208 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1951 



sive scale. It must mean that inside the atom there is some sort of mu- 

 tual interference between the electronic orbits, analogous to the inter- 

 ference between atoms or molecules that occurs in liquids. The neces- 

 sity for the nonlinearity in the relation between pressure and volume is 

 obvious, for, if it were not so, volumes would eventually become nega- 

 tive at sufficiently high pressure. Thus it can be calculated that if 

 the compressibility of cesium continued at its initial rate, the metal 

 would be squeezed out of existence altogether by a pressure of only 

 14,000 atmospheres. 



Although every volume-pressure curve must eventually be convex 

 toward the pressure axis, there may be an opposite curvature over 

 considerable pressure ranges. There is no mechanical or thermo- 

 dynamical reason why compressibility should not in some circum- 

 stances increase with increasing pressure. Examples of this are in 

 fact known; the most striking is perhaps quartz glass. Its com- 

 pressibility increases with pressure over a wide range. Such be- 

 havior cannot, however, continue indefinitely, and sooner or later 

 there must be a reversal. Experiment shows that the reversal occurs 

 at a pressure of 35,000 atmospheres, where the volume is still far above 

 zero, being in fact 89.3 percent of its initial value. Above 35,000, com- 

 pressibility decreases in the normal way with rising pressure. The 

 abnormality ceases so abruptly at 35,000 that there is a cusp on the 

 pressure- volume curve. It is as if there were some special mechanism 

 responsible for the abnormality, which abruptly goes out of action at 

 35,000 atmospheres. A plausible mechanism would assume some- 

 thing in the nature of lenticular cavities in the structure, which are 

 squeezed flat at 35,000 atmospheres. 



The pressure-volume curves in figure 4 contain several examples 

 of discontinuities. These are due to transitions of one kind or another. 

 In most cases they are ordinary polymorphic transitions resulting 

 from a change in the crystal lattice. The proof that they represent 

 transitions of this sort is usually indirect and presumptive, but in 

 some instances direct proof can be given. One method is by X-ray 

 analysis of the new phase while it is under pressure. Another is to 

 follow the transition to atmospheric pressure by suitably changing 

 the temperature, and then to establish the nature of the transition at 

 atmospheric pressure by some convenient method not subject to the 

 limitations of high-pressure measurements. 



It will be seen from figure 4 that in some cases a substance may 

 show more than one discontinuity. One of the most interesting of 

 such substances is bismuth. At atmospheric pressure, bismuth is 

 abnormal in many ways ; in particular it is one of the few substances 

 which, like water, expand when they freeze. Thermodynamics de- 

 mands that for substances of this sort the effect of pressure should be 



