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Giant Magnetocaloric Effect

September 10, 2018

While it's common for experimental physicists to invent something that's patentable, this is typically not true for theoretical physicists. However, it sometimes happens. The Hungarian-German-American physicist, Leo Szilard (1898-1964), and Italian-American physicist, Enrico Fermi (1901-1954), applied for a patent on the nuclear reactor in 1944. The 58 page patent, US patent no. 2,708,656, wasn't issued until a decade later for security reasons.[1]

Another example is Albert Einstein (1879-1955), who teamed with Szilard on the design of a refrigerator. As I wrote in a previous article (Ammonia Synthesis, March 6, 2017), ammonia was used as a refrigerant in household refrigerators in the early 20th century. It was a bad choice, based on its toxicity, but a good choice based on its thermodynamics. Ammonia has a low boiling point (-33.34 °C, -28.0 °F) and high enthaly of vaporization (23.35 kJ/mol, 5.56 kcal/mol at its boiling point). Methyl chloride and sulfur dioxide, likewise toxic chemicals, were also used in home refrigerators.

Einstein read how an entire family had been killed as they slept by leaking refrigerator fumes.[2] Moved by this tragedy, Einstein teamed with Szilard to invent and patent the "Einstein refrigerator."[3] This refrigerator still used the standard toxic gases, but it was safer since it had no moving parts and did not require rotary seals (see figure). The application of the first commercial freon (Freon-12, R-12, or CFC-12) to refrigeration in the 1930s likely saved many lives; but, as happens for many wonderful technologies, there were also unintended consequences. In the case of freon, it was destruction of atmospheric ozone.

Figure from US Patent No. 1,781,541, 'Refrigeration,' by Albert Einstein and Leo Szilard, November 11, 1930

Figure from US Patent No. 1,781,541, "Refrigeration," by Albert Einstein and Leo Szilard, dated November 11, 1930.

The "Einstein refrigerator" is an absorption refrigerator in which the cooling evaporate is absorbed by another liquid, which is run through a heat exchanger to recover the refrigerant for another refrigeration cycle.

(Via Google Patents.)[3]

As most people know, Einstein was quite familiar with patents, since he was employed by the Swiss patent office early in his career. Also, Jacob Einstein, his uncle, held seven patents, many of which concerned electric arc lamps.[4] Einstein was issued 19 patents in his lifetime. most of which were with collaborators such as Szilard, and many of these patents are the same invention patented in different countries.[4] One interesting invention is U.S. patent no. 1,017,566, "Design of a blouse," issued in 1936.[5]

Einstein design patent for a blouse, US 101,756

Albert Einstein's patent for a blouse, issued on October 27, 1936, was a design patent, not a utility patent.

My conjecture is that Einstein did this as a respite from more ponderous thought, just as one of today's scientists will view an entertaining video clip on his computer screen in the middle of a serious calculation.

(Via Google Patents.)[5]

Refrigeration is still being researched, and one important research area is magnetic refrigeration. This isn't about the best magnets to affix a child's artwork to a refrigerator door; rather, it's about a means of solid-state cooling using a magnetic material in a magnetic field using what's termed the magnetocaloric effect. I wrote about the magnetocaloric effect in an earlier article (Magnetic Refrigeration, September 3, 2014).

In 1881, German physicist, Emil Warburg, discovered that iron would cool upon application of a magnetic field. His iron specimen cooled about a degree Celsius when subjected to an applied field of one tesla (10,000 gauss), which is about 20,000 times the strength of Earth's magnetic field. While Warburg's experiment showed what is now called the magnetocaloric effect, there are arguments that the effect was only elucidated in 1917 by Pierre Weiss (1865-1940) and Auguste Piccard (1884-1962).[6] Weiss' name is associated with the important Curie–Weiss law.

The magnetocaloric effect uses entropy as a means of extracting heat from a substance. The magnetic field aligns the magnetic moments of the atoms in a solid, which allows a little more heat to be extracted from the material. This results in a temperature change, and the temperature can be lowered again by repeating the cycle. The thermodynamic cycle associated with the magnetocaloric effect can be seen in the figure. Magnetic refrigeration was first used as a means of cooling small volumes to temperatures near absolute zero. This method was developed by University of California, Berkeley, chemist and Nobel laureate, William Giauque (1895-1982).

Thermodynamic cycle of a magnetic refrigerator

The thermodynamic cycle of a magnetic refrigerator.

(Created using Inkscape. Click for a larger image.)

What material properties result in a good material for magnetic refrigeration? A cursory glance at the following equation that relates the change in temperature T to the change in magnetic field H tells the entire story.
Figure caption
In this case, instead of the usual heat capacities at constant volume (Cv) or constant pressure (Cp), the integral contains an expression for the particular heat capacity at each temperature and magnetic field (CH,T). Aside from the obvious fact that larger applied magnetic fields will give a greater temperature change, we see that materials with smaller heat capacity are better, and also that large temperature changes come from materials that have a large change in magnetization M with temperature.

This explains why gadolinium is the material used in the many YouTube demonstrations of the magnetocaloric effect. Gadolinium is about thirty times more expensive than iron, but it's commonly available. As can be seen in the graph, gadolinium has a Curie temperature quite near room temperature, so it has a large dM/dT at room temperature.

Ideal magnetization curve of Gadolinium as a function of temperature.

Ideal magnetization curve of gadolinium as a function of temperature.

The function shown gives the temperature dependence of magnetization of a ferromagnetic material according the the mean-field approximation.

(Created using Gnumeric.)

While pure gadolinium will function in a magnetic refrigerator, some compounds of gadolinium perform better. These include Gd85Er15, Gd5(Si2Ge2), and compounds of the general formula, Gd5(SixGe1−x)4.[6] Now, a research team from the U.S. Department of Energy's Ames Laboratory (Ames, Iowa), Iowa State University (Ames, Iowa), and the European Synchrotron Radiation Facility (Grenoble, France) has discovered a giant magnetocaloric effect in the rare earth intermetallic compound, Eu2In.[7-8] The magnetocaloric effect in this compound arises from a novel discontinuous magnetoelastic transition, and the discovery could lead to even better magnetocaloric materials.[7-8]

The first-order magnetic transition is marked by the presence of a latent heat of transformation, and few materials are known to have magnetoelastic first-order magnetic transitions at room temperature when at least one phase has a large magnetization.[7] Eu2In has such a transition at low magnetic fields and almost no hysteresis.[7-8]

Structure of Eu2In

Structure of Eu2In.

The two distinct europium lattice sites are important to this compound's functioning as an excellent magnetocaloric material.

(Ames Laboratory image.[9])

X-ray absorption and magnetic circular dichroism experiments were conducted at the European Synchrotron Radiation Facility to determine the physical mechanism of the transformation.[8] Says Durga Paudyal, a scientist at Ames and an author of the paper that describes this research, "The magnetic phase transition can be explained by an unusual exchange of electrons between the two elements in the compound, with indium electronic states overlapping with those of europium."[8] There is an electron transfer between a 5d electron state of europium and a 4p electron state of indium.[7]

Research team member Vitalij Pecharsky, who holds a joint appointment at Iowa State and Ames, explains the importance of the discovery the unusual mechanism of the compound's change in magnetic state.
"Now that we have seen this mechanism and are able to explain how it works, we can use this knowledge to look for similar but better materials, one that can be used in future applications like magnetic refrigeration."[8]


  1. E. Fermi and L. Szilard, "Neutronic reactor," U.S. patent no. 2,708,656, May 17, 1955.
  2. Gene Dannen, The Einstein-Szilard Refrigerators, Scientific American, January 1997, pp. 90-95.
  3. Albert Einstein and Leo Szilard, "Refrigeration," US patent No. 1,781,541, November 11, 1930.
  4. Asis Kumar Chaudhuri, "Einstein's Patents and Inventions," arXiv, September 5, 2017.
  5. Albert Einstein, "Design for a blouse," U.S. design patent no. 101,756, October 27, 1936.
  6. Anders Smith, "Who discovered the magnetocaloric effect?" The European Physical Journal H, vol. 38, no 4 (September, 2013), pp 507-517.
  7. V. K. Pecharsky and K. A. Gschneidner, Jr., "Giant Magnetocaloric Effect in Gd5(Si2Ge2)," Phys. Rev. Lett., vol. 78 (June 9, 1997), Document No. 4494, DOI: http://dx.doi.org/10.1103/PhysRevLett.78.4494.
  8. F. Guillou, A. K. Pathak, D. Paudyal, Y. Mudryk, F. Wilhelm, A. Rogalev, and V. K. Pecharsky, "Non-hysteretic first-order phase transition with large latent heat and giant low-field magnetocaloric effect," Nature Communications, vol. 9, Article no. 2925, July 26, 2018. This is an open access article with a PDF file here.
  9. Unusual rare earth compound opens doorway to new class of functional materials, Ames Laboratory Press Release, July 26, 2018.
  10. Stinus Jeppesen, "Magnetocaloric materials," Ph.D Thesis - University of Copenhagen, October, 2008, ISBN 978-87-550-3706-9.

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