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barkhausen_noise

Barkhausen noise

Stan Zurek, Barkhausen noise, Encyclopedia Magnetica
https://E-Magnetica.pl/barkhausen_noise

Barkhausen noise (BN) - the phenomenon of rapid changes of positions of domain walls during the process of magnetisation of a ferromagnetic material.1)2)3)

Barkhausen noise is caused by rapid changes of flux density B due to domain wall movements - this causes high-frequency noise-like changes in induced voltage V

These sudden jumps (also referred to as Barkhausen jumps) can be made audible by suppressing the large voltage induced in a search coil (with a high-pass filter) and amplifying the frequencies in the audible range (see the recording of audible noise with the animation).4)5)

Barkhausen noise was discovered by Heinrich Barkhausen in 1919.6)

A phenomenon similar to magnetic Barkhausen noise is also present in ferroelectric materials, which have ferroelectric domains and hence ferroelectric domain walls.7)8)

Recording of a real Barkhausen noise in grain-oriented electrical steel (with sound) (link to video file)
Barkhausen noise (BN) activity is greater at intervals during which the changes of flux density B are the most rapid
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Magnetisation process

Magnetisation process involves changes in the configuration of magnetic domains9)

Ferromagnetism is synonymous with spontaneous magnetisation of a material. Each part of the volume is magnetised to saturation and each such partial volume is known as a magnetic domain. The magnetic alignments of domains can point in different or opposing directions so that globally their contributions cancel partially or fully. Thus, the net volume magnetisation can be significantly smaller than saturation, and even zero for a demagnetised body (even though the individual domains remain saturated).10)

Magnetic domain structure (lancet combs switching during magnetisation) in high-permeability grain-oriented electrical steel. Bar domains are visible in the upper part. Copyright © Oles Hostanar

The magnetisation process, for example by applying external magnetic field, involves changes in the configuration of magnetic domains, which is accomplished by movement of the domain walls which separate domains. These movements can be impeded in several ways: crystal defects, grain boundaries, non-magnetic inclusions and precipitates, surface defects, etc.11) The phenomenon of “sticking” to local energy minima is called domain wall pinning.

Simplified animation of a domain wall crossing a non-magnetic void12)

The magnetisation process generates an effective pressure on the given domain wall to move. However, such domain wall can be pinned to one of the above-mentioned defect and therefore it will require additional pressure to overcome to pinning force. Once the pressure to move exceeds the pinning force the domain wall will be suddenly unpinned and it will move rapidly, until the forces are equalised, or for example when the wall encounters the next defect.

As a result, the process of magnetisation is not smooth, but comprises jittery jumps of domain walls. But a sudden movement of a domain wall is synonymous with a rapid change of local magnetisation M and hence also of the local flux density B. And according to the Faraday's law changes in B generate changes in electric field and thus to the voltage induced in a coil magnetically coupled to such material.

Single Barkhausen jumps

Typical Co-Fe amorphous microwires amorphous_co-fe_microwires_magnetica.jpg

There are magnetic materials which are magnetically very soft (very low coercivity) and because of their geometry can have just a single domain present (at least in some part of the volume).

Co-Fe amorphous core (red arrow) in glass coating (blue arrows and translucent tip), 0.1 mm diameter amorphous_co-fe_microwire_in_glass_magnetica.jpg

This is the case for example in microwires made from amorphous cobalt. Glass coating is added during the manufacturing process to help with the wire production, obtaining amorphous phase and applying internal stress. The magnetic domain structure is such that there is an inner core with the single-domain system, and the outer core with a cylindrical13) or multiple closure domains.14)

Closure domains can remain at the ends of the inner core. Once external magnetic field is applied, the main domain wall can rapidly change its position (even faster than 1000 m/s) travelling from one end of the wire to the other. Such a rapid transition constitutes a single Barkhausen jump.15)

When plotted as a B-H loop the rapid reversal of magnetisation makes the loop appear rectangular, because once the coercive field HC threshold is exceeded the corresponding B changes its polarity.16)

Structure of magnetic domains in a microwire17)
Single Barkhausen jump in a microwire creates a rectangular B-H loop18) charubin_et_al_single_barkhausen_jump_2019.jpg by T. Charubin, M. Nowicki, R. Szewczyk, CC-BY-4.0
Domain wall velocity in Co-based amorphous microwire19)

Measurement of BN

Simple search coil for detecting Barkhausen noise20) by F. Bohn, G. Durin, M.A. Correa, N.R. Machado, R.D. Della Pace, C. Chesman, R.L. Sommer, CC-BY-4.0

Barkhausen noise is generated by changes of magnetisation M and hence also by flux density B and it can be detected by a search coil (pick-up coil) whose operation is based on the Faraday's law of induction.

Any changes in B induce corresponding voltage V at the terminals of the search coil.

Voltage in a Barkhausen coil sensor
$$ V = N · A · \frac{dB}{dt}$$ (V)
$V$ - voltage induced in the coil (V), $N$ - number of turns of the coil (unitless), $A$ - active cross-sectional area of the coil (m2), $dB/dt$ - derivative of flux density $B$ (T) with respect to time $t$ (s)

However, typical changes of B (apart from the single-domain materials) comprise large-amplitude slower changes which induce low-frequency and high amplitude of the associated voltage. But the very fast Barkhausen events are of much smaller amplitude and thus create much smaller signal, which is superimposed on the slower large signal.

Therefore, before the BN can be analysed it is necessary either to filter out the slower, large amplitude signal, or to compensate it out. This can be achieved either by high-pass or band-pass filter in signal processing electronics, or by arranging the pick-up coils in such a way that the slow large signal is eliminated or not induced at all. Typical band-pass filtering can be from 300 Hz to 300 kHz.21)22)

For example, it is possible to use two search coil connected in series opposition. Barkhausen noise is quite random locally so noise detected at two different locations will just add to each other. But the slow large components of voltage will be similar in both coils and thus these will compensate out each other, leaving only the BN noise signature in the output voltage of such two coils.

Another approach is to use a pick-up coil on a ferromagnetic core positioned perpendicularly to the surface of the sample under test. The activity in the main sample will magnetically couple to the small magnetic core and thus it can be detected without the large voltage being induced in it. The additional magnetic core should be made of a material which has much lower Barkhausen noise activity than the main sample.23)

Typical ways of detecting Barkhausen noise:24) with two opposing B-coils and with a single B-coil perpendicular to the surface (with a small cylindrical magnetic core)

Analysis of BN activity

Barkhausen noise is stochastic (random) in nature and its analysis is not straightforward, because the induced noise depends on many factors, including the frequency, amplitude and waveshape of the magnetic excitation (e.g. magnetising current).

Many methods were devised by researchers internationally25), with some examples given below. However, there is no standardised method for performing such measurements so the numerical values from different publications cannot be compared in the absolute sense.

RMS of BN signal

RMS value of Barkhausen noise measured with two opposing B-coils (separated by 5 mm or 40 mm) at 50 Hz for a sample of grain-oriented electrical steel26)

RMS of the noise signal can be calculated after some high-pass or band-pass filtering. The RMS calculation follows the same method as measurement of RMS (root mean square) of any other signal, but it is applied to the Barkhausen noise waveform, typically digitised, with the calculations performed by a computer, for example over one cycle of magnetisation.

If the gain of the signal processing is calibrated, then the RMS of BN can be expressed in absolute units, which are typically quite small, e.g. less than 1 mV (as illustrated).

RMS of Barkhausen noise
(expressed
as integral)
$$ V_{BN,RMS} = \sqrt{\frac{1}{T} · \int_0^T {(V_{BN}(t))^2} dt } $$ (V)
(expressed
as sum
of samples)
$$ V_{BN,RMS} = \sqrt{\frac{1}{N_{BN}} · \sum_{i=0}^{N_{BN}-1} {(V_{BN,i})^2} } $$ (V)
where: $V_{BN}(t)$ - voltage signal after filtering (V), $V_{BN,i}$ - sampled (digitised) single value of voltage after filtering (V), $T$ - time interval (s), $N_{BN}$ - total number of sample (unitless), $i$ - index (unitless), $t$ - time (s)

Total sum of amplitudes (TSA)

Total sum of amplitudes (TSA) of Barkhausen noise for grain-oriented electrical steel, measured at 50 Hz excitation27)

The total sum of amplitudes (TSA) is a method in which all the instances of digitised signal are added up to produce a single value. Absolute values are used in order to include the negative numbers.

The TSA values are not comparable between different measurement systems, because they depend on the sampling frequency (more data points produces higher values, even if the amplitude of the noise is similar).

Total sum of amplitudes TSA
$$ V_{BN,TSA} = \sum_{i=0}^{N_{BN}-1} { | V_{BN,i} | } $$ (V)
where: $V_{BN,i}$ - sampled (digitised) single value of voltage after filtering (V), $N_{BN}$ - total number of sample (unitless), $i$ - index (unitless)

Total number of peaks (TNP)

Total number of peaks (TNP) of Barkhausen noise for non-oriented electrical steel, measured at 50 Hz excitation28)

Total number of peaks (TNP), as the name implies, is calculated simply as the number of detectable peaks in the filtered voltage. The result depends on the type of sensing, filtering, and criteria used for peak detection. Larger Barkhausen events which cause avalanches can cause fewer peaks.

The TNP value is unitless, because it reports the integer number of items.

Total number of peaks TNP
$$ TNP = \sum_{i=0}^{N_{BN}-1} { Peak_{V_{BN},i} } $$ (unitless)
where: $Peak_{V_{BN},i}$ - an instant of peak in the filtered voltage (unitless), $N_{BN}$ - total number of sample (unitless), $i$ - index (unitless)

Power spectrum

Power spectrum of Barkhausen noise at lower frequencies for grain-oriented electrical steel, measured at 50 Hz excitation29)

In the power spectrum method, the Barkhausen noise (after filtering) is processed by a Fourier transform, which detects the frequency spectrum of the noise.

By definition, the spectrum will be limited by the filtering used in the analogue and digital processing. In the illustration showing an example of such spectrum, the values reduce to zero below 50 Hz, which is cause by the high-pass filter characteristics of the signal processing.

With digital processing, the maximum frequency that can be detected is limited by the Shannon-Nyquist limit of the data acquisition device.

Also, the possibility of aliasing has to be considered, because the Barkhausen noise can extend up to MHz frequencies. Therefore, some analogue anti-aliasing has to be employed. As a consequence, the signal is processed with band-pass characteristics, because high-pass filter is required to suppress the high-amplitude low-frequency induced voltage, and low-pass filter is required for anti-aliasing. This is one the main reasons for digital methods to have limited upper frequency of BN processing.

Kurtosis

Kurtosis of Barkhausen noise for grain-oriented electrical steel, measured at 50 Hz excitation30)

Kurtosis is a method of statistical analysis of a given population of samples. It can quantify the “peakedness” or “flatness” of a statistical distribution. Using this method it is possible to compare the kurtosis value for example to that of ideal Gaussian distribution curve, thus studying the “randomness” of Barkhausen events.

The value of kurtosis has the units of V4 (volt to the power of 4).

Kurtosis K
$$ K = \frac{1}{N_{BN}} · \sum_{i=0}^{N_{BN}-1} { ( V_{BN,i} - V_{BN,mean} )^4 } $$ (V4)
where: $V_{BN,i}$ - subsequent voltage values (V), $V_{BN,mean}$ - mean value of voltage (V), $N_{BN}$ - total number of sample (unitless), $i$ - index (unitless)

Other types of analysis

Duration of Barkhausen events is correlated with their amplitude. One local Barkhausen jump can initiate others and the whole such sequence is sometimes referred to as Barkhausen avalanche.31)

The duration of avalanches can vary, and they can be analysed from the viewpoint of duration or frequency components. A whole range of analyses can be used even within the same study of the Barkhausen noise phenomenon.32)

Statistical analysis of Barkhausen avalanches in polycrystalline NiFe films of different thicknesses, from 20 to 1000 nm: a) distributions of avalanche sizes measured at 50 mHz, b) similar plot for the distributions of avalanche durations, c) average size as a function of the avalanche duration, d) power spectra.33) by F. Bohn, G. Durin, M.A. Correa, N.R. Machado, R.D. Della Pace, C. Chesman, R.L. Sommer, CC-BY-4.0

Magneto-acoustic emissions

If the moving domain walls separate domains which are not in the opposing directions (0-180°), but for example at 90° to each other, then the changes in domain wall position can cause changes of dimensions of the material due to magnetostriction.

Such low-amplitude local vibrations of the material are known as magnetoacoustic emissions (MAE). The frequency spectrum for studying such phenomenon is similar to the Barkhausen noise, and also the type of analysis is similar, for example by plotting the power spectrum. However, the detection is carried out with a very sensitive microphone or acceleration sensor, rather than an inductive coil.34)

Simplified block diagram of signal processing for magneto-acoustic emissions35) system_for_magnetoacustic_emissions.jpg

Non-destructive testing

Barkhausen noise activity is affected by crystallographic structure and defects in the given material. Materials exposed to mechanical stress can deform thus increasing the number of internal defects. Also other processes such as neutron irradiation in nuclear plants can degrade the crystallographic arrangements in the steel exposed to such radiation.

The image below shows an example of Barkhausen noise activity in two samples exposed to different mechanical stress, so that the elastic deformation was ε=2.5% and 15%, respectively. In the sample with larger deformation the BN activity is visibly reduced, and this can be correlated with the amount of damage sustained by the given steel.36)

Reduced Barkhausen noise activity in material exposed to larger deformation37) by M. Pitoňák, M. Neslušan, P. Minárik, J. Čapek, K. Zgútová, M. Jurkovič, T. Kalina, CC-BY-4.0
System for measuring residual mechanical stresses in rails by means of Barkhausen noise38) hwang_et_al_introscan_metal_analyzer_2021.jpg by Y.-I. Hwang, Y.-I. Kim, D.-C. Seo, M.-K. Seo, W.-S. Lee, S. Kwon, K.-B. Kim, CC-BY-4.0

Detection of mechanical properties through measurement of Barkhausen noise is beneficial, because it can be carried out on the surface of the material, without the need for cutting out a sample - hence it belongs to the class of non-destructive testing. The applicability of the method is limited, because the Barkhausen noise cannot be measured or correlated to the material damage in an absolute way.

Nonetheless, there are commercial devices capable of performing non-destructive measurements in an automated way. The excitation is typically applied by a small U-shaped magnetising yoke, and the sensing is carried out by pick-up coils, with processing and filtering similar to as described above. Parameters such as degradation in strength, increase in hardness or embrittlement can be automatically quantified to some extent.

XYZ scanner with transducer: a) block diagram, b) photo, c) 3D view of the transducer39) by M. Maciusowicz, G. Psuj, CC-BY-4.0

However, the correlation between Barkhausen noise and the mechanical properties of a given magnetic sample is not strict, and cannot be quantified independently of a material. It is therefore not possible to calibrate such system for a generic measurement.

Instead, a comparative measurement has to be carried out, when a known “good” sample is available for calibration. For example, degradation of surface of gears made of magnetic steel can be detected.40) In such applications the quality and thermal pre-processing is well known for the “good” steel and degradation with the Barkhausen noise system can give reliable results.

The BN method can be used for assessment of a large surface area for example by employing the scanning methods.41) A small-size detection head can be automatically moved around a large surface to perform the “scanning” action, and a computerised system can collate, analyse and display all the data accordingly.

See also

References


6) Heinrich Barkhausen (1919), Zwei mit Hilfe der neuen Verstärker entdeckte Erscheinungen, Phys. Z., 20, pp. 401–403
barkhausen_noise.txt · Last modified: 2021/11/14 21:16 by stan_zurek

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