Write for the exposed glass area. If is the blank-corrected dissolved mass concentration of element , its initial mass fraction in the glass and the leachate volume, thenThe numerator is the released element mass measured in solution. Dividing by converts this to an equivalent mass of the original glass, while dividing by expresses that mass per exposed area. With in and in , has units of glass-equivalent release. The fraction must be used as a fraction, not an unconverted percentage.
These corrections allow comparison of specimens of different size and composition without confusing a lower concentration with better durability. State how the area was measured; geometric area and a rough powder's accessible area need not coincide. For repeated sampling, include element mass removed in earlier aliquots and the volume remaining; for an initial blank in the leachant, subtract its corresponding inventory. Surface cracking and evolving porosity can make a rate based on initial area differ from a rate based on the true reactive area.
Under congruent glass dissolution, constituents enter solution in their bulk proportions, so their correctly normalised releases coincide. Preferential sodium release by ion exchange can instead give , while silicon retention in a gel or secondary precipitate can depress its dissolved release. Noncoincident curves show nonstoichiometric aqueous release, but do not uniquely identify the mechanism. Conversely, solution coincidence does not by itself establish that no secondary reactions occurred. A complete inference compares solution inventories with altered solids.
Normalisation removes composition and first-order area/volume scaling; it does not make different pH, temperature, solution composition or contact histories equivalent. In a batch test, even the same initial water changes composition and pH as reaction proceeds. Reporting those conditions and time is essential for a transferable comparison rather than treating as a condition-independent material constant.
Let be the measured mass concentration of element , its blank concentration, the leachate volume, the element's mass fraction in the original glass, and the exposed glass surface area. For one closed test, the normalised elemental release isIf concentration is in , volume in litres and area in square metres, is in of glass-equivalent release. Dividing by removes the trivial difference caused by loading different amounts of the measured element; dividing by removes the first-order geometrical scale difference. Normalising only by initial element content or reporting raw solution concentration does not accomplish both corrections.
For repeated sampling with leachant replacement, use cumulative released mass: add the mass removed in all earlier aliquots to the mass present in the final remaining solution, with the corresponding blank correction. A flow-through experiment instead integrates over time. State how surface area was determined and whether it is held at its initial value in the reported normalisation; cracks, fines and alteration can change the genuinely reactive area.
Compare for several constituents. In congruent glass dissolution, the different element-normalised curves coincide, provided the released elements remain in solution. Preferential early alkali release can indicate ion exchange, whereas lower dissolved silicon or actinide release can reflect an alteration layer, sorption or secondary-phase precipitation. boron is often useful as a relatively mobile dissolution tracer, but not if the leachant contains a large boron background or if it is itself retained. A low aqueous concentration of one constituent is therefore not automatically a low glass-dissolution rate.
A near-linear interval gives an approximately constant normalised elemental release rate. A square-root time dependence can be consistent with diffusion-limited transport, and decreasing slopes can indicate saturation or a protective alteration layer; no one curve shape proves a unique mechanism. Compare solution inventories with the altered solid by microscopy, composition and phase analysis. Differences in pH, temperature, leachant composition, duration and surface-area-to-volume ratio remain even after this mass-and-area normalisation. Careful background subtraction and control of solution conditions are experimentally consequential, as demonstrated in primary flow-through measurements.[ref]
Measurement of kinetic rate law parameters on a Na-Ca-Al borosilicate glass for low-activity waste by B. P. McGrail and others. Journal of Nuclear Materials 249, 175–189; abstract on duration, background subtraction and solution-condition dependence