October 6, 1923] 



NA TURE 



503 



a.s face development, etch figures, and the hke, is 

 discussed and finally dismissed as untrustworthy — 

 apparently on the sole ground that some crystals are 

 known to exhibit different geometrical symmetries 

 when grown or dissolved under different conditions. 



An examination of Wyckoff's and Tschermak's 

 japers would seem to leave no doubt concerning an 

 ~|tual clash between the two symmetries, but as 

 lyckoff's explanation is quite unacceptable I would 

 scuss it here and add a few suggestions, which may 

 itribute towards an eventual solution to a problem 

 great complexity. 

 [The question, whether symmetry of structure (there 

 no other real symmetry) can be deduced from sur- 

 :e observations, revolves round the following typical 

 3e, in which observations on etch figures can well be 

 lifted, for dissolution is the inverse of growth, 

 long the faces exhibited by a certain orthorhombic 

 Ibstance are those of a right tetrahedron, sometimes 

 nit not always accompanied by those of the corre- 

 ' I live left tetrahedron. In the former case the 

 -Ninmetry appears to be holoaxial, the crystal belong- 

 ing to the category of .enantiomorphous figures ; 

 while in the latter case the symmetry is apparently 

 holohedral, and the crystal is identical with its mirror 

 image. Even in the case of such apparently ambigu- 

 ous evidence the crystallographer believes he can 

 determine the correct symmetry of structure. 



In any crystal having the lower symmetry, similar 

 directions occur in sets of four, geometrically expres- 

 sible as normals to a tetrahedron. This offers a 

 simple structural interpretation of the observed fact 

 that if the conditions at the surface are suitable 

 for the appearance of one facet, the other three 

 are simultaneously developed. In other words, the 

 structure is controlling the surface. But the con- 

 ditions may simultaneously be favourable for a reveal- 

 ment by the structure of another set of morphogenetic 

 directions — with the production of the left tetrahe- 

 dron. The definitive choice of the lower symmetry 

 is still seen to afford a simple correlation between 

 structure and surface. Now consider the implication 

 of the selection of the higher symmetry, demanding 

 the structural subsistence of similar directions in 

 groups of eight instead of four. The simultaneous 

 appearance of the two tetrahedra is accounted for, 

 but not the occasional development of the right 

 tetrahedron alone (or alternatively of a left tetrahe- 

 dron alone, if this ever occurred). There is no longer 

 any simple explanation for a tetrahedral development, 

 as opposed to a development of four facets at one end 

 of the crystal (hemimorphic), or of three facets at one 

 end and the fourth at the other. The possibility of 

 'correlating form and structure vanishes just as utterly 

 ^ if the crystal were bounded by an irregular or 

 urved surface. 

 .\ow the above substance, like thousands of others, 

 lows no trace of curvature but obeys Haiiy's Laws of 

 \ mmetry and of Simple Multiple Intercepts. Some 

 rystals are, however, known which are partly bounded 

 iiy plane and partly by curved faces, and the question 

 naturally arises whether such curved boundaries 

 Imit of a simple structural interpretation. For- 

 mately, the invention of the two-circle goniometer 

 l>ormits of the exact exploration of a curved surface, 

 nul a recent observation in the Oxford laboratory may 

 now be put on record. A substance closely allied 

 to the one already discussed, in addition to plane facets 

 of negligible symmetry import, exhibits large curved 

 tracts arranged tetrahedrally. Moreover, there are 

 ' wo kinds of crystal, the curved tetrahedron of one 

 •ing the mirror image of that of the other. If the 

 r\'stals were mixed together, they could be separated 

 l>v hand. It is evident that the apparently irregular 



boundary of certain crystals is being reduced to the 

 same rule of law and order as is obeyed by the plane- 

 faced crystals of the text-books. 



Such results as the foregoing are held by a growing 

 body of X-ray workers to have no exact structural 

 implication, being contaminated, as it were, by the 

 non-crystalline influence of the surrounding fusion, 

 solution, or vapour. It therefore seems desirable to 

 press the argument home into the structure. Exactly 

 seventy-five years ago a young crystallographer was 

 examining a problem that had long vexed several 

 Academies of Science. The problem had in fact been 

 pronounced insoluble only three years previously, 

 but the tiny tetrahedral facets, occasionally observed 

 in certain crops of crystals and not in others (a fact I 

 know from experience), proved sodium ammonium 

 " racemate " to be an impostor, being in fact a 

 conglomerate of d- and /-tartrates. In this way 

 Pasteur showed there is something of unimpeachable 

 integrity on the surface of a crystal : something 

 which when properly interpreted can be made to found 

 a new province of a science dealing with liquids and 

 vapours. 



But this is not all. A later (as also an earlier, but 

 forgotten) advance in the classification of crystals led 

 to the recognition that out of thirty-two classes of 

 crystal symmetry, there are eleven enantiomorphous 

 classes : namely, the asymmetric class of the anorthic 

 system, the tartaric acid class of the monoclinic, the 

 Pasteur class of the orthorhombic, and two classes in 

 each of the rhombohedral, hexagonal, tetragonal and 

 cubic systems. It follows indubitably that every 

 substance which is optically active in solution belongs 

 to one of those classes. Happily, the most important 

 systems statistically are the first three mentioned, 

 and a recent count has shown that some 420 structures 

 (an isomorphous group being regarded as one struc- 

 ture), representing 93 per cent, of optically active 

 substances on the crystallographic record, are thus 

 definitely known as to their class of symmetry. There 

 are possibly two thousand more, lying indetermined 

 in the specimen cupboards of the chemist for want of 

 a crystallographer on the staff to examine them. 

 (Parenthetically, I would point out that Shearer's rule 

 could well be tested by an X-ray examination of those 

 substances, which in solution have a truly asymmetric 

 configuration. If, for example, the anorthic tetra- 

 hydrated acid strontium tartrate were found to 

 contain more than one molecule to the unit of structure 

 — or seignette salt more than four — the rule would be 

 infringed.) 



Unfortunately the Pasteur generalisation is not 

 applicable to all crystals, so that a careful examination 

 of the surface, eked out by a determination of certain 

 physical properties, is still demanded for the great 

 majority of substances, namely, those inactive in 

 solution and, owing to a certain limitation, those 

 which are only active in the crystalline condition. 



The above will, perhaps, be sufficient to show that 

 surface studies lead towards a real knowledge of 

 crystal symmetry, provided they are interpreted by 

 the principle of greatest common measure. In 

 individual cases the knowledge may not be complete 

 at the outset (every determination being in a sense 

 provisional). It may have to be modified with 

 accretion of evidence, in which connexion it is a liighly 

 significant fact that whenever there has been such a 

 modification in the past, as a result of a study of such 

 structure properties as pyro-electricity or optical 

 activity, the modification has always been towards a 

 lower symmetry, i.e. towards a symmetry which 

 experience proves might etjually well have been offered 

 (if only on one occasion) by the surface, if the crystal 

 had been grown or dissolved under a greater variety 



NO. 



2814, VOL. I 12] 



