Editing Magnetocaloric effect (section)

== Process ==

The MCE is a magneto-[[thermodynamic]] phenomenon in which a temperature change of a suitable material is caused by exposing the material to a changing magnetic field. This is also known by low temperature physicists as ''[[Adiabatic process|adiabatic]] demagnetization''. In that part of the refrigeration process, a decrease in the strength of an externally applied magnetic field allows the magnetic domains of a magnetocaloric material to become disoriented from the magnetic field by the agitating action of the thermal energy ([[phonon]]s) present in the material.  If the material is isolated so that no energy is allowed to (re)migrate into the material during this time, (i.e., an adiabatic process) the temperature drops as the domains absorb the thermal energy to perform their reorientation.  The randomization of the domains occurs in a similar fashion to the randomization at the [[Curie temperature]] of a [[ferromagnetic]] material, except that [[magnetic dipole]]s overcome a decreasing external magnetic field while energy remains constant, instead of magnetic domains being disrupted from internal [[ferromagnetism]] as energy is added.

One of the most notable examples of the magnetocaloric effect is in the chemical element [[gadolinium]] and some of its [[alloys]]. Gadolinium's temperature increases when it enters certain magnetic fields. When it leaves the magnetic field, the temperature drops. The effect is considerably stronger for the gadolinium [[alloy]] {{chem|Gd|5|(Si|2|Ge|2|)}}.<ref name="Ames">{{cite web|author=Karl Gschneidner Jr. |author2=Kerry Gibson |name-list-style=amp |title=Magnetic Refrigerator Successfully Tested |work=Ames Laboratory News Release |publisher=Ames Laboratory |date=December 7, 2001 |url=http://www.external.ameslab.gov/news/release/01magneticrefrig.htm |access-date=2006-12-17 |url-status=dead |archive-url=https://web.archive.org/web/20100323011159/http://www.external.ameslab.gov/news/release/01magneticrefrig.htm |archive-date=March 23, 2010 }}</ref> [[Praseodymium]] alloyed with [[nickel]] ({{chem|Pr|Ni|5}}) has such a strong magnetocaloric effect that it has allowed scientists to approach to within one millikelvin, one thousandth of a degree of [[absolute zero]].<ref>{{cite book | last = Emsley | first = John| title = Nature's Building Blocks | publisher = [[Oxford University Press]] |date= 2001 | page = 342 | isbn = 0-19-850341-5 }}</ref>

=== Equation ===

The magnetocaloric effect can be quantified with the following equation:

<math display="block">\Delta T_{ad}=-\int_{H_0}^{H_1}\left(\frac {T}{C(T,H)}\right)_H{\left(\frac {\partial M(T,H)}{\partial T}\right)}_H dH</math>

where <math>\Delta T_{ad}</math> is the adiabatic change in temperature of the magnetic system around temperature T, H is the applied external magnetic field, C is the heat capacity of the working magnet (refrigerant) and M is the [[magnetization]] of the refrigerant.

From the equation we can see that the magnetocaloric effect can be enhanced by:

* a large field variation
* a magnet material with a small heat capacity
* a magnet with large changes in net magnetization vs. temperature, at constant magnetic field

The adiabatic change in temperature, <math>\Delta T_{ad}</math>, can be seen to be related to the magnet's change in magnetic [[entropy]] (<math>\Delta S </math>) since<ref>{{Cite journal| last1=Balli|first1=M.|last2=Jandl|first2=S.|last3=Fournier|first3=P.|last4=Kedous-Lebouc|first4=A.|date=2017-05-24| title=Advanced materials for magnetic cooling: Fundamentals and practical aspects| journal=Applied Physics Reviews| volume=4|issue=2|pages=021305| doi=10.1063/1.4983612| bibcode=2017ApPRv...4b1305B|arxiv=2012.08176|s2cid=136263783}}</ref>

<math display=block> \Delta S(T) = \int_{H_0}^{H_1}\left(\frac{\partial M(T,H')}{\partial T} \right)dH'</math>

This implies that the absolute change in the magnet's entropy determines the possible magnitude of the adiabatic temperature change under a thermodynamic cycle of magnetic field variation. T

=== Thermodynamic cycle ===

[[Image:MCE_vectorized.svg|right|thumb|400px|Analogy between magnetic refrigeration and vapor cycle or conventional refrigeration. ''H'' = externally applied magnetic field; ''Q'' = heat quantity; ''P'' = pressure; Δ''T''<sub>ad</sub> = adiabatic temperature variation]]

The cycle is performed as a [[refrigeration cycle]] that is analogous to the [[Carnot cycle|Carnot refrigeration cycle]], but with increases and decreases in magnetic field strength instead of increases and decreases in pressure.  It can be described at a starting point whereby the chosen working substance is introduced into a [[magnetic field]], i.e., the magnetic flux density is increased.  The working material is the refrigerant, and starts in thermal equilibrium with the refrigerated environment.

* ''Adiabatic magnetization:''  A magnetocaloric substance is placed in an insulated environment.  The increasing external magnetic field (+''H'') causes the magnetic dipoles of the atoms to align, thereby decreasing the material's magnetic [[entropy]] and [[heat capacity]]. Since overall energy is not lost (yet) and therefore total entropy is not reduced (according to thermodynamic laws), the net result is that the substance is heated (''T'' + Δ''T''<sub>ad</sub>).
* ''Isomagnetic enthalpic transfer:'' This added heat can then be removed (-''Q'') by a fluid or gas&nbsp;— gaseous or liquid [[helium]], for example.  The magnetic field is held constant to prevent the dipoles from reabsorbing the heat.  Once sufficiently cooled, the magnetocaloric substance and the coolant are separated (''H''=0).
* ''{{Visible anchor|Adiabatic demagnetization}}:''  The substance is returned to another adiabatic (insulated) condition so the total entropy remains constant.  However, this time the magnetic field is decreased, the thermal energy causes the magnetic moments to overcome the field, and thus the sample cools, i.e., an adiabatic temperature change.  Energy (and entropy) transfers from thermal entropy to magnetic entropy, measuring the disorder of the magnetic dipoles.<ref>{{cite book |title=Introduction to Statistical Physics |edition=illustrated |first1=João Paulo |last1=Casquilho |first2=Paulo Ivo Cortez |last2=Teixeira |publisher=Cambridge University Press |year=2014 |isbn=978-1-107-05378-6 |page=99 |url=https://books.google.com/books?id=Hp-TBQAAQBAJ}} [https://books.google.com/books?id=Hp-TBQAAQBAJ&pg=PA99 Extract of page 99]</ref>
* ''Isomagnetic entropic transfer:''  The magnetic field is held constant to prevent the material from reheating. The material is placed in thermal contact with the environment to be refrigerated. Because the working material is cooler than the refrigerated environment (by design), heat energy migrates into the working material (+''Q'').

Once the refrigerant and refrigerated environment are in thermal equilibrium, the cycle can restart.

=== Applied technique ===

The basic operating principle of an adiabatic demagnetization refrigerator (ADR) is the use of a strong magnetic field to control the entropy of a sample of material, often called the "refrigerant". Magnetic field constrains the orientation of magnetic dipoles in the refrigerant. The stronger the magnetic field, the more aligned the dipoles are,  corresponding to lower entropy and [[specific heat capacity|heat capacity]] because the material has (effectively) lost some of its internal [[degrees of freedom (physics and chemistry)|degrees of freedom]]. If the refrigerant is kept at a constant temperature through thermal contact with a [[heat]] sink (usually liquid [[helium]]) while the magnetic field is switched on, the refrigerant must lose some energy because it is [[thermodynamic equilibrium|equilibrated]] with the heat sink. When the magnetic field is subsequently switched off, the heat capacity of the refrigerant rises again because the degrees of freedom associated with orientation of the dipoles are once again liberated, pulling their share of [[equipartition of energy|equipartitioned]] energy from the [[kinetic energy|motion]] of the [[molecule]]s, thereby lowering the overall temperature of a [[system]] with decreased energy. Since the system is now [[Thermal insulation|insulated]] when the magnetic field is switched off, the process is adiabatic, i.e., the system can no longer exchange energy with its surroundings (the heat sink), and its temperature decreases below its initial value, that of the heat sink.

The operation of a standard ADR proceeds roughly as follows.  First, a strong magnetic field is applied to the refrigerant, forcing its various magnetic dipoles to align and putting these degrees of freedom of the refrigerant into a state of lowered entropy. The heat sink then absorbs the heat released by the refrigerant due to its loss of entropy. Thermal contact with the heat sink is then broken so that the system is insulated, and the magnetic field is switched off, increasing the heat capacity of the refrigerant, thus decreasing its temperature below the temperature of the heat sink. In practice, the magnetic field is decreased slowly in order to provide continuous cooling and keep the sample at an approximately constant low temperature. Once the field falls to zero or to some low limiting value determined by the properties of the refrigerant, the cooling power of the ADR vanishes, and heat leaks will cause the refrigerant to warm up.