Johann F. C. Hessel
Encyclopedia
Johann Friedrich Christian Hessel (27 April 1796 – 3 June 1872) was a German physician (MD, University of Würzburg, 1817) and professor of mineralogy (PhD, University of Heidelberg, 1821) at the University of Marburg.
(the field concerned with the structures of crystalline solids), for which Hessel's work was noteworthy, can be traced back to eighteenth and nineteenth century mineralogy
. Hessel also made contributions to classical mineralogy (the field concerned with the chemical compositions and physical properties of minerals), as well.
in Euclidean space
, since only two-, three-, four-, and six-fold rotation axes can occur. A crystal form here denotes a set of symmetrically equivalent planes with Miller indices
enclosed in braces, {hkl}; form does not mean "shape". For example, a cube-shaped crystal of fluorite
(referred to as Flussspath by Hessel) has six equivalent faces. The entire set is denoted as {100}. The indices for each of the individual six faces are enclosed by parentheses and these are designated: (010), (001), (100), (010), (001), and (100). The cube belongs to the isometric
or tessular class, as do an octahedron and tetrahedron. The essential symmetry elements of the isometric class is the existence of a set of three 4-fold, four 3-fold, and six 2-fold rotation axes. In the earlier classification schemes by the German mineralogists Christian Samuel Weiss (1780 - 1856)
and Friedrich Mohs (1773 - 1839)
the isometric class had been designated sphäroedrisch (spheroidal) and tessularisch (tesseral), respectively. As of Hessel's time, not all of the 32 possible symmetries had actually been observed in real crystals.
Hessel's work originally appeared in 1830 as an article in Gehler’s Physikalische Wörterbuch (Gehler’s Physics Dictionary). It went unnoticed until it was republished in 1897 as part of a collection of papers on crystallography in Oswald’s Klassiker der Exakten Wissenschaften (Ostwald’s Classics of the Exact Sciences). Prior to this posthumous re-publication of Hessel's investigations, similar findings had been reported by the French scientist Auguste Bravais (1811–1863)
in Extrait J. Math., Pures et Applique ́es (in 1849) and by the Russian crystallographer Alex V. Gadolin (1828 - 1892) in 1867.
Interestingly, all three derivations (Hessel's, Bravais', and Gadolin's), which established a small finite number of possible crystal symmetries from first principles, were based on external crystal morphology rather than a crystal's internal structural arrangement (i.e. lattice symmetry). However, the 32 classes of crystal symmetry are one-and-the-same as the 32 crystallographic point group
s. After seminal work on space lattices by Leonhard Sohncke (1842-1897), Arthur Moritz Schönflies (1853–1928), Evgraf Stepanovich Fedorov (1853–1919)
, and William Barlow (1845–1934), the connection between space lattices and the external morphology of crystals was espoused by Paul Niggli (1888 - 1953), particularly in his 1928 Kristallographische und Strukturtheoretische Grundbegriffe.[2] For example, the repetition, or translation (physics)
, of a lattice plane produces a stack of parallel planes, the last member of which may be manifested morphologically as one of the external faces of the crystal.
Briefly, a crystal is similar to three-dimensional wallpaper, in that it is an endless repetition of some motif (a group of atoms or molecules). The motif is created by point group operations, while the wallpaper, which is called the space lattice, is generated by translation of the motif with or without rotation or reflection. The symmetry of the motif is the true point group symmetry of the crystal and it causes the symmetry of the external forms. Specifically, the crystal's external morphological symmetry must conform to the angular components of the space group symmetry operations, without the translational components. Under favorable circumstances, point groups (but not space groups) can be determined solely by examination of the crystal morphology, without the need for analysis of an X-ray diffraction pattern. This is not always possible because, of the many forms normally apparent or expected in a typical crystal specimen, some forms may be absent or show unequal development. The word habit
is used to describe the overall external shape of a crystal specimen, which depends on the relative sizes of the faces of the various forms present. In general, a substance may crystallize in different habits because the growth rates of the various faces need not be the same.[2]
, Hessel also gave specific examples of compound crystals (aka double crystals) for which Euler's formula for convex polyhedra failed. In this case, the sum of the valence (degree)
and the number of faces does not equal two plus the number of edges (V + F ≠ E + 2). Such exceptions can occur when a polyhedron
possesses internal cavities, which, in turn, occur when one crystal encapsulates another. Hessel found this to be true with lead sulfide
crystals inside calcium fluoride
crystals. Hessel also found Euler's formula disobeyed with interconnected polyhedra, for example, where an edge or vertex is shared by more than two faces (e.g. as in edge-sharing and vertex-sharing tetrahedra
).[5]
feldspar
s could be considered solid solutions of albite
and anorthite
. His analysis was published in 1826 (Taschenbuch für die gesammte Mineralogie, 20 [1826], 289–333) but, as with his work on the crystal classes, it did not garner much attention among his contemporaries. Rather, the theory of the composition of these feldspars was subsequently credited to Gustav Tschermak (1836 - 1927)
in 1865.[1]
and subsequently studied science and medicine at Erlangen
and Würzburg
.[1] After receiving his PhD in mineralogy under Karl C. von Leonhard (1779–1862), Hessel went to the University of Marburg as an associate professor of mineralogy and became full professor in 1825. He remained there until his death.[1] Hessel was also a Marburg city council member and was named an honorary citizen of Marburg on November 9, 1840.
Deutsch Wikipedia: Online German Academic Dictionaries and Encyclopedias (http://de.academic.ru/dic.nsf/dewiki/858817)
Contributions to Mineralogy and Crystallography
The origins of geometric crystallographyCrystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
(the field concerned with the structures of crystalline solids), for which Hessel's work was noteworthy, can be traced back to eighteenth and nineteenth century mineralogy
Mineralogy
Mineralogy is the study of chemistry, crystal structure, and physical properties of minerals. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization.-History:Early writing...
. Hessel also made contributions to classical mineralogy (the field concerned with the chemical compositions and physical properties of minerals), as well.
Derivation of the Crystal Classes
In 1830, Hessel proved that, as a consequence of Haüy’s law of rational intercepts, morphological forms can combine to give exactly 32 kinds of crystal symmetryCrystal system
In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals...
in Euclidean space
Euclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...
, since only two-, three-, four-, and six-fold rotation axes can occur. A crystal form here denotes a set of symmetrically equivalent planes with Miller indices
Miller index
Miller indices form a notation system in crystallography for planes and directions in crystal lattices.In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written , and each index denotes a plane orthogonal to a direction in the...
enclosed in braces, {hkl}; form does not mean "shape". For example, a cube-shaped crystal of fluorite
Fluorite
Fluorite is a halide mineral composed of calcium fluoride, CaF2. It is an isometric mineral with a cubic habit, though octahedral and more complex isometric forms are not uncommon...
(referred to as Flussspath by Hessel) has six equivalent faces. The entire set is denoted as {100}. The indices for each of the individual six faces are enclosed by parentheses and these are designated: (010), (001), (100), (010), (001), and (100). The cube belongs to the isometric
Cubic crystal system
In crystallography, the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals....
or tessular class, as do an octahedron and tetrahedron. The essential symmetry elements of the isometric class is the existence of a set of three 4-fold, four 3-fold, and six 2-fold rotation axes. In the earlier classification schemes by the German mineralogists Christian Samuel Weiss (1780 - 1856)
Christian Samuel Weiss
Christian Samuel Weiss was a German mineralogist born in Leipzig. After graduation he was a physics instructor in Leipzig from 1803 until 1808...
and Friedrich Mohs (1773 - 1839)
Friedrich Mohs
Carl Friedrich Christian Mohs was a German geologist/mineralogist.- Career :Mohs, born in Gernrode, Germany, studied chemistry, mathematics and physics at the University of Halle and also studied at the Mining Academy in Freiberg, Saxony...
the isometric class had been designated sphäroedrisch (spheroidal) and tessularisch (tesseral), respectively. As of Hessel's time, not all of the 32 possible symmetries had actually been observed in real crystals.
Hessel's work originally appeared in 1830 as an article in Gehler’s Physikalische Wörterbuch (Gehler’s Physics Dictionary). It went unnoticed until it was republished in 1897 as part of a collection of papers on crystallography in Oswald’s Klassiker der Exakten Wissenschaften (Ostwald’s Classics of the Exact Sciences). Prior to this posthumous re-publication of Hessel's investigations, similar findings had been reported by the French scientist Auguste Bravais (1811–1863)
Auguste Bravais
Auguste Bravais was a French physicist, well known for his work in crystallography...
in Extrait J. Math., Pures et Applique ́es (in 1849) and by the Russian crystallographer Alex V. Gadolin (1828 - 1892) in 1867.
Interestingly, all three derivations (Hessel's, Bravais', and Gadolin's), which established a small finite number of possible crystal symmetries from first principles, were based on external crystal morphology rather than a crystal's internal structural arrangement (i.e. lattice symmetry). However, the 32 classes of crystal symmetry are one-and-the-same as the 32 crystallographic point group
Crystallographic point group
In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind...
s. After seminal work on space lattices by Leonhard Sohncke (1842-1897), Arthur Moritz Schönflies (1853–1928), Evgraf Stepanovich Fedorov (1853–1919)
Yevgraf Fyodorov
Yevgraf Stepanovich Fyodorov, sometimes spelled Evgraf Stepanovich Fedorov , was a Russian mathematician, crystallographer, and mineralogist....
, and William Barlow (1845–1934), the connection between space lattices and the external morphology of crystals was espoused by Paul Niggli (1888 - 1953), particularly in his 1928 Kristallographische und Strukturtheoretische Grundbegriffe.[2] For example, the repetition, or translation (physics)
Translation (physics)
In physics, translation is movement that changes the position of an object, as opposed to rotation. For example, according to Whittaker:...
, of a lattice plane produces a stack of parallel planes, the last member of which may be manifested morphologically as one of the external faces of the crystal.
Briefly, a crystal is similar to three-dimensional wallpaper, in that it is an endless repetition of some motif (a group of atoms or molecules). The motif is created by point group operations, while the wallpaper, which is called the space lattice, is generated by translation of the motif with or without rotation or reflection. The symmetry of the motif is the true point group symmetry of the crystal and it causes the symmetry of the external forms. Specifically, the crystal's external morphological symmetry must conform to the angular components of the space group symmetry operations, without the translational components. Under favorable circumstances, point groups (but not space groups) can be determined solely by examination of the crystal morphology, without the need for analysis of an X-ray diffraction pattern. This is not always possible because, of the many forms normally apparent or expected in a typical crystal specimen, some forms may be absent or show unequal development. The word habit
Crystal habit
Crystal habit is an overall description of the visible external shape of a mineral. This description can apply to an individual crystal or an assembly of crystals or aggregates....
is used to describe the overall external shape of a crystal specimen, which depends on the relative sizes of the faces of the various forms present. In general, a substance may crystallize in different habits because the growth rates of the various faces need not be the same.[2]
Exceptions to Euler's Formula for Convex Polyhedra
Following the work of the Swiss mathematician Simon Antoine Jean L'Huilier (1750 - 1840)Simon Antoine Jean L'Huilier
Simon Antoine Jean L'Huilier was a Swiss mathematician of French Hugenot descent...
, Hessel also gave specific examples of compound crystals (aka double crystals) for which Euler's formula for convex polyhedra failed. In this case, the sum of the valence (degree)
Degree (graph theory)
In graph theory, the degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice. The degree of a vertex v is denoted \deg. The maximum degree of a graph G, denoted by Δ, and the minimum degree of a graph, denoted by δ, are the maximum and minimum degree...
and the number of faces does not equal two plus the number of edges (V + F ≠ E + 2). Such exceptions can occur when a polyhedron
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
possesses internal cavities, which, in turn, occur when one crystal encapsulates another. Hessel found this to be true with lead sulfide
Lead(II) sulfide
Lead sulfide is an inorganic compound with the formula Pb. It finds limited use in electronic devices. PbS, also known as galena, is the principal ore and most important compound of lead....
crystals inside calcium fluoride
Calcium fluoride
Calcium fluoride is the inorganic compound with the formula CaF2. This ionic compound of calcium and fluorine occurs naturally as the mineral fluorite . It is the source of most of the world's fluorine. This insoluble solid adopts a cubic structure wherein calcium is coordinated to eight fluoride...
crystals. Hessel also found Euler's formula disobeyed with interconnected polyhedra, for example, where an edge or vertex is shared by more than two faces (e.g. as in edge-sharing and vertex-sharing tetrahedra
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
).[5]
Feldspar Composition
In the field of classical mineralogy, Hessel showed that the plagioclasePlagioclase
Plagioclase is an important series of tectosilicate minerals within the feldspar family. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a solid solution series, more properly known as the plagioclase feldspar series...
feldspar
Feldspar
Feldspars are a group of rock-forming tectosilicate minerals which make up as much as 60% of the Earth's crust....
s could be considered solid solutions of albite
Albite
Albite is a plagioclase feldspar mineral. It is the sodium endmember of the plagioclase solid solution series. As such it represents a plagioclase with less than 10% anorthite content. The pure albite endmember has the formula NaAlSi3O8. It is a tectosilicate. Its color is usually pure white, hence...
and anorthite
Anorthite
Anorthite is the calcium endmember of plagioclase feldspar. Plagioclase is an abundant mineral in the Earth's crust. The formula of pure anorthite is CaAl2Si2O8.-Mineralogy :...
. His analysis was published in 1826 (Taschenbuch für die gesammte Mineralogie, 20 [1826], 289–333) but, as with his work on the crystal classes, it did not garner much attention among his contemporaries. Rather, the theory of the composition of these feldspars was subsequently credited to Gustav Tschermak (1836 - 1927)
Gustav Tschermak von Seysenegg
Gustav Tschermak von Seysenegg was an Austrian mineralogist.-Biography:He was born 19 April 1836 in Littau, Olomouc District, Moravia and studied at the University of Vienna where he obtained a teaching degree. He studied mineralogy at Heidelberg and Tübingen and obtained a PhD...
in 1865.[1]
Early life and education
Little is documented about Hessel's early life. He was a student at the Realschule in NurembergNuremberg
Nuremberg[p] is a city in the German state of Bavaria, in the administrative region of Middle Franconia. Situated on the Pegnitz river and the Rhine–Main–Danube Canal, it is located about north of Munich and is Franconia's largest city. The population is 505,664...
and subsequently studied science and medicine at Erlangen
Erlangen
Erlangen is a Middle Franconian city in Bavaria, Germany. It is located at the confluence of the river Regnitz and its large tributary, the Untere Schwabach.Erlangen has more than 100,000 inhabitants....
and Würzburg
Würzburg
Würzburg is a city in the region of Franconia which lies in the northern tip of Bavaria, Germany. Located at the Main River, it is the capital of the Regierungsbezirk Lower Franconia. The regional dialect is Franconian....
.[1] After receiving his PhD in mineralogy under Karl C. von Leonhard (1779–1862), Hessel went to the University of Marburg as an associate professor of mineralogy and became full professor in 1825. He remained there until his death.[1] Hessel was also a Marburg city council member and was named an honorary citizen of Marburg on November 9, 1840.
External links
Complete Dictionary of Scientific Bibliography," Charles Scribner's Sons, 2008. (http://www.encyclopedia.com/doc/1G2-2830901983.html)Deutsch Wikipedia: Online German Academic Dictionaries and Encyclopedias (http://de.academic.ru/dic.nsf/dewiki/858817)