33 



(b) Sub-Microns. 



Two methods each depending upon the appUcation of the T3Tidall 

 effect are available, but they cannot be appUed to the non-transparent 

 solid solutions encountered in metallurgical practice. 



1. Rayleigh's Formula. — It is well known that an incident beam 

 of light faUing upon particles, small compared with the wave length 

 of light, is not reflected but scattered and polarized. The intensity 

 of the scattered light varies according to the Rayleigh*^ formula 

 Is = Anr */A* where A is a factor which depends upon the experi- 

 mental conditions, " n " is the number of particles of radius " r " 

 scattering light of wave length "A" With a particular solution 

 where "n " is constant and the intensity of the scattered Ught may 

 be measured by means of a spectrograph and " r " found by substitution 

 in the Rayleigh formula. The method is considered by Henrii^ to 

 be very sensitive and to give exact results with hydrosols. But it is 

 neither so convenient nor so rapid as the method elaborated by 

 Zsigmondy^^ in his investigation of gold ruby glass and for which, 

 in collaboration with Siedentopf^^ the first ultra-microscope was 

 designed. 



2. Ultra- Microscopy. — Zsigmondy observed the scattered Ught in 

 a microscope set orthogonally to the illuminating beam. The particle 

 then looks like a planet, self-luminous in a dark field. The Ught 

 observed is sometimes coloured*" and appears as diffraction rings, 

 the size and colour of which is independent of the size of the particle, 

 but depends upon the numerical aperture of the objective and con- 

 denser, and the intensity of the Uluminating beam. The light used must 

 be of high specific intensity, and the iUumination system such that 

 in the solid under examination, a layer of known thickness, and less 

 than the depth of vision in the microscope, is illuminated, by a beam 

 of known mdth. Suitable apparatus made by Zeiss^* and Reichert^^ 

 is known as the Zsigmondy " slit " ultra-microscope, and the method 

 of manipulation has been well described by Heimstadt.^* 



The solid solution to be examined is cut so as to form at parallelo- 

 piped some 3 mm. thick, with two carefully polished faces at right 

 angles. This is placed on a special microscope stage so 'that the 

 illuminated layer can be observed at any point in the paraUelopiped. 

 By direct counting it is then possible to determine the number of 

 particles " N " in unit volume of the solid, containing a mass " M " 

 of the disperse phase of density D. By substitution in the formula 



L = /v/ YvM^ ^^^ linear dimension of the particle, considered as a 



cube,i s calculated (c.f. Wiegner^*). Errors may be introduced in the 

 determination of density and mass. It is usual to assume that the 

 density is constant and independent of the size of the particle, and 

 accordingly the ordinary density of the substance in microscopic 

 condition is used. For metal sols in soUd solution the error, if any, 

 is negUgible (Cholodny'), but for oxides, hj^droxides, and emulsions 

 this assumption may introduce an error making he estimated size 

 too large (Wintgen", Biichner*). The determination of mass per 



X 11404 C 



