Stress-Induced Migration and Partial Molar Volume of Sodium Ions in Glass

Abstract

The partial free energy Ḡi of a chemical species is altered by pressure according to the relation dḠi=V̄idP, where Vi is the partial molar volume. In a glass sheet under a bending stress, there is a gradient of hydrostatic pressure (as well as shear) through the sheet, tending to drive the mobile Na ions from regions of compression to regions of tension, and equilibrium will be reached when the space-charge buildup balances the driving force of the pressure gradient. The initial current prior to space-charge limitation was measured in a soda-lime—silica glass sheet, and the partial volume of the Na ion in this glass calculated to be 2.2 Å3. This figure is surprisingly high, about ⅗ of the cation volume. A naive calculation attributing the volume change to electrostrictive effects gives reasonable agreement with this result, but further experiments are needed to test this explanation.