The Photographic Reciprocity-Law Failure and the Ionic Conductivity of the Silver Halides*

Abstract

A method is given for determining from reciprocity-law failure measurements at different temperatures the value of the energy exponent ∊ in the equation for ionic conductivity of silver bromide (1)Ni=Ae−∊/kT ions/sec.According to present theory, the reciprocity-law failure at high intensities is due to the sluggishness of the secondary process of latent-image formation consisting of migration of Ag+ ions to the specks. The free electrons produced in the grains by exposure can move practically instantaneously and independently of temperature. However, if the Ag+ ions cannot move up to the specks at a sufficient rate to keep them discharged, an inefficiency is introduced. This inefficiency may be said to depend upon the number of free electrons produced in the grain per second, Ne, compared with the number of free Ag+ ions, Ni, available for ionic conduction. The number of free electrons produced can be controlled by the light intensity, I, whereas the number of conducting Ag+ ions can be controlled by temperature in accordance with Eq. (1). By choosing points on the reciprocity curves made at different temperatures such that the change of efficiency arising from a change of intensity I1 to I2 is equal to the change of efficiency arising from a change of temperature T1 to T2, the relation is shown to hold (2)logI2/I1=0.434∊k(1T1−1T2).Substitution of experimental values in this equation for I1, I2, and T1, T2 gives a value of ∊ = 0.69. Direct measurement of the ionic conductivity at different temperatures on a single crystal of AgBr gives the value of ∊ = 0.66. The close agreement between the ∊ values obtained by photographic means and by direct measurement affords quantitative evidence that the high intensity reciprocity-law failure is due to the ionic conductivity effect alone.