PHENOMENA OF PHOSPHORESCENCE. 211 



It thus appears that irregularities in the distribution of the active sub- 

 stance are sufficient to explain the deviation from linearity in all the decay- 

 curves thus far observed. Such irregularities of distribution are not merely 

 probable, but in many cases are perfectly obvious. But while the dis- 

 tribution of the active material is probably in all cases an important factor, 

 it can not be the only factor of importance. With Balmain's paint, Pierce 

 has found that the decay curve, which possesses the usual shoulder at 

 ordinary temperatures, becomes almost exactly linear at a temperature of 

 74, ' while for higher temperatures it again shows a curvature of the usual 

 kind. It appears highly improbable that such changes are brought about 

 by temporary changes in the distribution of the active substance. Non- 

 uniformity in the distribution of the active material also offers no explana- 

 tion of the phenomena of hysteresis or of the effect of the infra-red rays. 



DIFFUSION EFFECTS. 



Whenever irregularities exist in the distribution of the active substance 

 there will be a tendency for diffusion to occur. Under ordinary conditions 

 this tendency is probably neutralized by forces which act to keep the dis- 

 tribution unaltered, and so long as the substance remains in the molecular 

 form the condition is to be regarded as a stable one for the temperature and 

 pressure at which the phosphorescent substance normally exists. 



But when the material is excited to luminescence a part of the active 

 substance will be dissociated, and since the resulting ions will possess a 

 different mobility and will be acted upon by different forces from those 

 that determine the behavior of the original neutral molecules, the condition 

 of equilibrium will be destroyed, and some change in the distribution of 

 the active substance is to be expected. 



An exact discussion of the effects of diffusion would present great diffi- 

 culties; for the fact that diffusion and recombination occur at the same 

 time greatly complicates the analytical treatment. It is probable also 

 that in crystals the diffusion constant will be different for different direc- 

 tions. It is clear, however, that the influence of diffusion upon the form 

 of the decay curve must be similar to that produced by an irregular dis- 

 tribution of ions without diffusion. In fact, the discussion of the preceding 

 section applies without modification to the case of substances in which 

 diffusion of the ions may occur. Diffusion, however, will increase the 

 rapidity with which uniformity of ionic concentration is approached dur- 

 ing decay ; and since diffusion will be most active when large concentration 

 gradients exist, the effects of diffusion will be greatest in the early stages 

 of decay. In cases where diffusion is an important factor we should there- 

 fore expect a sharper curvature in the early part of the curve, and a more 

 rapid approach to linearity, than in cases where diffusion is absent. 



It is not impossible that diffusion is sometimes important even when 

 there is nearly complete uniformity in the distribution of the active sub- 

 stance. Owing to the absorption of the exciting light the ionization pro- 

 duced in the surface layer will be more intense than that produced at points 

 beneath the surface. If the absorption is large a large gradient may thus 



Physical Review, xxvi, p. 458. See also Chapter VI. 



