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| The '''Kadowaki–Woods ratio''' is the ratio of ''A'', the quadratic term of the [[resistivity]] and ''γ''<sup>2</sup>, the linear term of the [[specific heat]]. This ratio is found to be a constant for [[transition metal]]s, and for heavy-[[fermion]] compounds, although at different values. | | The person who wrote the article is called Jayson Hirano and he completely digs that title. Distributing manufacturing has been his profession for some time. Mississippi is where his home is. The favorite pastime for him and his kids is style and he'll be starting some thing else along with it.<br><br>Feel free to visit my blog [http://ustanford.com/index.php?do=/profile-38218/info/ online reader] |
| :<math>R_\mathrm{KW} = \frac{A}{\gamma^2}</math>
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| In 1968 M. J. Rice pointed out
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| <ref>
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| {{cite journal
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| |author=M. J. Rice
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| |year=1968
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| |title=Electron-electron scattering in transition metals
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| |journal=[[Phys. Rev. Lett.]]
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| |volume=20 |pages=1439
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| |doi=10.1103/PhysRevLett.20.1439
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| |bibcode = 1968PhRvL..20.1439R }}
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| </ref>
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| that the coefficient ''A'' should vary predominantly as the square of the linear electronic specific heat coefficient γ; in particular he showed that the ratio ''A/γ''<sup>2</sup> is material independent for the pure 3d, 4d and 5d transition metals. Heavy-fermion compounds are characterized by very large values of A and γ. Kadowaki and Woods
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| <ref>
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| {{cite journal
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| |author=K. Kadowaki, S.B. Woods
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| |year=1986
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| |title=Universal relationship of the resistivity and specific heat in heavy-fermion compounds
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| |journal=[[Solid State Communications]]
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| |volume=58 |issue=8| pages=507–509
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| |doi=10.1016/0038-1098(86)90785-4
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| |bibcode = 1986SSCom..58..507K }}
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| </ref> showed that ''A/γ''<sup>2</sup> is material-independent within the heavy-fermion compounds, and that it is about 25 times larger than in aforementioned transition metals.
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| According to the theory of electron-electron scattering <ref>{{cite journal
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| |author=W. G. Baber
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| |year=1937
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| |title=The contribution to the electrical resistance of metals from collisions between electrons
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| |journal=[[Proc. Roy. Soc. A]]
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| |volume= 158 |pages=383
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| |doi=10.1098/rspa.1937.0027
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| |bibcode = 1937RSPSA.158..383B }}
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| </ref>
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| <ref>
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| {{cite book
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| |author=P. Nozières and D. Pines
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| |title=The Theory of Quantum Liquids, Vol. 1
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| |publisher=Benjamin
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| |place=New York
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| |year=1966
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| }}
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| </ref>
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| <ref>
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| {{cite journal
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| |author= W. E. Lawrence and J. W. Wilkins
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| |year=1973
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| |title=Electron-electron scattering in the transport coefficients of simple metals
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| |journal=[[Phys. Rev. B]]
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| |volume= 7|pages=2317
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| |doi=10.1103/PhysRevB.7.2317
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| |bibcode = 1973PhRvB...7.2317L }}
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| </ref> | |
| the ratio ''A/γ''<sup>2</sup> contains indeed several non-universal factors, including the square of the strength of the effective electron-electron interaction. Since in general the interactions differ in nature from one group of materials to another, the same values of ''A/γ''<sup>2</sup> are only expected within a particular group.
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| In 2005 Hussey<ref>{{cite journal
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| |author=N. E. Hussey
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| |year=2005
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| |title=Non-generality of the Kadowaki-Woods ratio in correlated oxides
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| |journal=[[J. Phys. Soc. Jpn.]]
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| |volume=74 |pages=1107
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| |doi=10.1143/JPSJ.74.1107
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| |arxiv = cond-mat/0409252 |bibcode = 2005JPSJ...74.1107H }}
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| </ref> proposed a re-scaling of ''A/γ''<sup>2</sup> to account for unit cell volume, dimensionality, carrier density and multi-band effects. In 2009 Jacko, Fjaerestad, and Powell<ref>{{cite journal
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| |author=A.C. Jacko, J.O. Fjaerestad, B.J. Powell
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| |year=2009
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| |title=A unified explanation of the Kadowaki–Woods ratio in strongly correlated metals
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| |journal=[[Nature Physics]]
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| |volume=5 |pages=422–425
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| |doi=10.1038/nphys1249
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| |arxiv=0805.4275
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| |issue=6
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| |bibcode = 2009NatPh...5..422J }}
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| </ref> demonstrated ''f''<sub>dx</sub>''(n)A/γ''<sup>2</sup> to have the same value in transition metals, heavy fermions, organics and oxides with ''A'' varying over 10 orders of magnitude, where ''f''<sub>dx</sub>''(n)'' may be written in terms of the dimensionality of the system, the electron density and, in layered systems, the interlayer spacing or the interlayer hopping integral.
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| ==See also==
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| {{portal|Physics}}
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| * [[Wilson ratio]]
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Kadowaki-Woods ratio}}
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| [[Category:Condensed matter physics]]
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| [[Category:Fermions]]
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| {{physics-stub}}
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The person who wrote the article is called Jayson Hirano and he completely digs that title. Distributing manufacturing has been his profession for some time. Mississippi is where his home is. The favorite pastime for him and his kids is style and he'll be starting some thing else along with it.
Feel free to visit my blog online reader