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tibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field a related term is magnetizability the proportion between magnetic moment and vacuum magnetic field 3 a closely related parameter is the permeability which expresses the total magnetization of material and volume the volume magnetic susceptibility represented by the symbol χ v often simply χ sometimes χ m magnetic to distinguish from the electric susceptibility is defined in the international system of quantities which underlies the si in other systems there may be additional constants by the following relationship 4 5 m linear χ v h displaystyle mathbf m stackrel text linear chi _ text v mathbf h m is the magnetization of the material the magnetic dipole moment per unit volume with unit amperes per meter and h is the strength of the auxiliary magnetic field also with the unit amperes per meter χ v is therefore a dimensionless quantity using si units the magnetic field b is related to h by the relationship b μ 0 h m linear μ 0 1 χ v h μ h displaystyle mathbf b mu _ 0 mathbf h mathbf m stackrel text linear mu _ 0 1 chi _ text v mathbf h mu mathbf h where μ 0 is the vacuum permeability see table of physical constants and 1 χ v is the relative permeability of the material thus the volume magnetic susceptibility χ v and the magnetic permeability μ are related by the following formula μ def μ 0 1 χ v displaystyle mu stackrel text def mu _ 0 1 chi _ text v sometimes 6 an auxiliary quantity called intensity of magnetization i also referred to as magnetic polarisation j and with unit teslas is defined as i d e f μ 0 m displaystyle mathbf i stackrel mathrm def mu _ 0 mathbf m this allows an alternative description of all magnetization phenomena in terms of the quantities i and b as opposed to the commonly used m and h molar susceptibility and mass susceptibility edit there are two other measures of susceptibility the molar magnetic susceptibility χ m with unit m 3 mol and the mass magnetic susceptibility χ ρ with unit m 3 kg that are defined below where ρ is the density with unit kg m 3 and m is molar mass with unit kg mol χ ρ χ v ρ χ m m χ ρ m ρ χ v displaystyle begin aligned chi _ rho frac chi _ text v rho chi _ text m m chi _ rho frac m rho chi _ text v end aligned in cgs units edit the definitions above are according to the international system of quantities isq upon which the si is based however many tables of magnetic susceptibility give the values of the corresponding quantities of the cgs system more specifically cgs emu short for electromagnetic units or gaussian cgs both are the same in this context the quantities characterizing the permeability of free space for each system have different defining equations 7 b cgs h cgs 4 π m cgs 1 4 π χ v cgs h cgs displaystyle mathbf b text cgs mathbf h text cgs 4 pi mathbf m text cgs left 1 4 pi chi _ text v text cgs right mathbf h text cgs the respective cgs susceptibilities are multiplied by 4 π to give the corresponding isq quantities often referred to as si quantities with the same units 7 χ m si 4 π χ m cgs displaystyle chi _ text m text si 4 pi chi _ text m text cgs χ ρ si 4 π χ ρ cgs displaystyle chi _ text ρ text si 4 pi chi _ text ρ text cgs χ v si 4 π χ v cgs displaystyle chi _ text v text si 4 pi chi _ text v text cgs for example the cgs volume magnetic susceptibility of water at 20 c is 7 19 10 7 which is 9 04 10 6 using the si 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 cm 3 g or emu g oe 1 and the cgs molar susceptibility with unit cm 3 mol or emu mol oe 1 paramagnetism and diamagnetism edit if χ is positive a material can be paramagnetic in this case the magnetic field in the material is strengthened by the induced magnetization alternatively if χ is negative the material is diamagnetic 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 or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero field susceptibility experimental measurement edit 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 the gouy 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 a superconductive 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 the evans balance 9 for liquid samples the susceptibility can be measured from the dependence of the nmr 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 tensor susceptibility edit the magnetic susceptibility of most crystals is not a scalar quantity magnetic response m is dependent upon the orientation of the sample and can occur in directions other than that of the applied field h in these cases volume susceptibility is defined as a tensor m i h j χ i j displaystyle m_ i h_ j chi _ ij where i and j refer to the directions e g of the x and y cartesian 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 the i th direction from the external field applied in the j th direction differential susceptibility edit in ferromagnetic crystals the relationship between m and h is not linear to accommodate this a more general definition of differential susceptibility is used χ i j d m i h j displaystyle chi _ ij d frac partial m_ i partial h_ j where χ d ij is a tensor derived from partial derivatives of components of m with respect to components of h when the coercivity 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 the magnetic anisotropy when the material is not saturated the effect will be nonlinear and dependent upon the domain 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 of 1 h this behaviour is known as the de haas van alphen effect and relates the period of the susceptibility with the fermi surface of the material an analogue non linear relation between magnetization and magnetic field happens for antiferromagnetic materials 16 in the frequency domain edit when the magnetic susceptibility is measured in response to an ac magnetic field i e a magnetic field that varies sinusoidally this is called ac susceptibility ac susceptibility and the closely related ac permeability are complex 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 the ferromagnetic resonance frequency of the material with a given static applied field currently this effect is called the microwave permeability or network ferromagnetic resonance in the literature these results are sensitive to the domain wall configuration of the material and eddy currents in terms of ferromagnetic resonance the effect of an ac field applied along the direction of the magnetization is called parallel pumping table of examples edit magnetic susceptibility of some materials material temp pressure molar susceptibility mass susceptibility volume susceptibility molar mass density c atm χ si m m 3 mol χ cgs m cm 3 mol χ si ρ m 3 kg χ cgs ρ cm 3 g χ si v 1 χ cgs v 1 m g mol ρ g cm 3 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 1 200 000 15 900 55 847 7 874 sources of published data edit the crc 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 application in the geosciences edit in earth science magnetism is a useful parameter to describe and analyze rocks additionally the anisotropy of magnetic susceptibility ams within a sample determines parameters as directions of paleocurrents maturity of paleosol flow direction of magma 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 application in oil exploration edit 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 see also edit curie s law electric susceptibility iron magnetic flux density magnetochemistry magnetometer maxwell s equations paleomagnetism permeability electromagnetism quantitative susceptibility mapping susceptibility weighted imaging references edit roger grinter the quantum in chemistry an experimentalist s view john wiley sons 2005 isbn 0470017627 page 364 1 2 tauxe lisa 2019 essentials of paleomagnetism fifth web edition uc press magnetizability ξ iupac compendium of chemical terminology the gold book 2nd ed international union of pure and applied chemistry 1997 archived from the original on 2016 03 04 retrieved 2011 10 13 o handley robert c 2000 modern magnetic materials hoboken nj wiley isbn 9780471155669 freeman richard king james lafyatis gregory 2019 essentials of electricity and magnetism electromagnetic radiation oxford university press doi 10 1093 oso 9780198726500 003 0001 isbn 978 0 19 872650 0 retrieved 2022 02 18 richard a clarke magnetic properties of materials university of surrey archived from the original on 2012 06 03 retrieved 2011 11 08 1 2 bennett l h page c h swartzendruber l j 1978 comments on units in magnetism journal of research of the national bureau of standards 83 1 nist usa 9 12 doi 10 6028 jres 083 002 pmc 6752159 pmid 34565970 l n mulay 1972 a weissberger b w rossiter eds techniques of chemistry vol 4 wiley interscience new york p 431 magnetic susceptibility balances sherwood scientific com archived from the original on 2011 07 16 retrieved 2011 11 08 j r zimmerman and m r foster 1957 standardization of nmr high resolution spectra j phys chem 61 3 282 289 bibcode 1957jphch 61 282z doi 10 1021 j150549a006 robert engel donald halpern susan bienenfeld 1973 determination of magnetic moments in solution by nuclear magnetic resonance spectrometry anal chem 45 2 367 369 bibcode 1973anach 45 367b doi 10 1021 ac60324a054 pmid 4762356 kuchel p w chapman b e bubb w a hansen p e durrant c j hertzberg m p 2003 magnetic susceptibility solutions emulsions and cells concepts in magnetic resonance 18a 1 56 71 arxiv q bio 0601030 doi 10 1002 cmr a 10066 s2cid 13013704 k frei h j bernstein 1962 method for determining magnetic susceptibilities by nmr j chem phys 37 8 1891 1892 bibcode 1962jchph 37 1891f doi 10 1063 1 1733393 r e hoffman 2003 variations on the chemical shift of tms j magn reson 163 2 325 331 bibcode 2003jmagr 163 325h doi 10 1016 s1090 7807 03 00142 3 pmid 12914848 1 2 3 4 5 wapler m c leupold j dragonu i von elverfeldt d zaitsev m wallrabe u 2014 magnetic properties of m...
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