Solid Phosphorus

Phosphorus exhibits allotropy, and formerly was thought to exist in two forms, yellow and red. In addition, several other varieties, scarlet, violet, metallic and black phosphorus, were discovered later, some of which are perhaps not to be regarded as true allotropes.

White or yellow phosphorus is a colourless or pale yellow, translucent, lustrous solid of waxy appearance, soft at ordinary temperatures and brittle when cold (e.g. at 0° C.). It melts at about 44° C., giving a transparent liquid which can be supercooled many degrees below the melting-point without solidifying. The liquid catches fire in the air at about 60° C. and boils at about 280° C. in an indifferent atmosphere, giving a vapour which contains complex molecules (P₄). On long heating at temperatures slightly below its boiling-point it is transformed into red phosphorus. White phosphorus is almost insoluble in water, but is volatile with steam, to which it imparts a luminosity; this serves as a delicate test for the element. It is soluble in carbon disulphide and in most organic solvents.

It is one of the most easily oxidised of the non-metals, having a low ignition-point and burning in the air with great evolution of heat and the production of the pentoxide and some red phosphorus. It also combines vigorously with the halogens, and gives a more complete series of halides than any other non-metallic element.

Pure white phosphorus when slowly heated melts very sharply at 44.0° C. Under these conditions it behaves as a " unary " substance, i.e. one whose molecules are all the same, physically as well as chemically. But, in the account of the transformations which is given later, the theory is put forward that the liquid contains at least two kinds of molecules, which may be called Pα and Pβ. There will be a definite concentration of each in equilibrium at any one temperature, and if the temperature is lowered slowly, these relative concentrations will alter down to the melting-point, 44.0° C., at which the solid is in equilibrium with a particular mixture of Pα and Pβ. The solid is not necessarily in equilibrium at this melting-point with those proportions of Pα and Pβ which are found at a higher temperature. The expected alteration in the freezing-point was realised experimentally by cooling phosphorus very rapidly from 100° C. to temperatures just below or just above 44.0° in a capillary tube, then inoculating with solid phosphorus. Temperatures were read on a resistance thermometer which had a negligible heat capacity and lag, and hence took up the temperature of its surroundings practically instantaneously. After a slight fall, the temperature rose to 44.1, 44.25 and even above 45.0°, an extreme range of 1.8° being observed. The pseudo-binary character of the pure white form was thus revealed.

The degree of supercooling to which liquid phosphorus can be subjected without solidification also depends on its previous history. If the cooling be slow, pure liquid phosphorus may be kept for days at 18° C. If the liquid be heated to 100° C. and suddenly cooled to ordinary temperatures it crystallises spontaneously in a few seconds without inoculation.

As the fusion of phosphorus is accompanied by an increase of volume, the melting-point is raised by increase of pressure. The experimental results are expressed by the formula

t_m = 43.93 + 0.0275p – 0.0₆50p²

in which the pressure p is expressed in kilograms per square centimetre.

The mean specific heat of solid white phosphorus has been determined by several investigators with moderately concordant results:—

Temperature Interval (°C.).	Specific Heat.
(1) -78° to 4.10°	0.170-0.174
(2) +7° to +30°	0.185
(3) +13° to +36°	0.202
(4) -21° to +7°	0.1788
(5) -188° to +20°	0.169

The atomic heats are therefore 5.33, 5.74 and 6.26 over the three ranges of temperature (1), (2), (3). There is a slight deviation from Dulong and Petit's law at the lower temperatures, in the same sense as that met with in the case of the elements carbon, boron and silicon. But although phosphorus has a relatively low atomic weight, it also has a low melting-point, and the atomic heat as usual assumes the normal value at temperatures near the melting-point.

The latent heat of solidification at the melting-point, +44.2° C., is 5.034 calories per gram or 0.16 Calories per gram-atom — a very low value, which may be compared with that of sulphur, namely, 0.30 Calories per gram-atom. The latent heat, as usual, diminishes with fall of temperature. The following values were obtained on allowing the supercooled liquid to crystallise:—

t° C.	27.35	29.73	40.05
l	4.744	4.744	4.970 calories per gram.

The latent heat increases at the higher melting-points which are obtained at higher pressures; thus at t = 50.03° C. and p = 220 kg./sq. cm. l was 4.94, while at 69.98° C. and 959 kg. it was 5.28. At still higher pressures the increase in l continues, as is shown by the following results, which refer to white phosphorus:—

p	1	2000	4000	6000	8000
t	44.2	99.3	148.2	191.9	-2.4
l	2.09	2.41	2.63	2.78	18.61

Pressure and temperature are expressed in the units given above, and latent heats in kilogram-metres per gram. The last value refers to black phosphorus.

If the latent heat of fusion is taken as 5.0 calories absorbed per gram of phosphorus at the melting-point (T_m = 317.5° C. (abs.)), the high value of 40.4 is obtained as the cryoscopic constant for 1 mol of a solute in 1000 grams of phosphorus. The experimental value obtained by dissolving naphthalene in phosphorus was 33.2.

The density of solid white phosphorus is nearly twice as great as that of water. The following table is compiled from the results of different investigators:—

The densities of solid white phosphorus and of liquid phosphorus at the melting point

t° C.	0	18	20	40	44	44
D	1.8368	1.828	1.8232	1.8068	1.805	1.745 (liquid)

Hence the coefficient of expansion of solid phosphorus at ordinary temperatures is 0.0037 c.c. per degree Centigrade. The solid expands by about 3 per cent, on fusion; the ratio of the density of the solid to that of the liquid at this temperature is 1.035 or 1.0345 to 1.

The coefficient of compressibility is defined as the fractional change of volume produced by a change of pressure amounting to 1 megabar (10⁶ dynes per square centimetre). The range of pressure investigated was 100 to 500 megabars, and the compressibilities at room temperatures were 20.3 for white phosphorus and 9.2 for the red or violet variety. Thus, as usual, a high compressibility was found for an element of high atomic volume, and the more condensed form had the lower compressibility.

Crystalline Form.—It was shown by the earlier investigators that phosphorus crystallised from the liquid state in octahedra and dodecahedra, from carbon disulphide in octahedra, and that, when prepared by sublimation, the crystals had about 200 distinct faces. Well-shaped crystals of white phosphorus may be obtained by solidification of the liquid, by slow sublimation, or by evaporation of solutions in organic solvents. They belong to the regular system, and have a columnar shape if obtained from one set of solvents, e.g. carbon disulphide, benzene, alcohol, ether, petroleum, while they have shapes derived from the cube and dodecahedron if obtained from turpentine, oil of almonds, etc. By slow sublimation various forms of the regular system are obtained which may have every possible number of faces (except 48) up to 200. According to Bridgman white phosphorus crystallises both in the regular and in the hexagonal system, the transition temperature being raised by increase of pressure. Thus under 12,000 atmospheres the conversion occurs at +64.4° C., under atmospheric pressure at -76.9°, and under the pressure of its own vapour at -80°, which therefore appears to be the transition point between this β-form and the ordinary or α-form of white phosphorus. The β-form, stable under high pressures, is produced with a volume contraction of about 2 per cent. The density is 2.699.

As is to be expected from the brilliant gem-like appearance of the crystals and drops of liquid white phosphorus, the refractive index is high. At the ordinary temperature the refractive index for the D line (λ = 589.0 to 589.6 mμ) was found to be 2.144. The differences between the refractive indices of the solid and the liquid are shown in the table overleaf.

Electrical Conductivity.—Phosphorus is an electrical insulator. The conductivity of the solid element was found to be of the order of 10^-11 mhos per centimetre cube and that of the liquid 10^-6 mhos per centimetre cube. Black phosphorus, which must be considered the most metallic form of the element, is a relatively good conductor, the specific resistance being slightly less than 1 ohm per centimetre cube but diminishing with rise of temperature.

Refractive indices of solid and liquid phosphorus

State.	Temp. °C	Line and λ in mμ.
		D 589.0-589.6	Hα 656.3	Hβ 486.15	Hγ 434.07
Solid	25.0	2.144	...	...	...
Solid	37.5	...	2.08873	2.15388	2.1946
Liquid	37.5	...	2.05370	2.11675	2.15634
Liquid	44.0	...	2.05010	2.11311	2.15274

The dielectric constant of solid white phosphorus was found to be 4.1 at 20° C., and that of liquid phosphorus 3.85 at 45°. The electrochemical potential is said to lie between those of arsenic and tellurium. Phosphorus is diamagnetic. The magnetic susceptibility of the solid white element is about 0.9×10^-6 mass units, that of the red variety rather less.

Ionisation Potential, V_A.—This may be defined as the smallest difference of potential through which an electron must fall in an electric field in order that its kinetic energy, mv²/2, =eV_A (e is the electronic charge), may be sufficient to raise an atom after collision from state (1) with energy E₁ to another possible quantum state (2) with energy E₂. In changing back from quantum state (2) to (1) the atom will emit radiation of a frequency given by:

eV_A = hv (h= Planck's constant; v = wave number in waves per cm.) The wavelength λ_A of this radiation is calculated from:

λ_A =c/v (c is the velocity of light)

In the case of phosphorus, V_A = 5.80 ± 0.1 and λ_A = 2130 Å.

The ionisation potential has also been determined by the method of electronic collisions. Free electrons, from a heated platinum wire, are introduced into the vapour of an element under low pressure. By the application of increasing potentials increasing kinetic energies are imparted to the electrons. After a certain threshold value has been passed, the electrons strike the atoms in inelastic collisions, and monochromatic radiation is emitted by the atoms. When this method was applied to phosphorus vapour the value of the potential E was found to be 10.3 volts.

White phosphorus is almost insoluble in water. It dissolves easily in liquid ammonia, sulphur dioxide and cyanogen, also in such compounds as phosphorus trichloride which mix with typical organic solvents. It is moderately soluble in fatty oils, also in hydrocarbons, alcohols, ethers, halogenated hydrocarbons such as chloroform and especially methylene iodide. One of the best solvents for phosphorus, as for sulphur, is carbon disulphide, which seems to dissolve it in all proportions at ordinary temperatures; a solution has even

Solubility of white phosphorus in aqueous solvents and oils

Solvent	Water	Acetic Acid, 96 per cent	Paraffin	Oleic Acid	Almond Oil	Alcohol (absolute)	Glycerol (density 1.256)
Grams Phosphorus in 100 grams Solution	0.0003	0.105	1.45	1.06	1.25	0.208	0.25

Solubility in benzene

t° C.	0	5	8	10	15	18	20	23	25	30	35	40	45	50	55	60	65	70	75	81
Solubility in grams per 100 grams Solvent	1.513	1.99	2.31	2.4	2.7	3.1	3.2	3.4	3.7	4.60	5.17	5.75	6.11	6.80	7.32	7.90	8.40	8.90	9.40	10.03
Density of Solution	...	...	0.899	0.8985	0.894	0.892	0.890	0.8875	0.8861

Solubility in ether

t° C.	0	5	8	10	15	18	20	23	25	28	30	33	35
Grams Phosphorus in 100 grams Solution	0.434	0.62	0.79	0.85	0.90	1.01	1.04	1.12	1.39	1.60	1.75	1.80	2.00
Density of Solution	...	...	...	0.729	0.723	0.719	0.718	0.722	0.728

Solubility in carbon disulphide

t° C.	-10	-7.5	-5.0	-3.5	-3.2	-2.5	0.0	+5.0	+ 10.0
Grams Phosphorus in 100 grams Solution	31.40	35.85	41.95	66.14	71.72	75.0	81.27	86.3	89.8

been prepared containing 20 parts of phosphorus in 1 part of carbon disulphide. These solutions are dangerous; the volatile and endothermic disulphide forms an explosive mixture with air at ordinary temperatures, and the finely divided phosphorus which is left on evaporation ignites spontaneously. This is illustrated in the well-known lecture experiment in which the solution is allowed to evaporate on filter-paper.