en>Bender235: restructured according to MOS:APPENDIX

2014-12-07T17:26:11Z

restructured according to MOS:APPENDIX

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	~~[[File:Shottky Anomaly~~.~~png\|thumb\|Schottky anomalous heat capacity for a two-level system. T~~ is ~~the absolute temperature, k is the Boltzmann constant and E is the energy difference between the levels~~.]]		Let me first begin with introducing us. My name is Tanisha. The job he's been occupying hottest is a [https://Www.Flickr.com/search/?q=people+manager people manager] and he'll be promoted soon. To do archery can be something his wife doesn't delight in but he is doing. Some [http://www.reddit.com/r/howto/search?q=time+ago time ago] I chose to exist [http://Uuabq.org/blogs/index.php?blog=10&c=1&page=1&more=1&title=new_life_for_an_old_faith_7&tb=1&pb=1&disp=single apartments in westwood mqsa] Connecticut. My wife with regards to maintain an online site. You might desire to check it here: http://Uuabq.org/blogs/index.php?blog=10&c=1&page=1&more=1&title=new_life_for_an_old_faith_7&tb=1&pb=1&disp=single

	The '~~''Schottky anomaly'''~~ is ~~an observed effect in solid state physics where the [[specific heat capacity]] of~~ a ~~solid at~~ [~~[low temperature physics\|low temperature]] has a peak~~. ~~It is called anomalous because the [[heat capacity]] usually increases with temperature, or stays constant~~. ~~It occurs in systems with a limited number of energy levels so that E(T) increases with sharp steps, one for each energy level that becomes available. Since Cv~~ =~~(dE/dT), it will experience a large peak as the temperature crosses over from one step to the next~~.

	~~This effect~~ can be ~~explained by looking at the change~~ in ~~entropy of the system. At zero temperature only the lowest energy level is occupied, entropy is zero, and there~~ is ~~very little probability of a transition to a higher energy level~~. ~~With increasing temperature the probability of a transition, and thus an increase in entropy, goes up~~. ~~As the temperature approaches the difference between the energy levels there is a broad peak in the specific heat corresponding to a large change in entropy for a small change in temperature~~. ~~At high temperatures all of the levels are populated evenly, so there is again little change in entropy for small changes in temperature and thus a lower specific heat capacity.~~

	~~: <math>S~~ = ~~\int_0^T \! \left(\frac{C_{v}}{T}\right)dT \,</math>~~

	~~For a two level system the specific heat coming from the Schottky anomaly has the form~~:

	~~: <math>C_{\rm Schottky} = R\left(\frac{\Delta}{T}\right)^{2} \frac{e^{\Delta~~ / ~~T}}{[1 + e^{\Delta~~ / ~~T}]^{2}} \,<~~/~~math>~~

	~~Where k<sub>B<~~/~~sub>Δ is the energy between the two levels~~.~~<ref name~~=~~Tari2003p250/>~~

	~~This anomaly is usually seen~~ in ~~[[paramagnetic salt~~]~~]s or even ordinary glass (due~~ to ~~paramagnetic iron impurities) at low temperature~~. ~~At high temperature the paramagnetic spins have many spin states available, however at low temperatures some of the spin states are "frozen out" (having too high energy due~~ to ~~[[crystal field splitting]]) and the entropy per impurity is lowered~~.

	~~It was named after [[Walter H. Schottky]]~~.

	==~~References~~==
	~~{{reflist\|refs~~=
	~~<ref name~~=~~Tari2003p250>Tari, A: ''The Specific Heat of Matter at Low Temperatures'', page 250. Imperial College Press, 2003.</ref>~~
	}}

	~~[[Category:Thermodynamic properties]]~~

	~~{{physics-stub}}~~

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en>Bender235: restructured according to MOS:APPENDIX

150.108.238.30 at 18:31, 14 December 2012

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