Allotropy, Theory

A review of the alleged allotropes of phosphorus reduces their number to four, namely, the a- and/3-forms of yellow phosphorus, red or violet phosphorus, and black phosphorus. Most of the work of various investigators has been directed towards elucidating the nature of red phosphorus, and of the transformation of yellow to red phosphorus and conversely. Red phosphorus was formerly considered to be amorphous, and it was often called amorphous phosphorus. The term amorphous, however, here referred more to the general appearance of the powder rather than to its minute structure. J. W. Retgers 5 showed that the particles of ordinary red phosphorus are rhombohedral crystals, which are well developed in those of W. Hittorf s violet phosphorus. All four varieties are therefore crystalline. J. W. Terwen has reviewed this subject in a general way and M. Copisarow discussed the theory of allotropy,... 

Smits, Theory of Allotropy translated by Thomas (Longmans, 1922), p. 240. 

An examination of the behaviour of red and violet phosphorus (and indeed all solid forms) in the light of this theory leads to the conclusion that they are mixtures, with the difference that while violet phosphorus is capable of behaving in a unary manner, red phosphorus is not. Violet phosphorus is a mixture, because when it is heated to 360° C. in a vacuum, and the vapour is thus rapidly removed, the vapour pressure falls.2 The inner equilibrium has not in these circumstances time to adjust itself to the loss of the volatile Pa molecules, the residue becomes poorer in this kind and therefore has a lower vapour pressure. The production of red phosphorus below 400° C. may be explained partly by an increase in the proportion of Pa molecules in the solid solution of the pseudo-components, but principally by a delay in the establishment of the equilibrium, which leads to the production of solid solutions still richer in Pa, which are not in equilibrium but which constitute the ordinary red phosphorus. This therefore is not an allotropie modification, if such a modification is defined as a substance which can exist in inner equilibrium and which is able to behave in a unary manner. 

Equilibrium in heterogeneous systems, in the absence of electrical, capillary, Or gravitational effects—The Phase Rule and some of its applications—The theory of Allotropy... 

The Significance of Meltmg-pomt Determinations from the Standpoint of the Theory of Allotropy... 

Complexity of the Solid State. Theory of Allotropy.— Attention has already been drawn to the fact that liquids, under ordinary conditions (that is, in presence of traces of moisture), behave as equilibrium mixtures of simple and associated molecules (p. 20). According to the theory of allotropy put forward by.S.riiit. .gt4aystal-... 

On the basis of his theory of allotropy, according to which there separates from a liquid mixture in dynamic equilibrium, not a pure solid substance but a solid phase consisting also of an equilibrium mixture (a solid solution), Smits has suggested a diagram for the equilibrium relations of sulphur. This diagram, however, has not yet... 

Phosphorus as Pseudo-binary System.—For the purpose of illustrating the behaviour of a one-component system as interpreted by means of the theory of allotropy put forward by Smits, a brief discussion of the behaviour of phosphorus may be given. ... 

In order to make possible a more systematic treatment of the subject and a fuller and better-adjusted consideration of recent advances, it has been found advisable to make somewhat extensive alterations in the now twenty-three-year-old general framework of the book. These changes affect, more especially, those chapters which deal with equilibria in one and two component systems. These chapters have not only been revised, but have been re-cast, re-arranged, and, to a considerable extent, rewritten. In these sections, the nature of the equilibria in intensively dried systems and the Smits theory of allotropy have also been discussed, although the limitations of space have necessitated brevity. Greater emphasis, also, has been laid on the applications of the Clausius-CIapeyron equation to the calculation of changes of equilibria with pressure and temperature. 

Univariant Systems.—Equilibrium between liquid and vapour. Vaporisation curve. Upper limit of vaporisation curve. Theorems of van t Hoff and of Le Chatelier. The Clausius-Clapeyron equation. Presence of complex molecules. Equilibrium between solid and vapour. Sublimation curve. Equilibrium between solid and liquid. Curve of fusion. Equilibrium between solid, liquid, and vapour. The triple point. Complexity of the solid state. Theory of allotropy. Bivariant systems. Changes at the triple point. Polymorphism. Triple point Sj—Sg— V. Transition point. Transition curve. Enantiotropy and monotropy. Enantiotropy combined with monotropy. Suspended transformation. Metastable equilibria. Pressure-temperature relations between stable and metastable forms. Velocity of transformation of metastable systems. Metastability in metals produced by mechanical stress. Law of successive reactions. 

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