Chemical crystallography before X-rays

During the 19th century crystallography was progressively transformed into an empirical and mathematical science by the adoption of symmetry concepts.{{sfnm|Scholz|1989a|Scholz|1989b|Scholz|1994|Katzir|2004}} In 1832 Franz Ernst Neumann used symmetry considerations when studying double refraction in crystals.{{sfn|Neumann|1832}} 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".{{sfn|Neumann's principle}}{{sfnm|Lalena|2006|1pp=145–146|Authier|2014|2p=11}} Neumann's principle is sometimes referred to as the Neumann–Minnigerode–Curie principle based on later work by Bernhard Minnigerode{{sfnm|Minnigerode|1884|Minnigerode|1886|Minnigerode|1887}} (another student of Neumann) and Pierre Curie.{{sfn|Brandmüller|1986}} Curie's principle "the symmetries of the causes are to be found in the effects" is a generalization of Neumann's principle.{{sfnm|Curie|1894|Curie|1982|Shubnikov|1988}}

The relations between symmetry and physical and chemical properties were established throughout the 19th century: the notion of hemihedry{{sfn|Alworth|1972|p=1|loc="Crystals that display unequal development or modification of related parts and thus lack points or planes of symmetry are said to be hemihedral"}} (Weiss, 1819; Delafosse, 1840), the 7 crystal systems (Mohs, 1822), the notion of point lattice (Seeber, 1824), the 32 crystal classes (Frankenheim, 1826; Hessel, 1830; Gadolin, 1869), molecular chirality (Pasteur, 1848), the 14 Bravais lattices (Bravais, 1850), the 65 chiral groups that contain only proper symmetry operations – rotations, translations and roto-translations (Sohncke 1879), and, finally, the 230 space groups (Fedorov, 1891; Schoenflies, 1891; Barlow, 1894).{{sfnm|1a1=Malgrange|1a2=Ricolleau|1a3=Schlenker|1y=2014|1p=viii|Authier|2013|2pp=318–400|2loc=The Birth and Rise of the Space-Lattice Concept|Katzir|2004|Darvas|2007|4pp=59–61}}

File:Fortres Monroe 1861 - Cannon-balls.jpg lattices.]]

In the first half of the 16th century Paracelsus proposed a theory of mineral formation as an analogy to fruit-bearing plants.{{sfn|Oldroyd|1974|pp=134–135|loc="Similarly, thinks Paracelsus, the matrix element, water, nourishes the seeds of minerals and metals, which grow into mature specimens within the earth. The matrix of minerals, the element water – forms a ‘tree’ within the body of the earth, which deposits its fruits in due season, later to be harvested by man"}} In 1550 Gerolamo Cardano made an early attempt to explain the shape of crystals as the result of a close packing of spheres.{{sfnm|Cardano|2013|1p=392|Authier|2013|2p=277}} In 1591 Thomas Harriot studied the close packing of cannonballs (spheres).{{sfn|Authier|2013|pp=277–278}} In 1597 Andreas Libavius recognized the geometrical characteristics of crystals and identified salts from their crystal shape.{{sfn|Cuevas-Diarte|Reverter|2014|p=3}}

File:Kepler conjecture 1.jpg (1611) of square (A) and hexagonal (B) packings{{sfnm|Kepler|1611|1p=9|Kepler|1966|2p=14}}]]

File:Huyghens - Traité de la lumière - Fig. 49-50.svg in a crystal of Iceland spar (Huygens, 1690) {{sfn|Huyghens|1690|p=94}}]]

In 1611 Johannes Kepler studied the packing of spheres, in order to explain the hexagonal symmetry of snow crystals.{{sfnm|Kepler|1611|Kepler|1966}} Kepler demonstrated that in a compact packing each sphere has six neighbours in the same plane, three in the plane above, and three in the plane below, for a total of twelve touching spheres.{{sfnm|1a1=Cuevas-Diarte|1a2=Reverter|1y=2014|1p=3|Kepler|1611}} Kepler concluded that {{pi}}/(3{{sqrt|2}}) = 0.74084 is the maximum possible density amongst any arrangement of spheres — this became known as the Kepler conjecture.{{sfn|Authier|2013|pp=284–286,289–290}} The conjecture was finally proved by Thomas Hales in 1998.{{sfnm|Hales|2006|Szpiro|2003|2pp=201–214,264–278}}

By the second half of the 17th century the ideas of Paracelsus had been displaced by a more scientific approach to chemistry, geology, mineralogy, and the emerging field of crystallography.{{sfnm|Boas|1969|Mauskopf|2012}} In his book The Sceptical Chymist of 1661,{{sfnm|Boyle|1661|Boyle|2007}} Robert Boyle criticized the traditional composition of materials, as represented by the teaching of Aristotle and Paracelsus, and initiated the modern understanding of chemical elements using the words "perfectly unmingled bodies". Boyle argued that matter's basic elements consisted of various types of particles, termed "corpuscles", which were capable of arranging themselves into groups (molecules).{{sfn|Authier|2013|p=17}} Boyle was one of the earliest researchers to use the term crystal for crystalline substances apart from quartz.{{sfn|Authier|2013|p=271}} In 1665 Robert Hooke attempted to explain crystal morphology based on the stacking of atoms. In his work Micrographia{{sfn|Hooke|1665}} he reported on the regularity of quartz crystals observed with the recently invented microscope, and proposed that they are formed by spherules.{{sfnm|1a1=Cuevas-Diarte|1a2=Reverter|1y=2014|1p=4|Authier|2013|2pp=294–296}}

Nicolas Steno rejected Paracelsus's proposed organic origin for crystals.{{sfn|Oldroyd|1974|p=153|loc="The accretion of crystalline matter provides the basis of the proposed explanations of crystal formation and an organic origin of mineral crystals is explicitly denied"}} Steno first observed the law of constancy of interfacial angles when studying quartz crystals{{sfn|Senechal|1990a|p=44}} (De solido intra solidum naturaliter contento, Florence, 1669),{{sfnm|Steno|1669|Steno|1916}} and noted that, although the crystals of a substance differed in appearance from one to another, the angles between corresponding faces were always the same.{{sfn|Ladd|2014}} Steno's work can be considered as the beginning of crystallography as an independent discipline.{{sfn|Cuevas-Diarte|Reverter|2014|p=5}}

In 1678 Christiaan Huygens proposed a structural explanation of the double refraction of calcite based on ellipsoidal atoms.{{sfn|Moser|Robinson|2024}} Huygens discovered the polarization of light by Iceland spar, a transparent form of calcite, and published his results in his Traité de la Lumière.{{sfnm|1a1=Cuevas-Diarte|1a2=Reverter|1y=2014|1p=5|Authier|2013|2pp=305–306|Huyghens|1690}}

Domenico Guglielmini's publications of 1688 (Riflessioni filosofiche dedotte dalle figure de Sali) and 1705 (De salibus dissertatio epistolaris physico-medico-mechanica) concluded that the earliest forms (he noted cube, rhombohedral parallelepiped, hexagonal prism, and octahedron) of various salt crystals are characteristic of each substance, are identical in form, indivisible, and have faces with identical inclinations to each other.{{sfnm|Whewell|2011|Authier|2013|2pp=306–307}}

File:Contact Goniometer.jpg of the Carangeot type]]

File:Calcite scalenohedron constructed using Haüy's integrant molecules.png scalenohedron crystal constructed from small building blocks (molécules intégrantes) using the law of decrements of René Just Haüy.{{sfn|Haüy|1801|loc=pl. III, fig. 17}}]]

In 1723 Moritz Anton Cappeller published Prodromus Crystallographiae, the first treatise on crystal shapes.{{sfn|Cappeller|1723}} The introduction of the term crystallography is attributed to Cappeller.{{sfnm|1a1=Cuevas-Diarte|1a2=Reverter|1y=2014|1p=5|Authier|2013|2p=272}} In 1735 Carl Linnaeus, who is known for his system of classification of biological species in his Systema Naturae, also classified minerals and stated that "their transparency is derived from their atomical construction".{{sfn|Linnaeus|1806|p=6}} In 1745 Guillaume-François Rouelle carried out a microscopic analysis of sea salt and proposed that the crystals were composed of cubic particles.{{sfnm|Rouelle|1745|Mauskopf|2012|2p=18}} In 1758 Roger Joseph Boscovich published{{sfn|Boscovich|1922}} his atomic theory which stated that particles of matter were linked by attractive and repulsive forces and that the solid so formed was compressible rather than rigid; this would become relevant in the 19th century when Haüy theorised that crystals were constructed from identical units stacked up without spaces.{{sfn|Rowlinson|2002|pp=49–51, 105–107}}

The idea of a polyhedral molecular unit of crystal structure was promoted by Pierre-Joseph Macquer in his handbook Dictionnaire de chymie of 1766.{{sfnm|Macquer|1766|Macquer|1771|Mauskopf|1976|3pp=8–10}} In 1767 :de:Christian Friedrich Gotthard Westfeld wrote that calcite crystals could be built from rhombohedra.{{sfnm|Westfeld|1767|Authier|2013|2p=318}} In 1773 Torbern Bergman, a leader in the field of chemical analysis, described the crystal forms of calcite and stated that all the forms could be built up from the cleavage rhombohedron.{{sfnm|Bergman|1773|Bergman|1780}} Bergman developed a classification of minerals based on chemical characteristics (extending the work of Linnaeus), with subclasses organized by their external shapes, and defined seven primary crystal forms.{{sfn|Authier|2013|pp=307–313}}

With Jean-Baptiste L. Romé de l'Isle's Essai de cristallographie published in 1772{{sfnm|Romé de L'Isle|1772|Mauskopf|1976|2p=10}} and Cristallographie published in 1783{{sfn|Romé de L'Isle|1783}} the scientific approach to crystal structure began. Romé de l'Isle described over 500 crystal forms and accurately measured the interfacial angles of a great variety of crystals, using the goniometer designed by his student Arnould Carangeot. Romé de l'Isle noted that the angles are characteristic of a substance, thus generalizing the law of constancy of angles postulated by Steno.{{sfnm|Metzger|1969|Phillips|1963}} Romé de l'Isle considered that the shape of a crystal is a consequence of the packing of elemental particles, and defined six primitive forms.{{sfn|Authier|2013|pp=313–317}}

In 1781 René Just Haüy (often termed the "Father of Modern Crystallography"){{sfnm|Brock|1913|Kraus|1918|2p=127|Fock|1895|3p=5}} discovered that crystals always cleave along crystallographic planes. Based on this observation, and the fact that the inter-facial angles in each crystal species always have the same value, Haüy concluded that crystals must be periodic and composed of regularly arranged layers of tiny polyhedra (molécules intégrantes).{{sfnm|Haüy|1782a|Haüy|1782b|Authier|2013|3pp=320–322}} This theory explained why all crystal planes are related by small rational numbers (the law of rational indices). In 1784 René-Just Haüy published Essai d'une théorie sur la structure des cristaux, appliquée à plusieurs genres de substances cristallisées in which he stated his law of decrements: a crystal is composed of molecules arranged periodically in three dimensions without leaving any gaps.{{sfnm|Haüy|1784|Authier|2013|2pp=322–325}} Haüy's molecular crystal structure theory assumed that molécules intégrantes were specific in shape and composition for every compound.{{sfn|Mauskopf|2012|p=23}} Haüy developed a mathematical theory of crystal structure that turned out to be remarkably accurate and gave crystallography a legitimate place among the sciences.{{sfnm|1a1=Cuevas-Diarte|1a2=Reverter|1y=2014|1pp=6–7|Authier|2013|2pp=318–328}}

File:A New System of Chemical Philosophy - DPLA - 530ddba5e875f88a834d3aa2d9b82d10 (page 19).jpg, 1808).{{sfn|Dalton|1808|loc=Plate 3}}]]

File:Plate from On the Elementary Particles of certain Crystals by William Hyde Wollaston 1813.pngs (Wollaston, 1813).{{sfn|Wollaston|1813}}]]

From the late 18th century it became apparent that a crystal of a substance was composed of units, whether thought of as atoms, ions, molecules, or polyhedra, in a regular spatial arrangement, termed its crystal structure.{{sfn|Moore|1990|p=78}}

The most notable early theory for crystal structures was that of René Just Haüy. In 1801 Haüy, published his Traité de Minéralogie{{sfn|Haüy|1801}} in four volumes, the last of which was an atlas of plates which was considered "among the most wonderful of the 19th century".{{sfn|Kubbinga|2012|p=2}} It has been described as "a work of comprehensive insight, and much of it, written with literary fluency".{{sfn|Gratacap|1918|p=101}} In this work Haüy described how the law of rational indices establishes relationships between the orientations of the crystal faces, and explains that crystalline solids are formed by replicas of what would now be considered a unit cell.{{sfnm|1a1=Cuevas-Diarte|1a2=Reverter|1y=2014|1p=7|Authier|2013|2p=328}} Haüy's theory called for fixed mineral species (based on their molécule intégrante), fixed crystal morphology, and constant chemical composition. This was a mineralogical equivalent to the law of definite proportions in chemistry.{{sfn|Mauskopf|2012|p=26}}

John G. Burke (1966) and :de:Hans-Werner Schütt (1984) proposed Haüy's crystal structure theory as an example of a paradigm in the sense of The Structure of Scientific Revolutions by Thomas S. Kuhn (1962).{{sfnm|Burke|1966|pp=8–9|Schütt|1984}} In 1822 Haüy published Traité de Cristallographie and updated version of his work of 1801. Haüy postulated, "to each specific substance with a well defined chemical composition, capable of existence in a crystalline form, there corresponds a shape that is specific and characteristic of that substance."{{sfnm|Haüy|1822|Authier|2013|2pp=329–333|3a1=Cuevas-Diarte|3a2=Reverter|3y=2014|3p=11}}

In 1808 John Dalton published his atomic theory of matter. In Dalton’s theory, there were four key assertions: "matter is made up of roughly spherical atoms, which were indivisible and indestructible; all atoms of a given element are identical in mass and properties; compounds are formed by a combination of two or more different kinds of atoms; and chemical reactions involve the rearrangement of atoms".{{sfnm|Lalena|2006|1p=148|Cahn|1999}} In his book A New System of Chemical Philosophy,{{sfn|Dalton|1808}} crystals are considered as a periodic arrangement of spherical atoms.{{sfn|Cuevas-Diarte|Reverter|2014|p=8}} However, Dalton stated that it was premature to form any theory of crystallization.{{sfn|Dalton|1808|pp=210–211|loc="Crystallization exhibits to us the effects of the natural arrangement of the ultimate particles of various compound bodies ; but we are scarcely yet sufficiently acquainted with chemical synthesis and analysis to understand the rationale of this process"}} Kuhn proposed Dalton's atomic theory as an example of a paradigm in which Dalton asserted that atoms can only combine in simple, whole-number ratios (law of multiple proportions). Under this new paradigm, any reaction which did not occur in fixed proportion could not be a chemical process.{{sfn|Kuhn|1962|pp=130-132}}

There was a contradiction between the crystallographic and chemical paradigms. Haüy's theory asserted that crystals were composed of polyhedral units stacked up in three dimensions without gaps; Dalton's theory, by contrast, implied that crystals were constructed by a periodic arrangement of spherical atoms in space.{{sfn|Cahn|1999}} Haüy's theory was generally accepted by his fellow mineralogists in the period 1801–1815{{sfn|Ferraris|2019|p=133}} but then came under attack from the German dynamist school led by Christian Samuel Weiss.{{sfn|Nicol|1878|p=674}} Weiss and his followers studied the external symmetry of crystals rather than their internal structure.{{sfn|Authier|2013|pp=337–347}} In 1819, Weiss demonstrated the generality of the phenomenon of hemihedry (half of the vertices/edges/faces of a crystal act differently from the other half), thus challenging Haüy's holohedral approach (all vertices/edges/faces of a crystal act in the same manner).{{sfnm|Pasteur|1860|1pp=11–12|Authier|2013|2pp=372–375}} Haüy's crystal structure theory was criticised as over-simplistic by William Hyde Wollaston in 1809{{sfn|Wollaston|1809}} and by Henry James Brooke in 1819.{{sfn|Brooke|1819|p=454}} Haüy also tended to ignore experimental results that contradicted his structural theory, such as those achieved with the more accurate reflection goniometer{{sfn|Usselman|1986}} invented by Wollaston in 1809.{{sfnm|Mohs|1823|1p=289|Burke|1966|2p=103|Authier|2013|3p=332}}

In 1813 Wollaston adopted Dalton's ideas and proposed using sphere packing to model crystal structures.{{sfnm|Wollaston|1813|Authier|2013|2pp=333–337}} In 1814 André-Marie Ampère published a theory of the chemical combination of substances, based on Haüy's polyhedral forms.{{sfnm|Ampère|1814|Mauskopf|1976|2p=33,35–37}} However, Ampère's work had little impact on contemporary chemists.{{sfnm|Authier|2013|1p=372|Laszlo|2010}}

In 1819 David Brewster classified crystals according to their optical properties, as isotropic, uniaxial, or biaxial.{{sfnm|Brewster|1819|Lalena|2006|2p=144}} In a paper published in 1830 Brewster attempted to relate the phenomenon of double refraction to the arrangement of the molecules in crystals. If a crystal has three axes at right angles to each other then, if they are equivalent, the crystal is isotropic, if two are equivalent and the third different, the crystal is uniaxial, and if all three are different, the crystal is biaxial.{{sfnm|Brewster|1830|Authier|2013|2pp=347–349}} In 1822 John Herschel proposed a causal relationship between the handedness of quartz crystals (right- or left-handed) and the direction of their optical rotation.{{sfnm|Herschel|1822|2a1=Cuevas-Diarte|2a2=Reverter|2y=2014|2p=11|Authier|2013|3p=374}}

In 1840 :de:Friedrich Ludwig Hünefeld described the first crystallization of a protein; Hünefeld obtained lamellar crystals (later identified as haemoglobin) by putting the blood of an earthworm between two slides.{{sfnm|Giegé|2013|Hünefeld|1840|2pp=160–161|2loc=Fig. 7, p. xvii|Zimmer|2025}}

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Originally, René Just Haüy considered that each chemical compound had a characteristic crystalline form.{{sfn|Authier|2013|p=230}} However, based on his 1808 work with aragonite{{sfn|Haüy|1808}} and his earlier studies of calcite, which are two different forms of calcium carbonate (CaCO₃), Haüy had to concede that substances with the same chemical composition but different molecular arrangements could have different crystalline forms.{{sfn|Authier|2013|p=331}}

In 1819 Eilhard Mitscherlich discovered the law of isomorphism which states that compounds which contain the same number of atoms, and have similar structures, tend to exhibit similar crystal forms.{{sfnm|Mitscherlich|1819|Tutton|1911|Tutton|1922|3pp=1221–1254|Melhado|1980}} Mitscherlich carried out the first systematic research on the dependence of crystal forms on their chemical nature.{{sfnm|Mitscherlich|1824|Hoddeson|1992|2p=73}} The discovery of isomorphism was the first major step in chemical crystallography{{sfn|Moore|1990|p=78}} and Emil Wohlwill regarded Mitscherlich's work on isomorphism as a milestone in the history of the atomic-molecular theory.{{sfnm|Wohlwill|1866|Salvia|2013|Schütt|1984}} The discovery of the phenomena of isomorphism and polymorphism dealt a clear blow to Haüy's crystal structure theory.{{sfnm|Burke|1966|1p=132|Goodman|1969|Fock|1895|3pp=82–88}}

Mitscherlich’s findings were a central consideration of the atomic weight determinations in 1819 by Jöns Jacob Berzelius, a leading proponent of Dalton’s atomic theory. Berzelius classified minerals by their chemical composition rather than by their crystal morphology, as was the established practice.{{sfn|Bowden|1997|p=27}} Mitscherlich’s research, together with the work of Alexis Thérèse Petit and Pierre-Louis Dulong that heat capacities of solids vary with temperature and inversely with atomic weight, led Berzelius to declare them as a positive confirmation of the atomic theory.{{sfnm|Cahn|1999|Mauskopf|1976|2p=32|Lalena|2006|3p=148}}

A contemporary historical review of the development of isomorphism in the 19th century was written by Andreas Artsruni.{{sfn|Arzruní|1893|pp=77–218}}

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In crystallography, polymorphism is the phenomenon where a compound can crystallize into more than one crystal structure; in the case of elements the term allotropy is sometimes used.{{sfnm|Tutton|1922|1pp=1255–1272|Arzruní|1893|2pp=22–76}} An example of polymorphism is titanium dioxide (TiO₂), which occurs in four known natural polymorphic forms (minerals with the same composition but different structure): brookite (orthorhombic), akaogiite (monoclinic), anatase (tetragonal) and rutile (tetragonal).

Eilhard Mitscherlich discovered polymorphism ("dimorphism") in his studies of sodium phosphate (1821) and sulphur (1823).{{sfnm|Mitscherlich|1821|Mitscherlich|1823|Authier|2013|3p=331}} In the 1830s the development of the microscope enhanced observations of polymorphism and aided Moritz Ludwig Frankenheim’s studies.{{sfn|Buerger|Bloom|1937|pp=183–184}} Frankenheim was able to demonstrate methods to induce crystal phase changes, for example the use of solvents or physical scratching, and formally summarized his findings on the nature of polymorphism.{{sfnm|Frankenheim|1839|Bernstein|2002|2p=20}} Soon after, the more sophisticated polarized light microscope came into use, and it provided better visualization of crystalline phases allowing crystallographers to distinguish between different polymorphs. The hot stage was invented and fitted to a polarized light microscope by Otto Lehmann in about 1877. This invention helped crystallographers determine melting points and observe polymorphic transitions.{{sfnm|Bernstein|2002|Tutton|1922|2pp=1172,1258–1259|3a1=Buerger|3a2=Bloom|3y=1937|3pp=183–184}}

The first polymorphic organic substance, benzamide, was discovered by Friedrich Wöhler and Justus von Liebig in 1832.{{sfnm|1a1=Wöhler|1a2=Liebig|1y=1832|Bernstein|2002|2p=73|Tutton|1922|3pp=1266–1272|4a1=Molčanov|4a2=Stilinović|4y=2014|4p=10}}

In 1870 Paul Groth defined wikt:morphotropy as the state of two crystals whose similar physical structure is due to similar chemical composition.{{sfnm|Groth|1870|Arzruní|1893|2pp=219–297|Wahl|1913|3p=354}} Groth examined the change in symmetry of a crystal as a result of the replacement of a hydrogen atom by another univalent atom or radical.{{sfnm|Jaeger|1920|1pp=138–139|Fock|1895|2pp=173–184|Groth|1906|3pp=36–65}} Morphotropy is also referred to as isogonism{{sfn|Tutton|1922|p=1266}} in which each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.

In 1897 Wilhelm Ostwald introduced Ostwald's rule,{{sfnm|Ostwald|1897|2a1=Buerger|2a2=Bloom|2y=1937|2pp=186–187}} to describe the formation of polymorphs. The rule states that usually the less stable polymorph crystallizes first.{{sfn|Van Stanten|1984}} Ostwald's rule is not a universal law but a common tendency observed in nature.{{sfnm|Threlfall|2003|Bernstein|2002|2pp=23–24}}

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In 1811 François Arago constructed a polariscope and used it to discover that quartz crystals would rotate the plane of polarization of polarized light.{{sfnm|Arago|1811|Bernal|1953|2p=184}} Shortly after Jean-Baptiste Biot found a similar optical rotation effect for solutions, for example tartaric acid, and concluded that the effect was a inherent property of certain molecules.{{sfnm|Biot|1812a|Biot|1812b|Glusker|1990|3p=91}}

In 1830 Jöns Jacob Berzelius discovered that tartaric and racemic acids have the same elementary composition, and concluded that a difference in the arrangement of the atoms in the molecules creates compounds with different chemical properties; in the same paper Berzelius suggested the term “isomerism” for the phenomenon.{{sfnm|Berzelius|1830|Jorpes|1966|2pp=108-109}}

In 1831 Mitscherlich was asked by Berzelius to study the tartrates in order to determine the differences between two isomers, tartaric acid and racemic acid.{{sfn|Kostyanovsky|2003}} By 1832, Jean-Baptiste Biot had discovered that tartaric acid from grape juice was dextrorotatory and that racemic acid was optically inactive. In 1844 Mitscherlich found that the solution of sodium ammonium tartrate was optically active, but that of sodium ammonium paratartrate was optically inactive.{{sfn|Kostyanovsky|2003}} The work of Biot and Mitscherlich was the starting point for research by the French chemist Louis Pasteur, a doctoral student of Gabriel Delafosse and a colleague of Auguste Laurent.{{sfn|Mauskopf|2012|p=35}}

In 1848 Louis Pasteur gave the general relation between crystal morphology and rotatory polarization.{{sfnm|Pasteur|1848a|Pasteur|1848b}} Pasteur solved the mystery of polarized light acting differently with chemically identical crystals and solutions by discovering the phenomenon of molecular asymmetry, that is that molecules could be chiral and exist as a pair of enantiomers.{{sfnm|Pasteur|1860|1p=30|Richardson|1901|2pp=1–34|Tutton|1922|3pp=1272–1286|Mauskopf|1976|4pp=68–80}} 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.{{sfnm|1a1=Geison|1a2=Secord|1y=1988|2a1=Debré|2y=1998|3a1=Kauffman|3a2=Myers|3y=1998|4a1=Flack|4y=2009}} Pasteur's research was in part informed by considerations of molecular symmetry.{{sfn|Katzir|2004|pp=43–45}} Pasteur also proposed two other methods for the isolation of optically active enantiomers from racemic mixtures: by the use of optically active bases, e.g. strychnine, or by means of living organisms, e.g. bacteria or yeasts.{{sfn|Jaeger|1920|pp=217–228}}

William Thomson (Lord Kelvin) introduced the word "chiral" in 1904 to describe handed figures.{{sfnm|Thomson|1904|Ollis|1972|2pp=22–26}} Objects that do not exhibit optical isomerism are said to be "achiral", that is their image in a plane mirror can be made congruent with itself.{{sfn|Lalena|2006|pp=147–149}} The term chirality has almost completely displaced the term "dissymmetry" which was used by Pasteur.{{sfnm|Gal|2011|Gal|2013}}

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In 1888 Friedrich Reinitzer examined the properties of various derivatives of cholesterol which now belong to the class of materials known as cholesteric liquid crystals. Previously, other researchers had observed distinct colour effects when cooling cholesterol derivatives just above the freezing point, but had not associated it with a new phenomenon.{{sfnm|Mitov|2014|1p=1246|Kelker|1973|2p=7|Kelker|1988|3pp=2–9}} Reinitzer found that cholesteryl benzoate does not melt in the same way as most substances, but has two melting points. At {{convert|145.5|°C|°F}} it melts into a cloudy liquid, and at {{convert|178.5|°C|°F}} it melts again and the cloudy liquid becomes clear. The phenomenon is reversible. Reinitzer sought assistance to understand the phenomenon and, on 14 March 1888, he wrote to Otto Lehmann. They exchanged letters and samples.{{sfnm|Mitov|2014|1p=1246|2a1=Kelker|2a2=Knoll|2y=1989|2pp=30–35}} Lehmann examined the intermediate cloudy fluid, and reported seeing crystallites. Reinitzer's colleague Victor von Zepharovich{{sfn|Korbel|1993}} also indicated that the intermediate "fluid" was crystalline. Reinitzer published his results, with credit to Lehmann and von Zepharovich, on 3 May 1888.{{sfnm|Reinitzer|1888|Reinitzer|2004|3a1=Sluckin|3a2=Dunmur|3a3=Stegemeyer|3y=2004|3pp=3–6}}

By that time, Reinitzer had discovered and described three important features of liquid crystals (the term was coined by Lehmann in a 1904 monograph):{{sfn|Lehmann|1904}} the existence of two melting points, the reflection of circularly polarized light, and the ability to rotate the direction of polarized light.

Reinitzer did not pursue the study of liquid crystals further, although in 1908 he had to defend his role in their discovery when Lehmann claimed the priority.{{sfnm|Lehmann|1908|Reinitzer|1908|Mitov|2014|3pp=1246–1247}} The research was continued by Lehmann who started a systematic study, first of cholesteryl benzoate, and then of related compounds which exhibited the double-melting phenomenon. He was able to make observations in polarized light, and his microscope was equipped with a hot stage (sample holder equipped with a heater) enabling high temperature observations. The intermediate cloudy phase clearly sustained flow, but other features, particularly the signature under a microscope, convinced Lehmann that he was dealing with a solid. By the end of August 1889 he had published his results.{{sfnm|Lehmann|1889|Lehmann|2004}} Lehmann's paper prompted work by Ludwig Gattermann who in 1890 published a paper on the synthesis of azoxyphenol ethers, such as para-azoxyanisole, which exhibited the same double-melting behaviour.{{sfnm|1a1=Gattermann|1a2=Ritschke|1y=1890|2a1=Sluckin|2a2=Dunmur|2a3=Stegemeyer|2y=2004|2pp=54–62|Kelker|1988|3pp=25–26}}

Lehmann's interpretation of his results was controversial, and was not accepted by Gustav Heinrich Tammann, Georg Hermann Quincke, and Walther Nernst.{{sfnm|Mitov|2014|Kelker|1973|2p=8|3a1=Dunmur|3a2=Sluckin|3y=2011|3pp=17–40}} In 1905 :de:Rudolf Schenck's research addressed and largely resolved the objections of Tamman, Quincke and Nernst.{{sfnm|Schenck|1905|2a1=Sluckin|2a2=Dunmur|2a3=Stegemeyer|2y=2004|2pp=64–75|Kelker|1973|3pp=13–15}} Lehmann's work was continued and significantly expanded by the German chemist Daniel Vorländer who from the beginning of the 20th century had synthesized most of the liquid crystals known.{{sfnm|Vorländer|1906|Vorländer|1907|3a1=Sluckin|3a2=Dunmur|3a3=Stegemeyer|3y=2004|3pp=76–88|4a1=Dunmur|4a2=Sluckin|4y=2011|4pp=43–49|Kelker|1973|5pp=15–17|Sackmann|1989|6pp=43–48}} In 1910–1922 research on liquid crystals, led by Georges Friedel, was carried on in France.{{sfnm|Lagerwall|2013|Leslie|2016}} In the period before X-rays liquid crystals were seen as merely a curiosity by scientists, and the field did not yield applications until the second half of the 20th century.{{sfn|Sluckin|Dunmur|Stegemeyer|2004|pp=3–16}}

Liquid crystals are now known to have one- or two-dimensional periodicity, with rod or layer symmetry respectively.{{sfnm|1a1=Shubnikov|1a2=Kopt︠s︡ik|1y=1974|1pp=103–127,189–198|Moore|1990|2p=87}}

{{multiple image

|align = right

| total_width = 300

| image1 = Jacobus van 't Hoff by Perscheid 1904.jpg

| alt1 = Photograph of Jacobus van 't Hoff

| caption1 = Jacobus van 't Hoff

| image2 = Joseph Achille Le Bel.jpg

| alt2 = Photograph of Joseph Le Bel

| caption2 = Joseph Le Bel

| footer = Discoverers of the tetrahedral carbon atom (1874)

| footer_align = center

}}

File:J. H. van 't Hoff enantiomers of tetrahedral carbon 1874.png, 1874){{sfn|van 't Hoff|1874}}]]

File:Sphere packing by William Barlow 1897.png, 1897 representing the structure of rock-salt (NaCl){{sfn|Barlow|1897|p=547}}]]

From the 1830s Haüy’s molecular crystal structure theory started to be combined with the atomic theory of the chemists to produce a view of a crystal as the regular arrangement of atoms or molecules in space. In 1849 Auguste Bravais related the symmetry of the crystal, considered as one of 14 space lattices, to that of its constituting molecules and formalized the reticular interpretation of hemihedry given by Gabriel Delafosse.{{sfnm|Authier|2013|1pp=372–382|Mauskopf|1976|2pp=51–55|Delafosse|1843}} In 1852 Delafosse attempted to relate the structure of the molecule to the external shape of the crystal.{{sfn|Authier|2013|p=372}}

During the 1850s and 1860s a "quiet revolution" took place in structural chemistry according to Alan J. Rocke, a historian of chemistry.{{sfnm|Rocke|1993}} The main features of the revolution were the clarification of the concept of atomic weight (Stanislao Cannizzaro), the definition of the idea of valence (then known as atomicity), and new chemical structural ideas, such as the benzene structure of a ring of alternating double and single carbon bonds (August Kekulé).{{sfn|Mauskopf|2012|p=44}} These developments in chemistry were largely independent of the mathematical and geometrical direction of crystallography in the period 1850–1895 which had little concern with the practicalities of atomic and molecular arrangement.{{sfn|Mauskopf|2012|p=51}}

In 1874 Jacobus Henricus van 't Hoff and Joseph Le Bel independently proposed the tetrahedral arrangement of the atoms bound to carbon in organic molecules.{{sfnm|van 't Hoff|1874|van 't Hoff|1898|Richardson|1901|3pp=35–46|Le Bel|1874|Le Bel|1963|Richardson|1901|6pp=47–60}}{{sfnm|1a1=Riddell|1a2=Robinson|1y=1974|Glusker|1990|2p=92}} Van't Hoff's theory validated and explained Pasteur's results with tartrate crystals, and Johannes Wislicenus' work with isomeric lactic acids,{{sfnm|Ramberg|2003|1pp=42–52|Mauskopf|2006}} and was fundamental to the further development of stereochemistry.{{sfnm|1a1=Hargittai|1a2=Hargittai|1y=2024|Rocke|2010}}

Until the use of X-rays there was no way to determine the actual crystal structure of even the simplest substances such as salt (NaCl).{{sfn|Authier|2013|p=230}} For example in the 1880s, William Barlow proposed several crystal structures based on close-packing of spheres{{sfnm|Barlow|1883a|Barlow|1883b|Sohncke|1884|Barlow|1884|Kubbinga|2012|5pp=21–22|Mauskopf|2015}} some of which were validated later by X-ray crystallography; however the available data were too scarce in the 1880s to accept his models as conclusive. In the period between the discovery of X-rays (1895) and X-ray diffraction (1912) Barlow and William Jackson Pope developed the principles of packing, and showed how to deduce the structures of some simple compounds.{{sfnm|Barlow|1897|2a1=Barlow|2a2=Pope|2y=1906|3a1=Barlow|3a2=Pope|3y=1907|4a1=Barlow|4a2=Pope|4y=1910|Paufler|2019}} In the 1930s Linus Pauling was impressed that Barlow had assigned many crystal structures of metals (copper, silver, and gold to cubic close packing, and magnesium, zinc, and cadmium to hexagonal close packing) and salts (sodium, potassium and caesium chlorides) which were subsequently proved to be correct by X-ray crystallography.{{sfn|Pauling|1981|p=1}} William Johnson Sollas emphasised the importance of different atomic sizes in constructing simple crystals, and correctly concluded that the sodium and chlorine atoms in salt would be of different sizes.{{sfnm|Sollas|1898|Stillwell|1938|2pp=33–34}}

In 1887 Johannes Wislicenus published a study of stereoisomerism in unsaturated compounds.{{sfnm|Wislicenus|1887|Richardson|1901|2pp=61–132}}

Groth made a systematic classification of minerals based on their chemical composition and crystal structure and published his results in his 5-volume Chemische Kristallographie in 1906–1919, which contained crystalline morphology and physical property data on nearly 10,000 substances.{{sfnm|Groth|1906–1919|2a1=Black|2a2=Seton|2y=2024|Glusker|1990|3p=92}}

In 1913 Walter Wahl summarised the known connections between chemical composition and crystalline form as isomorphism (Mitscherlich), morphotropism (Groth), and enantiomorphism (Pasteur and van 't Hoff).{{sfn|Wahl|1913}}

In his preface to Andreas Fock's An introduction to chemical crystallography Pope summarised the state of chemical crystallography in 1895 as follows:

{{Blockquote|"Our knowledge of the physical and geometrical properties of crystals is now very complete, but their relations to chemical constitution and composition are as yet but little known."{{sfn|Fock|1895|p=xiii}}}}

After 1912 crystallography would develop dramatically with the widespread adoption of X-ray diffraction to determine crystal structures.{{sfn|Authier|2013|pp=1–8}}

{{multiple image

| align = right

| total_width = 300

| image1 = Theodor Hilsdorf - Paul Heinrich von Groth (1910).jpg

| alt1 = Photograph of Paul Groth

| caption1 = Paul Groth

| image2 = Zeitschrift für Krystallographie und Mineralogie, title page, volume 1, 1877.png

| alt2 = Title page of the first issue of the journal Zeitschrift für Krystallographie

| caption2 = Z. Kryst., 1, 1877

| footer = Founder of Zeitschrift für Krystallographie

| footer_align = center

}}

Before the 20th century crystallography was not a well-established academic discipline. There were no academic positions specifically in crystallography. Workers in the field normally carried out their crystallographic research as an ancillary to other employment(s), or had independent means. The leading workers in the field of chemical crystallography were employed as follows:

• Professors
• Mathematics or science: Arago,{{sfnm|Hahn|1970|MacTutor|2loc=Dominique François Jean Arago}} Berzelius,{{sfnm|Jorpes|1966|Melhado|1981}} Biot,{{sfnm|Crosland|1970|MacTutor|2loc=Jean-Baptiste Biot}} Curie,{{sfnm|Curie|1923|Wyart|1971}} Frankenheim,{{sfn|Correns|1972}} Lehmann,{{sfnm|Burke|1973|Mitov|2014}} Liebig,{{sfnm|Brock|1997|Science History Institute|2016|Shenstone|1901}} Mitscherlich,{{sfnm|Schütt|1992|Szabadváry|1974}} Ostwald,{{sfnm|Wilhelm Ostwald Biography|2a1=Hiebert|2a2=Körber|2y=1981}} Pasteur,{{sfnm|Debré|1998|Geison|1974}} Reinitzer,{{sfn|Mitov|2014}} Wöhler{{sfnm|Keen|2005|Science History Institute|2016}}
• Mineralogy: Delafosse,{{sfnm|Authier|2013|1p=370|Taylor|1978}} Groth,{{sfnm|Fischer|1972|H.A.M.|1928}} Haüy,{{sfnm|Authier|2013|1p=319|Hooykaas|1972|Kunz|1918|4a1=Boulliard|4a2=Cabaret|4a3=Giura|4y=2022}} Neumann,{{sfnm|Authier|2013|1p=354|MacTutor|2loc=Franz Ernst Neumann}}
• Other employment: Brewster (editor),{{sfnm|Authier|2013|p=349|Morse|1970}} Romé de l'Isle (cataloguer),{{sfnm|Authier|2013|1p=313|Hooykaas|1981}} Sohncke (meteorological service),{{sfnm|Authier|2013|1p=383|Burke|1970}} Wollaston (physician){{sfnm|Authier|2013|p=335|Usselman|2015|Goodman|1976}}
• Independently wealthy: Barlow,{{sfnm|Authier|2013|1p=387|Holser|1981}} Herschel,{{sfnm|Evans|1972|MacTutor|2loc=John Frederick William Herschel}} Huygens{{sfnm|Authier|2013|1p=34|MacTutor|2loc=Christiaan Huygens}}

In the nineteenth century there were informal schools of crystallography researchers in France (Arago, Biot, Curie, Delafosse, Haüy, Pasteur),{{sfnm|Mauskopf|1976|Kubbinga|2012|Lalena|2006}} Germany (Frankenheim, Groth, Lehmann, Liebig, Mitscherlich, Neumann, Reinitzer, Sohncke, Wöhler){{sfnm|Scholz|1989b|Kubbinga|2012|Lalena|2006}} and England (Barlow, Brewster, Herschel, Wollaston).{{sfnm|Deas|1959|Authier|2013|2pp=333–337,355–359,386–400}}

Until the founding of Zeitschrift für Krystallographie und Mineralogie by Paul Groth in 1877 there was no lead journal for the publication of crystallographic papers. The majority of crystallographic research was published in the journals of national scientific societies, or in mineralogical journals.{{sfn|Schuh|2007a|pp=371–373}} The inauguration of Groth’s journal marked the emergence of crystallography as a mature science independent of geology.{{sfn|Kahr|McBride|1992|p=12}}

• History of atomic theory
• History of molecular theory
• Physical crystallography before X-rays
• Timeline of chemistry
• Timeline of crystallography

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• {{cite book |last1=Brock |first1=William H. |title=Justus von Liebig: the chemical gatekeeper |date=1997 |publisher=Cambridge University Press |location=Cambridge, U.K. |isbn=9780521562249 |edition=1st}}
• {{cite journal |last1=Brooke |first1=H. J. |title=Observations on a Memoir by the Abbé Haüy on the Measurement of the Angles of Crystals |journal=Annals of Philosophy |date=1819 |volume=14 |pages=453–456 |url=https://www.biodiversitylibrary.org/item/53907#page/479/mode/1up |access-date=5 June 2025 |quote=His [Haüy's] theory contains a principle which has in some instances conduced to error and which may affect its worth as a theory more than any consideration of the comparative merit of the goniometer. This principle is an imaginary simplicity which he supposes to exist naturally in the ratios of certain lines either upon or traversing a crystal ... and he is disposed to regard generally the disagreement of an observed measurement with this character rather as an error of the observation than a correction of his theoretic determination.}}
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• {{cite book |last1=Burke |first1=John G. |title=Origins of the science of crystals |date=1966 |publisher=University of California Press |location=Berkeley, CA |url=https://archive.org/details/originsofscience0000burk |access-date=10 May 2024}}
• {{cite book |last1=Burke |first1=John G. |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |date=1970 |publisher=Charles Scribner's Sons |location=New York |isbn=0684129248 |pages=511–512 |url=https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/sohncke-leonhard |access-date=8 February 2025 |archive-url=https://archive.org/details/dictionaryofscie12gill/page/510/mode/2up |archive-date=16 November 2010 |chapter=Sohncke, Leonhard |volume=12 |url-status=live}}
• {{cite book |last1=Burke |first1=John G. |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |date=1973 |publisher=Charles Scribner's Sons |location=New York |isbn=068410119X |pages=148–149 |url=https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/lehmann-otto |access-date=27 February 2025 |archive-url=https://archive.org/details/dictionaryofscie08gill/page/148/mode/2up |archive-date=16 November 2010 |chapter=Lehmann, Otto |volume=8 |url-status=live}}

• {{cite journal |last1=Cahn |first1=Robert W. |title=Slaying the crystal homunculus |journal=Nature |date=12 August 1999 |volume=400 |issue=6745 |page=625 |doi=10.1038/23161|bibcode=1999Natur.400..625C }}
• {{cite book |last1=Cappeller |first1=Moritz Anton |title=Prodromus Crystallographiae De Crystallis Improprie Sic Dictis Commentarium |trans-title=Preliminary treatise on crystallography: a commentary on improperly named crystals |date=1723 |doi=10.3931/e-rara-86385 |publisher=Typis Henrici Rennwardi Wyssing |location=Lucerne |url=https://www.e-rara.ch/zhb/content/titleinfo/24541158 |access-date=8 May 2025 |language=Latin}}
• {{cite book |last1=Cardano |first1=Gerolamo |editor1-last=Forrester |editor1-first=John M. |title=The De subtilitate of Girolamo Cardano |date=2013 |orig-date=1550 |publisher=Arizona Center for Medieval and Renaissance Studies |location=Tempe AZ |isbn=978-0-86698-484-3}}
• {{cite book |last1=Clarke |first1=Frank Wigglesworth |editor1-last=Rogers |editor1-first=Howard J. |title=International Congress of Arts and Science |date=1908 |publisher=University Alliance |location=London |pages=221–240 |chapter-url=https://archive.org/details/internationalcon07inteiala/page/220/mode/2up |access-date=31 May 2025 |chapter=The Progress and Development of Chemistry in the Nineteenth Century |volume=7: Physics and Chemistry}}
• {{cite book |last1=Correns |first1=Carl W. |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |date=1972 |publisher=Scribner |location=New York |isbn=0684101165 |page=124 |url=https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/frankenheim-moritz-ludwig |access-date=8 February 2025 |archive-url=https://archive.org/details/dictionaryofscie0005unse/page/124/mode/2up |archive-date=19 October 2022 |chapter=Frankenheim, Moritz Ludwig |volume=5 |url-status=live}}
• {{cite book |last1=Crosland |first1=M. P. |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |volume=2 |date=1970 |publisher=Charles Scribner's Sons |location=New York |isbn=0-684-16963-0 |pages=133–140 |url=https://www.encyclopedia.com/people/science-and-technology/physics-biographies/jean-baptiste-biot |access-date=24 April 2025 |archive-url=https://archive.org/details/dictionaryofscie02gill/page/132/mode/2up |archive-date=16 November 2010 |url-status=live |chapter=Biot, Jean-Baptiste}}
• {{cite journal |last1=Cuevas-Diarte |first1=Miguel Ángel |last2=Reverter |first2=Álvarez Santiago |title=Commented chronology of crystallography and structural chemistry |url=https://hdl.handle.net/2445/120608 |website=Dipòsit Digital |publisher=Universitat de Barcelona |access-date=21 January 2025 |date=2014|hdl=2445/120608 }}
• {{cite book |last1=Curie |first1=Marie |title=Pierre Curie |date=1923 |publisher=The Macmillan Company |location=New York |translator-last1=Kellogg |translator-first1=Charlotte and Vernon |url=https://archive.org/details/pierrecurie0000curi/page/n7/mode/2up |access-date=27 February 2025}}
• {{cite journal |last1=Curie |first1=Pierre |title=Sur la symétrie dans les phénomènes physiques, symétrie d'un champ électrique et d'un champ magnétique |trans-title=On symmetry in physical phenomena, symmetry of an electric field and a magnetic field |journal=Journal de Physique, 3rd series |date=1894 |volume=3 |pages=393–415 |url=https://archive.org/details/oeuvresdepierrec00curi/page/118/ |access-date=6 February 2025 |language=French}}
• {{cite book |last1=Curie |first1=Pierre |editor1-last=Rosen |editor1-first=Joe |translator-last1=Rosen |translator-first1=Joe |translator-last2=Copié |translator-first2=P. |title=Symmetry in physics: selected reprints |year=1982 | orig-date=1894 |publisher=American Association of Physics Teachers |location=Stony Brook, NY |pages=17–25 |chapter=On symmetry in physical phenomena, symmetry of an electric field and of a magnetic field}}

• {{cite book |last1=Dalton |first1=John |title=A new system of chemical philosophy |date=1808 |publisher=R. Bickerstaff |location=London |url=https://digital.sciencehistory.org/works/ff365590j |archive-url=https://archive.org/details/newsystemofchemi01daltuoft/page/n3/mode/2up |archive-date=15 January 2008 |url-status=live |access-date=1 June 2025}}
• {{cite book |last1=Darvas |first1=Gyorgy |title=Symmetry: Cultural-historical and Ontological Aspects of Science-Arts Relations; the Natural and Man-made World in an Interdisciplinary Approach |date=2007 |publisher=Birkhäuser |location=Basel |isbn=9783764375546 }}
• {{cite journal |last1=Deas |first1=Herbert D. |title=Crystallography and crystallographers in England in the early nineteenth century: a preliminary survey |journal=Centaurus |date=June 1959 |volume=6 |issue=2 |pages=129–148 |doi=10.1111/j.1600-0498.1959.tb00253.x|bibcode=1959Cent....6..129D }}
• {{cite book |last1=Debré |first1=Patrice |title=Louis Pasteur |date=1998 |publisher=The Johns Hopkins University Press |location=Baltimore |translator-last1=Forster |translator-first1=Elborg |pages=29–51 |chapter=Crystals: A New Law |isbn=9780801865299 }}
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• {{cite book |last1=Dunmur |first1=David |last2=Sluckin |first2=Tim |title=Soap, science, and flat-screen TVs: a history of liquid crystals |date=2011 |publisher=Oxford University Press |location=New York |isbn=9780199549405 |pages=17–33 |url=https://archive.org/details/soapscienceflats0000davi/page/16/mode/2up |access-date=24 April 2025}}

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• {{cite journal |last1=Ferraris |first1=Giovanni |title=Early contributions of crystallography to the atomic theory of matter |journal=Substantia |date=31 March 2019 |volume=3 |issue=1 |pages=131–138 Pages |doi=10.13128/Substantia-81}}
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• {{cite journal |last1=Flack |first1=H. D. |url=http://crystal.flack.ch/dox/sh5092.pdf |title=Louis Pasteur's discovery of molecular chirality and spontaneous resolution in 1848, together with a complete review of his crystallographic and chemical work |date=2009 |archive-url=https://web.archive.org/web/20190908211420/http://crystal.flack.ch/dox/sh5092.pdf |archive-date=8 September 2019 |journal=Acta Crystallographica, Section A |volume=65 |issue=5 |pages=371–389 |doi=10.1107/S0108767309024088 |pmid=19687573 |bibcode=2009AcCrA..65..371F |access-date=13 February 2025}}
• {{cite book |last1=Fock |first1=Andreas |title=An introduction to chemical crystallography |editor-last1=Pope |editor-first=William J. |date=1895 |publisher=Clarendon Press |location=Oxford |url=https://babel.hathitrust.org/cgi/pt?id=mdp.39015058461206&seq=9 |access-date=16 June 2025}}
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• {{cite book |last1=Groth |first1=P. |title=An introduction to chemical crystallography |date=1906 |translator-last1=Marshall |translator-first1=Hugh |publisher=Gurney & Jackson |location=London |url=https://wellcomecollection.org/works/hfyh69vg/items?canvas=7 |access-date=6 June 2025}}
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• {{cite journal |last=Hales |first=Thomas C. |date=2006 |title=Historical Overview of the Kepler Conjecture |url=http://link.springer.com/10.1007/s00454-005-1210-2 |journal=Discrete & Computational Geometry |volume=36 |issue=1 |pages=5–20 |doi=10.1007/s00454-005-1210-2 |issn=0179-5376}}
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• {{cite book |last1=Haüy |first1=René-Just |title=Traité de Minéralogie |trans-title=Mineralogical treatise |date=1801 |publisher=Chez Louis |location=Paris |volume=1–5 |url=https://gallica.bnf.fr/ark:/12148/bpt6k9760845h/f13.item |access-date=8 January 2025 |language=French}}
• {{cite journal |last1=Haüy |first1=René-Just |date=1 April 1808 |title=Sur l'arragonite |trans-title=On aragonite |journal=Journal des Mines |volume=23 |issue=136 |pages=241–270 |url=https://www.annales.org/archives/annales/1808-1/126-140.pdf |access-date=16 June 2025 |language=French}}
• {{cite book |last1=Haüy |first1=René Just |title=Traité de cristallographie |trans-title=Crystallographic treatise |date=1822 |publisher=Bachelier |location=Paris |url=https://archive.org/details/traitdecristal00ha/page/8/mode/2up |url-access=registration |access-date=7 January 2025 |language=French}}

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• {{cite book |last1=Hooke |first1=Robert |title=Micrographia |date=1665 |publisher=The Royal Society |location=London |url=https://archive.org/details/mobot31753000817897/page/n1/mode/2up |access-date=7 May 2025}}
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• {{cite book |last1=Hooykaas |first1=R. |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |date=1981 |publisher=Charles Scribner's & Sons |location=New York |isbn=0684169681 |pages=520–524 |url=https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/rome-de-l |access-date=8 February 2025 |archive-url=https://archive.org/details/dictionaryofscie1112gill/page/n539/mode/2up |archive-date=24 October 2011 |chapter=Romé De L’Isle, Jean-Baptiste Louis |volume=11 |url-status=live}}
• {{cite book |last1=Hünefeld |first1= F. L. |title=Der Chemismus in der thierischen Organisation |trans-title=Chemical Properties in Animal Organization |location=Leipzig |publisher=F. A. Brockhaus |year=1840 |url=https://archive.org/details/b21710478/page/160/mode/2up |access-date=5 June 2025 |language=German}}
• {{cite book |last1=Huyghens |first1=Christiaan |title=Traité de la lumière |trans-title=Treatise on light |date=1690 |publisher=Pieter van der Aa |location=Leiden |url=https://archive.org/details/bub_gb_kVxsaYdZaaoC/page/n105/mode/2up |access-date=10 February 2025 |language=French}}

• {{cite book |last1=Jaeger |first1=Francis Mauritius |title=Lectures on the principle of symmetry and its applications in all natural sciences |date=1920 |publisher=Elsevier |location=Amsterdam |edition=2nd |url=https://archive.org/details/lecturesonprinci00jaegrich/page/n5/mode/2up |access-date=6 February 2025}}
• {{cite book |last1=Jorpes |first1=J. Erik |title=Jac. Berzelius: his life and work |date=1966 |publisher=Almqvist & Wiksell |location=Stockholm}}

• {{cite journal |last1=Kahr |first1=Bart |last2=McBride |first2=J. Michael |title=Optically Anomalous Crystals |journal=Angewandte Chemie International Edition in English |date=January 1992 |volume=31 |issue=1 |pages=1–26 |doi=10.1002/anie.199200013}}
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• {{cite journal |last1=Kauffman |first1=George B. |last2=Myers |first2=Robin D. |title=Pasteur's Resolution of Racemic Acid: A sesquicentennial Retrospect and a New Translation |journal=The Chemical Educator |date=December 1998 |volume=3 |issue=6 |pages=1–4 |url=http://192.129.24.144/licensed_materials/00897/papers/0003006/36kau897.pdf |access-date=13 February 2025 |doi=10.1007/s00897980257a|archive-url=https://web.archive.org/web/20060117144722/http://192.129.24.144/licensed_materials/00897/papers/0003006/36kau897.pdf |archive-date=17 January 2006 }}
• {{cite book |last1=Keen |first1=Robin |editor1-last=Buttner |editor1-first=Johannes |title=The life and works of Friedrich Wöhler (1800–1882) |date=2005 |publisher=Traugott Bautz |location=Nordhausen |isbn=9783883092249 |url=https://content.bautz.de/neuerscheinungen-2005/pdf/9783883092249.pdf |access-date=28 February 2025}}
• {{cite journal |last1=Kelker |first1=H. |title=History of Liquid Crystals |journal=Molecular Crystals and Liquid Crystals |date=January 1973 |volume=21 |issue=1–2 |pages=1–48 |doi=10.1080/15421407308083312|bibcode=1973MCLC...21....1K }}
• {{cite journal |last1=Kelker |first1=H. |title=Survey of the Early History of Liquid Crystals |journal=Molecular Crystals and Liquid Crystals Incorporating Nonlinear Optics |date=December 1988 |volume=165 |issue=1 |pages=1–43 |doi=10.1080/00268948808082195|bibcode=1988MCLCI.165....1K }}
• {{cite journal |last1=Kelker |first1=Hans |last2=Knoll |first2=Peter M. |title=Plenary Lecture. Some pictures of the history of liquid crystals |journal=Liquid Crystals |date=July 1989 |volume=5 |issue=1 |pages=19–42 |doi=10.1080/02678298908026350|bibcode=1989LoCr....5...19K }}
• {{cite book|last1=Kepler |first1=Johannes |title=Strena seu de Nive Sexangula |trans-title=A New Year's Gift of Hexagonal Snow|date=1611 |publisher=G. Tampach |location=Frankfurt |language=Latin |url=https://archive.org/details/ioanniskepleriss00kepl/page/n21/mode/2up}}
• {{cite book|last1=Kepler |first1=Johannes |title=The Six-Cornered Snowflake |date=1966 |editor-last1=Hardie |editor-first1=Colin |publisher=Oxford University Press |location=Oxford |isbn=978-0-19-858120-8 |url=https://archive.org/details/sixcorneredsnowf0000joha |url-access=registration |access-date=24 February 2025}}
• {{cite book |last1=Korbel |first1=Petr |editor1-last=Höck |editor1-first=Volker |editor2-last=Koller |editor2-first=Friedrich |title=125 Jahre Knappenwand; Proceedings of a Symposium held in Neukirchen am Großvenediger (Salzburg/Austria) September 1990 |date=1993 |publisher=Geologische Bundesanst |location=Wien |isbn=3-900312-85-0 |pages=159–161 |chapter-url=https://www.zobodat.at/pdf/AbhGeolBA_49_0159-0161.pdf |access-date=16 June 2025 |chapter=To the 100th Anniversary of the Death of Victor Leopold Ritter von Zepharovich}}
• {{cite journal |last1=Kostyanovsky |first1=Remir G. |title=Louis Pasteur did it for us especially |journal=Mendeleev Communications |date=January 2003 |volume=13 |issue=3 |pages=85–90 |doi=10.1070/mc2003v013n03abeh001828}}
• {{cite journal |last1=Kraus |first1=Edward H. |title=Haüys contribution to our knowledge of isomorphism |journal=The American Mineralogist |date=1918 |volume=3 |issue=6 |pages=126–130 |url=http://www.minsocam.org/msa/collectors_corner/arc/hauyvi.htm |access-date=16 May 2025}}
• {{cite journal |last1=Kubbinga |first1=Henk |title=Crystallography from Haüy to Laue: controversies on the molecular and atomistic nature of solids |journal=Zeitschrift für Kristallographie |date=January 2012 |volume=227 |issue=1 |pages=1–26 |doi=10.1524/zkri.2012.1459|bibcode=2012ZK....227....1K }}
• {{cite book |last1=Kuhn |first1=Thomas S. |title=The Structure of Scientific Revolutions |authorlink=Thomas Kuhn |year=1962 |publisher=University of Chicago Press |edition=1st |lccn=62019621}}
• {{cite journal |last1=Kunz |first1=George F. |title=The life and work of Haüy |journal=The American Mineralogist |date=1918 |volume=3 |pages=60–89 |url=http://www.minsocam.org/msa/collectors_corner/arc/hauyii.htm |access-date=8 February 2025}}

• {{cite book |last1=Ladd |first1=Marcus Frederick Charles |title=Symmetry of crystals and molecules |date=2014 |publisher=Oxford University Press |location=Oxford |isbn=9780199670888 |pages=13–15}}
• {{cite journal |last1=Lagerwall |first1=Sven T. |title=On some important chapters in the history of liquid crystals |journal=Liquid Crystals |date=December 2013 |volume=40 |issue=12 |pages=1698–1729 |doi=10.1080/02678292.2013.831134|bibcode=2013LoCr...40.1698L }}
• {{cite journal |last1=Lalena |first1=John N. |title=From quartz to quasicrystals: probing nature's geometric patterns in crystalline substances |journal=Crystallography Reviews |date=April 2006 |volume=12 |issue=2 |pages=125–180 |doi=10.1080/08893110600838528|bibcode=2006CryRv..12..125L }}
• {{cite web |last1=Laszlo |first1=Pierre |title=Ampère and the "Representative Shape" of Molecules |url=http://www.bibnum.education.fr/chimie/theorie-chimique/lettre-d-ampere-berthollet |website=bibnum |access-date=5 May 2025 |date=2010}}
• {{cite journal |last1=Le Bel |first1=J. A. |title=Sur les relations qui existent entre les formules atomiques des corps organiques, et le pouvoir rotatoire de leurs dissolutions |journal=Bulletin de la Société chimique de Paris |date=1874 |volume=22 |pages=337–347 |url=https://babel.hathitrust.org/cgi/pt?id=hvd.hc1j13&seq=351 |access-date=3 June 2025 |trans-title=On the relations that exist between the atomic formulas of organic compounds and the rotary power of their solutions |language=French}}
• {{cite book |last1=Le Bel |first1=J. A. |editor1-last=Benfy |editor1-first=O. T. |title=Classics in the Theory of Chemical Combinations |date=1963 |publisher=Dover |location=New York |chapter=On the relations that exist between the atomic formulas of organic compounds and the rotary power of their solutions |pages=161–171 |chapter-url=https://archive.org/details/classicsintheory0000unse/page/160/mode/2up |access-date=17 June 2025}}
• {{cite journal |last1=Lehmann |first1=O. |title=Über fliessende Krystalle |journal=Zeitschrift für Physikalische Chemie |date=1889 |volume=4 |issue=1 |pages=462–472 |doi=10.1515/zpch-1889-0434 |url=https://archive.org/details/zeitschriftfurp10hoffgoog/page/462/mode/2up |access-date=24 April 2025 |trans-title=On flowing crystals |language=German |s2cid=92908969}}
• {{cite book |last1=Lehmann |first1=O. |title=Flüssige Kristalle sowie Plastizität von Kristallen im allgemeinen, molekulare Umlagerungen und Aggregatzustandsänderungen |trans-title=Liquid crystals as well as plasticity of crystals in general, molecular replacements and changes in the state of aggregates |date=1904 |publisher=Verlag von Wilhelm Engelmann |location=Leipzig |url=https://archive.org/details/bub_gb_OfZaAAAAQAAJ/page/n1/mode/2up |access-date=2 May 2025 |language=German}}
• {{cite journal |last1=Lehmann |first1=O. |title=Zur Geschichte der flüssigen Kristalle |journal=Annalen der Physik |date=January 1908 |volume=330 [25] |issue=5 |pages=852–860 |doi=10.1002/andp.19083300503 |bibcode=1908AnP...330..852L |url=https://archive.org/details/sim_annalen-der-physik_1908_25_5/page/852/mode/2up |access-date=3 May 2025 |trans-title=The history of liquid crystals |language=German}}
• {{cite book |last1=Lehmann |first1=O. |title=Crystals that flow: classic papers from the history of liquid crystals |date=2004 |pages=42–53 |publisher=Taylor & Francis |location=London; New York |isbn=9780415257893 |editor-last1=Sluckin |editor-first1=Tim |editor-last2=Dunmur |editor-first2=David |editor-last3=Stegemeyer |editor-first3=Horst |chapter=On flowing crystals |language=English}}
• {{cite book |last1=Leslie |first1=Esther |title=Liquid Crystals: The Science and Art of a Fluid Form |date=2016 |publisher=Reaktion Books |location=London |isbn=9781780236933 |pages=23–29 |edition=Ebook |url=https://books.google.com/books?id=ks8ZDgAAQBAJ&pg=PA23 |access-date=1 May 2025}}
• {{cite book |last1=Linnaeus |first1=Carl |title=A general system of nature |date=1806 |orig-date=1735 |volume=7 |publisher=Lackington, Allen, and Co. |location=London |url=https://archive.org/details/generalsystemna7linn/page/n9/mode/2up |access-date=9 May 2025}}

• {{cite journal |last1=M. |first1=H. A. |title=Prof. P. H. Von Groth, For. Mem. R.S. |journal=Nature |date=21 January 1928 |volume=121 |issue=3038 |pages=98–107 |doi=10.1038/121098a0 |bibcode=1928Natur.121...98H |ref={{sfnref|H.A.M.|1928}}}}
• {{cite book |last1=Macquer |first1=Pierre-Joseph |title=Dictionnaire de chymie |trans-title=Dictionary of chemistry |volume=1 |publisher=Laurent Durand |location=Paris |year=1766 |language=French |url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=8626805 |access-date=11 May 2025 |chapter=Aggrégation |pages=55–57}}
• {{cite book |last1=Macquer |first1=Pierre-Joseph |title=Dictionary of chemistry |volume=1 |publisher=Printed for T. Cadell, and P. Elmsly, in the Strand; J. Robson, in Bond-Street; and S. Bladon, in Paternoster Row |location=London |year=1771 |page=28 |chapter-url=https://archive.org/details/bim_eighteenth-century_a-dictionary-of-chemistr_macquer-pierre-joseph_1771_1/page/28/mode/2up |access-date=11 May 2025 |chapter=Aggregation |quote=By the integrant parts of a body are to be understood the smallest molecules or particles into which this body can be reduced without decomposition. We may conceive that a neutral salt, for instance common salt, may be divided into molecules still smaller and smaller, without separation of the acid and alkali which constitute the salt; so that these molecules, however small, shall always be common salt, and possessed of all its essential properties. If we should now suppose that these molecules are arrived at their utmost degree of smallness, so that each of them shall be composed of one atom of acid and of another atom of alkali, and that they cannot be further divided without a separation of the acid and the alkali, then these last molecules are those which Mr. Macquer in his Chemical Lectures calls primitive integrant molecules.}}
• {{cite book |last1=Malgrange |first1=Cécile |last2=Ricolleau |first2=Christian |last3=Schlenker |first3=Michel |title=Symmetry and Physical Properties of Crystals |date=2014 |publisher=Springer |location=Dordrecht |isbn=978-94-017-8992-9}}

• {{cite journal |last1=Mauskopf |first1=Seymour H. |title=Crystals and compounds: molecular structure and composition in nineteenth-century French science |date=July 1976 |journal=Transactions of the American Philosophical Society, New Series |volume=66 |issue=3 |pages=5–82 |doi=10.2307/1006279 |jstor=1006279 |isbn=0871696630 |url=https://archive.org/details/transactions-of-the-american-philosophical-society/TAPhS%2066%2C%203%20Seymour%20H.%20Mauskopf%20-%20Crystals%20and%20Compounds_Molecular%20Structure%20and%20Composition%20in%20Nineteenth-Century%20French%20Science/mode/2up|access-date=1 March 2025}}
• {{cite book |last1=Mauskopf |first1=Seymour |editor1-last=Busch |editor1-first=Kenneth L. |editor2-last=Busch |editor2-first=Marianna A. |title=Chiral analysis |date=2006 |publisher=Elsevier |location=Amsterdam Boston Heidelberg |isbn=978-0-444-51669-5 |pages=3–24 |chapter=A history of chirality |doi=10.1016/B978-044451669-5/50001-6}}
• {{cite web |last1=Mauskopf |first1=Seymour |title=Seeds to Symmetry to Structure: Crystallography and the Search for Atomic-Molecular Arrangement |url=https://xray-exhibit.scs.illinois.edu/keynoteLecture.php |website=Crystallography: Defining the Shape of Our Modern World |publisher=University of Illinois at Urbana-Champaign |access-date=7 May 2025 |date=30 April 2012}}
• {{cite journal |last1=Mauskopf |first1=Seymour H. |title=William Barlow and the Determination of Atomic Arrangement in Crystals: Essay in Honour of Alan J. Rocke |journal=Annals of Science |date=3 April 2015 |volume=72 |issue=2 |pages=206–223 |doi=10.1080/00033790.2015.1007524|pmid=26104165 }}
• {{cite journal |last1=Melhado |first1=Evan M. |title=Mitscherlich's Discovery of Isomorphism |journal=Historical Studies in the Physical Sciences |date=1 January 1980 |volume=11 |issue=1 |pages=87–123 |doi=10.2307/27757472|jstor=27757472 }}
• {{cite book |last1=Melhado |first1=Evan M. |title=Jacob Berzelius: the emergence of his chemical system |date=1981 |publisher=Almqvist & Wiksell |location=Stockholm |isbn=91-85286-21-4 |url=https://archive.org/details/jacobberzeliusem0000melh/page/n5/mode/2up |access-date=25 April 2025}}
• {{cite book |last1=Metzger |first1=Hélène |title=La Gènese de la Science de Cristaux |trans-title=The genesis of the science of crystals |year=1969 |orig-year=1918 |publisher=Albert Blanchard |location=Paris |pages=67–68 |url=https://gallica.bnf.fr/ark:/12148/bpt6k260731/f66.item |url-status=live |archive-url=https://archive.org/details/metzger-helene-la-genese-de-la-science/page/67/mode/2up |archive-date=2 October 2021 |language=French |access-date=8 January 2025}}
• {{cite journal |last1=Minnigerode |first1=B. |title=Untersuchungen über die Symmetrieverhältnisse und die Elasticität der Krystalle |trans-title=Investigation of the symmetry relations and elasticity of the crystal |journal=Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen |year=1884 |pages=374–384 |url=http://eudml.org/doc/180034 |access-date=30 March 2025 |language=German}}
• {{cite journal |last1=Minnigerode |first1=B. |title=Ueber Wärmeleitung in Krystallen |trans-title=About heat conduction in crystals |journal=Neues Jahrbuch für Mineralogie, Geologie und Paläontologie |year=1886 |volume=1 |pages=1–13 |url=https://archive.org/details/neuesjahrbuchfrm18861leon/page/n25/mode/2up |access-date=21 March 2025}}
• {{cite journal |last1=Minnigerode |first1=B. |title=Untersuchungen über die Symmetrieverhältnisse der Krystalle |trans-title=Investigation of the symmetry relations of the crystal |journal=Neues Jahrbuch für Mineralogie, Geologie und Paläontologie |year=1887 |volume=5 |pages=145–166 |url=https://archive.org/details/neuesjahrbuchfr83unkngoog/page/144/mode/2up |access-date=21 March 2025}}
• {{cite journal |last1=Mitov |first1=Michel |title=Liquid-Crystal Science from 1888 to 1922: Building a Revolution |journal=ChemPhysChem |date=19 May 2014 |volume=15 |issue=7 |pages=1245–1250 |doi=10.1002/cphc.201301064|pmid=24482315 |url=https://hal.science/hal-01764620 }}
• {{cite journal |last1=Mitscherlich |first1=E. |title=Ueber die Krystallisation der Salze, in denen das Metall der Basis mit zwei Proportionen Sauerstoff verbunden ist |trans-title=About the crystallisation of salts in which the base metal is connected with two proportions of oxygen |journal=Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin |year=1819 |pages=427–437 |url=https://play.google.com/store/books/details/Mitscherlich_Eilhard_Ueber_die_Krystallisation_der?id=SyRs2RswQ58C&pli=1 |access-date=20 March 2025 |language=German |archive-url=https://archive.org/details/abhandlungenderp18akad/page/426/mode/2up |archive-date=12 January 2019}}
• {{cite journal |last1=Mitscherlich |first1=E. |title=Sur la Relation qui existe entre la forme cristalline et les proportions chimique. IIme Mémoire: Sur les Arséniates et les Phosphates |trans-title=On the relationship between crystalline form and chemical proportions. Second memoir on arsenates and phosphates |journal=Annales de chimie et de physique |year=1821 |volume=19 |pages=350–419 |url=https://gallica.bnf.fr/ark:/12148/bpt6k6571078m/f356.item |access-date=9 June 2025 |language=French}}
• {{cite journal |last1=Mitscherlich |first1=E. |title=Sur la rapport qui existe entre la forme cristalline et les proportions chimique. IIIme Mémoire: Sur les corps qui affectent deux formes cristallines différentes |trans-title=On the relationship between crystalline form and chemical proportions. Third memoir on bodies that affect two different crystalline forms |journal=Annales de chimie et de physique |year=1823 |volume=24 |pages=264–280 |url=https://gallica.bnf.fr/ark:/12148/bpt6k65687889/f274.item |access-date=9 June 2025 |language=French}}
• {{cite journal |last1=Mitscherlich |first1=E. |title=Ueber das Verhältniss der Form der krystallisirten Körper zur Ausdehnung durch die Wärme |trans-title=On the relationship between the form of crystals and their expansion by heat |journal=Annalen der Physik |date=January 1824 |volume=77 [1] |issue=5 |pages=125–127 |doi=10.1002/andp.18240770507 |bibcode=1824AnP....77..125M |url=https://archive.org/details/sim_annalen-der-physik_1824_1/page/n137/mode/2up |access-date=24 March 2025 |language=German}}
• {{cite journal |last1=Mohs |first1=F. |date=1823 |title=On the crystallographic discoveries and systems of Weiss and Mohs |journal=The Edinburgh Philosophical Journal |volume=8 |pages=275–290 |url=https://archive.org/details/sim_edinburgh-philosophical-journal_october-01-1822-april-01-1823_8/page/274/mode/2up |access-date=7 February 2025 |quote=But the measurements, or rather the indications of the angles of Haüy, have, in so. many instances, been found incorrect, that we can no longer attach any certainty to their exactness}}
• {{cite journal |last1=Molčanov |first1=Krešimir |last2=Stilinović |first2=Vladimir |title=Chemical Crystallography before X-ray Diffraction |date=2014 |journal=Angewandte Chemie International Edition |volume=53 |issue=3 |pages=638–652 |pmid=24065378 |doi=10.1002/anie.201301319}}
• {{cite book |last1=Moore |first1=Paul B. |editor1-last=Lima-de-Faria |editor1-first=J. |title=Historical atlas of crystallography |date=1990 |publisher=Published for International Union of Crystallography by Kluwer Academic Publishers |location=Dordrecht ; Boston |isbn=079230649X |chapter=Brief history of chemical crystallography. I: Inorganic compounds |chapter-url=https://archive.org/details/historicalatlaso0000unse_p0f2/page/76/mode/2up |chapter-url-access=registration |pages=77–90|access-date=9 February 2025}}
• {{cite book |last1=Morse |first1=Edgar W. |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |volume=2 |date=1970 |publisher=Charles Scribner's Sons |location=New York |isbn=0-684-16963-0 |pages=451–454 |url=https://www.encyclopedia.com/people/science-and-technology/physics-biographies/david-brewster |access-date=24 April 2025 |archive-url=https://archive.org/details/dictionaryofscie02gill/page/450/mode/2up |archive-date=16 November 2010 |url-status=live |chapter=Brewster, David}}
• {{cite book |last1=Moser |first1=Tijmen Jan |last2=Robinson |first2=Enders A. |title=Walking with Christiaan Huygens: from Archimedes' influence to unsung contributions in modern science |date=2024 |publisher=Springer |location=Cham |isbn=978-3-031-46157-6 |pages=74–80 |chapter=Anisotropy and Ellipsoidal Wavelets |doi=10.1007/978-3-031-46158-3}}

• {{cite journal |last1=Neumann |first1=F. E. |title=Theorie der doppelten Strahlenbrechung, abgeleitet aus den Gleichungen der Mechanik |trans-title=Theory of double beam refraction, derived from the equations of mechanics |journal=Annalen der Physik |date=January 1832 |volume=101 |issue=7 |pages=418–454 |doi=10.1002/andp.18321010703 |bibcode=1832AnP...101..418N |url=https://archive.org/details/theoriederdoppe00wanggoog/page/n2/mode/2up |access-date=23 March 2025 |language=German}}
• {{cite web |title=Neumann's principle |url=https://dictionary.iucr.org/Neumann%27s_principle |website=Online Dictionary of Crystallography |publisher=International Union of Crystallography |access-date=20 March 2025 |ref={{sfnref|Neumann's principle}} |date=16 November 2017}}
• {{cite book |last1=Nicol |first1=James |title=Encyclopedia Britannica |date=1878 |pages=671–677 |edition=9th |publisher=Charles Scribner's Sons |location=New York |url=https://digital.nls.uk/encyclopaedia-britannica/archive/194413309 |access-date=10 June 2025 |chapter=Crystallography |volume=6}}

• {{cite journal |last1=Oldroyd |first1=D. R. |title=Some Neo-Platonic and Stoic Influences on Mineralogy in the Sixteenth and Seventeenth Centuries |journal=Ambix |date=1 November 1974 |volume=21 |issue=2–3 |pages=128–156 |doi=10.1179/000269874790223614}}
• {{cite journal |last1=Ollis |first1=W. D. |title=Models and molecules |journal=Proceedings of the Royal Institution of Great Britain |date=1972 |volume=45 |pages=1–31 |url=https://archive.org/details/proceedingsofroy0045unse/page/n11/mode/2up |access-date=6 May 2025}}
• {{cite journal |last1=Ostwald |date=1897 |first1=W. |title=Studien über die Bildung und Umwandlung fester Körper 1. Abhandlung: Übersättigung und Überkaltung |trans-title=Studies on the formation and transformation of solid bodies: over-saturation and over-cooling |journal=Zeitschrift für Physikalische Chemie |volume=22U |issue=1 |pages=289–330 |doi=10.1515/zpch-1897-2233 |url=https://commons.wikimedia.org/wiki/File:Wilhelm_Ostwald_-_Studien_%C3%BCber_die_Bildung_und_Umwandlung_fester_K%C3%B6rper.pdf |language=German}}

• {{cite journal |last1=Pasteur |first1=Louis |title=Mémoire sur la relation qui peut exister entre la forme cristalline et la composition chimique, et sur la cause de la polarisation rotatoire |journal=Comptes Rendus de l'Académie des Sciences de Paris |date=1848a |volume=26 |pages=535–538 |url=https://www.biodiversitylibrary.org/item/21163#page/545/mode/1up |trans-title=Memoir on the relationship which can exist between crystalline form and chemical composition, and on the cause of rotary polarization |language=French |archive-url=https://gallica.bnf.fr/ark:/12148/bpt6k2983p/f539.item |archive-date=15 October 2007}}
• {{cite journal |last1=Pasteur |first1=Louis | title=Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire |trans-title=On the relations that can exist between crystalline form, and chemical composition, and the sense of rotary polarization |date=1848b |url=https://books.google.com/books?id=gJ45AAAAcAAJ&pg=PA442 |journal=Annales de Chimie et de Physique, 3rd series |volume=24 |pages=442–459 |access-date=16 February 2025 |language=French}}
• {{cite book |last1=Pasteur |first1=Louis |title=Researches on the molecular asymmetry of natural organic products |date=1905 |orig-date=1860 |publisher=Alembic Club |location=Edinburgh |url=https://wellcomecollection.org/works/nrqmkuvh |access-date=24 April 2025 |ref={{sfnref|Pasteur|1860}}}}
• {{cite journal |last1=Paufler |first1=Peter |title=William Barlow's early publications in the 'Zeitschrift für Krystallographie und Mineralogie' and their influence on crystal structure research |journal=Zeitschrift für Kristallographie - Crystalline Materials |date=18 December 2019 |volume=234 |issue=11–12 |pages=769–785 |doi=10.1515/zkri-2019-0044}}
• {{cite book |last1=Pauling |first1=Linus |chapter=Historical Perspective |title=Structure and Bonding in Crystals |date=1981 |pages=1–12 |doi=10.1016/B978-0-12-525101-3.50007-3 |isbn=978-0-12-525101-3 |publisher=Academic Press |editor-last1=O'Keeffe |editor-first1=Michael |editor-last2=Navrotsky |editor-first2=Alexandra |volume=1}}
• {{cite book |last1=Phillips |first1=F. C. |title=An Introduction To Crystallography |date=1963 |publisher=John Wiley & Sons |location=New York |pages=12–14 |edition=3rd |url=https://archive.org/details/introductiontocr0000fcph/page/12/mode/2up |url-access=registration |access-date=8 January 2025}}
• {{cite web |title=Polymorphism |url=https://dictionary.iucr.org/Polymorphism |website=Online Dictionary of Crystallography |publisher=International Union of Crystallography |access-date=20 March 2025 |ref={{sfnref|Polymorphism}} |date=13 March 2018}}

• {{cite book |last1=Ramberg |first1=Peter J. |title=Chemical structure, spatial arrangement: the early history of stereochemistry, 1874-1914 |date=2003 |publisher=Ashgate |location=Aldershot, England ; Burlington, VT |isbn=0-7546-0397-0}}
• {{cite journal |last1=Reinitzer |first1=Friedrich |title=Beiträge zur Kenntniss des Cholesterins |journal=Monatshefte für Chemie |date=December 1888 |volume=9 |issue=1 |pages=421–441 |doi=10.1007/bf01516710 |url=https://www.biodiversitylibrary.org/page/7209119#page/195/mode/1up |access-date=24 April 2025 |trans-title=Contributions to the understanding of chloresterol |language=German |s2cid = 97166902 |archive-url=https://web.archive.org/web/20221104084215/https://www.biodiversitylibrary.org/part/232475 |archive-date=4 November 2022 |url-status=live}}
• {{cite journal |last1=Reinitzer |first1=Fr. |title=Zur Geschichte der flüssigen Kristalle |journal=Annalen der Physik |date=January 1908 |volume=332 [27] |issue=11 |pages=213–224 |doi=10.1002/andp.19083321111 |bibcode=1908AnP...332..213R |url=https://archive.org/details/sim_annalen-der-physik_1908_27_11/page/212/mode/2up |access-date=3 May 2025 |trans-title=The history of liquid crystals |language=German}}
• {{cite book |last1=Reinitzer |first1=Friedrich |title=Crystals that flow: classic papers from the history of liquid crystals |date=2004 |pages=26–41 |publisher=Taylor & Francis |location=London; New York |isbn=9780415257893 |editor-last1=Sluckin |editor-first1=Tim |editor-last2=Dunmur |editor-first2=David |editor-last3=Stegemeyer |editor-first3=Horst |chapter=Contributions to the understanding of chloresterol |language=English}}
• {{cite book |editor1-last=Richardson |editor1-first=George M. |title=The Foundations of Stereochemistry: Memoirs by Pasteur, Van't Hoff, Lebel, and Wislicenus |date=1901 |publisher=American Book Company |location=New York; Cincinnati; Chicago |url=https://archive.org/details/foundationsofste00richrich/page/n7/mode/2up |access-date=28 April 2025}}
• {{cite journal |last1=Riddell |first1=F. G. |last2=Robinson |first2=M. J. T. |title=J. H. van't Hoff and J. A. Le Bel—their historical context |journal=Tetrahedron |date=January 1974 |volume=30 |issue=13 |pages=2001–2007 |doi=10.1016/S0040-4020(01)97330-2}}
• {{cite web |last1=Robertson |first1=Edmund F. |last2=O'Connor |first2=John J. |title=The MacTutor History of Mathematics Archive: Biographies |url=https://mathshistory.st-andrews.ac.uk/Biographies/ |publisher=School of Mathematics and Statistics, University of St Andrews | access-date=27 February 2024 |ref={{sfnref|MacTutor}}}}
• {{cite book |last1=Rocke |first1=Alan J. |title=The quiet revolution: Hermann Kolbe and the science of organic chemistry |date=1993 |publisher=University of California press |location=Berkeley Los Angeles London |isbn=0-520-08110-2}}
• {{cite book |last1=Rocke |first1=Alan J. |title=Image and reality: Kekulé, Kopp, and the scientific imagination |date=2010 |publisher=The University of Chicago Press |location=Chicago |isbn=978-0-226-72332-7 |pages=228–260 |chapter=Dimensional Molecules}}
• {{cite book |last1=Romé de L'Isle |first1=Jean Baptiste Louis de |title=Essai de cristallographie: ou, Description des figures géométriques, propres à différens corps du regne minéral connus vulgairement sous le nom de Cristaux |trans-title=Crystallographic essay, or, Description of geometric figures, specific to different bodies of the mineral kingdom known vulgarly as crystals |date=1772 |publisher=Didot jeune |location=Paris |page=10 |url=https://archive.org/details/essaidecristall00lisgoog/page/n45/mode/2up |language=French |access-date=8 January 2025 |quote=Germs being inadmissible for explaining the formation of crystals, it is necessary to suppose that the integrant molecules of bodies have each, according to its own nature, a constant and determinate figure. [translation]}}
• {{cite book |last1=Romé de L'Isle |first1=Jean Baptiste Louis de |title=Cristallographie, ou, Description des formes propres à tous les corps du regne minéral |trans-title=Crystallography, or, Description of the forms specific to all bodies in the mineral kingdom |date=1783 |publisher=De l'imprimerie de Monsieur |location=Paris |url=https://archive.org/details/cristallographi01unkngoog/page/n4/mode/2up |language=French |access-date=8 January 2025}}
• {{cite journal |last1=Rouelle |first1=G.-F. |title=Sur la crystallisation du sel marin |journal=Histoire de l'Académie royale des sciences |date=1745 |pages=32–34 |url=https://gallica.bnf.fr/ark:/12148/bpt6k3543t/f39.item |access-date=11 May 2025 |trans-title=On the crystallization of sea salt |language=French}}
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• {{cite web |vauthors=((Science History Institute)) |title=Justus von Liebig and Friedrich Wöhler |url=https://www.sciencehistory.org/historical-profile/justus-von-liebig-and-friedrich-wohler |website=sciencehistory.org |date=June 2016 |access-date=28 February 2025}}
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• {{cite journal |last1=Scholz |first1=Erhard |title=The rise of Symmetry Concepts in the Atomistic and Dynamistic Schools of Crystallography, 1815-1830 |journal=Revue d'histoire des sciences |date=1989b |volume=42 |issue=1–2 |pages=110–112 |doi=10.3406/rhs.1989.4136 |url=https://www.persee.fr/doc/rhs_0151-4105_1989_num_42_1_4136 |access-date=20 January 2025}}
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• {{cite book |last1=Schütt |first1=Hans-Werner |title=Eilhard Mitscherlich, Baumeister am Fundament der Chemie |trans-title=Eilhard Mitscherlich, master builder of the foundation of chemistry |date=1992 |publisher=In Kommission bei R. Oldenbourg |location=München |isbn=3486262734 |url=https://archive.org/details/eilhardmitscherl0000schu/page/n5/mode/2up |access-date=28 February 2025 |language=German |url-access=registration}}
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• {{cite book |last1=Shenstone |first1=William Ashwell |title=Justus von Liebig, his life and work (1803–1873) |date=1901 |publisher=Cassell |location=London |url=https://archive.org/details/justusvonliebigh00shenrich/page/n9/mode/2up |access-date=28 February 2025}}
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• {{cite book |last1=Sluckin |first1=Tim |last2=Dunmur |first2=David |last3=Stegemeyer |first3=Horst |title=Crystals that flow: classic papers from the history of liquid crystals |date=2004 |publisher=CRC Press, Taylor & Francis Group |location=Boca Raton |isbn=978-0-415-25789-3}}
• {{cite journal |last1=Sohncke |first1=L. |title=Probable Nature of the Internal Symmetry of Crystals |journal=Nature |volume=29 |pages=383–384 |year=1884 |doi= 10.1038/029383a0 |issue=747 |bibcode =1884Natur..29..383S |s2cid=4072817}}
• {{cite journal |last1=Sollas |first1=W. |title=On the intimate structure of crystals. Parts I, II & III. Crystals of the cubic system with cubic cleavage |journal=Proceedings of the Royal Society of London |date=1898 |volume=63 |pages=270–300 |doi=10.1098/rspl.1898.0035}}
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• {{cite book |last1=Steno |first1=Nicolaus |title=The prodromus of Nicolaus Steno's dissertation concerning a solid body enclosed by process of nature within a solid |year=1916 |orig-year=1669 |translator-last1=Winter |translator-first1=John Garrett |publisher=The Macmillan Company |location=New York, London |page=272 |url=https://archive.org/details/prodromusnicola00stengoog/page/n128/mode/2up |access-date=9 January 2025 |language=English |quote=Figures 5 and 6 belong to the class of those which I could present in countless numbers to prove that in the plane of the axis both the number and the length of the sides are changed in various ways without changing the angles.}}
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• {{cite journal |date=1 July 1915 |title=The Evolution of the Goniometer |journal=Nature |volume=95 |issue=2386 |pages=564–565 |doi=10.1038/095564a0 |bibcode=1915Natur..95..564. |issn=1476-4687 |doi-access=free |ref={{SfnRef|The Evolution of the Goniometer|1915}}}}
• {{cite book |last1=Thomson |first1=William |title=Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light |date=1904 |publisher=C. J. Clay and Sons |location=London |pages=602–642 |chapter-url=https://archive.org/details/baltimorelecture00kelviala/page/602/mode/2up |access-date=6 May 2025 |chapter=On the molecular tactics of a crystal |quote=I call any geometric figure, or group of points, chiral and say it has chirality if its image in a plane mirror cannot be brought to coincide with itself.}}
• {{cite journal |last=Threlfall |first=T. |year=2003 |title=Structural and thermodynamic explanations of Ostwald's Rule |journal=Organic Process Research & Development |volume=7 |issue=6 |pages=1017–1027 |doi=10.1021/op030026l |issn=1083-6160}}
• {{cite book |last1=Tutton |first1=A. E. H. |title=Crystals |date=1911 |publisher=Kegan Paul, Trench, Trubner & Co. Ltd. |location=London |pages=70–97 |chapter-url=https://archive.org/details/crystals00tuttiala/page/70/mode/2up |access-date=25 April 2025 |chapter=The work of Eilhardt Mitscherlich and his discovery of isomorphism}}
• {{cite book |last1=Tutton |first1=A. E. H. |title=Crystallography and practical crystal measurement |date=1922 |publisher=Macmillan |location=London |volume=2 |url=https://archive.org/details/crystallographyp02tuttrich/crystallographyp02tuttrich/page/n7/mode/2up |access-date=6 May 2025}}

• {{cite book |last1=Usselman |first1=Melvyn C. |chapter=The Reflective Goniometer and its Impact on Chemical Theory |title=The History and Preservation of Chemical Instrumentation |editor-last1=Stock |editor-first1=J. T. |editor-last2=Orna |editor-first2=M. V. |date=1986 |pages=33–40 |doi=10.1007/978-94-009-4690-3_4|isbn=978-94-010-8585-4 }}
• {{cite book |last1=Usselman |first1=Melvyn C. |title=Pure intelligence: the life of William Hyde Wollaston |date=2015 |publisher=The University of Chicago Press |location=Chicago ; London |isbn=9780226245737}}

• {{cite book |last1=van 't Hoff |first1=J. H. |title=Voorstel tot uitbreiding der tegenwoordig in de scheikunde gebruikte structuur-formules in de ruimte; benevens een daarmee samenhangende opmerking omtrent het verband tusschen optisch actief vermogen en chemische constitutie van organische verbindingen |trans-title=Proposal to extend the structural formulas in space used today in chemistry; in addition to a related comment regarding the relationship between optical active power and chemical constitution of organic compounds |date=1874 |publisher=J. Greven |location=Utrecht |url=https://www.gutenberg.org/ebooks/66255 |access-date=3 June 2025 |language=Dutch}}
• {{cite book |last1=van 't Hoff |first1=J. H. |title=The arrangement of atoms in space |date=1898 |publisher=Longman, Green and Co. |location=London |url=https://archive.org/details/arrangementatom01werngoog/page/n5/mode/2up |access-date=3 June 2025}}
• {{cite journal |last1=Van Stanten |first1=R. A. |title=The Ostwald step rule |journal=Journal of Physical Chemistry |date=1 November 1984 |volume=88 |issue=24 |pages=5768–6769 |doi=10.1021/j150668a002 |url=https://pure.tue.nl/ws/files/1957949/591388.pdf |access-date=7 June 2025}}
• {{cite journal |last1=Vorländer |first1=D. |title=Ueber krystallinisch-flüssige Substanzen |journal=Berichte der Deutschen Chemischen Gesellschaft |date=January 1906 |volume=39 |issue=1 |pages=803–810 |doi=10.1002/cber.190603901126 |trans-title=On crystalline-liquid substances |language=German}}
• {{cite journal |last1=Vorländer |first1=D. |title=Einfluß der molekularen Gestalt auf den krystallinisch-flüssigen Zustand |journal=Berichte der Deutschen Chemischen Gesellschaft |date=March 1907 |volume=40 |issue=2 |pages=1970–1972 |doi=10.1002/cber.190704002101 |trans-title=Influence of molecular configuration on the crystalline-liquid state |language=German}}

• {{cite journal |last1=Wahl |first1=Walter |title=The relation between the crystal-symmetry of the simpler organic compounds and their molecular constitution.—Part I |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |date=2 June 1913 |volume=88 |issue=604 |pages=354–361 |doi=10.1098/rspa.1913.0036 |jstor=93436|bibcode=1913RSPSA..88..354W }}
• {{cite book |last1=Westfeld |first1=Christian Friedrich Gotthard |title=Mineralogische Abhandlungen |trans-title=Mineralogical Papers |date=1767 |publisher=J. C. Dieterich |location=Göttingen und Gotha |doi=10.3931/e-rara-50829 |url=https://www.e-rara.ch/zuz/doi/10.3931/e-rara-50829 |access-date=8 May 2025|language=German}}
• {{cite book |last1=Whewell |first1=William |title=History of the Inductive Sciences: From the Earliest to the Present Times |date=2011 |orig-date=1837 |publisher=Cambridge University Press |location=Cambridge |pages=191–197 |edition=Online |chapter=Prelude to the Epoch of De L'Isle and Haüy |doi=10.1017/cbo9780511734359.027 |isbn=978-1-108-01926-2 |quote=Nevertheless since there is here a principle of crystallization, the inclination of the planes and of the angles is always constant.}}
• {{cite web |title=Wilhelm Ostwald Biographical |url=https://www.nobelprize.org/prizes/chemistry/1909/ostwald/biographical/ |website=nobelprize.org |publisher=Nobel Media AB |access-date=17 June 2020 |ref={{sfnref|Wilhelm Ostwald Biography}}}}
• {{cite journal |last1=Wislicenus |first1=Johannes |title=Ueber die räumliche Anordnung der Atome in organischen Molekülen und ihre Bestimmung in geometrischisomeren ungesättigten Verbindungen |trans-title=On the spatial arrangement of atoms in organic molecules and their determination in geometrically isomeric unsaturated compounds |journal=Abhandlungen der Mathematisch-Physischen Classe der Königlich Sächsischen Gesellschaft der Wissenschaften |date=1887 |volume=14 |pages=1–78 |language=German |url=https://books.google.com/books?id=EJEKAAAAIAAJ&pg=PA1 |access-date=9 June 2025}}
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• {{cite journal |last1=Wohlwill |first1=Emil |title=Die Entdeckung des Isomorphismus. Eine Studie zur Geschichte der Chemie |journal=Zeitschrift für Völkerpsychologie und Sprachwissenschaft |date=1866 |volume=4 |pages=1–67 |url=https://archive.org/details/ZeitschriftFurVolkerpsychologie4/page/n15/mode/2up |access-date=24 April 2025 |trans-title=The discovery of isomorphism, a study in the history of chemistry |language=German}}
• {{cite journal |last1=Wollaston |first1=William Hyde |title=Description of a reflective goniometer |journal=Philosophical Transactions of the Royal Society of London |date=1809 |volume=99 |pages=253–258 |doi=10.1098/rstl.1809.0018 |url=https://archive.org/details/philtrans00599893 |access-date=5 June 2025}}
• {{cite journal |last1=Wollaston |first1=William Hyde |title=The Bakerian Lecture. On the elementary particles of certain crystals |journal=Philosophical Transactions of the Royal Society of London |date=31 December 1813 |volume=103 |pages=51–63 |doi=10.1098/rstl.1813.0008 |url=https://archive.org/details/s3id13528510/page/50/mode/2up |access-date=23 April 2025 |jstor=107387}}
• {{cite book |last1=Wyart |first1=Jean |editor1-last=Gillispie |editor1-first=Charles Coulston |title=Dictionary of scientific biography |date=1971 |publisher=Scribner |location=New York |isbn=0684169649 |pages=503–508 |url=https://www.encyclopedia.com/people/science-and-technology/physics-biographies/pierre-curie |access-date=27 February 2025 |archive-url=https://archive.org/details/dictionaryofscie0003unse/page/502/mode/2up |archive-date=23 February 2024 |chapter=Curie, Pierre |volume=3 |url-status=live}}

• {{cite news |last1=Zimmer |first1=Carl |date=12 June 2025 |title=Shining a Light on the World of Tiny Proteins |url=https://www.nytimes.com/2025/06/12/science/genes-dna-microproteins.html |work=New York Times |access-date=17 June 2025}}

{{refend}}

{{Crystallography|state=collapsed}}

Category:Crystallography

Category:History of chemistry

Category:History of crystallography