Apkil 14, 1922] 



SCIENCE 



403 



TABLE I. 



Atomic and Ionic Kadii (X I''*) for the Halogens. 



line, and the molecular volumes of numerous 

 halogen-substituted compounds; for salts, the 

 molecular volumes of praeticalh^ all metal 

 halides, the volume change in solution, the 

 melting points, boiling points, latent heat of 

 vaporization, heat of formation and specific 

 compressibilities of the alkali halides and many 

 others, the percentage contraction for halides 

 of small cations, the distance between the cen- 

 ters of oppositely charged ions in crystals, and 

 the radii of ionic halogens. 



There are many interesting details of each 

 item in the above enumeration of which space 

 does not admit detailed consideration. For 

 example the percentage contraction undergone 

 when a salt is formed from the fi'ee elements, 

 is found in this work to be related in a funda- 

 mental way to the properties of the complex 

 compound formed from it. Thus when a 

 nickel halide is formed by the union of nickel 

 with any of the halogens (fluorine, chlorine, 

 bromine, or iodine) the percentage contraction 

 is the same (22.5 per cent.) in each of the four 

 cases. In the case of the cobalt and cupric 

 halides the magnitude of the contraction is not 

 quite constant, but increases slightly from the 

 fluoride to the iodide. The constancy of the 

 percentage contraction is also found when any 

 halogen is combined in turn with the alkali 

 metals (lithium, sodimn, potassium, and ru- 

 bidium). The contraction amounts to 60 per 

 cent, each for the four fluorides, 43 per cent. 

 each for the four chlorides, 38 per cent, each 

 for the four bromides, and 30 per cent, for 

 the four iodides. It is seen that the relative 

 contraction decreases with increasing number 

 of non-nuclear electrons in the halogen atom. 

 The contraction for the cfesium halides is 

 greater than that given above for the other 

 alkali halides. However in the oxy-aeid salts 

 caesium shows the same contraction as the other 

 salts of the alkalis, and in molten halides it is 



also perfectly normal as indicated by the care- 

 ful researches of Jaeger. The anomaly of 

 csBsium is therefore to be attributed to differ- 

 ence in crystal form. As a matter of fact 

 ca3sium halides possess cube-centered lattices, 

 while all other alkali halides are simple cubic. 



The ionic radii can be derived from experi- 

 mentally determined crystal distances only by 

 means of some assumption. The following 

 table shows the widely varying values, multi- 

 plied by 10^, which have been presented by 

 eight workers. 



It is a singular fact that in spite of the luide 

 discrepancies all of the values except those of 

 Richards are quite accurately linearly related 

 to the atomic volumes of the halogens at the 

 boiling point, showing that whatever basis of 

 calculation may be the closely similar halogens 

 are still related to each other in relatively the 

 same way. Richards' values are calculated 

 from the atomic volumes of chlorine, bromine 

 and iodine at 25° whei'e the three values are 

 practicallj' coincident, and this may explain 

 the deviations in this case. However the third 

 powers of the radii values, as direct functions 

 of the volumes of single combined atoms, are 

 found to be linearly related to gram-atomic vol- 

 umes. This is apparently of greater signifi- 



- From close-packing in crystals. 



3 From equality in size of ions with same num- 

 ber of external electrons: K+ = C1-, Kb+ =: Br-, 

 Cs+ :;= I-. 



* From viscosity of gaseous halogens, hence 

 radii of atoms. 



'' From various aspects of Bohr theory. Repre- 

 sents actual distance from nucleus to outermost 

 electron orbit. 



« From extrapolation of compressibility-con- 

 traction curve to zero compressibility. 



■? From empirical considerations of linearity to 

 molecular volumes, Zelt. anorg. allgem. Chem,., 

 120: 77 (December 14, 1921). 



