi-frequency EM sensor measurements, μ r , the initial permeability extrapolated from incremental permeability for the minor loop amplitude sweep, μ i , or the maximum incremental permeability for the minor loop excursions from a major loop major max μ Δ as described in Table 3. The consistency in the permeability behaviour between different measurements and/or techniques indicates that the underlying domain processes are similar. Note the major max μ Δ occurs near H c , where B 0 ≈ and the effective field experienced by the domains is comparable with the small field applied for EM sensor measurements for μ r , the small   Fig. 8. Size distribution of the precipitates for the as-tempered (T22T) and the service exposed T22 (T22ES) sample [6].

Major loop properties and domain processes
Consider the domain processes during the upper part of a major loop, where the applied field H changes from H m to H m − . At H m most of the magnetic dipoles are expected to orientate along the applied field direction so as to minimise the free energy due to the external field (also known as Zeeman energy E z ), forming nearly a single domain across the whole sample. The saturation magnetic induction ( B s ≈ ) is thus determined by the magnetic moments associated with each atoms. Substituting Fe with nonferromagnetic alloy elements such as Cr and Mo (present in power generation steels such as P9 and T22) reduces the average magnetic moment and hence B s . This account for the generally lower B s values for the T22 samples and the lower still for the P9 ones than that of about 2.17 T for pure iron [28]. The significantly lower B s values for the normalised samples (P9N and T22N) than the astempered and the ex-service ones can be attributed to the supersaturated interstitial carbon in solid solution causing lattice distortion and significantly disturbing the coupling between the neighbouring magnetic moments on the lattice. This effect is analogical with interstitial elements e.g. carbon in steels causing more electron diffraction and hence having a more significant effect on residual resistivity in steels than substitutional elements e.g. Cr [29].
As H decreases E z becomes less competitive, that is, the change in the Zeeman energy, E z Δ , due to the magnetic moments rotating away from the applied field direction decreases. At the same time the anisotropy energy, E an , due to the deviation of magnetic moments from their easy magnetisation axes becomes a more influential component of the total free energy and hence needs minimising; as a result the magnetic moments rotate towards and eventually align with one of their easy directions associated with  the crystallographic orientations of each grain that is closest to the applied field direction to minimise E an , with a minimum increase in the E z . It follows that the single domain splits into a number of domains orientated along one of the easy directions closest to the applied field direction, with accommodative DWs formed at grain boundaries. Meanwhile, domains of reverse magnetisation tend to nucleate at the grain boundaries [30] enabling the domain within each grain to split into a group of alternate anti-parallel domains separated by 180°DWs to minimise the demagnetising energy or magneto-static energy, E d , without affecting E an . As H continues decreasing the growth of the reverse domains, which is against the applied field direction i.e. their direction vector makes an obtuse angle with the direction of H, is favoured at the expense of the anti-parallel neighbouring domains, accompanied by 180°DW motion until H¼0. At H ¼0 the 180°DWs are expected to be uniformly spaced provided that there are no imperfections pinning DW motion. Work must be done to overcome the energy barrier for domain nucleation due to the introduction of DW energy. Low-angle boundaries such as martensitic lath boundaries are not energetically favourable nucleation centres for 180°DWs due to the relatively low free magnetic pole density on these boundaries and hence lower driving force for the nucleation. Note I cos cos , where I s is the spontaneous magnetisation, θ 1 and θ 2 the angles between the domain directions of the neighbouring grains and the normal of their common boundaries [30]. It is reported that granular imperfections such as the carbide precipitates within grains do not contribute to the formation of 180°DWs as the critical field required for the nucleation is much larger than the H c for most soft magnetic materials according to the calculation by Goodenough [30]. Dislocation tangles within the untempered martensite or cold-worked steels can be regarded as point pinning features and hence are expected to have a similar effect as carbide precipitates. However, carbide precipitates within grains may be preferable nucleation centres for closure domains about them so as to minimise the demagnetising energy associated with the magnetic poles present on the surface of the particles so long as their radius is larger than a critical size R c , which was reported to be approximately 0.1 μm for iron [30]. Most of the precipitates on the lath boundaries in the as-tempered P9 and T22 samples are smaller than R c , see Figs. 3 and 8. Moreover, they are expected to have relatively low magnetic pole density compared to the equilibrium precipitates occurring within the ferrite grains in the ex-service samples because (a) part of their associated magnetic poles are expected to be counteracted by the lath boundaries intersecting the precipitates; (b) enriching with alloy elements such as Cr, Mo during long service exposure reduces the ferromagnetism of the precipitates and hence increases the density of magnetic poles according to Neel's theory [31]. By contrast, some of the large and equilibrium precipitates observed within the ferrite grains for the ex-service samples (whose diameters are larger than 0.2 μm, Figs. 3 and 8) are possible nucleation centres for closure domains. Thus, the low B r values for the ex-service samples may be attributed to the formation of closure domains around the large intra-grain carbide precipitates as well as the presence of free poles around the surface of the relatively fine precipitates in the ex-service samples, both promoting the demagnetising process. The low B r value for the as-normalised samples can be ascribed to the high density of free poles associated with the high density of dislocations within the highly strained martensitic laths providing extra demagnetising energy and promoting the demagnetising process. Meanwhile these microstructural imperfections including the martensitic lath boundaries with precipitates present on them in the as-tempered samples, the dislocation tangles within the laths in the as-normalised samples as well as the precipitates within the ferrite grains in the ex-service samples can be effective pinning features to the 180°D Ws and leave them still non-uniformly spaced, with those Table 3 Major/minor loop properties for all the studied steels.
Sample   oriented against the applied field direction being narrower than their anti-parallel neighbours, when H decreases to 0. In other words 180°DWs can be trapped by the potential well associated with these pinning features. Extra driving force is needed to allow further 180°DW movements. Then, as H is reversed and increases in magnitude the 180°D Ws that were originally pinned will eventually overcome the pinning with the narrower parallel domains growing until uniformly spaced, where the B value returns to 0 at H c . The significant drop in H c values for both steels after tempering can be attributed to the recovery of the dislocations, coarsening of the martensitic or bainitic laths; and the further drop after service exposure can be attributed to the coarsening of the precipitates and the lath boundaries. These microstructural changes reduce the number density of the pinning features to DW motion and hence H c . The parallel domains within each grain, which are oriented in favour of the applied field direction, grow at the expense of their anti-parallel neighbours to minimise the Zeeman energy E z without affecting the anisotropy energy E an with a further increase in the magnitude of H. This domain process results in a rapid increase in the B value. As E z becomes more and more competitive with the increase of H and eventually overthrows the dominance of E an domains start rotating away from their easy directions towards the applied field direction with the increase of B values slowing down, or the decrease of the differential permeability, and eventually B plateauing at approximately B s .     parameters are influenced by the probability distribution of f pin as well as the spatial distribution between the pinning features. Thus, it is expected that the probability distribution of f pin will have a similar shape to the incremental permeability profiles shown in Fig. 14(a). It is worth clarifying that f pin in this paper is defined as the minimum applied field H required to enable a domain wall to just overcome the pinning of a microstructural feature. Driving force or E z Δ , provided by the applied field, is required to overcome two terms of free energy (a) E d Δ to give a domain wall potential to move and (b) the domain wall energy change due to intersecting the pinning features to enable de-pinning. E d Δ is influenced by the number density of domains, which is in turn affected by a number of microstructural parameters such as grain size, dislocation density, number density or interparticle spacing of precipitates; DW energy change is influenced by the DW thickness and the size of the pinning feature. It follows that one can characterise the microstructural feature distribution by correlating it with f pin distribution.

Unbiased minor loop properties
The broad μ Δ profile of the as-normalised P9 sample (P9N) indicates a broad distribution of f pin (with a lower and wide peak), which in turn is associated with an expectedly broad spatial distribution of pinning features including intra-lath dislocation tangles and martensitic lath boundaries (made of dislocation networks). The peak occurring at a higher H value is due to a high number density of dislocations increasing E d Δ and hence f pin . The peak for the as-tempered P9 (P9T) narrowing and shifting to a lower H value is expected of the recovery of dislocations within the martensitic laths and coarsening of the laths. These microstructural changes narrow the spatial distribution of the pinning features, which become predominantly tempered martensitic laths, as compared to dislocation tangles and untempered martensitic laths for the P9N sample, and increase the mode of the distribution, during tempering. These changes in the microstructural feature distribution alter the corresponding f pin distribution and hence the μ Δ profile. Further increase in max μ Δ for the ex-service sample indicates a narrower f pin distribution due to the coarsening of the martensitic laths into ferrite grains with coarsened precipitates present within the ferrite grains increasing the spacing between the pinning features (i.e. the inter-particle spacing for the intra-grain precipitates compared to martensitic lath width for the as tempered sample). Further shifting to the left after service exposure can be attributed to a significantly reduced area fraction of the precipitates (Table 2) and increased interparticle spacing (see Fig. 4) compared to the lath width (Table 2), which decreases E d Δ and the number density of domains, shifting the f pin distribution to a lower H value. The as-normalised and as-tempered T22 samples follow the same trend as the P9 counterparts. The lower max μ Δ of the ex-service T22 indicates a broader distribution of the inter-particle spacing for the precipitates within the ferrite grains in the T22ES samples compared to that of the bainitic laths in the T22T sample. This can be attributed to the coarsening of the very fine precipitates within the bainitic laths, which were not effective pinning features to DWs [6], into larger and less magnetic precipitates that can pin domain walls altering the f pin distribution. The similar peak position is probably due to a similar area fraction of precipitates (Table 2) and comparable spacing between the pinning features i.e. mode value of interparticle spacing distribution (Fig. 9) and the lath width (Table 2).
For H H a m c > many pinning features are passed through by the DWs. The 180°DWs may also be annihilated as a result of merging of the antiparallel domains and domains will start to rotate away from the easy direction and towards the applied field direction. The pinning forces, from the high-angle boundaries such as many ferrite grain boundaries or martensitic packet boundaries, are expected to be overcome and the incremental permeability decreases with the increase of H m a . Whilst the microstructural the nearest neighbour spacing distribution of the precipitates within the ferrite grains for the ex-service P9 or T22 samples as these precipitates are predominant pinning features to DWs before domains start rotating away from the easy direction towards the applied field direction. The wider the spacing, the smaller f pin is expected to be as illustrated in [32]. Fig. 18 illustrates a qualitative mapping of f pin to the nearest neighbour spacing distribution. For a given bias field at f the precipitates with a nearest neighbour spacing d d nn < are expected to be effective pinning features and the number of these precipitates can be characterised by the CDF (d). The MFP and hence the major init , μ Δ for small amplitude will decrease with f shifting to the left in Fig. 18. It follows that the H major init m , 0 μ ( ) Δ profile is expected to be of qualitatively similar shape to the CDF d nn ( ) mirrored with respect to d 0 nn = , as can be observed by comparing Fig. 17 with Fig. 4 or Fig. 9 for the ex-service P9 and T22 samples respectively. In the case of excursion from major loops, f pin has to take into account the effect of B r of the sample on the domain structure. The shifting of the peak position for the major μ Δ profiles for excursion from the lower part of a major loop compared to the corresponding init μ Δ can be ascribed to a minus B r at H¼ 0 counteracting the applied field by H c . The consistency in peak values between minor loops excursions from an initial magnetisation curve and a major loop as well as μ r can be attributed to the same underlying microstructural feature distribution that affecting the domain processes.
Similarly, the microstructural features involved in irreversible domain processes during a minor loop can be characterised by the cross-hatched area in Fig. 18 or , which will not be discussed in detail in this paper as only a very small amplitude was used and hence the measured H m c , W m h and B m r values are more or less comparable to the scatter for H and B measurements.

Conclusions
Various magnetic properties measured from major loops and minor loops have been found to be sensitive to different microstructural features and have shown different behaviours in response to microstructural changes for power generation steel P9 and T22 in the different conditions (normalised, tempered and exservice). The different sensitivities and behaviours have been ascribed to various microstructural feature distribution affecting domain processes differently. It has been demonstrated that one can separate out the microstructural features whose pinning strength f H pin m 0 ≤ | | by applying a bias field H m 0 , at the same time, examining the features with f H pin m 0 > | | by looking at the incremental permeability for a small amplitude H m 0 , and/or further selecting the features that are actively impeding domain walls and eventually passed through during a minor loop by varying the minor loop amplitude H m a . It was found that the initial permeability values evaluated by different techniques were in good agreement with each other including the initial permeability approximated by extrapolating the incremental permeability for unbiased minor loop measurements to zero amplitude (μ i ), the maximum incremental permeability by biased minor loop excursions from a major loop ( major max μ Δ ) or an initial magnetisation curve ( init max μ Δ ) and the initial permeability approximated by multi-frequency electromagnetic sensors that apply a very small magnetic field (μ r ). It was also found that the maximum incremental permeability for both unbiased minor loops with a range of amplitude and biased minor loop excursions from a major loop occur approximately at coercivity H c for all the studied samples. This consistency in magnetic behaviours between different techniques has been attributed to similar underlying domain processes due to a same effective field (B ¼0), regardless of the externally applied field, experienced by the domain walls and hence similar microstructural features that are affecting the domain processes.