Physical crystallography before X-rays

Did You Know?

• Franz Ernst Neumann used symmetry considerations when studying double refraction in 1832.
• Woldemar Voigt formalized Neumann's principle in 1885: a crystal's physical properties are invariant under its symmetry operations.
• Before the 20th century, crystallography had no dedicated academic positions; researchers worked in other roles such as professor, physician, or engineer.

Interaction with electromagnetic radiation

Double refraction, the splitting of light into two polarized rays, was first recorded in 1669 by Rasmus Bartholin in calcite (Iceland spar). Christiaan Huygens analyzed this in 1690, attributing the cleavage rhombohedron to stacked spherical particles and the optical behavior to crystal asymmetry. Étienne-Louis Malus in 1810 discovered that natural light reflected at a certain angle behaves like one of the rays from a double-refracting crystal, coining the term polarization.

Jean-Baptiste Biot defined optically positive and negative crystals in 1812, and David Brewster classified all crystals as isotropic, uniaxial, or biaxial in 1819. Augustin-Jean Fresnel published a detailed 1827 paper on double refraction, explaining it via transverse polarization of light waves. François Arago discovered rotary polarization in quartz in 1811, and Biot established its laws in 1812, noting that rotation direction and magnitude depend on crystal thickness and light wavelength.

Comprehensive accounts of crystal optics were published by Lazarus Fletcher, Theodor Liebisch (both 1891), and Friedrich Pockels (1906).

Effect of electricity and magnetism

Henri Hureau de Sénarmont in 1850 first observed anisotropic electrical conductivity in 36 crystals, correlating symmetry axes with conductivity extremes. Carlo Matteucci experimented on bismuth in 1855, and Helge Bäckström measured hematite's conduction in 1888. Electrical conductivity is now described as a second-rank symmetric tensor relating current density to electric field. Siméon Denis Poisson's 1826 magnetic theory predicted crystal behavior in magnetic fields, verified by Julius Plücker in 1847.

Plücker found quartz and other crystals were repelled (diamagnetic), while some were slightly attracted (paramagnetic). John Tyndall studied diamagnetism in crystals from 1850 to 1856. By the late 19th century, ferromagnetic, diamagnetic, and paramagnetic types were established, with theories linking diamagnetism and paramagnetism to crystal symmetry. Pierre Weiss in 1896 explained ferromagnetic hysteresis by postulating permanent atomic magnetic poles that align under a field and remain aligned via mutual dipole effects, also proposing domains with uniform dipole orientation.

Effect of temperature change

Eilhard Mitscherlich in 1824 observed that calcite's cleavage angles changed with temperature, concluding it contracts perpendicular to the trigonal axis (negative expansion) and expands along it (positive expansion), implying a cone of zero expansion. Hippolyte Fizeau used optical interferometry in 1864 to measure thermal expansion in many crystals. Non-cubic crystals exhibit anisotropic expansion; in monoclinic and triclinic systems, even axial angles change.

The thermal expansion coefficient is a symmetric second-rank tensor, a term introduced by Woldemar Voigt in 1898. Joseph Fourier's 1822 work on heat conduction preceded Jean-Marie Duhamel's 1832 experiments on crystals. Sénarmont demonstrated thermal anisotropy by showing that a point heat source in a non-cubic crystal produces an elliptical isothermal envelope whose orientation relates to crystallographic axes. Duhamel analyzed these findings in 1848.

Effect of mechanical force

Early elasticity theories for solids emerged in the 1820s, with Augustin-Louis Cauchy and Siméon Denis Poisson (1823, 1829) modeling non-cubic particle arrays, and Claude-Louis Navier (1827) treating isotropic bodies. Friedrich Mohs introduced his hardness scale in the 1820s. Franz Ernst Neumann published on homohedral crystal elasticity in 1834. Cauchy in 1828 required 36 constants for crystal elasticity; George Green in 1837 reduced this to 21 by assuming forces act along inter-element lines.

William Thomson in 1857 showed thermodynamics alone mandates 21 constants. Woldemar Voigt measured rock salt's elasticity (1874), G. Baumgarten calcite's (1874), and Wilhelm Röntgen with J. Schneider measured cubic compressibility of sodium and potassium chlorides (1887). Lambros Koromilas twisted gypsum and mica bars (1877), and H. Klang tested fluorites (1881). Voigt (1874–1888) led the field, showing symmetry reduces constants: triclinic 21, monoclinic 13, rhombic 9, hexagonal 7, tetragonal 6, cubic 3.