Moritz Ludwig Frankenheim


Moritz Ludwig Frankenheim was a German physicist, geographer, and crystallographer.

Life and education

Moritz Ludwig Frankenheim was born in 1801 in Brunswick. His family was Jewish. He attended the Gymnasium there and in Wolfenbüttel. Afterwards he went to Berlin to attend the Alma Mater Berolinensis to study physics. In 1823 he completed a dissertation titled Dissertatio de Theoria Gasorum et Vaporum Meditationes. Inspired by the research of his teacher Christian Samuel Weiss, he became interested in crystallography. In 1827 he moved to the University of Breslau, where he was assistant professor of physics, geography, and mathematics from 1827 to 1850. In 1850 he was promoted to the position of professor of these subjects. After his retirement, he first moved to Leipzig and then to Dresden, where he died in 1869 at the age of 67.

Work

Frankenheim's focus of research was crystallography, particularly studies of crystal structure and the mathematical and theoretical basis of the symmetry of crystals. By 1826, he was already using the integer reciprocals of Weiss' coefficients to describe the spatial positions of crystal surfaces, from which the British crystallographer William Hallowes Miller developed the concept of Miller indices in 1839.
By assigning symmetry elements to the crystal systems defined previously by Weiss and Friedrich Mohs, Frankenheim was able, for the first time, to define 32 point groups and to classify them into four crystal systems. He published this result in his 1826 paper "Crystallonomische Aufsätze".
Later, Frankenheim derived 15 lattice types for crystals, which were later reduced by Auguste Bravais to 14 and today are referred to as Bravais lattices. On pages 311-312 of his 1835 book Die Lehre von der Cohäsion, Frankenheim says that application of symmetry ideas shows that there are 15 crystal families, but in this book he doesn’t actually describe them. On page 15 of his 1842 treatise System Der Krystalle, however, he says – in reference to what he calls the Grundform of crystals – that “there are a total of fifteen, three of which are tesseral crystals, two are tetragonal, two are hexagonal, four are isoclinic, three belong to monoclinic and one to triclinic crystals.” All these are the correct numbers except the three for monoclinic, which should be two. Later, on page 102, he discusses monoclinic crystals in more detail. Frankenheim’s three monoclinic shapes correspond to what we today call primitive, body-centered, and end-centered monoclinic unit cells. The primitive cell describes the primitive monoclinic lattice, but the body-centered and end-centered monoclinic cells describe the same non-primitive lattice: the two different cells can be transformed into one another by a simple redefinition of one of the cell axes. Bravais got the number right in a paper he read to the French Academy of Sciences in 1848 and also gave a good discussion of why there are exactly 14 lattices. For these reasons we refer to them today as Bravais lattices. Bravais mentions in a footnote that Frankenheim in his 1842 treatise listed 3 “modes of the oblique prismatic system of Hauy” . Bravais goes on to say in the footnote that the last two of Frankenheim’s three modes are in fact identical. Interestingly, in 1856 Frankenheim revisited the question in a journal article, published in 1852.

Publications

  • Dissertatio de Theoria Gasorum et Vaporum Meditationes, Berlin 1823.
  • Crystallonomische Aufsätze, ISIS, Vol. 19, pp.,, Jena 1826.
  • Populäre Astronomie, Brunswick 1827.
  • De Crystallorum Cohäsione, Breslau 1829.
  • Die Lehre von der Cohäsion, umfassend die Elasticität der Gase, die Elasticität und Cohärenz der flüssigen und festen Körper und die Krystallkunde, Breslau 1835.
  • System der Krystalle, Breslau 1842.
  • Krystallisation und Amorphie, Breslau 1851.
  • Völkerkunde, Breslau 1852.
  • Ueber das Entstehen und das Wachsen der Krystalle nach mikroskopischen Beobachtungen, 1860.
  • Zur Krystallkunde. I. Characteristiken der Krystalle., Leipzig 1869.