Original title: Lorenz-Gini method for quantitative assessment of particle distribution in composite microstructures from SEM feature areas
Festus Ben · September 2026
Scientists make composite materials by mixing small particles into metals, such as agro-waste-reinforced metal matrix composites. To check if particles spread out evenly, researchers usually just look at microscope pictures and guess. This visual check is subjective and can be inconsistent. To solve this, researchers created a math-based method using microscope pictures. First, software finds each particle and measures its area. Next, the method arranges these particle areas to build a cumulative distribution. Then, it uses a Lorenz curveA graph that shows how a total amount (like total area of particles) is shared across different portions of the sample, often used in economics to show income inequality., a type of graph, to plot the distribution pattern. Finally, it calculates a single number called the Gini coefficientA single number between 0 and 1 that measures inequality: 0 means everyone has the same share, 1 means one person has everything. to measure area inequality. This gives scientists a reproducible way to measure and compare particle spread across samples without relying on guesswork.
Imagine you are pouring toppings on a pizza and you want each slice to have a similar amount. If you look at the pizza and just judge by eye, one person might think it is even while another disagrees. Here, the method turns each topping piece into a number, plots how those numbers add up across slices, and produces a single score that tells you how evenly they are spread. In this paper, the toppings are reinforcing particles in a composite material, the pizza slices represent different parts of the sample, and the score is the Gini coefficient.
Engineers who make composite materials—like car parts or airplane panels—need to know if tiny strengthening particles are evenly mixed. Until now, judging that often meant staring at microscope images and guessing. This method turns each image into one number, so different batches or recipes can be compared fairly and automatically.
The abstract does not state a numerical threshold or benchmark for what Gini value constitutes 'good' dispersion. It also does not validate the metric against mechanical properties or compare it to existing quantitative methods. The method assumes particles are fully segmented, which may fail for touching or overlapping features in crowded micrographs.
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Lorenz-Gini method for quantitative assessment of particle distribution in composite microstructures from SEM feature areas — Festus Ben — MethodsX — doi:10.1016/j.mex.2026.104141
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper.