ISOMORPHISM, ISOSTENISM AND COVALENCE 251 



TABLE VII 

 Sulfates and Phosphates, Type 14 (c). Orthorhombic Bipyramidal 



a. b c. 



SrHPOi' 0.8581 I 1. 9431 



KHSO< 0.8609 > 1-9344 



Both substances form 8- or 4-sided plates parallel to c(ooi) with (iii) as the next 

 most important face. The plane of the optic axis is (001). 



4 like that of carbon in carbonates. In chlorates and nitrates the central 

 atom is supposed to have a valence of 5. By the octet theory, however, the 

 covalence of sulfur in normal sulfites is 3, while that of carbon in car- 

 bonates is 4. In chlorates the covalence of chlorine is 3, while in meta- 

 phosphates that of the phosphorus is 4. A great deal of effort has been 

 expended by chemists and crystallographers to prove cases of isomorphism 

 between nitrates and chlorates. Groth says that carbonates and sulfites 

 should be expected to be isomorphous and recommends that much more 

 work be done in a comparative study of these salts — especially he advises 

 attempting to prepare mixed crystals. -In spite of this effort and the belief 



TABLE VIII 



Selenates and Arsenates, Type 21. Orthorhombic Bipyramidal 



a. h. c. 



MnSe04.2H20 0.8849 i 0.9959 



FeAs04.2H20 0.8658 i 0.9541 



Plane of the optic axis (100) in both. 



* The measurements on SrHPOi and on CaHPOi given in Table VI were made by 

 Schulten, Bull. Soc. frang mineral 2j, 120 (1904). 



According to Groth the ratio of the axes for SrHPO* was found to be 

 0.6477:1:0.8581 and the only faces measured were (100), (133), (203), (130), (230), 

 (010). Groth states that the chosen orientation of the CaHPOi crystals was adopted 

 because of the relationships to those of SrHPO*. 



For the substance BaHPO* which Schulten finds to be orthorhqpibic he gives the 

 ratios 0.7133:1 :o.8ii7, and considers that these ratios are related to those given above 

 for SrHPOi (see Groth, p. 815) although the crystals are of "entirely different form." 

 These facts make it clear that Schulten chose for this orthorhombic crystal the axial 

 ratio a:h: '.0.6477 -.i simply to make this ratio agree with a:b: :o.6467:i which he had 

 obtained for the triclinic crystals of CaHP04 and which he supposed isomorphous with 

 SrHP04 notwithstanding that they belonged to a different crystal system. If we 

 multiply the a intercept 0.6477 by 3 and then interchange the a and c axes we obtain 

 the ratios given above in Table VII. The crystal faces which Schulten measured 

 should thus be denoted by (100), (in), (201), (no), (210), and (010) instead of the 

 absurd set of faces (100), (133), (203), (130), (230) and (010) given by Schulten. 

 There is thus ample internal evidence for making this change in Schulten's data. We 

 may conclude that there is no similarity in the ratios between the axes of the triclinic 

 CaHPOi, the orthorhombic SrHP04 and the orthorhombic BaHP04, but they repre- 

 sent 3 distinctly different crystal types. 



