Methods for determining a weathering index using x-ray diffraction (XRD) data are provided. An exemplary method includes obtaining XRD data of a weathered rock sample, and calculating the weathering index using a formula developed to use the XRD data.

The invention provides a system and method for characterising at least part of a material comprising: a source of incident X-rays (4, 28) configured to irradiate at least part of the material; one or more detectors (300,302,312,1701,1704,1600,1607,1608,1604) adapted to detect radiation emanating from within or passing through the material as a result of the irradiation by the incident radiation (1700) and thereby produce a detection signal (313); and one or more digital processors (304-311,2000-2009) configured to process the detection signal (313) to characterise at least part of the material; wherein the one or more detectors (300,302,312,1701, 1704,1600,1607,1608,1604) and one or more digital processors (304-311,2000-2009) are configured to characterise at least part of the material by performing energy resolved photon counting X-ray transmission spectroscopy analysis.

Methods and systems for spectroscopic analysis of focused ion beam induced optical emission include accessing a spectrum acquired from a sample responsive to irradiating the sample with an ion beam and identifying the spectral peaks of the spectrum. The emission type of the spectral peak is determined based on a spectral resolution of a light collection system for collecting the spectrum. The emission types include elemental emission, molecular emission, and bandgap emission.

A correction apparatus for correcting a structure factor includes a structure factor acquisition section that acquires the structure factor; a PDF calculation section that calculates PDF from the acquired structure factor; a correction function preparation section that prepares a first correction function that is Fourier-transformed in a predetermined range, and a second correction function that is Fourier-transformed in the predetermined range, the first correction function comprising data of the PDF and a cut-off function for cutting off data on a long distance side of the PDF and the second correction function comprising the cut-off function; a correction amount calculation section that calculates a correction amount comprising the first correction function, the second correction function, and a scale factor; a structure factor correction section that corrects the structure factor; and an R-factor value calculation section that calculates an R-factor value indicating correction accuracy.

A method for analyzing secondary ion mass spectrum data representing respective secondary ion counts for a range of masses at a given mass resolution. The mass spectrum data is obtained by Secondary Ion Mass Spectrometry, SIMS. Automatic quantification of the ion species and/or cluster ions detected in the analyzed spectrum data is provided.

A material characterization system and method for characterizing a stream of material emanating from a material identification, exploration, extraction or processing activity, the system including a source of incident radiation configured to irradiate the stream of material in an irradiation region, one or more detectors adapted to detect radiation emanating from within or passing through the stream of material as a result of the irradiation by the incident radiation and thereby produce a detection signal, and one or more digital processors configured to process the detection signal to characterise the stream of material, wherein the source of incident radiation and the one or more detectors are adapted to be disposed relative to the stream of material so as to irradiate the stream of material and detect the radiation emanating from within or passing through the stream as the stream passes through the irradiation region.

In order to increase reproducibility of a reconstructed tomographic image without increasing the computational load, detection is performed by oversampling in (N+n) directions during imaging for detection by N detection elements. A vector having N×(N+n) elements is obtained, and vector decimation step is performed in which a total of n×N elements corresponding to a sequence {k} 30 denoting a decimation order are removed. In a discrete Radon transform step, a corresponding discrete Radon inverse matrix W.sub.SQ.sup.−140 is operated, and in an image data generation step, de-vectoring is performed, thereby tomographic image data are acquired. When oversampling is used, a discrete Radon inverse matrix W.sub.SQ.sup.−1 is obtained. Therefore, a tomographic image is obtained by matrix computation without resorting to iterative approximation.

A method for analyzing secondary ion mass spectrum data representing respective secondary ion counts for a range of masses at a given mass resolution. The mass spectrum data is obtained by Secondary Ion Mass Spectrometry, SIMS. Automatic quantification of the ion species and/or cluster ions detected in the analyzed spectrum data is provided.

In order to increase reproducibility of a reconstructed tomographic image without increasing the computational load, detection is performed by oversampling in (N+n) directions during imaging for detection by N detection elements. A vector having N×(N+n) elements is obtained, and vector decimation step is performed in which a total of n×N elements corresponding to a sequence {k} 30 denoting a decimation order are removed. In a discrete Radon transform step, a corresponding discrete Radon inverse matrix W.sub.SQ.sup.−140 is operated, and in an image data generation step, de-vectoring is performed, thereby tomographic image data are acquired. When oversampling is used, a discrete Radon inverse matrix W.sub.SQ.sup.−1 is obtained. Therefore, a tomographic image is obtained by matrix computation without resorting to iterative approximation.

Atomic position data may be obtained from x-ray diffraction data. The x-ray diffraction data for a sample may be squared and/or otherwise operated on to obtain input data for a neural network. The input data may be input to a trained convolutional neural network. The convolutional neural network may have been trained based on pairs of known atomic structures and corresponding neural network inputs. For the neural network input corresponding to the sample and input to the trained convolutional neural network, the convolutional neural network may obtain an atomic structure corresponding to the sample.