ISOMORPHISM, ISOSTENISM AND COVALENCE 247 



method of X-ray analysis, substances can now be studied in powdered form 

 so that we may hope to see whether in fact these two substances are iso- 

 niorphous. Other pairs of substances which may be isomorphous are potas- 

 sium chloride and calcium sulfide, potassium sulfide and calcium chloride, 

 cuprous sulfide and zinc chloride, etc. 



A still more interesting class of isomorphous substances which are pre- 

 dicted by the octet theory is that represented by sodium nitrate and calcium 

 carbonate. Since the nitrate and carbonate ions are isosteric we should 

 expect sodium nitrate and magnesium carbonate to be isomorphous, Na" 

 and Mg"^ being isosteric. As a matter of fact, both substances are given 

 by Groth as trigonal scalenohedral with the ratio of the axes 1 10.8297 and 

 1 : 0.8095, respectively. 



The practical identity in all the crystallographic properties of sodium 

 nitrate and calcium carbonate has long been known. In Mitscherlich's 

 early theory before clear ideas of valence were developed, no difficulty 

 was experienced in regarding these two substances as isomorphous and as 

 having similar structures. The theory of valence, however, gave formulas 



Ca< >C = O and Na — O — N^ 



so that they could no longer be regarded as of similar structure. It was 

 necessary either to abandon Mitscherlich's rule or to re-define isomorphism 

 so as to exclude cases of this kind. Therefore Kopp ^ and Retgers ^ re- 

 garded substances as isomorphous only when they are capable of forming 

 mixed crystals. This effectually eliminated such cases as sodium nitrate 

 and calcium carbonate because mixed crystals can naturally only be ob- 

 tained when the solubilities of the two substances are not too widely 

 different. The crystal form depends, of course, exclusively, on the arrange- 

 ment of the atoms and the electrons in them, while the ability to form 

 mixed crystals depends on both similarity of arrangement and on similarity 

 in the magnitude of the forces acting between the atoms. Thus Kopp 

 found a practical rule by which nearly all those cases inconsistent with the 

 ordinary valence theory, could be excluded. In order to be isomorphous in 

 Kopp's sense, two substances must have atoms which are not only linked 

 together in the same manner, but also have the same number of available 

 electrons in corresponding atoms. 



T. V. Barker,^ however, and a few other crystallographers have main- 

 tained that isomorphism should be used to denote similarity of crystal 

 form. Barker pointed out a great many new cases of isomorphism be- 



'Ber., 12,868 (1879). 



®Z. physik. Chem., 3, 497 (1889), and later papers in 1889 to 1896. 



' Trans. Chem. Soc, loi, 2484 (1912), 



