1 88 



NATURE 



[August ii, 1910 



the liquid substance at the ordinary temperature, the liquid 

 mass is seen to immediately crystallise. This well-known 

 substance, hitherto known only in the liquid state at 

 ordinary temperatures, really exists in a more stable con- 

 dition as a crystalline solid. 



Many substances are capable of crystallising in two or 

 more distinct crystalline forms, of which one is, in general, 

 the more stable at any particular temperature. The 

 physical properties of the several crystalline modifications 

 of any one substance are quite distinct and characteristic 

 for the particular crystalline form, and in many instances 

 even the colours of the several modifications are different. 

 An example of this is afforded by pouring boiling water 

 into a beaker coated with cuprous mercuric iodide ; the 

 brilliant scarlet crystalline form, stable at ordinary 

 temperatures when heated in this way, becomes converted 

 into another crystalline modification which is nearly black. 

 The change is a reversible one, and the differences between 

 the properties of the two crystalline modifications are to 

 be attributed to diliferences in the mode of arrangement of 

 the molecules in the two cases ; the two modifications, in 

 fact, possess different crystalline structures. 



Although vast numbers of observations, such as the pre- 

 ceding, lead to the conclusion that crystals are arranged 

 structures, it is not essential that the crystal should be a 

 solid substance ; during recent years large numbers of 

 crystalline liquids have been discovered. On allowing 

 melted cholesteryl chloride to cool rapidly, a brilliant dis- 

 play of interference colours is seen, owing to the particles 

 of the substance assuming crystalline or orderly arrange- 

 ment, whilst still retaining the' liquid condition. 



Having very briefly reviewed some of the many reasons 

 for concluding that crystals are structured edifices, the 

 nature of the architecture which they exhibit may now be 

 considered. All the properties . of crystalline, solids 

 harmonise .with one simple assumption as to the manner 

 m which the parts of the structure are arranged; this 

 assumption is that the structure is a geometrically " homo- 

 geneous " one, that is, a structure the parts of which are 

 uniformly repeated throughout, corresponding points having 

 a similar environment everywhere within the edifice. The 

 assumption of geometrical homogeneity as the characteristic 

 of crystalline solids leads at once to the great problem 

 solved by the crystallographers of the nineteenth century. 

 This consisted in the inquiry as to how many types of 

 homogeneous arrangement of points in space are possible, 

 to the study of those types and to their identification, in 

 symmetry and other, respects, with the known systems into 

 which crystalline solids fall. This work was commenced 

 by the German crystallographer Frankenheim in 1830, and 

 completed by the English geometrician Barlow in 1894. 

 Briefly stated, the final conclusion has been attained that 

 230 geometrically homogeneous modes exist of distributing 

 material, or points representing material throughout space, 

 and that these 230 homogeneous types of structure, the 

 so-called homogeneous "point-systems," fall into the 

 lf"!!-^"'^° '-^'f"^' °' ^.^■"■"etry exhibited by crystalline solids. 

 Models of a number of homogeneous point-systems illus- 

 trating some of these types are exhibited. 

 ,.}}-. '*• however, obvious that the limitation of the possi- 

 bilities of solid crystalline arrangement to 230 types marks 

 but one stage in the determination of the nature of crystal 

 structure, and throws no direct light on the relation 

 between crystal structure and chemical constitution. 

 Although by the end of the nineteenth century we had 

 learnt that corresponding points of the units of 'crystalline 

 structures form homogeneous point-systems, the great 

 problem still remained of determining what are the entities 

 which become homogeneously arranged, for what reason 

 they become .so arranged, and in what way the conclusions 

 drawn by modern chemistry are reflected 'in crystal struc- 

 ture. _ This problem was a legacy to the twentie'th century, 

 and It now remains to indicate briefly the extent to which 

 "u- u r'^^" solved and the results of chemical importance 

 which have accrued during its investigation. 



The problem may be most easily visualised in connection 

 with some comparatively simple case, that, for instance, 

 presented by the crystalline forms assumed by the elements 

 themselves. It is generally admitted that 'an elementary 

 substance consists of identical atoms, each of which act's 

 as a centre of operation of attractive and repulsive forces. 



NO. 2128, VOL. 84] 



In a solid crystalline structure the atoms are obiously not 

 free to travel through the mass, each, if not indeed fi.xed 

 to a particular spot, being retained within a certain minute 

 domain ; each of these domains must be regarded as possess- 

 ing a centre which marks the mean position of the atom. 



The crystalline condition of an element may consequently 

 be defined as one of equilibrium between forces of attrac- 

 tion and repulsion emanating from or referable to a flock 

 of points homogeneously arranged in space, that is to say, 

 conditions, the space 

 occupied by a crystal- 

 line element, a homo- 

 geneous assemblage of 

 identically s i m i I ar 



atoms, may be par- 

 titioned into identically 

 similar cells in such a 

 manner that the bound- 

 aries of a single cell 

 shall enclose the entire 

 domain throughout 

 which a particular atom 

 exercises predominant 

 influence. Since it is 

 postulated that every 

 point in the space is 

 subject to the domin- Fin. 1. 



ating influence of some 



next neighbouring atomic centre, it follows that the cells 

 fit together so as to occupy the whole available space with- 

 out interstices. Nothing' is here said about the shape of 

 the cells; but since, in the case of an elementary sub- 

 stance, the atomic, centres are all alike, so too will be 

 the cells. Before proceeding to discuss the actual shapes 

 of the cells referred to, it will be convenient to illustrate 



more graphically the mode of treating the problem which 

 is here introduced with the aid of a particular point-system 

 connected with the crystalline structure of elementary 

 substances. 



The point-system in question may be derived in the 

 following manner. Space is first partitioned into cubes by 

 three sets of parallel planes at right angles to one another 

 (Fig. i) ; a point is then placed at each cube corner and 

 .It the centre of each cube face. The cubes of the partition- 

 ing, iiaving ser\'ed iheir purpose, may now be removed. 



