Real and reciprocal space order parameters for porous arrays from image analysis

A real space technique based on the pair distribution function (PDF) and a reciprocal space method utilizing a 2D fast Fourier transform (FFT) quantify the order in porous arrays. Porous arrays fabricated from nanoscience technology are analyzed. The PDFs are fit with a series of Gaussian curves and the widths of the Gaussian peaks are used to model the linear strain in the array. An order parameter is defined from the PDF and takes values from [0,1], where the value 1 represents an ideal array. The radial distribution function (RDF) is also determined for the porous arrays. The FFT of the porous arrays is used to generate an order parameter as a ratio of intensity to the full width at half maximum (σ) of the peaks. Defined as relative intensity , this parameter takes values from [0,∞], where larger values represent more order in the array. We use a variety of available software to generate this data.