2o8 STUDIES IN LUMINESCENCE. 



INFLUENCE OF IRREGULARITIES IN DISTRIBUTION OF THE ACTIVE MATERIAL. 



Luminescent substances are in most cases solid solutions. In fact it is 

 doubtful whether luminescence can occur in an absolutely pure substance. 

 Pure calcium sulphide for example is not phosphorescent; but the addition 

 of a small amount of some other metal, such as manganese or copper, gives 

 it the power to phosphoresce brilliantly. The method of preparing the 

 phosphorescent sulphides is such as to bring about a very intimate mixture 

 of the constituents, and it is natural to think of the manganese, copper, or 

 other active material as being dissolved in the sulphide. 



So little is known regarding the nature of solid solutions that we can not 

 say with certainty whether such substances are to be regarded as strictly 

 homogeneous or not. Especially in the case of crystals it seems probable 

 that the molecules of the solute may not be uniformly distributed through- 

 out the mass of the solvent, but may to a greater or less extent collect in 

 groups or minute crystals. Any lack of uniformity in the distribution of 

 the active substance will cause a corresponding variation in the concentra- 

 tion of the ions produced by the exciting light; and if the nature of the 

 solvent is such as to permit of diffusion the phenomena will be complicated 

 by the fact that a redistribution of the ions will occur during excitation and 

 decay. Even without diffusion, however, the form of the decav curve will 

 be modified. For, since the rate of recombination is proportional to the 

 square of the ionic concentration the intensity of phosphorescence will 

 decay at different rates in different parts of the mass. The effect on the 

 decay curve will be similar to that produced by absorption; in fact, the decay 

 curve is modified by absorption of the exciting light only because of the 

 resulting lack of uniformity in the ionic concentration at different depths 

 below the surface. 



Our complete ignorance of the distribution of the active material makes 

 it almost useless to attempt any exact treatment of the problem. It is 

 possible, however, without questionable assumptions or great analytical 

 complexity, to predict the general character of the effect to be expected. 



Let n be the number of ions per unit mass at any point ; /; is then some 

 unknown function of the position of the point in question and of the time 

 that has elapsed since the decay began. The number of recombinations 

 per second will be an- per unit volume, and the number of recombinations 

 for the whole mass will hejairdr, where dr is an element of volume. Dis- 

 regarding the absorption of the emitted light we have 



= ka ( ir< 



Since ions are destroyed only by recombination 



dN r 2 , 



= a I ii-dr 

 dt J 



where N is the total number of ions. 



If n is the volume average of ;/, and n- the volume average of n 2 , so that 



A i /. , , dN 



n 



= - I ndr=- , ii-= - I trdr, = am- 



t *' t t J dt 



