# In situ measurements of the axial expansion of palladium microdisks during hydrogen exposure using diffraction phase microscopy

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We measured the height of Pd microdisks during H2 exposure using epi-illumination diffraction phase microscopy, a quantitative phase imaging technique for capturing nanoscale dynamics in situ. From these microdisk height measurements, we extracted the axial expansion coefficient as a function of H2 concentration as well as image sequences that show the instantaneous rate of axial expansion in a spatially and temporally resolved manner. Quantifying these two parameters is important in modeling Pd-based H2 sensors. For H2 concentrations below 0.5%, i.e. an order of magnitude below the lower explosive limit, the axial expansion coefficient followed the Freundlich distribution: Δh(c) = 1.28 c0.51 where Δh is the percentage change in height of the Pd microdisk and c is the percent concentration of H2 in N2. The fit agrees well with the anticipated square root dependence for diatomic gas.