C411,(OH)(NO), 0.937:1:0.974 CaH4(NOh 0.943:1:0.538 0.954:1:0.733 The study of the changes which result in the crystal structures of different substances when certain atoms or atomic groups are re placed by others necessitates extremely accu rate physical and chemical determinations. A deeper insight into the results has been obtained by use of the so-called ratios* or "molecular distance" ratios of Muthmann, which may be explained as follows: In any space lattice the crystal elements a, Q, y, and a, b, c are theoretically the angles and relative lengths of the sides of the elementary parallelopipedon of the crystal structure, but the parameters a : b : c cannot be used directly for comparison between volumes of elementary parallelopipedons because in each such propor tion one term is unity and the ratio between the unities is not known.
The assumption, however, is that the volumes of the elementary parallelopipeda are directly as their molecular weights and inversely as their specific gravities and the quotient of the first by the second is called the molecular vol ume. By appropriate formulae the relative molecular volumes of different substances may be combined with their respective crystal ele ments and the topical parameters x: ob tained and the relative dimensions of the ele mentary parallelopipeda of different substances with the same type of space lattice compared term by term, thus making clear the changes which will be produced in any structure by the substitution of one element for another.
For instance, the rhombic series of isomor phous sulphates and selenates of potassium, rubidium and caesium exhibit the same forms and their corresponding angles vary less than one degree. The calculated topical ratios are: Kst304 3.8810 3.8754 4.9964 AboSO4 4.0340 4.0039 5.2366 Co.504 4.2187 4.1849 5.2366 1C,seo, 4.0291 4.0068 5.1171 RbvSe04 4.1672 4.1315 5.3461 CaSe04 4.34S7 4.3040 5.6058 From these Tutton concludes that one atom of sulphur or selenium lies between two of the alkali metal and all three extended in the direc tion of w because in passing from the sulphate of one metal to that of the next in the periodic classification or from selenate to selenate the principal change is the vertical direction w whereas in passing from sulphate to selenate of the same metal the horizontal directions X and IP are more changed.
Such a series as that mentioned, Tutton calls a Eutropic series, the interchangeable ele ments belonging to the same group in the periodic system, and in such a series the angles and the physical properties of the crystals are functions of the atomic weights of the inter changeable elements. He uses the term Iso morphous in a broad sense to include sub stances which bear some definite chemical anal ogy, crystallize in the same symmetry class, develop the same forms and differ in angles only by a few degrees, rarely over three.
Possibly the most important general result of the study of morphotropic changes is the proof that the atom has a definite place and exerts a definite influence on the structure, for this must be so if the substitution of one par ticular element for another produces a quanti tative and definitely oriented change in struc ture in whatever salt the substitution is made.
Polymorphism or Physical Isomerism.— That an element or compound may occur in two or more distinct crystalline forms was first observed by Mitscherlich in 1821, who found that by slowly cooling fused sulphur, mono clinic crystals were developed and that these on standing passed spontaneously, without again being fused, into the usual orthorhombic aystals.
This property, now known as polymorphism, was formerly attributed to a difference in the number of the chemical molecules in the so called physical molecules, but is now regarded as due to the existence of different positions of equilibrium in the homogeneous arrangement of the atoms, each position being most stable at a particular temperature.