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| In [[electromagnetism]], the '''magnetic susceptibility''' <math>\chi</math> ([[latin]]: ''susceptibilis'' “receptive”) 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 [[magnetic field|magnetic flux density]].<ref>{{cite encyclopedia |year=1997 |title =magnetizability, ξ |encyclopedia=IUPAC Compendium of Chemical Terminology—The Gold Book |publisher=[[International Union of Pure and Applied Chemistry]] |edition=2nd |url=http://goldbook.iupac.org/search.py?search_text=magnetizability}}</ref> A closely related parameter is the [[Permeability (electromagnetism)|permeability]], which expresses the total magnetization of material and volume.
| | Environmental Study Scientist Chong from St. Jacobs, has lots of pursuits which include ghost hunting, herpes cure and bringing food to the. During the previous year has completed a journey to Prehistoric Caves of Yagul and Mitla in the Central Valley of Oaxaca.<br><br>My blog post [http://gentlecharlatan49.yolasite.com/contact herpes virus] |
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| ==Definition of volume susceptibility==
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| ::''See also '' [[Permeability (electromagnetism)#Relative permeability|Relative permeability]].
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| The ''volume magnetic susceptibility'', represented by the symbol <math>\chi_v</math> (often simply <math>\chi</math>, sometimes <math>\chi_m</math> – magnetic, to distinguish from the [[electric susceptibility]]), is defined in the [[International System of Units]] — in other systems there may be additional constants — by the following relationship, it is same as residual magnet.
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| :<math>
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| \mathbf{M} = \chi_v \mathbf{H}
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| </math>
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| where
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| :'''M''' is the [[magnetization]] of the material (the [[magnetic dipole moment]] per unit volume), measured in [[ampere]]s per meter, and
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| :'''H''' is the [[Effective magnetic field|magnetic field strength]], also measured in amperes per meter.
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| The [[magnetic field|magnetic induction]] '''B''' is related to '''H''' by the relationship
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| :<math>
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| \mathbf{B} \ = \ \mu_0(\mathbf{H} + \mathbf{M}) \ = \ \mu_0(1+\chi_v) \mathbf{H} \ = \ \mu \mathbf{H}
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| </math>
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| where μ<sub>0</sub> is the [[magnetic constant]] (see table of [[physical constant]]s), and
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| <math> (1+\chi_v) </math> is the [[Permeability (electromagnetism)#Relative permeability|relative permeability]] of the material.
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| Thus the ''volume magnetic susceptibility'' <math>\chi_v</math> and the [[magnetic permeability]] <math>\mu</math> are related by the following formula:
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| :<math>\mu = \mu_0(1+\chi_v)\,</math> .
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| Sometimes<ref>{{cite web|author=Richard A. Clarke |url=http://info.ee.surrey.ac.uk/Workshop/advice/coils/mu/#itns |title=Magnetic properties of materials |publisher=Info.ee.surrey.ac.uk |date= |accessdate=2011-11-08}}</ref> an auxiliary quantity, called ''intensity of magnetization'' (also referred to as magnetic polarisation ''J'') and measured in [[Tesla (unit)|teslas]], is defined as
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| :<math>\mathbf{I} = \mu_0 \mathbf{M} \,</math> .
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| 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'''.
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| ==Conversion between SI and CGS units==
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| Note that these definitions are according to [[International System of Units|SI]] conventions. However, many tables of magnetic susceptibility give [[Centimetre gram second system of units|CGS]] values (more specifically [[Centimetre gram second system of units#Electromagnetic units (EMU)|emu-cgs]], short for electromagnetic units, or [[Gaussian units|Gaussian-cgs]]; both are the same in this context) that rely on a different definition of the permeability of free space:<ref name=bennett>{{
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| cite journal
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| | author = Bennett, L. H.; Page, C. H.; and Swartzendruber, L. J.
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| | title = Comments on units in magnetism
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| | year = 1978
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| | journal = Journal of Research of the National Bureau of Standar
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| | volume = 83
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| | issue = 1
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| | publisher = [[NIST]], USA
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| | pages = 9–12
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| | doi = }}</ref>
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| :<math>
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| \mathbf{B}^{\text{cgs}} \ = \ \mathbf{H}^{\text{cgs}} + 4\pi\mathbf{M}^{\text{cgs}} \ = \ (1+4\pi\chi_{v}^{\text{cgs}}) \mathbf{H}^{\text{cgs}}
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| </math>
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| The [[dimensionless]] CGS value of volume susceptibility is multiplied by 4π to give the dimensionless [[International System of Units|SI]] volume susceptibility value:<ref name=bennett/>
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| :<math>\chi_v^{\text{SI}}=4\pi\chi_v^{\text{cgs}}</math>
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| For example, the [[Centimetre gram second system of units|CGS]] volume magnetic susceptibility of water at 20°C is −7.19×10<sup>−7</sup> which is −9.04×10<sup>−6</sup> using the [[International System of Units|SI]] convention.
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| ==Mass susceptibility and molar susceptibility==
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| There are two other measures of susceptibility, the ''mass magnetic susceptibility'' (χ<sub>mass</sub> or χ<sub>g</sub>, sometimes χ<sub>m</sub>), measured in m<sup>3</sup>·kg<sup>−1</sup> in SI or in cm<sup>3</sup>·g<sup>−1</sup> in CGS and the ''molar magnetic susceptibility'' (χ<sub>mol</sub>) measured in m<sup>3</sup>·mol<sup>−1</sup> (SI) or cm<sup>3</sup>·mol<sup>−1</sup> (CGS) that are defined below, where ρ is the [[density]] in kg·m<sup>−3</sup> (SI) or g·cm<sup>−3</sup> (CGS) and M is [[molar mass]] in kg·mol<sup>−1</sup> (SI) or g·mol<sup>−1</sup> (CGS).
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| :<math>\chi_\text{mass} = \chi_v/\rho</math>
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| :<math>\chi_\text{mol} = M\chi_\text{mass} = M\chi_v/\rho</math>
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| ==Sign of susceptibility: diamagnetics and other types of magnetism==
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| If χ is positive, the 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]]. As a result, the magnetic field in the material is weakened by the induced magnetization. Generally, non-magnetic materials are said to be para- or diamagnetic because they do not possess permanent magnetization without external magnetic field. [[Ferromagnetic]], [[ferrimagnetism|ferrimagnetic]], or [[antiferromagnetic]] materials, which have positive susceptibility, possess permanent magnetization even without external magnetic field.
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| ==Experimental methods to determine susceptibility==
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| Volume magnetic susceptibility is measured by the force change felt upon the application of a magnetic field gradient.<ref>{{cite book
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| | author=L. N. Mulay
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| | title=Techniques of Chemistry
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| | editor=A. Weissberger and B. W. Rossiter
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| | publisher=Wiley-Interscience: New York
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| | volume=4
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| | page = 431
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| | year=1972}}</ref> 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]].<ref>{{cite web|url=http://www.sherwood-scientific.com/msb/msbindex.html |title=Magnetic Susceptibility Balances |publisher=Sherwood-scientific.com |date= |accessdate=2011-11-08}}</ref> For liquid samples, the susceptibility can be measured from the dependence of the [[Nuclear magnetic resonance|NMR]] frequency of the sample on its shape or orientation.<ref>{{ SAM_ @dreamlyf10
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| cite journal
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| | author=J. R. Zimmerman, and M. R. Foster
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| | title=Standardization of NMR high resolution spectra
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| | journal=J. Phys. Chem.
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| | volume=61
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| | year=1957
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| | pages=282–289
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| | doi=10.1021/j150549a006
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| | issue=3}}</ref><ref>{{
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| cite journal
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| | author=Robert Engel, Donald Halpern, and Susan Bienenfeld
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| | title=Determination of magnetic moments in solution by nuclear magnetic resonance spectrometry
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| | journal=Anal. Chem.
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| | volume=45
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| | year=1973
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| | pages=367–369
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| | doi=10.1021/ac60324a054
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| | issue=2}}</ref><ref>{{
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| cite journal
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| | author=P. W. Kuchel, B. E. Chapman, W. A. Bubb, P. E. Hansen, C. J. Durrant, and M. P. Hertzberg
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| | title=Magnetic susceptibility: solutions, emulsions, and cells
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| | journal=Concepts Magn. Reson.
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| | volume=A 18
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| | year=2003
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| | pages=56–71
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| | doi=10.1002/cmr.a.10066}}</ref><ref>{{
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| cite journal
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| | author=K. Frei and H. J. Bernstein
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| | title=Method for determining magnetic susceptibilities by NMR
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| | journal=J. Chem. Phys.
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| | volume=37
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| | year=1962
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| | pages=1891–1892
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| | doi=10.1063/1.1733393|bibcode = 1962JChPh..37.1891F
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| | issue=8 }}</ref><ref>{{
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| cite journal
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| | author=R. E. Hoffman
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| | title=Variations on the chemical shift of TMS
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| | journal=J. Magn. Reson.
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| | volume=163
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| | year=2003
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| | pages=325–331
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| | doi=10.1016/S1090-7807(03)00142-3
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| | pmid=12914848
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| | issue=2|bibcode = 2003JMagR.163..325H }}</ref>
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| ==Tensor susceptibility==
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| The magnetic susceptibility of most [[crystal]]s is not a scalar. 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]]
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| :<math> M_i=\chi_{ij}H_j </math>
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| where ''i'' and ''j'' refer to the directions (e.g., ''x'' and ''y'' in [[Cartesian coordinates]]) of the applied field and magnetization, respectively. The [[tensor]] is thus rank 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.
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| ==Differential susceptibility==
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| In [[ferromagnetic]] crystals, the relationship between '''M''' and '''H''' is not linear. To accommodate this, a more general definition of ''differential susceptibility'' is used
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| :<math>\chi^{d}_{ij} = \frac{\part M_i}{\part H_j}</math>
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| where <math>\chi^{d}_{ij}</math> is a [[tensor]] derived from [[partial derivative]]s of components of '''M''' with respect to components of '''H'''.
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| 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 (magnetism)|domain wall]] configuration of the material.
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| ==Susceptibility in the frequency domain==
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| When the magnetic susceptibility is measured in response to an [[Alternating current|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|complex]] quantities, and various phenomena (such as resonances) can be seen in AC susceptibility that cannot 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 (magnetism)|domain wall]] configuration of the material and [[eddy currents]].
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| In terms of [[ferromagnetic resonance]], the effect of an ac-field applied along the direction of the magnetization is called ''parallel pumping''.
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| For a tutorial with more information on AC susceptibility measurements, see [http://www.qdusa.com/resources/pdf/1078-201.pdf here (external link)].
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| ==Examples==
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| {| class="wikitable" style="margin:auto; text-align:center;"
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| |+ Magnetic susceptibility of some materials
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| ! Material !![[Temperature]]!![[Pressure]] !!colspan="2" | <math>\chi_{\text{mol}}</math> (molar susc.)!! colspan="2" | <math>\chi_{\text{mass}}</math> (mass susc.) !! colspan="2" | <math>\chi_{v}</math> (volume susc.) !! ''M'' ([[molar mass]]) !!<math>\rho</math> ([[density]])
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| |-
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| | style="text-align:right;"| [[Units of measurement|Units]] || style="text-align:center;"|([[Celsius|°C]])|| style="text-align:center;"|([[Atmosphere (unit)|atm]])|| style="text-align:center;"|SI<br/>([[cubic meter|m<sup>3</sup>]]·[[Mole (unit)|mol]]<sup>−1</sup>)|| style="text-align:center;"|CGS<br/>([[cubic centimeter|cm<sup>3</sup>]]·[[Mole (unit)|mol]]<sup>−1</sup>)|| style="text-align:center;"|SI<br/>([[cubic meter|m<sup>3</sup>]]·[[kg]]<sup>−1</sup>)|| style="text-align:center;"|CGS<br/>([[cubic centimeter|cm<sup>3</sup>]]·[[gram|g]]<sup>−1</sup>)|| style="text-align:center;"|SI<br/>|| style="text-align:center;"|CGS<br/> (''[[electromagnetic unit|emu]]'')|| style="text-align:center;"|(10<sup>−3</sup> [[kg]]/[[Mole (unit)|mol]])<br/>or ([[gram|g]]/[[Mole (unit)|mol]])|| style="text-align:center;"|(10<sup>3</sup> [[kg]]/[[cubic meter|m<sup>3</sup>]])<br/>or ([[gram|g]]/[[cubic centimeter|cm<sup>3</sup>]])
| |
| |-
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| |align="left" | [[Water (data page)|water]] <ref>{{
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| cite journal
| |
| | author=G. P. Arrighini, M. Maestro, and R. Moccia
| |
| | title=Magnetic Properties of Polyatomic Molecules: Magnetic Susceptibility of H<sub>2</sub>O, NH<sub>3</sub>, CH<sub>4</sub>, H<sub>2</sub>O<sub>2</sub>
| |
| | journal=J. Chem. Phys.
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| | volume=49
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| | year=1968
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| | pages=882–889
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| | doi=10.1063/1.1670155|bibcode = 1968JChPh..49..882A
| |
| | issue=2 }}</ref> ||20||1 ||−1.631×10<sup>−10</sup>||−1.298×10<sup>−5</sup> ||−9.051×10<sup>−9</sup> ||−7.203×10<sup>−7</sup> ||−9.035×10<sup>−6</sup> ||−7.190×10<sup>−7</sup> ||18.015 ||0.9982
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| |-
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| |align="left" | [[bismuth]] <ref>{{
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| cite journal
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| | author = S. Otake, M. Momiuchi and N. Matsuno
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| | title = Temperature Dependence of the Magnetic Susceptibility of Bismuth
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| | year = 1980
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| | journal = J. Phys. Soc. Jap.
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| | volume = 49
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| | issue = 5
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| | pages = 1824–1828
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| | doi = 10.1143/JPSJ.49.1824|bibcode = 1980JPSJ...49.1824O }}
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| The tensor needs to be averaged over all orientations: <math>\chi=(1/3)\chi_{||}+(2/3)\chi_{\perp}</math> .</ref>|| 20 ||1||−3.55×10<sup>−9</sup> ||−2.82×10<sup>−4</sup>||−1.70×10<sup>−8</sup> ||−1.35×10<sup>−6</sup> ||−1.66×10<sup>−4</sup> ||−1.32×10<sup>−5</sup>|| 208.98
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| ||9.78
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| |-
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| |align="left" | [[Carbon|Diamond]] <ref>{{
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| cite journal
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| | author = J. Heremans, C. H. Olk and D. T. Morelli
| |
| | title = Magnetic Susceptibility of Carbon Structures
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| | year = 1994
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| | journal = Phys. Rev. B
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| | volume = 49
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| | issue = 21
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| | pages = 15122–15125
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| | doi = 10.1103/PhysRevB.49.15122|bibcode = 1994PhRvB..4915122H }}</ref> || [[Room temperature|R.T.]]||1 ||−7.4×10<sup>−11</sup> ||−5.9×10<sup>−6</sup>|| −6.2×10<sup>−9</sup>||−4.9×10<sup>−7</sup> || −2.2×10<sup>−5</sup> ||−1.7×10<sup>−6</sup> || 12.01|| 3.513
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| |-
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| |align="left" | [[Carbon|Graphite]] <ref name=graphite1>{{
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| cite journal
| |
| | author = N. Ganguli and K.S. Krishnan
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| | title = The Magnetic and Other Properties of the Free Electrons in Graphite
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| | year = 1941
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| | journal = Proceedings of the Royal Society
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| | volume = 177
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| | issue = 969
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| | pages = 168–182
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| | doi = 10.1098/rspa.1941.0002|bibcode = 1941RSPSA.177..168G
| |
| | unused_data = stable URL: http://www.jstor.org/stable/97544 }}</ref> <math>\chi_{\perp}</math>(to c-axis) || [[Room temperature|R.T.]]||1 ||−7.5×10<sup>−11</sup> ||−6.0×10<sup>−6</sup>|| −6.3×10<sup>−9</sup>||−5.0×10<sup>−7</sup> || −1.4×10<sup>−5</sup> ||−1.1×10<sup>−6</sup> || 12.01|| 2.267
| |
| |-
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| |align="left" | [[Carbon|Graphite]] <ref name=graphite1/> <math>\chi_{||}</math> || [[Room temperature|R.T.]]||1 ||−3.2×10<sup>−9</sup> ||−2.6×10<sup>−4</sup>|| −2.7×10<sup>−7</sup> ||−2.2×10<sup>−5</sup> || −6.1×10<sup>−4</sup> ||−4.9×10<sup>−5</sup> || 12.01|| 2.267
| |
| |-
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| |align="left" | [[Carbon|Graphite]] <ref name=graphite1/> <math>\chi_{||}</math> || -173||1 ||−4.4×10<sup>−9</sup> ||−3.5×10<sup>−4</sup>|| −3.6×10<sup>−7</sup>||−2.9×10<sup>−5</sup> || −8.3×10<sup>−4</sup> ||−6.6×10<sup>−5</sup> || 12.01|| 2.267
| |
| |-
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| |align="left" | [[Helium|He]] <ref name=gases1>{{
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| cite journal
| |
| | author = R. E. Glick
| |
| | title = On the Diamagnetic Susceptibility of Gases
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| | year = 1961
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| | journal = J. Phys. Chem.
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| | volume = 65
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| | issue = 9
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| | pages = 1552–1555
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| | doi = 10.1021/j100905a020}}</ref> ||20 ||1
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| ||−2.38×10<sup>−11</sup>||−1.89×10<sup>−6</sup>||−5.93×10<sup>−9</sup> ||−4.72×10<sup>−7</sup> ||−9.85×10<sup>−10</sup> || −7.84×10<sup>−11</sup> ||4.0026 || 0.000166
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| |-
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| |align="left" | [[Xenon|Xe]] <ref name=gases1/> ||20 ||1 ||−5.71×10<sup>−10</sup>||−4.54×10<sup>−5</sup>|| −4.35×10<sup>−9</sup>||−3.46×10<sup>−7</sup> ||−2.37×10<sup>−8</sup> ||−1.89×10<sup>−9</sup> || 131.29||0.00546
| |
| |-
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| |align="left" | [[Oxygen|O<sub>2</sub>]] <ref name=gases1/> || 20|| 0.209 ||4.3×10<sup>−8</sup>||3.42×10<sup>−3</sup>||1.34×10<sup>−6</sup> ||1.07×10<sup>−4</sup> || 3.73×10<sup>−7</sup>||2.97×10<sup>−8</sup> || 31.99||0.000278
| |
| |-
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| |align="left" | [[Nitrogen|N<sub>2</sub>]] <ref name=gases1/> || 20|| 0.781 ||−1.56×10<sup>−10</sup>||−1.24×10<sup>−5</sup>||−5.56×10<sup>−9</sup> ||−4.43×10<sup>−7</sup> || −5.06×10<sup>−9</sup>||−4.03×10<sup>−10</sup> || 28.01 ||0.000910
| |
| |-
| |
| |align="left" | [[Aluminium|Al]] || ||1 || 2.2×10<sup>−10</sup> ||1.7×10<sup>−5</sup>||7.9×10<sup>−9</sup> ||6.3×10<sup>−7</sup> ||2.2×10<sup>−5</sup> ||1.75×10<sup>−6</sup> ||26.98 ||2.70
| |
| |-
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| |align="left" | [[Silver|Ag]] <ref>{{
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| cite journal
| |
| | author = R. Dupree and C. J. Ford
| |
| | title = Magnetic susceptibility of the noble metals around their melting points
| |
| | year = 1973
| |
| | journal = Phys. Rev. B
| |
| | volume = 8
| |
| | issue = 4
| |
| | pages = 1780–1782
| |
| | doi = 10.1103/PhysRevB.8.1780|bibcode = 1973PhRvB...8.1780D }}</ref> || 961 ||1|| || || || ||−2.31×10<sup>−5</sup>||−1.84×10<sup>−6</sup> || 107.87||
| |
| |}
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| | |
| ==Sources of confusion in published data==
| |
| There are tables of magnetic susceptibility values published on-line that seem to have been uploaded from a substandard source,<ref>{{cite web|url=http://www.reade.com/Particle_Briefings/magnetic_susceptibilities.html |title=Magnetic Properties Susceptibilities Chart from |publisher=READE |date=2006-01-11 |accessdate=2011-11-08}}</ref>
| |
| which itself has probably borrowed heavily from the [[CRC Press|CRC Handbook of Chemistry and Physics]]. Some of the data (e.g. for Al, Bi, and diamond) are apparently in cgs '''Molar Susceptibility''' units, whereas that for water is in '''Mass Susceptibility''' units (see discussion above). The susceptibility table in the CRC Handbook is known to suffer from similar errors, and even to contain sign errors. Effort should be made to trace the data in such tables to the original sources, and to double-check the proper usage of units.
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| ==See also==
| |
| * [[Curie constant]]
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| * [[Electric susceptibility]]
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| * [[Iron]]
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| * [[Magnetic constant]]
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| * [[Magnetic flux density]]
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| * [[Magnetism]]
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| *[[Magnetochemistry]]
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| * [[Magnetometer]]
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| * [[Maxwell's equations]]
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| * [[Paleomagnetism]]
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| * [[Permeability (electromagnetism)]]
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| * [[Quantitative susceptibility mapping]]
| |
| * [[Susceptibility weighted imaging]]
| |
| | |
| ==References and notes==
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| {{Reflist}}
| |
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| {{DEFAULTSORT:Magnetic Susceptibility}}
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| [[Category:Physical quantities]]
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| [[Category:Magnetism]]
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| [[Category:Electric and magnetic fields in matter]]
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| [[Category:Scientific techniques]]
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