Inelectromagnetism, themagnetic susceptibility (from Latin susceptibilis 'receptive'; denotedχ,chi) is a measure of how much a material will become magnetized in an appliedmagnetic field. It is the ratio ofmagnetizationM (magnetic moment per unitvolume) to the appliedmagnetic field intensityH. This allows a simple classification, into two categories, of most materials' responses to an applied magnetic field: an alignment with the magnetic field,χ > 0, calledparamagnetism, or an alignment against the field,χ < 0, calleddiamagnetism.
Magnetic susceptibility indicates whether a material is attracted into or repelled out of a magnetic field. Paramagnetic materials align with the applied field and are attracted to regions of greater magnetic field. Diamagnetic materials are anti-aligned and are pushed away, toward regions of lower magnetic fields. On top of the applied field, the magnetization of the material adds its own magnetic field, causing thefield lines to concentrate in paramagnetism, or be excluded in diamagnetism.[1] Quantitative measures of the magnetic susceptibility also provide insights into the structure of materials, providing insight intobonding andenergy levels. Furthermore, it is widely used ingeology forpaleomagnetic studies andstructural geology.[2]
The magnetizability of materials comes from the atomic-level magnetic properties of the particles of which they are made. Usually, this is dominated by the magnetic moments ofelectrons. Electrons are present in all materials, but without any external magnetic field, the magnetic moments of the electrons are usually either paired up or random so that the overall magnetism is zero (the exception to this usual case isferromagnetism). The fundamental reasons why the magnetic moments of the electrons line up or do not are very complex and cannot be explained byclassical physics. However, a useful simplification is to measure the magnetic susceptibility of a material and apply themacroscopic form of Maxwell's equations. This allows classical physics to make useful predictions while avoiding the underlyingquantum mechanical details.
Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. A related term ismagnetizability, the proportion betweenmagnetic moment and (vacuum)magnetic field.[3] A closely related parameter is thepermeability, which expresses the total magnetization of material and volume.
Thevolume magnetic susceptibility, represented by the symbolχv (often simplyχ, sometimesχm – magnetic, to distinguish from theelectric susceptibility), is defined in theInternational System of Quantities, which underlies theSI – in other systems there may be additional constants – by the following relationship:[4][5]were
χv is therefore adimensionless quantity.
UsingSI units, themagnetic fieldB is related toH by the relationshipwhereμ0 is thevacuum permeability (see table ofphysical constants), and(1 +χv) is therelative permeability of the material. Thus thevolume magnetic susceptibilityχv and themagnetic permeabilityμ are related by the following formula:
Sometimes[6] an auxiliary quantity calledintensity of magnetizationI (also referred to asmagnetic polarisationJ) and with unitteslas, is defined as
This allows an alternative description of all magnetization phenomena in terms of the quantitiesI andB, as opposed to the commonly usedM andH.
There are two other measures of susceptibility, themolar magnetic susceptibility (χm) with unit m3/mol, and themass magnetic susceptibility (χρ) with unit m3/kg that are defined below, whereρ is thedensity with unit kg/m3 andM ismolar mass with unit kg/mol:
The definitions above are according to theInternational System of Quantities (ISQ) upon which theSI is based. However, many tables of magnetic susceptibility give the values of the corresponding quantities of theCGS system (more specificallyCGS-EMU, short for electromagnetic units, orGaussian-CGS; both are the same in this context). The quantities characterizing the permeability of free space for each system have different defining equations:[7]
The respective CGS susceptibilities are multiplied by 4π to give the corresponding ISQ quantities (often referred to as SI quantities) with the same units:[7]
For example, the CGS volume magnetic susceptibility of water at 20 °C is7.19×10−7, which is9.04×10−6 using theSI convention, both quantities being dimensionless. Whereas for most electromagnetic quantities, which system of quantities it belongs to can be disambiguated by incompatibility of their units, this is not true for the susceptibility quantities.
In physics it is common to see CGS mass susceptibility with unit cm3/g or emu/g⋅Oe−1, and the CGS molar susceptibility with unit cm3/mol or emu/mol⋅Oe−1.
Ifχ is positive, a material can beparamagnetic. In this case, the magnetic field in the material is strengthened by the induced magnetization. Alternatively, ifχ is negative, the material isdiamagnetic. In this case, the magnetic field in the material is weakened by the induced magnetization. Generally, nonmagnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field.Ferromagnetic,ferrimagnetic, orantiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.
Volume magnetic susceptibility is measured by the force change felt upon a substance when a magnetic field gradient is applied.[8] Early measurements are made using theGouy balance where a sample is hung between the poles of an electromagnet. The change in weight when the electromagnet is turned on is proportional to the susceptibility. Today, high-end measurement systems use asuperconductive magnet. An alternative is to measure the force change on a strong compact magnet upon insertion of the sample. This system, widely used today, is called theEvans balance.[9] For liquid samples, the susceptibility can be measured from the dependence of theNMR frequency of the sample on its shape or orientation.[10][11][12][13][14]
Another method using NMR techniques measures the magnetic field distortion around a sample immersed in water inside an MR scanner. This method is highly accurate for diamagnetic materials with susceptibilities similar to water.[15]
The magnetic susceptibility of mostcrystals is not a scalar quantity. Magnetic responseM is dependent upon the orientation of the sample and can occur in directions other than that of the applied fieldH. In these cases, volume susceptibility is defined as atensor:wherei andj refer to the directions (e.g., of thex andyCartesian coordinates) of the applied field and magnetization, respectively. The tensor is thus degree 2 (second order), dimension (3,3) describing the component of magnetization in theith direction from the external field applied in thejth direction.
Inferromagnetic crystals, the relationship betweenM andH is not linear. To accommodate this, a more general definition ofdifferential susceptibility is used:whereχd
ij is a tensor derived frompartial derivatives of components ofM with respect to components ofH. When thecoercivity of the material parallel to an applied field is the smaller of the two, the differential susceptibility is a function of the applied field and self interactions, such as themagnetic anisotropy. When the material is notsaturated, the effect will be nonlinear and dependent upon thedomain wall configuration of the material.
Several experimental techniques allow for the measurement of the electronic properties of a material. An important effect in metals under strong magnetic fields, is the oscillation of the differential susceptibility as function of1/H. This behaviour is known as theDe Haas–Van Alphen effect and relates the period of the susceptibility with theFermi surface of the material.
An analoguenon-linear relation between magnetization and magnetic field happens forantiferromagnetic materials.[16]
When the magnetic susceptibility is measured in response to anAC magnetic field (i.e. a magnetic field that variessinusoidally), this is calledAC susceptibility. AC susceptibility (and the closely related "AC permeability") arecomplex number quantities, and various phenomena, such as resonance, can be seen in AC susceptibility that cannot occur in constant-field (DC) susceptibility. In particular, when an AC field is applied perpendicular to the detection direction (called the "transverse susceptibility" regardless of the frequency), the effect has a peak at theferromagnetic resonance frequency of the material with a given static applied field. Currently, this effect is called themicrowave permeability ornetwork ferromagnetic resonance in the literature. These results are sensitive to thedomain wall configuration of the material andeddy currents.
In terms of ferromagnetic resonance, the effect of an AC-field applied along the direction of the magnetization is calledparallel pumping.
| Material | Temp. | Pressure | Molar susceptibility | Mass susceptibility | Volume susceptibility | Molar mass | Density | |||
|---|---|---|---|---|---|---|---|---|---|---|
| (°C) | (atm) | χSI m (m3/mol) | χCGS m (cm3/mol) | χSI ρ (m3/kg) | χCGS ρ (cm3/g) | χSI v (1) | χCGS v (1) | M (g/mol) | ρ (g/cm3) | |
| Helium[17] | 20 | 1 | −2.38×10−11 | −1.89×10−6 | −5.93×10−9 | −4.72×10−7 | −9.85×10−10 | −7.84×10−11 | 4.0026 | 1.66×10−4 |
| Xenon[17] | 20 | 1 | −5.71×10−10 | −4.54×10−5 | −4.35×10−9 | −3.46×10−7 | −2.37×10−8 | −1.89×10−9 | 131.29 | 5.46×10−3 |
| Oxygen[17] | 20 | 0.209 | +4.3×10−8 | +3.42×10−3 | +1.34×10−6 | +1.07×10−4 | +3.73×10−7 | +2.97×10−8 | 31.99 | 2.78×10−4 |
| Nitrogen[17] | 20 | 0.781 | −1.56×10−10 | −1.24×10−5 | −5.56×10−9 | −4.43×10−7 | −5.06×10−9 | −4.03×10−10 | 28.01 | 9.10×10−4 |
| Air (NTP)[18] | 20 | 1 | +3.6×10−7 | +2.9×10−8 | 28.97 | 1.29×10−3 | ||||
| Water[19] | 20 | 1 | −1.631×10−10 | −1.298×10−5 | −9.051×10−9 | −7.203×10−7 | −9.035×10−6 | −7.190×10−7 | 18.015 | 0.9982 |
| Paraffin oil, 220–260 cSt[15] | 22 | 1 | −1.01×10−8 | −8.0×10−7 | −8.8×10−6 | −7.0×10−7 | 0.878 | |||
| PMMA[15] | 22 | 1 | −7.61×10−9 | −6.06×10−7 | −9.06×10−6 | −7.21×10−7 | 1.190 | |||
| PVC[15] | 22 | 1 | −7.80×10−9 | −6.21×10−7 | −1.071×10−5 | −8.52×10−7 | 1.372 | |||
| Fused silica glass[15] | 22 | 1 | −5.12×10−9 | −4.07×10−7 | −1.128×10−5 | −8.98×10−7 | 2.20 | |||
| Diamond[20] | r.t. | 1 | −7.4×10−11 | −5.9×10−6 | −6.2×10−9 | −4.9×10−7 | −2.2×10−5 | −1.7×10−6 | 12.01 | 3.513 |
| Graphite[21]χ⊥ | r.t. | 1 | −7.5×10−11 | −6.0×10−6 | −6.3×10−9 | −5.0×10−7 | −1.4×10−5 | −1.1×10−6 | 12.01 | 2.267 |
| Graphite[21]χ∥ | r.t. | 1 | −3.2×10−9 | −2.6×10−4 | −2.7×10−7 | −2.2×10−5 | −6.1×10−4 | −4.9×10−5 | 12.01 | 2.267 |
| Graphite[21]χ∥ | −173 | 1 | −4.4×10−9 | −3.5×10−4 | −3.6×10−7 | −2.9×10−5 | −8.3×10−4 | −6.6×10−5 | 12.01 | 2.267 |
| Aluminium[22] | 1 | +2.2×10−10 | +1.7×10−5 | +7.9×10−9 | +6.3×10−7 | +2.2×10−5 | +1.75×10−6 | 26.98 | 2.70 | |
| Silver[23] | 961 | 1 | −2.3×10−10 | −1.8×10−5 | −2.31×10−5 | −1.84×10−6 | 107.87 | |||
| Bismuth[24] | 20 | 1 | −3.55×10−9 | −2.82×10−4 | −1.70×10−8 | −1.35×10−6 | −1.66×10−4 | −1.32×10−5 | 208.98 | 9.78 |
| Copper[18] | 20 | 1 | −1.0785×10−9 | −9.63×10−6 | −7.66×10−7 | 63.546 | 8.92 | |||
| Nickel[18] | 20 | 1 | 600 | 48 | 58.69 | 8.9 | ||||
| Iron[18] | 20 | 1 | 200000 | 15900 | 55.847 | 7.874 | ||||
TheCRC Handbook of Chemistry and Physics has one of the few published magnetic susceptibility tables. The data are listed as CGS quantities. The molar susceptibility of several elements and compounds are listed in the CRC.[25] Another compilation of magnetic susceptibility data is published in Tables of Physical Values (Таблицы физических величин), 1976.[26]
InEarth science, magnetism is a useful parameter to describe and analyze rocks. Additionally, theanisotropy of magnetic susceptibility (AMS) within a sample determines parameters as directions ofpaleocurrents, maturity ofpaleosol, flow direction ofmagma injection,tectonic strain, etc.[2] It is a non-destructive tool which quantifies the average alignment and orientation of magnetic particles within a sample.[27]
In oil exploration, magnetic susceptibility can determine prospective hydrocarbon deposites. In 2014, a research conducted in western Ukraine revealed that prospective hydrocarbon deposit locations presented higher values of mass-specific magnetic susceptibility that was calculated in laboratory from rock samples obtained on field. Moreover, magnetic susceptibility can distinguish crude oil from different worldwide oil reservoir. Measuring magnetic susceptibility, it is possible to quantify clay content in clastic shoreface reservoir; minerals as illite and quartz can be measured through mass magnetic susceptibility, high amounts of these components are highly correlated with the presence of clay contents into the reservoir. Final results show that magnetic susceptibility measurements have good correspondences compared with traditional methods of measuring minerals in rocks as gamma ray and XDR.
Furthermore, magnetic susceptibility can characterize permeability of reservoir rock. Comparing low field and high field magnetic susceptibility measurements, in the high ones exists a higher correlation between the magnetic susceptibility and the permeability of the reservoir. In a shoreface North Sea oil reservoir was observed a slightly higher correlation with permeability in high field susceptibility (Potter and Ivakhnenko, 2008), and a much higher correlation with permeability and porosity in an Arab-D carbonate reservoir (Potter et al., 2011).
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