Physical crystallography before X-rays
Physical crystallography before X-rays describes how physical crystallography developed as a science up to the discovery of X-rays by Wilhelm Conrad Röntgen in 1895. In the period before X-rays, crystallography can be divided into three broad areas: geometrical crystallography culminating in the discovery of the 230 space groups in 1891–1894, chemical crystallography and physical crystallography.
Physical crystallography is concerned with the physical properties of crystals, such as their optical, electrical, magnetic, thermal, and mechanical properties.
- The interaction between crystals and electromagnetic radiation is covered in the following sections: double refraction, [|rotary polarization], [|conical refraction], [|absorption and pleochroism], [|luminescence], [|reflection from opaque materials], and [|infrared optics].
- The effect of electricity and magnetism on crystals is covered in: [|electrical conduction], [|magnetic properties], and [|dielectric properties].
- The effect of temperature change on crystals is covered in: [|thermal expansion], [|thermal conduction], [|thermoelectricity], and [|pyroelectricity].
- The effect of mechanical force on crystals is covered in: [|elasticity], [|photoelasticity], and [|piezoelectricity].
Symmetry
During the 19th century crystallography was progressively transformed into an empirical and mathematical science by the adoption of symmetry concepts. In 1832 Franz Ernst Neumann used symmetry considerations when studying double refraction. Woldemar Voigt, who was a student of Neumann, in 1885 formalized Neumann's principle as "if a crystal is invariant with respect to certain symmetry operations, any of its physical properties must also be invariant with respect to the same symmetry operations". Neumann's principle is sometimes referred to as the Neumann–Minnigerode–Curie principle based on later work by Bernhard Minnigerode and Pierre Curie. Curie's principle "the symmetries of the causes are to be found in the effects" is a generalization of Neumann's principle. At the end of the 19th century Voigt introduced tensor calculus to model the physical properties of anisotropic crystals.Interaction with electromagnetic radiation
Double refraction
Double refraction occurs when a ray of light incident upon a birefringent material, is split by polarization into two rays taking slightly different paths. The double refraction and rhomboidal cleavage of crystals of calcite, or Iceland spar, were first recorded in 1669 by Rasmus Bartholin In 1690 Christiaan Huygens analyzed double refraction in his book Traité de la lumière. Huygens reasoned that the cleavage rhombohedron resulted from the stacking of spherical particles and that the peculiarities of the transmission of light can be traced to the particular asymmetry of the crystal.In 1810 Étienne-Louis Malus determined that natural light, too, when reflected through a certain angle, behaves like one of the rays exiting a double-refracting crystal. Malus called this phenomenon polarization. In 1812 Jean-Baptiste Biot defined optically positive and negative crystals for the first time. In 1819 David Brewster found that all crystals could be classified as isotropic, uniaxial or biaxial. Augustin-Jean Fresnel was a significant researcher in the whole field of crystal optics, and published a detailed paper on double refraction in 1827 in which he described the phenomenon in terms of polarization, understanding light as a wave with field components in transverse polarization. Crystal optics was an active research area during the 19th century and comprehensive accounts of the field were published by Lazarus Fletcher, Theodor Liebisch and Friedrich Pockels.
Rotary polarization
In 1811 François Arago, who favoured the corpuscular theory of light, discovered the rotation of the plane of polarization of light travelling through quartz. In 1812 Jean-Baptiste Biot, who favoured the wave theory of light, enunciated the laws of rotary polarization and their application to the analysis of various substances. Biot discovered that while some crystals rotate the light to the right others rotate it to the left, and determined that the rotation is proportional to the thickness of substance traversed and to the wavelength of the light.In 1821 John Herschel pointed out the relation between the direction of rotation and the development of faces on quartz crystals. Suspecting that rotatory polarization is an effect of a lack of symmetry, Herschel established that quartz crystals often present faces placed in such a way that those belonging to certain crystals are mirror images of the corresponding faces of other crystals. He explained the connection between this arrangement and the respective rotation of light to the right and to the left. In 1822 Augustin-Jean Fresnel explained the rotation by postulating oppositely circularly polarized beams travelling with different velocities along the optic axis. In 1831 George Biddell Airy gave an explanation of the formation of the spirals which bear his name. In 1846 Michael Faraday discovered that the plane of polarization may also be rotated when light passes through an isotropic medium when it is in a magnetic field. The corresponding Kerr effect can be observed on reflecting plane-polarized light from a polished ferromagnetic mirror when in a magnetized state.
In 1848 Louis Pasteur gave the general relation between crystal morphology and rotatory polarization. Pasteur solved the mystery of polarized light acting differently with chemically identical crystals and solutions. Pasteur discovered the phenomenon of molecular asymmetry, that is that molecules could be chiral and exist as a pair of enantiomers. Pasteur's method was to physically separate the crystals of a racemic mixture of sodium ammonium tartrate into right- and left-handed crystals, and then dissolve them to make two separate solutions which rotated polarized light in opposite directions.
In 1855 discovered that crystals of sodium chlorate, sodium bromate, sodium ammonium sulfate and sodium amyl acetate have the property of rotating the polarization plane. In 1857 Alfred Des Cloizeaux advanced a general theory of rotatory polarization whilst studying cinnabar and strychnine sulphate. In 1864 Josef Stefan introduced the banded spectrum in the study of rotatory polarization. Theories of magnetic optics in ferromagnetic crystals were published in 1892 by D. A. Goldhammer, and in 1893 by Paul Drude.
Conical refraction
is an optical phenomenon in which a ray of light, passing through a biaxial crystal along certain directions, is refracted into a hollow cone of light. There are two possible conical refractions, one internal and one external.In 1821–1822 Augustin-Jean Fresnel developed a theory of double refraction in both uniaxial and biaxial crystals. Fresnel derived the equation for the wavevector surface in 1823, and André-Marie Ampère rederived it in 1828. Many others investigated the wavevector surface of the biaxial crystal, but they all missed its physical implications.
William Rowan Hamilton, in his work on Hamiltonian optics, discovered the wavevector surface has four conoidal points and four tangent conics. This implies that, under certain conditions, a ray of light could be refracted into a cone of light within the crystal. He termed this phenomenon "conical refraction" and predicted two distinct types: internal and external, corresponding respectively to the conoidal points and tangent conics. Hamilton announced his discovery on 22 October 1832. He then asked Humphrey Lloyd to prove his theory experimentally. Lloyd first observed conical refraction on 14 December 1832 with a specimen of aragonite, and published his results in early 1833. In 1833 James MacCullagh claimed that Hamilton's work was a special case of a theorem he had published in 1830. Hamilton also exchanged letters with George Biddell Airy who was skeptical that conical refraction could be observed experimentally but became convinced after Lloyd's report.
Hamilton and Lloyd's discovery was a significant victory for the wave theory of light and solidified Fresnel's theory of double refraction. The discovery of conical refraction is an example of a mathematical prediction being subsequently verified by experiment.
Later theoretical work on conical refraction was published in 1860 by Robert Bellamy Clifton and in 1874 by Jules Antoine Lissajous, and experimental work in 1888 by Theodor Liebisch and in 1889 by Albrecht Schrauf.
Absorption and pleochroism
In 1809 Louis Cordier discovered the phenomenon of pleochroism while investigating a new mineral that he named dichröıte, whereby its crystals showed different colors when viewed along different axes. From 1817 to 1819 David Brewster made a systematic study of light absorption and pleochroism in various minerals and showed that, in uniaxial crystals, the absorption is smallest in the direction of, and greatest at right angles to, the optical axis. In 1820 John Herschel studied the absorption of light in biaxial crystals and explained the interference rings first observed by David Brewster. In 1838 Jacques Babinet discovered that the greatest absorption in a crystal generally coincided with the direction of greatest refractive index. In 1845 Wilhelm Haidinger published a general account of pleochroism in crystals. In 1854 Henri Hureau de Sénarmont showed that transparent crystals stained by a dye during crystal growth became pleochroic.In 1877 performed photometric observations on absorption. In 1880 pointed out the existence of absorption axes. He investigated certain biaxial crystals and found that the absorption axes, although subject to the symmetry of the crystal, did not necessarily coincide with the principal directions of the indicatrix. In 1888 Henri Becquerel made qualitative and quantitative observations. Woldemar Voigt and Paul Drude presented theories of the absorption of light in crystals. In 1906 Friedrich Pockels published his Lehrbuch der Kristalloptik which gave an overview of the subject.