Previous page     Contents     Next page

There have been numerous attempts to relate chemical diffusivities in silicate melts to melt viscosity. For example, the Stokes-Einstein equation states that Dη= kT/6¶r where D is the chemical diffusivity, η is the melt viscosity, k is Boltzmann's constant, and r is the radius of the diffusing species. Simple relations such as the Stokes-Einstein equation fail to predict diffusivities for most elements; however our recent work on diffusivities of U and Th revealed that the activation energy of diffusion was in some cases equal to that of viscous flow. We have performed several tracer diffusion experiments on a haplogranitic base composition whose viscosity is controlled by the addition of Na₂O and H₂O. The base composition is HPG8 (79.1 % SiO₂, 12.1 % Al₂O₃, 4.6 % Na₂O, 4.2 % K₂O), a haplogranite near the minimum melt composition whose properties have already been exhaustively studied in Bayreuth. The peralkaline equivalent, HPG8+20, has had 20 wt% Na₂O added to it; hydrous compositions contain 2 or 5 wt% added H₂O. Diffusion profiles are being measured by ion microprobe at Nancy and by electron microprobe at BGI. Diffusivities of all 22 elements studied (Li, Be, B, Mg, Ca, Ti, Ge, Rb, Sr, Y, Zr, Nb, Cs, Ba, Nd, Tb, Lu, Hf, Ta, W, U, Th; 1000 ppm concentration of each element) are Arrhenian; activation energies of diffusion of all elements in each melt composition are similar, and are close to activation energies of viscous flow. However there are large systematic variations in the relative magnitudes of the diffusivities within groups of the periodic table (Figure 3.8-2). An increase in ionic radius is correlated with increasing diffusivity within groups IIa and IIIb (including lanthanides), but is inversely correlated with increasing diffusivity in group IVb. The results indicate that diffusivities of these elements can be predicted within an order of magnitude from melt viscosity over a wide range of conditions and compositions.
 

Fig. 3.8-2: Log diffusivity versus reciprocal temperature. Diffusivities shown for Be, Mg, Ca, Sr, Ba, Nd, Tb, Lu, Ti, Zr, Hf in HPG8 and HPG8+20 Na2O melts. Shown for comparison are the diffusivities of Si predicted from the Stokes-Einstein relation based on melt viscosities measured by concentric cylinder viscometry.