[ULY IO, . I913] 



NATURE 



493 



facts have recently been brought forward by Barker 

 which tend to show that it will not hold in many 

 cases of inorganic substances. Barker, who has had 

 the good fortune to have worked in St. Petersburg 

 with von Fedorow for more than a year, shows that, 

 as the lecturer has always held, the true unit of 

 volume is the molecular or atomic volume, as deter- 

 mined for the particular substance itself. The molecular 

 volume is determinable by dividing the molecular 

 iveight of the substance by the specific gravity of its 

 en stals at a definite comparable temperature, such as 

 20° C, but the determination of the atomic volume 

 oilers peculiar difficulty, and so far only comparative 

 and indirect methods have been employed, chiefly by 

 Sollas. By taking the volumes of the spherical units 

 to be proportional to the atomic volumes (not those of 

 the element in the free state, as enormous compression 

 occurs on combination), and also determining the 

 amount of free interstitial space by comparative 

 methods of calculation, Sollas has achieved some re- 

 markable explanations of the crystallographic char- 

 acters of the two polymorphous forms of silver iodide 

 and of the three forms of titanium dioxide, rutile, 

 anatase, and brookite. It would not be surprising if 

 the valencv volumes of Barlow and Pope, in the cases 

 of those elements for which their theory appears to 

 work in a satisfactory' manner, turn out to be iden- 

 tical with the atomic volumes as determined by the 

 method of Sollas. As regards the compounds of 

 carbon and hydrogen, Barlow and Pope have been 

 most successful in accounting for crystallographic and 

 chemical relationships, and it is at least significant 

 that both Le Bas, from experimental work on the 

 molecular volumes of liquid hydrocarbons, and Traube 

 from an entirely different point of view, concur in 

 assigning th< relative volumes 4 and 1 to carbon and 

 hydrogen atoms in combination respectively. If 

 Traube 's results for carbon and hydrogen be 

 acccepted, so must also those for the relative 

 volumes of the atoms of the halogens, sulphur, 

 oxygen, and nitrogen, his values being : F=i ; CI, Br, 

 and 1=7 each; S = 6; = 2; and N = 3. As regards 

 oxygen and nitrogen, he agrees with Barlow and 

 Pope, but the latter take all the halogens as of unit 

 valency volume, and sulphur as of valency volume 2. 

 Barker shows that while in the binary sulphides, 

 such as zinc sulphide ZnS, the sulphur is probably 

 of volume 2, in the sulphates, such as K..SO, and 

 BaSO,, it is probably 6, as Traube insists; this con- 

 clusion is also in agreement with other work of Barker 

 on some extraordinary cases of isomorphism, includ- 

 ing that of barium sulphate with potassium per- 

 chlorate KCIO,, potassium permanganate KMnO t . 

 and the extraordinary compound potassium boro- 

 fluoride KBF,. 



While it would thus appear that the atomic volume 

 fin the substance itself, and including any interspace) 

 is the true effective volume concerned in crystal struc- 

 ture, and that it may be only a coincidence that, in 

 the cases of a few prominent elements, it happens to 

 be approximately proportional to the valencies of those 

 elements (as certainly appears to be true in the cases 

 of hydrogen and carbon, and possibly oxygen and 

 nitrogen), there is a very considerable amount of the 

 joint work of Barlow and Pope which is of permanent 

 value. Their explanations of the preponderating cubic 

 and hexagonal crystalline forms of the elements them- 

 selves, and of binary compounds such as ZnS, are 

 doubtless correct, and it will be of great interest, in 

 view of the next development to which attention must 

 be directed, to illustrate the case of zinc sulphide. 



Barlow and Pope's idea of the structure of zinc 

 blende, which merely assumes that the volumes of the 

 atoms of zinc and sulphur are approximately equal, is 

 NO. 2280,. VOL. 2l] 



that sixteen molecules ZnS gu lo form the grosser 

 unit of the crystal structure, the combined system or 

 space-lattice unit — that is, sixteen atoms of zinc and 

 sixteen of sulphur. Only one zinc or one sulphuratom 

 in every sixteen is sameways orientated, and if we 

 adopt von Groth's definition, we may give the struc- 

 ture of zinc blende as follows : — The crystals of zinc 

 blende consist of two interpenetrating regular point- 

 systems, one formed from zinc atoms, and the other 

 from sulphur atoms; each of these two point-systems 

 is built up from sixteen interpenetrating space-lattices, 

 each of the latter being formed from zinc atoms or 

 from sulphur atoms occupying parallel positions. All 

 the thirty-two space-lattices 

 of the combined system are ,--^~-"--^ — r-.-------j© 



geometrically identical. ^^~~l*^J^-~-~-"ii~'s* 



Barlow and Pope have i'\\/i \ / :'-'' ■' ' 

 shown that the space- j \ ,'-.• *•,•'' _,<*, . ; 



lattice in zinc blende is the ; >^ .'. / Q ' 'A '■ 

 third cubic one, in which a ; V, • jg .-' \j $ ; 

 point is situated at each '. / '^ ;-• -\ \\[ , ; 



cube corner and also in the ; ,' ,-','• ,-' \ ' ;"\\i 

 centre of each cube face. i/-^'--^---v>;--v c -ii-.- J J^ 

 For this is the space-lattice # : -------"-Y-VAv^-- ' 



corresponding to an assem- VlGi 4 ._ S p ace .iattice of centred- 

 blage of spheres of equal face cube, 



volume in closest pat Ic- 

 ing. The space-lattice in question is shown 

 on" the screen (Fig. 4), and a pair of models 

 of the arrangement are illustrated in the next 

 two pictures, *" in the first of which the points 

 are expanded into spheres of considerable size, and in 

 the second they appear still further expanded into 

 actual contact. "The third stage, in which the expan- 

 sion proceeds until all interstices are filled up and the 

 spheres are converted into polvhedra, is left to the 

 imagination. In the second picture (reproduced in 

 black and white in Fig. s) the mutual arrangement 



of the spheres of the two elements in zinc blende, 

 zinc and sulphur, is indicated by the yellow colouring 

 of the sulphur spheres and the grey tinting of those 

 of zinc. The tetrahedral mode of derivation of the 

 structure, accounting for the observed hemihedrism, 

 is also shown in another slide (Fig. 6). The eight 

 larger cubes which together form the grosser unit 

 are each supposed to be occupied by four smaller 

 cubes of the same element, arranged tetrahedrally, 

 and of zinc and of sulphur alternately in different 



