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Theory of the Allotropic Forms of Phosphorus

Pressure-temperature Diagram
Pressure-temperature Diagram of Phosphorus
Pressures at lower temperatures are magnified in order to show all changes on one diagram. Lines are lettered, as usual, with the phases which can coexist; W2= white phosphorus formed at high pressures, W1= ordinary white phosphorus, L = liquid phosphorus, G = vapour or gaseous phosphorus, V = violet phosphorus.

Curves which refer to unstable forms are represented by dotted lines, as also are the transformations of the condensed forms. The slopes of these curves can be calculated when the specific volumes of the two forms are known; thus the W1 + L line should slope slightly to the right, since the specific volume of liquid phosphorus is greater than that of solid white phosphorus near + 44.1° C. The melting-point is therefore raised by an increase of pressure.

The solid white form really is only in a state of false equilibrium, being unstable with respect to the polymerised forms at all realisable temperatures. There are also the other forms—red, scarlet and black phosphorus—the behaviour of which under definite conditions of pressure and temperature cannot be stated with any certainty. Further, the melting-point even of the well-crystallised white phosphorus can be made to vary under certain conditions. In fact, all the condensed phases, liquid and solid, behave as mixtures rather than as single pure substances.

The existence of two or more molecular species is definitely postulated by Smits as follows:—
  1. "Every phase, and therefore also every crystalline phase, of an allotropic substance is a state which, in certain circumstances, can behave as a poly-component phase."
  2. "The cause of this behaviour must be assumed to be the complexity, i.e. the existence of different molecular species, which are in inner equilibrium when the behaviour of the system is unary, or in other words when it behaves as a one- component system."
In the case of phosphorus there are probably several " molecular species," but the phenomena at temperatures which are not too high can be explained rationally by assuming only two—Pα, which is white, with a low melting-point and high vapour pressure, and Pβ, which is violet, with a high melting-point and low vapour pressure, and which probably is highly polymerised.

The density of the vapour is the same whether it is derived from white or red phosphorus, and at lower temperatures and not too low pressures corresponds to molecules P4.

In the liquid the pseudo-components are supposed to be in a state of dynamic equilibrium which shifts with the temperature, but does not readjust itself instantaneously on sudden changes.

The solids, at any rate the polymerised forms, are regarded as solid solutions of Pα and Pβ in varying proportions. Temperature-concentration diagrams similar to those representing a two-component system have been constructed for these pseudo-components.

When the liquid is heated to between 400° and 500° C. it is highly supercooled with respect to violet phosphorus, which crystallises with explosive violence. When, however, the vapour is cooled rapidly so that the liquid passes rapidly through this range down to 30° C., the liquid white phosphorus, which is richer in Pα, and thus approximates more closely to the composition of the vapour, is deposited first, and subsequently solid white phosphorus, which also resembles the liquid and the vapour much more closely than does the polymerised form. This appearance of a metastable rather than a stable form was pointed out long ago by Frankenheim, and stated formally as a generalisation, called by Ostwald the Law of Successive Transformations, thus: " When a given chemical system is left in an unstable state it tends to change, not into the most stable form, but into the form the stability of which most nearly resembles its own, i.e. into that transient or permanently stable modification whose formation from the original state is accompanied by the smallest loss of free energy."

The condensation of phosphorus vapour, however, does not necessarily yield white phosphorus; much depends upon the temperature to which the vapour has been heated and the rate of cooling.

It was noted by Hittorf that the vapour evolved by red phosphorus at 440° C. was deposited in the yellow form. But Arctowski found that when red phosphorus was heated in a vacuum at 100° C. it sublimed and condensed in the same form. This phenomenon was investigated in detail by Stock, Schroder and Stamm. The phosphorus was introduced in varying amounts into a sealed quartz tube, heated to various temperatures and suddenly cooled by immersion in water. Cooling from the temperatures stated in the first column of the following table gave the products described in the second column:—

Temperatures, °C., from which Sudden Cooling was effected.Appearance of Product.
400Colourless drops.
450Pale yellow drops.
550Distinctly yellow drops.
600Drops with a few purple flakes.
700Some brownish-red solid.
900Opaque brownish-red solid.
1000Denser and more opaque.
1200Phosphorus vapour at 5 mm. gave entirely red phosphorus.

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. The inner equilibrium has not in these circumstances time to adjust itself to the loss of the volatile Pα 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 Pα 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 allotropic 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.

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