# Who discovered anisotropic materials, and what were they studying?

Thinking of properties of materials, who discovered anisotropy and what materials were they studying?

I had read a claim that the first recorded experiments to study anisotropy are those by Duhamel who in 1832 studied anisotropic conductivity by measuring the elliptic shape of the melting front around a small heat source embedded in crystals coated with paraffin. Thus, the relation $$q_i =-k_{ij} \partial_j T$$ is known as the Fourier-Duhamel law of heat conduction.

• Crystalline? molecular? You might want to refine the question a bit – Carl Witthoft Oct 3 '19 at 13:26

It depends on what counts as "discovery". Interestingly, optical anisotropy was discovered before the elastic one, and the first anisotropic "material" modeled was... the luminiferous ether.

Bartholinus discovered double refraction in calc-spar, a type of calcite, back in 1669, and Huygens showed in 1690 that two rays arising from refraction by calcite are extinguished by passing them through the same crystal rotated about the direction of the rays. Thus, calcite was optically anisotropic. Newton explained it by suggesting that light particles have "sides", and used it as an argument against Hooke's wave optics. At the time, only longitudinal (acoustic) waves were known, and they could not explain transverse polarization.

The phenomenon was not much investigated until Malus's polarization experiments with calcite in 1808, and Arago's with quartz in 1811, see Brief History of the Discovery of Phenomena Concerning Light Polarization. At that time, Young and Fresnel made wave optics indispensable, and that posed a problem. In isotropic elastic media transverse waves were always accompanied by longitudinal waves, but polarization experiments ruled out their presence. If light propagated in elastic ether, that ether had to be anisotropic. Elastic theories of ether became quite popular, with Cauchy, Lame, Green and others studying them. Green's 1838 equations already took anisotropy into account, but it was Kelvin's Elements of a Mathematical Theory of Elasticity (1856) that redirected the theory towards real solid materials rather than the hypothetical ether, see 75-plus years of anisotropy by Helbig and Thomsen:

"Thus, the first articles on elasticwave propagation already took anisotropy into account. For example, Green (1838) was the first to use strain energy, and he strongly supported the notion that there could be as many as 21 elastic constants. In 1856, Lord Kelvin published “Elements of a mathematical theory of elasticity”, which exclusively discussed solids. This is not to be taken as an indication that he did not believe in the elastic ether, but only that he was interested in metals at that time and thus needed a solid foundation of the theory of elasticity.

For this purpose, he invented concepts that became common only much later, such as vectors and vector spaces (in 6D space!), tensors, and eigensystems. With these tools, he could describe the elastic tensor in coordinate-free form. His ideas were so much ahead of his time that his paper — and a re-publication (in the “Elasticity” listing of the 1886 edition of the Encyclopedia Britannica) — were regarded by some of his contemporaries as scientifically unsound (despite his stature) and thus made no impact on the development of the theory of anisotropy... Kelvin was also the first to formulate the elastic-wave equation for anisotropic media. (He solved it for a simple case.) Since this achievement was published as part of his “no impact” papers, it was also overlooked. Hence, today the solution of the wave equation is attributed to Christoffel (1877)."

In the end, anisotropic ether did not work out either, but the elasticity theory motivated by it came in handy in material science.

• And over in biology, chirality of some complex organic substances – Carl Witthoft Oct 3 '19 at 13:27
• I suggest that anisotropy of materials was know to prehistoric smiths. Working metals results in anisotropic behaviors pretty readily. – Jon Custer Oct 4 '19 at 18:38
• @JonCuster It depends on what counts as "known". Cavemen made use of minerals that are easier to chip one way rather than another even before metals. On the other hand, asking for a clear conceptualization of "isotropy" vs "anisotropy" pushes it up into 18-19th century, the words do not even appear until 1850s. – Conifold Oct 4 '19 at 20:37