His findings were first published in a paper in 1773 [26] and a considerably
extended version appeared in the second volume of his Opuscula Physica et
Chemica in 1780 [27]. The introduction to Bergman’s paper gives a good indication
of his views on crystallography:
“Crystals are bodies which, though destitute of organic structure, yet externally resemble
geometrical figures, more or less regular. If we attend to the numerous collections of these,
we shall be ready to conclude, that nature has effectually eluded our research by the infinite
variety; for frequently bodies widely differing in their nature and properties resemble one
another in figure; and, on the contrary, those which are exactly alike in properties put on
external appearances entirely different; yet, upon a careful examination and comparison of
this variety of figures, we shall find, that a great number of them, though their surfaces differ
with respect to their angles and sides, may be derived from and referred to a very small
number of simple figures” [28].
Bergman’s approach was to use the rhombohedral calcite kernel as a primitive
form and stack thin lamella on its faces. First, Bergman used lamella of the same
size and form as the kernel faces and, in that manner, he arrived at the crystal form
of several crystals including garnet and hyacinth (yellow zircon; ZrO 2 ). Here,
Bergman went too far, as he did not pay close attention to the angles between the
crystal faces. Bergman’s system was only valid for crystals of the same symmetry
displaying different crystal habits,
3 such as the rhombohedral and scalenohedral
forms of calcite [24]; both belong to the trigonal system while garnets belong to the
cubic and zircon to the tetragonal systems, respectively. Inspired by his apparent
success, he also attempted to relate the hyacinth crystal to a cruciform interpenetrating twin
4 of staurolite (monoclinic system).
Next, Bergman applied lamella with the same form but with continuously
decreasing dimensions. By doing so, he correctly arrived at the scalenohedral
calcite form. So far, Bergman’s theory was based on the cleavage of crystals but the
next step, introduced in order to describe an even larger number of crystals based on
a common primitive form, was a purely geometrical construction: he now applied
truncated lamellae. Although Bergman, through his qualitative approach, tried to
relate unrelated crystals, his theory contained one important discovery: he could
relate the morphologically very different rhombohedral and scalenohedral forms of
calcite, and thus pointing in the direction of the basis for modern crystallography:
the unit cell.
In the extended 1780 version of the paper, Bergman had come across a work on
ice by French physicist and biologist Jean-Jacques d’Ortous de Mairan (1678–
1771), published in 1716. By observing striation (lines that form on the faces of
crystals; Fig. 25.2), de Mairan had concluded that crystals were built up by tiny
fibres arranging themselves into hollow pyramids. As the direction of these fibres
was not the same throughout the crystal, it would represent twinned crystals in
3
Due to different growth rates of different crystal faces, crystals may have different forms although
the atomic arrangements in the crystals are the same.
4
A twinned crystal is a crystal where crystal domains are related by a symmetry element not
described by the space group of the crystal.
350
25 Bergman’s Contributions to Mineralogy
extended version appeared in the second volume of his Opuscula Physica et
Chemica in 1780 [27]. The introduction to Bergman’s paper gives a good indication
of his views on crystallography:
“Crystals are bodies which, though destitute of organic structure, yet externally resemble
geometrical figures, more or less regular. If we attend to the numerous collections of these,
we shall be ready to conclude, that nature has effectually eluded our research by the infinite
variety; for frequently bodies widely differing in their nature and properties resemble one
another in figure; and, on the contrary, those which are exactly alike in properties put on
external appearances entirely different; yet, upon a careful examination and comparison of
this variety of figures, we shall find, that a great number of them, though their surfaces differ
with respect to their angles and sides, may be derived from and referred to a very small
number of simple figures” [28].
Bergman’s approach was to use the rhombohedral calcite kernel as a primitive
form and stack thin lamella on its faces. First, Bergman used lamella of the same
size and form as the kernel faces and, in that manner, he arrived at the crystal form
of several crystals including garnet and hyacinth (yellow zircon; ZrO 2 ). Here,
Bergman went too far, as he did not pay close attention to the angles between the
crystal faces. Bergman’s system was only valid for crystals of the same symmetry
displaying different crystal habits,
3 such as the rhombohedral and scalenohedral
forms of calcite [24]; both belong to the trigonal system while garnets belong to the
cubic and zircon to the tetragonal systems, respectively. Inspired by his apparent
success, he also attempted to relate the hyacinth crystal to a cruciform interpenetrating twin
4 of staurolite (monoclinic system).
Next, Bergman applied lamella with the same form but with continuously
decreasing dimensions. By doing so, he correctly arrived at the scalenohedral
calcite form. So far, Bergman’s theory was based on the cleavage of crystals but the
next step, introduced in order to describe an even larger number of crystals based on
a common primitive form, was a purely geometrical construction: he now applied
truncated lamellae. Although Bergman, through his qualitative approach, tried to
relate unrelated crystals, his theory contained one important discovery: he could
relate the morphologically very different rhombohedral and scalenohedral forms of
calcite, and thus pointing in the direction of the basis for modern crystallography:
the unit cell.
In the extended 1780 version of the paper, Bergman had come across a work on
ice by French physicist and biologist Jean-Jacques d’Ortous de Mairan (1678–
1771), published in 1716. By observing striation (lines that form on the faces of
crystals; Fig. 25.2), de Mairan had concluded that crystals were built up by tiny
fibres arranging themselves into hollow pyramids. As the direction of these fibres
was not the same throughout the crystal, it would represent twinned crystals in
3
Due to different growth rates of different crystal faces, crystals may have different forms although
the atomic arrangements in the crystals are the same.
4
A twinned crystal is a crystal where crystal domains are related by a symmetry element not
described by the space group of the crystal.
350
25 Bergman’s Contributions to Mineralogy