Compute Geometric Material Properties

In filtration, energy storage, catalysis, or the development of new materials, microstructure determines success or failure. But how precise is your understanding of the solid structure of porous materials?

MatDict is a specialized analysis module designed to extract and quantify key geometric properties of the solid phase - including material thickness, heterogeneity, particle size distribution, surface area, and connectivity.

The data basis: high-resolution 3D models from CT, µCT, FIB/SEM, or geometries generated with GeoDict.
The result: A reliable assessment of structural parameters that significantly determine mechanical strength, service life, and functional efficiency.

• Battery electrodes: Structural insights for increasing energy density and service life.
• Fuel cells: Analysis of the gas diffusion layer for higher system efficiency. 
• Reservoir analysis: Reliable evaluation of complex sandstone structures. 
• Filter media: Optimization of fabrics and nonwovens for high-performance filter systems.

Whether you're designing new materials or refining existing ones, MatDict provides the deep structural insight needed to make informed decisions - faster and with greater confidence.

MatDict provides multiple options to compute all relevant geometric properties of the solid material phase.

The Structure Information option enables the computation of fundamental material properties, such as porosity, density, grammage, and material fractions. These calculations can be performed in all three spatial directions, providing comprehensive insights into the material's characteristics.

Accurate Thickness Estimation is key for characterizing material microstructures and understanding their impact on performance. Advanced imaging combined with computational analysis enables precise mapping of thickness variations across a sample [1]. This detailed measurement not only informs quality control but also guides material design by correlating thickness with properties such as mechanical strength and thermal behavior.

The 2D Density Map option analyzes the spatial heterogeneity of materials by computing the distribution of grammage, solid volume fraction (SVF), and object count across planes in a specified direction. Each pixel in these planes represents the averaged property value along the direction of interest, providing detailed insights into variations such as cloudiness within the material.

The 3D Inhomogeneity tool analyzes material heterogeneity by dividing the structure into defined sub-volumes and calculating histograms of solid volume fraction or material fraction. This provides a clear visualization of spatial variations within the material.

With the option Solid Size Distribution, one characterizes the solid material size distribution by fitting spheres into the solid material phase. This purely geometrical method does not distinguish between single objects / grains in the material (single grains can be identified with the module GrainFind).

Computing Connected Components distinguishes separate regions within a microstructure, highlighting connectivity and isolation. This insight is vital for understanding percolation, transport behavior, and structural integrity, which helps optimize material performance.

The Percolation Path option calculates the maximum diameter of a spherical particle that can traverse the medium through the solid material phase. It also determines the corresponding shortest path. Additionally, users can compute specific cases, such as the five largest path diameters (along with their shortest paths) or the eight shortest paths for a given path diameter. The movement of spheres along these paths is visualized and animated.

The feature Estimate Surface Area is vital for characterizing material microstructures as it quantifies the total interfacial region where key physical and chemical processes occur. This metric reveals critical information about reaction sites, diffusion paths, and interphase interactions, enabling researchers to predict and optimize material behavior in applications such as catalysis, adsorption, and energy storage.

Reference: J. Ohser, F. Mücklich, Statistical Analysis of Microstructures in Materials Science, Wiley and Sons (2000)

With Estimate Three-Phase Contact Line one captures the regions where three distinct phases converge. This analysis provides valuable insights into wetting dynamics, capillary forces, and interfacial reactivity, which are critical for optimizing processes like emulsification, catalysis, and energy conversion.

Minkowski Parameters offer a powerful way to quantify the geometry and topology of complex microstructures. By calculating these parameters—such as volume, surface area, curvature, and connectivity, researchers can objectively describe features that are otherwise difficult to characterize visually. This quantitative insight is essential for correlating microstructural characteristics with material properties.

Reference: J. Ohser, F. Mücklich, Statistical Analysis of Microstructures in Materials Science, Wiley and Sons (2000)

The option GAD Object Orientation allows you to compute the orientation tensor for a given object type. In this way one can check the orientation for all geometries created with GeoDict, for example with GrainGeo or FiberGeo.

The Chord Length Distribution (CLD) enables precise comparison of complex media geometries. Unlike traditional size distribution methods, CLD is particularly useful for 2D cross-sections where direct size measurements are impractical. By analyzing chord lengths - linear segments traversing the solid phases - it provides insights into solid connectivity, anisotropy, and heterogeneity.

Geodesic Tortuosity quantifies the complexity of transport pathways in complex material geometries by measuring the ratio of the shortest actual path through the medium to the straight-line distance. It provides insights into conductivity, diffusion, and connectivity, helping to assess effective conductivity and transport efficiency. Higher tortuosity indicates more convoluted pathways, which can impede transport.

The option 2-Point Correlation function offers a concise statistical description of a material's microstructure by quantifying the likelihood that two points, separated by a specific distance, belong to the same phase. This measure effectively captures essential spatial patterns, aiding in the prediction of material properties and guiding the optimization of material design.

The Analyze Objects feature computes various properties, distributions, and statistics of material models based on objects information like GeoDict’s analytic data, whether created within GeoDict or derived from CT scans analyzed using modules like GrainFind and FiberFind. These analyses can yield results like contact area histograms and coordination numbers, offering insights into the interactions and connectivity within the material.

Computing the Euclidean Distance Transform (EDT) for complex materials is essential for accurately characterizing their microstructure. The EDT calculates the shortest distance from any point within the pore space to the nearest solid boundary, providing a spatial map of local pore sizes.

The option Skeletonizer computes the material skeleton of structures and provides a simplified representation of their complex geometry, capturing essential features such as connectivity and topology.

One powerful GeoApp to analyze complex materials is also included: The app Compute Fractal Dimension allows to compute the fractal dimension for a given complex structure using the box counting algorithm.