Mapping of mechanical properties for diagnostics of inclusions in complex multi-phase Minerals
A method of the instrumental indention or nanoindention [1, 2] performed well as a non-destructive method to measure mechanical properties of various objects. This method allows of estimating properties of small objects like thin coatings or micron size grains because of light load and penetration depth . Local measurements make it possible to study distribution of the non-uniform sample properties of complex shape and composition [4, 5], including an inhomogeneity due to external influence [6, 7]. The deformation area of the material is so small that it allows of studying the inhomogenuity with micron lateral resolution, which is useful when studying the border regions in the heterogeneous materials [8, 9].
Besides, there is a competing method for the mechanical properties mapping based on the probe contact scanning of the material’s surface in the dynamical mode [10, 11]. This method has a high measurement rate and a better lateral resolution due to the lower applied force but it has a couple of limitations. The most important limitations of this method are: purity of the surface and high requirements to treatment of the surface, moreover, the calibration procedure is too complicated, hence, the accuracy of the meaningful measurements is hardly obtained. However, it is useful to apply different methods of mapping in order to study the materials in various scales . Indention method and mapping can be applied to study a large number of materials ranging from the soft organic tissues  to the super hard composites . Statistical data manipulation of the indention allows us to isolate and analyze the separate phase properties of the multi-component samples including porous minerals [15–17].
Automated mapping method is an important instrument to investigate the spatial inhomogenuity of complex multi-phase material mechanical properties, especially in geology. This method is advantages in comparison with other methods in the cases when inclusions similar in chemical composition appear to be identical though they possess significantly different mechanical properties.
In this paper we present a mapping method of the natural mineral sample properties and determine the phases different by their mechanical properties using a NanoScan nano-hardness tester.
RESEARCH AND EQUIPMENT
Nano-indention method is based on an impression of a known shape hard tip (indenter) into the sample to be studied. Measured are the loading force and the displacement of the indenter when testing.
Analysis of the force versus displacement curve (depth of penetration) allows of calculating the surface area and rigidity corresponding to the contact area of the indenter with the material when testing. These data are used to determine hardness and modulus of elasticity of the sample.
The sample hardness is defined as the average contact pressure under the indenter and is calculated as the ratio of the applied force to the contact area.
The modulus of elasticity during indention is calculated from the slope of the tangent to the unloading curve. Its value is close to the value of the Young’s modulus of the material (modulus of longitudinal elasticity).
Indention tests were performed using a NanoScan 4D nano-hardness tester (Fig.1) [18, 19]. Optical images were obtained by Mitutoyo VMU-V inner optical module equipped with a polarizing filter.
Mechanical properties data, including calculations of mechanical properties and construction of multi-layer maps, was carried out with the software developed for the NanoScan devices.
The software for creating and processing the multi-layered interactive maps of the tested sample surfaces presents a graphical user interface in which the video stream from the microscope is available to the researcher, frames from this video stream are captured, the layers are created and edited (combination of some frames into one cluster according to the researcher’s tasks), viewing of the resulting sample maps, installation of planned tests and viewing of a mini-map for easy navigation with a microscope on a sample.
The process of "stitching" frames occurs due to coordinates of the centers of each image obtained from the microscope positioning system, as well as the calibration data. To get the latest frames, the user must select the current camera settings (resolution) and microscope objective (magnification) and start the calibration process. The software takes a set of snapshots of overlapping areas and detects and maps particular points (using the open-source OpenCV library and AKAZE algorithm). Based on the matched pairs of points, a conclusion is drawn about the geometry of the original image and a frame displacement relative to each other. This process should be performed for each camera-microscope-magnifying lens set.
To obtain a sample map dynamically, an algorithm is used that loads only those frames with a dynamically selected resolution from the hard disk of the device (to save RAM) which are necessary to build the viewed area of the map and construct the resulting image from the calibration data. Due to the rigid binding of coordinates to the image, it is possible to obtain a one-to-one correspondence between each pixel and the device coordinate. The indentations can be applied to this sample map in places where the measurements have been or will be taken. The results of indentation data processing are attached to the coordinates of the optical image, which allows mapping of the mechanical properties. The overlay of several layers of different levels of transparency allows of obtaining a visualization of the inhomogenuity of the sample.
This algorithm with dynamic mapping and storing the original images on the hard disk allows of performing the additional calibration at any time, selection of displayed frames and layers and continuation of the previously saved experiment.
Fig.2 and 3 demonstrate the same area of the sample in different modes. Fig.2 is an optical micrograph of the surface in polarized light. Fig.3 is a black and white optical image with a superimposed color hardness map. Gradient scale shows the dependence of color on the hardness measured in the corresponding area of the sample.
In the photo obtained in the polarized light, four phases are clearly distinguished (Fig.2). Phase 1 has a minimum hardness of 7.5 GPa and an elastic modulus of 230 GPa. Phases 2, 3, and 4 are almost twice as hard as the first, about 14 GPa. The modulus of elasticity is also higher: 3 and 4 phases have a modulus of 270 GPa, with a second phase of 260 GPa.
Analysis of the phase composition can be estimated by constructing the frequency distribution of the mechanical properties. Figure 4 presents such a distribution in the form of histograms, which is a visual representation of the function of a probability density of measured random variables: hardness and elastic modulus. Analysis of statistical data allows of calculating the share of a particular phase in the material, as well as such parameters of their properties as the mean value and dispersion.
The nanoindention method is a method of local measurement of mechanical properties allowing of detecting separate phases in multi-component materials. Especially well this method can be used in mineralogy, where multiphase samples of a close chemical composition occur often though they differ in their physical properties. Mapping of mechanical properties is a visual instrument to study inhomogenuities of materials under testing and complements well the optical research methods. ■