CRYSTAL - Cross and ovals with scenes of the Passion in rock crystal, work by Valerio De Belli of Vicenza (16th century) - Vatican, Christian Museum.
to establish his kingdom in Jerusalem with the twelve tribes reunited. His kingdom was to last 1,000 years, after which there would be the second resurrection, and then the just would be rewarded with eternal life and the wicked with eternal death (that is, with annihilation). This sect has about 4,000 adherents and has missions in Germany, France, Norway and in some other parts of Europe.
Cristaldi, Belisario. - Cardinal, b. in Rome on 11 July 1764, d. there on 25 Feb. 1831. Descended from a noble baronial family, he first studied literature and philosophy at the Roman College, then devoted himself to legal studies and graduated in both civil and canon law. For some time he practised law successfully, and after the occupation of Rome by Neapolitan troops he was appointed secretary of the Supreme State Commission. Chosen to be sent on a mission to Venice to the new pope Pius VII, upon his return he was enrolled among the advocates of the Consistorial Court.
During the French occupation he directed the orphanage of “Tata Giovanni.” Disliked by the French commander of Rome, he was transferred to Bologna and, after returning to Rome following the restoration, he was appointed by Pius VII as advocate of the treasury and of the Roman people. Having completed the
presumed life, both because in living beings the crystalline structure is the basis of many morphological dispositions, which, although not representing life, constitute its supposed material (v. Colloids; Protoplasm). The polyhedral form of crystals is not causal but a consequence of the growth rate, which varies with direction in a discontinuous manner, and this is due to a triperiodic ordering by which the atoms or ions that enter into the chemical constitution of the crystal are arranged.
The number and type of possible forms are regulated by symmetry rules and by the law of the rationality of indices.
A substance is isotropic with respect to a vectorial physical property (growth, solubility, cohesion, light refraction, magnetic susceptibility, etc.), if the value of said property remains constant in all directions; it is anisotropic if instead the value changes with direction in a continuous or discontinuous manner.
The solid state comprises two phases or modifications of matter: the crystalline phase and the amorphous phase. Crystalline substances are discontinuously anisotropic with respect to at least one vectorial physical property, and this character is clearly evidenced by different phenomena: formation of crystals, cleavage, etc. Amorphous substances (glasses, some colloids) are isotropic with respect to all vectorial physical properties, and therefore do not exhibit any of the aforementioned phenomena.
In seeking the cause that determines such different behaviour, it has been necessary to admit that it lies in a different structure which can be expressed as follows: amorphous substances are made up of leptons (a generic term to indicate atoms, ions, molecules) arranged in space without order. Crystalline substances, on the other hand, are made up of leptons ordered with regular periodicity in the three directions of space. Consider, in fact, a disordered set of molecules or atoms; a line passing through it will encounter, after a path very large compared to the dimensions of its constituents, a number of atomic particles independent of the direction; a disordered set is therefore isotropic because all directions are equivalent. If the same atoms or the same molecules are aligned in space with regular periodicity, some directions become denser than others and to the different densities there corresponds a different behaviour with respect to one or more physical properties; the ordered set must therefore be anisotropic.
The first hypothesis, organically developed, on the structure of crystals is due to Abbot R. J. Haüy (1743-1822). He had noted that some crystals, when broken, resolved into fragments which, however small, were not shapeless but small polyhedra of constant form for each species of mineral (cubic in rock salt, rhombohedral in calcite, octahedral in fluorite). From this he deduced that, even if subdivision could be carried down to particles of molecular size, these too would have to present the form of the cleavage polyhedron. Haüy had also noted that cleavage subdivision took place along planes always parallel to one another: he therefore formulated the hypothesis that crystals were constituted by the perfect contact juxtaposition of parallelepipedal molecules, called integral molecules, having the form of the cleavage solid.
The three forms that a rock salt crystal can assume may be supposed to derive one from the other by truncating edges and vertices with the removal of a decreasing number of rows in the successive layers of molecules; the rhombic dodecahedron, for example, can be derived from the cube by eliminating, for each edge, some rows of integral molecules, so that each edge is replaced by a new face.
The conception of a solid state characterized by polyhedral molecules in perfect contact with one another, without intermolecular voids, contrasted too openly with the principle of the compressibility of matter. The phenomenon of crystal anisotropy had therefore to be related not to the shape of the molecules but to the regular and periodic distribution of them in space. Reduced to this simpler expression, Haüy’s hypothesis allowed the conception of molecular shapes such as to permit the existence of intermolecular voids. To the hypothesis of regular and continuous structure there was therefore substituted that of regular and discontinuous structure, advanced by Seeber, Delafosse, and L. Frankenheim.
If we imagine concentrating the masses of the molecules at their equilibrium centres, the crystalline structure reduces to a set of points or nodes which repeat in space with the same periodicity as the molecules themselves; this ordered set is given the name of crystal or space lattice because the points are distributed in space like the nodes of a three-dimensional network. From the abstract space lattice we pass to the concrete crystalline structure by clothing the nodes with material particles (atoms, in the case of chemical elements, molecules or complexes of atoms in compounds). Establishing in how many ways the material particles repeat in a crystalline structure is equivalent to establishing what types of lattices are compatible with the morphological properties of crystals. Two nodes are said to be identical if the distribution of atomic masses around each of them is perfectly equal so that one can be considered as derived from the other by translation (parallel displacement) of a certain segment T. The nodes of a space lattice are all identical and the distance T between two nodes is constant for each bundle of parallel rows. A crystal lattice can therefore be decomposed into so many equal, contiguous and parallel parallelepipeds, and its geometric, physical and chemical properties are identifiable with those of one of these elementary parallelepipeds.
perfectly identical in such a way that one can be considered derived from the other by a translation (parallel displacement) of a certain segment T. The nodes of a spatial lattice are all identical, and the distance T between two nodes is constant for each bundle of parallel rows. A crystalline lattice can therefore be decomposed into many equal, contiguous, and parallel parallelepipeds, and its geometric, physical, and chemical properties can be identified with those of one of these elementary parallelepipeds.
The elementary parallelepiped, or fundamental cell, thus represents the smallest particle of crystalline substance that can be imagined, in the same way that the molecule represents the smallest quantity of a liquid or amorphous substance.
From the foregoing, it follows that the problem of defining the different possible types of lattices reduces to that of determining the possible types of elementary cells compatible with the morphological properties of crystals. A. Bravais, a student of Haüy, who was the first to systematically study spatial lattices, established that for crystals there are 14 possible types of elementary cells with sides parallel to the crystallographic axes.
Diffraction teaches that an ordered system of small material particles (diffraction lattice), struck by a thin beam of light, produces light rays that propagate, in addition to the direction of incidence, also in other directions; thus, a diffraction spectrum is obtained, consisting of a central luminous image, due to the rays propagating in the direction of incidence, surrounded by other images corresponding to the deviated rays. For the phenomenon to manifest, it is not enough for the diffracting bodies to have an ordered constitution; it is necessary that the dimensions of the individual material elements and the intervals separating them be of the same order of magnitude as the wavelengths of the incident beam. The atoms and the empty spaces they delimit, when in contact with each other, have dimensions on the order of a few Angstrom units (1 Å = 10^-8 cm.); to obtain diffraction spectra with crystals and thus provide experimental confirmation of the lattice theory, it was necessary to resort to wave radiations with wavelengths much smaller (about a thousand times) than those of light.
Max von Laue, a physicist at the University of Munich, guided by this principle, in 1912 conceived the idea of irradiating a rock salt crystal with X-rays, for which a wavelength of the order of magnitude of atomic particles was predicted.
The experiment, carried out with a very simple experimental device, fully confirmed the validity of the theory on the regular and discontinuous structure of crystals. Laue's experiment marks a very important date in the history of science, because it represents the starting point for new achievements in the field of morphological, physical, and chemical crystallography.
The English physicists W. L. Bragg and L. Bragg, father and son, in 1913, modifying Laue's experimental device, demonstrated that the effects of X-ray diffraction could also be considered as images reflected by layers of atoms, parallel to the possible faces of crystals, at certain angles of incidence (law of selective reflection).
Such an interpretation so simplified the analytical expression given by Laue that the two English physicists, starting from Bravais's theoretical premises, were able to indicate the way to establish the first criteria for determining crystalline structure.