Method of material analysis and manufacturing

Abstract

A method (100) of analysing a material comprises obtaining atomic data relating to the location of atoms within the material (110); performing a calculation on the atomic data to generate a plurality of mathematical functions relating to the spatial distribution of the atoms according to one or more predefined parameters (120); calculating a statistical distribution of the generated mathematical functions (130); and determining the detected microstructure of the material based on the statistical distribution (140). An alternative analysis method (500) uses a plurality of k-Nearest Neighbour (kNN) distributions as the mathematical functions and calculates one or more Short Range Order (SRO) values from the plurality of kNN distributions. A method (300) of manufacturing a product using the analysis method (100) and related system (400) are also provided.

Description

Method of Material Analysis and ManufacturingCross-Reference to Priority Application

[0001] This application claims priority to Australian Provisional Patent Application No. 2024901772 filed on 12 June 2024, the contents of which are hereby incorporated by reference in their entirety.Field of the Disclosure

[0002] The disclosure relates to a method of material analysis and in a particular to a method of manufacturing using the method of material analysis. The disclosure has been developed primarily for use as a method of analysing materials at the microstructure level and its application in a method of manufacturing a product comprising the analysed material, and will be described hereinafter by reference to this application. It will be appreciated that the invention may be used in many manufacturing applications for a variety of materials, including metal alloys, ceramics and semiconductors.Background of the Disclosure

[0003] The following discussion of the prior art is intended to present the disclosure in an appropriate technical context and allow its advantages to be properly appreciated. Unless clearly indicated to the contrary, however, reference to any prior art in this specification should not be construed as an express or implied admission that such art is widely known or forms part of common general knowledge in the field.

[0004] The smallest building block for both synthetic and natural structures is the atom. This means that the design-critical engineering properties of materials depend fundamentally on the arrangement of the atoms within the material. For example, mechanical properties like ductility and tensile strength, and chemical properties like corrosion resistance, are a consequence of the particular arrangements of the constituent atoms of the material, also known as the microstructure of the material. The critical parameters of these atomic arrangements are their spacings, symmetries and chemical distributions. These determine the local electronic density of states which govern the state of the material. This information together with the grain size, phase,defect and textural distribution information are typically key variables that control the macro-behaviour of solid-state materials.

[0005] Hence, the properties of a material are governed by its microstructure, which is a consequence of the manufacturing process used to produce the material, especially where the material is being manufactured into a particular part or component of a machine or other device. Determining quantitatively how the microstructure (and hence properties) of materials are affected by the manufacturing process remains an enormous challenge in materials science, engineering and industry. This challenge is primarily due to the difficulty of quantifying the microstructure of the manufactured material.

[0006] Consequently, it is difficult to ensure that manufactured materials (and the parts or components made of that material) have the desired properties initially designed for when commencing the manufacturing process. That is, frequently the initial design of a material or part to be manufactured may not exhibit the desired properties due to variances in the microstructure that form during the manufacturing process and cannot be designed around. This results in significant wastage of resources and time due to the need to produce and test prototypes or samples to check that the desired properties are exhibited by the manufactured material or part based on the initial design requirements. This creates further problems when the manufactured material or part needs to be certified or qualified before it can be used, such as being certified as meeting an industry or regulatory standard, or meeting a contractual design requirement. For example, electronic components are manufactured with semiconductor material having a required number of dopant atoms to control or improve their conductivity, optical properties and / or physical properties. Similarly, the thermomechanical processing of metal alloys frequently require specific final physical or mechanical properties in the metal alloy that have to be achieved via complex, multi-stage thermomechanical processing (manufacturing).

[0007] Often, a manufacturer will design a specific part that has certain requirements as to its mechanical, chemical and / or physical properties, and invest capital expenditure into manufacturing equipment, but find it difficult to manufacture the specific part with satisfactory reliability, such that it can pass end-user certification and qualification requirements.

[0008] It is an object of the present disclosure to overcome or substantially ameliorate one or more of the disadvantages of prior art, or at least to provide a useful alternative. It is an object of the disclosure in at least one preferred form to provide a method for analysing materials based on their microstructure, and a method and system for manufacturing a product incorporating the analysis method.Summary of the Disclosure

[0009] A first aspect of the disclosure provides a method of analysing a material, comprising: obtaining atomic data relating to the location of atoms within the material; performing a calculation on the atomic data to generate a plurality of mathematical functions relating to the spatial distribution of the atoms according to one or more predefined parameters; calculating a statistical distribution of the generated mathematical functions; and determining a detected microstructure of the material based on the statistical distribution.

[0010] In one or more embodiments, the method comprises determining one or more properties of the material from the detected microstructure.

[0011] In one or more embodiments, determining the detected microstructure comprises determining the concentration and / or arrangement of atoms according to the one or more predefined parameters from the statistical distribution. In one or more embodiments, the concentration of the atoms according to the one or more predefined parameters indicates a clustering effect of the atoms to exhibit the one or more properties of the material.

[0012] In one or more embodiments, the plurality of mathematical functions comprises k-Nearest Neighbour (kNN) distributions. In one or more other embodiments, the plurality of mathematical functions comprises Short Range Order (SRO) values. In one or more other embodiments, the SRO values are calculated from the kNN distributions. In one or more further embodiments, the plurality of mathematical functions comprises probability functions representing local composition parameters. In one or more further embodiments, the plurality of mathematical functions comprises voxelisation of the spatial distribution of atoms.

[0013] In one or more embodiments, the method comprises assigning weights to one or more of the mathematical functions. In one or more embodiments, the method comprises calculating the statistical distribution based on the weighted mathematical functions.

[0014] In one or more embodiments, the method comprises selecting one or more of the plurality of mathematical functions as a representative mathematical function of a subset of mathematical functions. In one or more embodiments, the method comprises calculating the statistical distribution based on the representative mathematical functions.

[0015] In one or more embodiments, the method comprises obtaining the atomic data using a microscopy method. In one or more embodiments, the microscopy method comprises one or more of light-optical microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), atom probe microscopy (APM), X-ray scattering and neutron scattering. In one or more embodiments, the SEM method comprises at least one of backscattered electron imaging (BSI), secondary electron imaging (SEI), transmission Kikuchi diffraction (TKD), electron backscattered diffraction (EBSD) and energy dispersive X-ray spectroscopy (EDXS). In one or more embodiments, the TEM method comprises at least one of scanning TEM (STEM), electron energy loss spectrometry (EELS), EDXS and a TEM based diffraction technique. In one or more embodiments, the APM method comprises at least one of mass spectrometry, field ion microscopy (FIM), field evaporation microscopy (FEM) and atom probe tomography (APT).

[0016] In one or more embodiments, the method comprises retrieving a sample of the material to obtain the atomic data. In one or more embodiments, the sample is retrieved using a focussed ion beam (FIB) specimen extraction method. In one or more embodiments, the sample is retrieved using precision mechanical sectioning, further cutting or electrolytic polishing.

[0017] In one or more embodiments, the atomic data comprises data relating to the state of the material at one or more predetermined times and / or locations. The state of the material may relate to a thermal state of the material. In one or more embodiments, the atomic data comprises thermal data relating to the temperature of the atoms within the material based on their location over a predetermined time period. In one or more embodiments, the atomic data comprises atomic-scale microstructural data.

[0018] In one or more embodiments, local measurements of properties may be made from the material at one or more locations adjacent or in proximity to where the sample was obtained. These local measurements may be local mechanical property measurements, such as hardness, but may also comprise local magnetic property measurements, or electrical property measurements.

[0019] In one or more embodiments, the one or more predefined parameters comprises atomic species. In one or more other embodiments, the one or more predefined parameters comprises distances between a designated atom from one or more other atoms.

[0020] In one or more embodiments, the method comprises altering the material in response to the detected microstructure of the material. In one or more embodiments, the material is altered in response to the detected microstructure being substantially different to a target microstructure.

[0021] In one or more embodiments, the method comprises generating the target microstructure of the material and comparing the detected microstructure to the target microstructure. In one or more embodiments, the target microstructure is generated from an initial set of data relating to the material. In one or more embodiments, the initial set of data is derived from theoretical values relating to the material or measurements taken prior to formation of the material.

[0022] In one or more embodiments, the method comprises determining one or more properties of the material from the detected microstructure of the material. In one or more embodiments, the one or more properties of the material comprises one or more of tensile strength, shear strength, yield strength, ductility, malleability, combustibility, density, hardness, plasticity, elasticity, stiffness, fracture resistance, fatigue resistance, corrosion resistance, wear resistance, electrical conductivity, and both soft and hard magnetic properties.

[0023] A second aspect of the disclosure provides a method of manufacturing a product comprising at least a first material, comprising: performing one or more manufacturing steps on the first material for producing the product having a target microstructure;performing a method of analysis of the first material, wherein the analysis method is in accordance with the first aspect; comparing the detected microstructure to the target microstructure; and adjusting at least one of the manufacturing steps in response to the detected microstructure being substantially different to the target microstructure.

[0024] In one or more embodiments, the adjusting step comprises changing one of the manufacturing steps to modify the detected microstructure of the first material to the target microstructure. In one or more embodiments the adjusting step comprises modifying a first manufacturing step to modify the detected microstructure.

[0025] In one or more embodiments, there is at least a first manufacturing step, wherein the adjusting step comprises performing a second manufacturing step on the first material to modify the detected microstructure of the first material to the target microstructure. In one or more embodiments, the adjusting step comprises performing the second manufacturing step after stoppage or completion of the first manufacturing step

[0026] In one or more embodiments, the adjusting step further comprises adjusting one or more design parameters of the product prior to repeating the one or more manufacturing steps.

[0027] In one or more embodiments, the obtaining and analysis steps are repeated after the adjusting step. In one or more embodiments, the obtaining, analysis and adjusting steps are repeated until the detected microstructure is substantially the same as the target microstructure.

[0028] In one or more embodiments, the atomic data is obtained directly from the first material during the one or more manufacturing steps. In one or more other embodiments, a sample of the first material is taken during the one or more manufacturing steps and the atomic data is obtained from the sample.

[0029] In one or more embodiments, the method comprises generating the target microstructure of the first material. In one or more embodiments, the target microstructure is generated from an initial set of data relating to the first material. In one or more embodiments, the initial set of data may be derived from theoretical values orfrom data acquired from the first material prior to performing the one or more manufacturing steps.

[0030] In one or more embodiments, the product comprises at least a second material, wherein the method is also performed in relation to the second material. That is, the one or more manufacturing steps are performed on the second material for producing a second target microstructure, the atomic data obtaining and analysis steps are performed in respect of the second material and the one or more manufacturing steps are adjusted to modify the detected microstructure of the second material to the second target microstructure. In one or more embodiments, the one or more manufacturing steps are performed simultaneously on the first and second materials. In one or more embodiments, the one or more manufacturing steps are performed sequentially on the first and second materials.

[0031] In one or more embodiments, the first material comprises a metal or metal alloy. In one or more embodiments, the metal alloy comprises a multicomponent alloy or a medium or a high entropy alloy (M / HEA). In one or more embodiments, the first material comprises a ceramic material. In one or more embodiments, the first material comprises a semiconductor material

[0032] In one or more embodiments, the product comprises an electronic component comprising semiconductor material. In one or more embodiments, the product comprises a machine component or part.

[0033] One or more embodiments of the second aspect may have the features of one or more embodiments of the first aspect of the disclosure stated above, where applicable. In particular, the analysis step may be performed in accordance with one or more embodiments of the first aspect.

[0034] A third aspect of the disclosure provides a system for manufacturing a product comprising at least a first material, comprising: one or more manufacturing machines for performing one or more manufacturing steps on the first material to produce the product having a target microstructure; a control unit configured to control the one or more manufacturing machines;a data retrieval unit for obtaining atomic data relating to the location of atoms within the first material; and a processor configured to perform a method of analysis of the first material, wherein the analysis method comprises: performing a calculation on the atomic data to generate a plurality of mathematical functions relating to the spatial distribution of the atoms according to one or more predefined parameters; calculating a statistical distribution of the generated mathematical functions; determining a detected microstructure of the first material based on the statistical distribution; and comparing the detected microstructure to the target microstructure; wherein the control unit is configured to adjust operation of the one or more manufacturing machines in response to the detected microstructure being substantially different to the target microstructure.

[0035] In one or more embodiments, the control unit is configured to adjust operation of the one or more manufacturing machines such that the detected microstructure of the first material is modified to the target microstructure.

[0036] In one or more embodiments, the one or more manufacturing machines modifies a first manufacturing step to modify the detected microstructure. In one or more embodiments, there is at least a first manufacturing step, and the one or more manufacturing machines performs a second manufacturing step on the first material to modify the detected microstructure. In one or more embodiments, the one or more manufacturing machines perform the second manufacturing step after stoppage or completion of the first manufacturing step.

[0037] In one or more embodiments, the data retrieval unit obtains the atomic data directly from the first material during operation of the one or more manufacturing machines. In one or more other embodiments, data retrieval unit obtains the atomic data from a sample of the first material taken during operation of the one or more manufacturing machines.

[0038] In one or more embodiments, the data retrieval unit comprises a microscopy instrument. In one or more embodiments, the data retrieval unit comprises one or moreof a light-optical microscope, an electron microscope, an atomic force microscope (AFM), a scanning tunnelling microscope, an atom probe microscope, and an X-ray microscope.

[0039] In one or more embodiments, the processor is configured to generate the target microstructure from an initial set of data relating to the first material. The initial set of data may be derived from theoretical values or from data acquired from the first material prior to performing the one or more manufacturing steps.

[0040] In one or more embodiments, the data retrieval unit obtains an additional set of the atomic data and the processor performs the analysis method on the additional set of the atomic data after the control unit adjusts operation of the one or more manufacturing machines. In one or more embodiments, the system is configured so that the data retrieval unit obtains the atomic data, the processor performs the analysis method and the control unit adjusts operation of the one or more manufacturing machines iteratively until the detected microstructure is substantially the same as the target microstructure.

[0041] In one or more embodiments, the product comprises at least a second material, wherein the system is configured to perform the method in relation to the second material. That is, the one or more manufacturing machines performs the one or more manufacturing steps on the second material for producing a second target microstructure, the data retrieval unit obtains atomic data relating to the location of atoms in the second material, the processor performs the analysis method in relation to the second material and the control unit adjusts operation of the one or more manufacturing machines in response to the detected microstructure of the second material being substantially different to the second target microstructure.

[0042] One or more embodiments of the third aspect may have the features of one or more embodiments of the first and / or second aspects of the disclosure stated above, where applicable. In particular, the processor may perform the analysis step in accordance with one or more embodiments of the first aspect.

[0043] A fourth aspect of the disclosure provides a method of analysing a material, comprising: obtaining atomic data relating to the location of atoms within the material; performing a calculation on the atomic data to generate a plurality of k-Nearest Neighbour (kNN) distributions according to one or more predefined parameters;calculating one or more Short Range Order (SRO) values from the plurality of kNN distributions; and determining a detected microstructure of the material based on the one or more SRO values.

[0044] In one or more embodiments, the method comprises determining one or more properties of the material from the detected microstructure.

[0045] In one or more embodiments, determining the detected microstructure comprises using the one or more SRO values to determine whether the atoms have a clustering effect to cause the material to exhibit the one or more properties of the material. In one or more embodiments, determining the detected microstructure comprises using the one or more SRO values to determine whether the atoms have a random or anti-clustering effect to cause the material not to exhibit the one or more properties of the material.

[0046] In one or more embodiments, the calculation of SRO values comprises selecting a representative kNN distribution from the plurality of kNN distributions and calculating the SRO values for that representative kNN distribution. In one or more embodiments, the calculation of SRO values comprises calculating the SRO values from some or all of the kNN distributions.

[0047] In one or more embodiments, the calculation of SRO values comprises applying a correction or calibration factor to take into account variances occurring when the atomic data is obtained. In one or more embodiments, the correction or calibration factor comprises assigning a true SRO value based on a theoretical value and dividing the true SRO value by the measured SRO value.

[0048] One or more embodiments of the fourth aspect may have the features of one or more embodiments of the first aspect of the disclosure stated above, where applicable, including the steps relating to the atomic data, altering the material in response to the detected microstructure of the material, generating the target microstructure of the material, determining one or more properties of the material from the detected microstructure of the material, the one or more predefined parameters and the one or more properties of the material.

[0049] A fifth aspect of the disclosure provides a method of manufacturing a product comprising at least a first material, comprising: performing one or more manufacturing steps on the first material for producing the product having a target microstructure; performing a method of analysis of the first material, wherein the analysis method is in accordance with the fourth aspect; comparing the detected microstructure to the target microstructure; and adjusting at least one of the manufacturing steps in response to the detected microstructure being substantially different to the target microstructure.

[0050] One or more embodiments of the fifth aspect may have the features of one or more embodiments of the second and / or fourth aspects of the disclosure stated above, where applicable, including the steps relating to adjusting the manufacturing step(s).

[0051] Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.

[0052] Furthermore, as used herein and unless otherwise specified, the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.Brief Description of the Drawings

[0053] Preferred embodiments of the disclosure will now be described, by way of example only, with reference to the accompanying drawings in which:

[0054] Figure 1 is a schematic drawing of the various scales by which a material can be viewed;

[0055] Figure 2 is a schematic drawing illustrating the connection between the atomic arrangement of a material and the material’s properties;

[0056] Figure 3 is a schematic drawing of a method of analysing a material according to an embodiment of the disclosure;

[0057] Figure 4 is a schematic drawing of an APT method to acquire atomic data;

[0058] Figure 5 is a tomogram or atom map showing atoms within an exemplary material obtained by using the APT method of Figure 4;

[0059] Figure 6 is a schematic drawing of a typical spatial distribution of the map;

[0060] Figure 7A(a) illustrates atom maps of copper in a material, simulated and experimental;

[0061] Figure 7A(b) is a schematic graph of SRO values for a copper-copper pair;

[0062] Figure 7A(c) is a schematic graph of a distribution of the spatial distributions relating to Figures 7A(a) and 7A(b);

[0063] Figure 7B is a schematic drawing illustrating nearest neighbour relationships between atomic species;

[0064] Figure 8 is a schematic drawing illustrating a method of manufacturing a material according to another embodiment of the disclosure;

[0065] Figure 9 is a schematic drawing illustrating a system for manufacturing a material according to another embodiment of the disclosure;

[0066] Figure 10 is a schematic drawing of a method of analysing a material according to another embodiment of the disclosure;

[0067] Figures 11 (a) to 11 (g) are schematic graphs illustrating the calculation of SRO values based on a kN N distribution of atoms and includes the effects of detector efficiency and spatial resolution in the case of a kN N distribution of atoms measured using atom probe tomography;

[0068] Figure 12(a) is a schematic drawing of an atom map;

[0069] Figures 12(b) to 12(e) are schematic graphs of density maps for an example alloy that demonstrate an approach to validate or range the in-depth resolution of the atom probe tomography method;

[0070] Figures 13(a) to 13(d) are schematic graphs illustrating “measured” SRO values against “true” SRO values at different resolutions for a simulated model;

[0071] Figures 14(a) and 14(b) are schematic graphs illustrating “measured” SRO values against “true” SRO values at different resolutions for a simulated model;

[0072] Figures 15(a) to 15(d) are schematic graphs illustrating “measured” SRO values against “true” SRO values after simulation of the instrumental effects of atom probe on the measurement;

[0073] Figures 16(a) to 16(d) are schematic graphs comparing SRO values in two different samples of the same alloy following different heat treatment (or manufacturing) processes;

[0074] Figures 17(a) to 17(d) are schematic graphs illustrating mass to charge ratios for the two samples;

[0075] Figures 18(a) and 18(b) are TEM diffraction patterns and intensity graphs for the two samples;

[0076] Figures 19(a) to 19(d) are schematic TEM diffraction graphs for the two samples;

[0077] Figures 20(a) to 20(j) are schematic diagrams and graphs comparing spatial distribution maps for atom pairs;

[0078] Figures 21(a) to 21(f) are schematic density hit maps for the two samples;

[0079] Figures 22(a) is a schematic diagram of a three-dimensional reconstruction of an APT sample;

[0080] Figure 22(b) are schematic concentration maps for the elements of the sample in Figure 22;

[0081] Figure 23 is a schematic graph showing X-ray diffraction results for the two samples;

[0082] Figure 24(a) is a schematic atom map of pure aluminium;

[0083] Figures 24(b) and 24(c) are schematic graphs showing spatial distributions of aluminium atoms from Figure 24(a);

[0084] Figures 25(a) and 25(b) are schematic graphs compare the SRO parameter values for random and experimental results based on kNN distributions;

[0085] Figures 26(a) to 26(c) are schematic diagrams and graphs illustrating the concentration of atomic elements;

[0086] Figures 27(a) to 27(d) are schematic graphs shows SRO values for the two samples; and

[0087] Figures 28(a) to 28(i) are schematic atomic concentration maps for the two samples.Preferred Embodiments of the Disclosure

[0088] The present disclosure will now be described with reference to the following examples which should be considered in all respects as illustrative and non-restrictive. Although the disclosure has been described with reference to specific examples, it will be appreciated by those skilled in the art that the disclosure may be embodied in many other forms. In the Figures, corresponding features within the same embodiment or common to different embodiments have been given the same reference numerals.

[0089] The microstructure of a material, especially a crystalline material, such as a semiconductor, a ceramic or a metal, may be conceived of as a multi-scale set of parameters that define the phenomenological attributes of, variously, the grain structure (including the size, shape and texture), the various defect structures (dislocations, twins, etc.), any precipitation that may occur, any segregation across relevant microstructural interfaces, and any clustering or anti-clustering that may occur throughout the atoms within the crystal. Multiple matrix phases may exist adding further complexity. This description of microstructure of a material may be represented schematically in Figure 1,which illustrates the multi-scale conception ranges from the atomic scale 10 at the left through to what could be tens of microns (or larger) scale 20 at the right.

[0090] This microstructure is in turn dependent on the arrangement of atoms within the crystalline material. Hence, the phenomenological attributes of the microstructure are the result of the particular arrangements of the constituent atoms within the material. The critical parameters of these atomic arrangements are their spacings, symmetries and chemical distributions. These determine the local electronic density of states which govern the state of the material, as illustrated in Figure 2. That is, the electronic structure 50 (i.e. the arrangement of atoms) dictates the structural, electronic, magnetic, optical and mechanical properties 60 of the material. These properties 60 in turn influence directly other related properties 70 of the material or combined with another property to influence additional properties 80 of the material. For example, the mechanical properties 60a of the material directly determines the stress-strain relationship or the bulk / Young's / shear modulus 70a and in combination with the optical properties 60b determines the optomechanical 80b of the material.

[0091] Combined with the grain size, phase, defect information and textural distribution information, the above set of data represents the key variables that control the macro-behaviour of solid-state materials. This macro-behaviour results in a particular material exhibiting its properties, such as tensile strength, shear strength, yield strength, ductility, malleability, combustibility, density, hardness, plasticity, conductivity, elasticity, stiffness, fracture resistance, fatigue resistance, corrosion resistance and wear resistance. This list is not exhaustive, and other mechanical, physical or other material properties can be measured, such as nanoindentation to uniaxial tensile strength.

[0092] The details of the atomic arrangements (their spacings, symmetries and chemical distributions), grain size, phase, defect information and textural distribution information are effectively captured, quantitatively, in atomic nearest neighbour (NN) distributions. These distributions are frequency histograms of the first (and / or second, third, fourth, up to a kth) atomic nearest neighbours in a material. For example, the 1st to kth NN distributions of an intragranular (matrix) region of a grain in a crystalline material will, for example, reflect the local tendency for clustering, segregation, precipitation, or other microstructural phenomena. Moreover, the 1st to kth NN distributions may change from region to region throughout the microstructure depending on the local thermodynamic and kinetic influences on the materials imposed by themanufacturing process. As another example, the 1st to kth NN distributions of a region of a grain boundary that contains segregation will be different from the 1st to kth NN distributions of an interior region of the grain, which will also be very different from regions containing crystal defects or second phase precipitates.

[0093] The present inventor has developed a novel methodology for analysing materials based on this quantified atomic data. Accordingly, there is provided a method 100 of analysing a material, comprising obtaining atomic data relating to the location of atoms within the material at step 110 and performing a calculation on the atomic data to generate a plurality of mathematical functions relating to the spatial distribution of the atoms according to one or more predefined parameters at step 120. The method 100 then involves calculating a statistical distribution of the generated mathematical functions at step 130 and determining a detected microstructure of the material based on the statistical distribution at step 140. Optionally, the method 100 comprises the step 150 of determining one or more properties of the material from the detected microstructure.

[0094] In this embodiment, the plurality of mathematical functions comprises k- Nearest Neighbour (kNN) distributions, as they best quantify the above information that determines the macro-behaviour of a material and thus the physical and mechanical properties that are exhibited by that material, such as conductivity, tensile strength, ductility, and so on. However, in other embodiments, the plurality of mathematical functions may comprise Short Range Order (SRO) values, probability functions representing local composition parameters, or voxelisation of the spatial distribution of atoms. Each of these alternative mathematical functions also describe or indicate the macro-behaviour resulting in the above physical and mechanical properties.

[0095] By using a distribution of generated mathematical functions, the overall microstructure of the material can be viewed holistically. For example, using a distribution of kNN distributions (which may also be called a mosaic of kNN distributions) allows full microstructural picture of the material to be constructed for analysis. This means that patterns of particular concentrations of atoms can be recognised, which indicate that the material is likely or will have a particular microstructure at those locations, and thus exhibit a particular physical or mechanical property. For example, the addition of n-type or p-type dopant atoms at certain locations within a semiconductor material will control the conductivity at those locations in the semiconductor material. In other words, one can determine the microstructure by determining the concentrationand / or arrangement of atoms according to the one or more predefined parameters from the statistical distribution. The concentration of atoms may indicate a clustering or anticlustering effect that results in the material exhibiting (where there is a clustering effect) or not exhibiting (where there is an anti-clustering effect) a particular property or set of properties. Other possibilities include segregation effects as in segregation to a microstructural interface such as a grain boundary or a defect, or alternatively, a near random solute distribution. Thus, this method 100 can validate the location-specific microstructure across a real world part composed of the material at multiple lengthscales (nm to mm)

[0096] The predefined parameters may comprise atomic species, groups or pairings of different atomic species and / or distances between a designated atom from one or more other atoms. For example, in an aluminium alloy containing small additions of magnesium and silicon, the mathematical functions are generated according to the spatial distribution of magnesium atoms and / or silicon atoms. That is, there can be a set of mathematical functions for the spatial distribution of magnesium atoms and / or a set of mathematical functions for the spatial distribution of silicon atoms. As another example, the mathematical functions are generated according to the distances between the magnesium atoms and / or silicon atoms. Again, there can be a set of mathematical functions for the distances between magnesium atoms only, a set of mathematical functions for the distances between silicon atoms only and / or a set of mathematical functions for the distances between magnesium atoms and silicon atoms. As a further example, in an aluminium-copper-magnesium alloy, there can be a set of mathematical functions for the spatial distribution of aluminium atoms only, a set of mathematical functions for the spatial distribution of copper atoms only, a set of mathematical functions for the spatial distribution of magnesium atoms only, a set of mathematical functions for the spatial distribution of aluminium to copper atoms, a set of mathematical functions for the spatial distribution of aluminium to magnesium atoms, a set of mathematical functions for the spatial distribution of copper to magnesium atoms, a set of mathematical functions for the spatial distribution of aluminium to magnesium or copper atoms, etc.

[0097] In addition, depending on the predefined parameters selected, it is also possible to assign weights to one or more particular mathematical functions when calculating the distribution of mathematical functions. For example, it may be desirable for the material to exhibit a particular property (like conductivity or ductility) at a particularlocation of the material. Consequently, the mathematical functions, like kNN distributions, can be assigned weighting to place emphasis when calculating the distribution of a particular set of kNN distributions, or when examining the distribution of a particular set of kNN distributions to determine if the material will exhibit the desired property at the desired location of the material.

[0098] A mathematical function in a subset of mathematical functions may also be taken or selected as a representative of the subset; this so-called representative mathematical function can then be used as a substitute or proxy for the subset when calculating the distribution of mathematical functions. The representative mathematical function is generally selected from a wide sample of mathematical functions in the subset, and is usually indicative of or has significance in the material exhibiting a particular microstructure and hence property. Consequently, the use of a representative mathematical function may reduce the need for calculating each mathematical function in the subset. For example, instead of calculating the NN distribution from the 1st NN distribution up to the 250th NN distribution, where 1 < k < -250, a NN distribution, like the 34th NN distribution, may be selected as the representative kNN distribution and is generated for that location and / or atom type (atomic element). When the distribution of kNN distributions is calculated, the 34th NN distribution is used for the subset. This may be repeated for each location and / or atomic element. Accordingly, the distribution of kNN distributions can be calculated more quickly while still retaining its usefulness as an indicator of the microstructure (and hence properties) of the material.

[0099] In further embodiments, the representative mathematical function may be used as an effective proxy for the entire microstructure, and thus all or most of the microstructural attributes shown in Figure 1. This involves giving the representative mathematical functions more weight in assessing the distribution of mathematical functions to determine the microstructure of the material. For example, the 34th NN distribution may be shown to be particularly sensitive or significant in indicating whether a particular microstructure is present in the material and thus a particular property will be exhibited. Thus, the 34th NN distribution is given more weight in the distribution of kNN distributions when the microstructure is determined in step 140.

[0100] The atomic data obtained in step 110 may be acquired either directly from the material prior to the manufacturing process, after the manufacturing process, or in situ at some point during the manufacturing process. The atomic data may be obtained fromsamples of the material. The samples may be excised using a focussed ion beam (FIB) specimen extraction method. Other methods include the use of precision mechanical sectioning, further cutting, and electrolytic polishing may be used.

[0101] The atomic data in step 110 may be obtained from the sample through various methods, but preferably a microscopy method is used. The microscopy method may be based on transmission electron microscopy (TEM), atom probe microscopy (APM), X-ray scattering or neutron scattering. The TEM method may comprise at least one of scanning TEM (STEM), electron energy loss spectrometry (EELS), energy dispersive X- ray spectroscopy (EDXS) and a TEM based diffraction technique. The APM method may comprise at least one of mass spectrometry, field ion microscopy (FIM), field evaporation microscopy (FEM) and atom probe tomography (APT).

[0102] APT is preferred to be used to obtain the atomic data in step 110, as this method provides a unique range of information compared to other microscopy methods related to the local arrangement of the individual atomic species and there is a relative ease of computation. The extremely high chemical and spatial resolution analyses provided in APT enable the direct microscopic imaging of atomic arrangements including the nature of atomic clusters which can represent a subtle, but significant, local chemistry perturbation that may contain just a few atoms in a solid solution. This distinguishes APT from many other techniques because it provides direct three-dimensional chemical information on this length scale, whereas other microscopies cannot achieve the combined levels of chemical and spatial resolution required for such measurements. Thus, APT eliminates the substantial effort of measuring the atomic data using diffuse scattering experiments. With APT, it is possible to reconstruct the position and chemical identity of tens-of millions of atoms from a material in 3D with a resolution <1 nm in the lateral direction, and < 0.1 nm in the depth direction. This allows nanoscale microstructural features to be imaged in great detail, and in some cases crystallographic information may be determined. Accurate APT data reconstructions effectively transform detector ion-hit positions into atomic spatial coordinates.

[0103] Figure 4 shows the process of obtaining the atomic data using an APT method. In APT, surface atoms from a needle-shaped specimen 200 under a positive electrical potential undergo ionisation due to stimulation from either a high voltage pulse or an ultra-short laser pulse. That is, the surface atoms are evaporated and the created ions 210 are accelerated by an electric field (generated by electrode 220) toward a positionsensitive detector 230 that registers the impact position and the time taken for each ion 210 to travel from the specimen to the detector. This enables a time-of-flight mass spectrometry to identify the ionised atomic species. The impact position and order of the detection can be used to approximate the original location of each atomic species in the specimen 200. An exemplary tomogram illustrating the location of various atoms is shown in Figure 5, where the spatial locations of aluminium 245 (blue), magnesium 247 (green) and copper 249 (red) atoms in a metal alloy specimen are shown.

[0104] While the atomic data obtained through APT relates to the spatial location of the atoms, in other embodiments the atomic data may relate to the state of the material at one or more predetermined times and / or locations. The state of the material may relate to a thermal state of the material. For example, the atomic data may comprise thermal data relating to the temperature of the atoms within the material based on their location over a predetermined time period. In further embodiments, the atomic data comprises atomic-scale microstructural data.

[0105] The distribution of the spatial locations of the atoms can be described by a mathematical function. In one embodiment, the kNN distribution of the atoms may be chosen. That is, the frequency distribution of the distances from a designated atom to its 1st nearest neighbour (NN) atom, its 2nd NN atom, its 3rd NN atom, up to the kth NN atom. This may be repeated for each atom. In the case of the exemplary tomogram of Figure 5, the kNN distributions may comprise the kNN distribution of a designated aluminium atom to other aluminium atoms (the distances from the designated aluminium atom to its 1st NN aluminium atom, its 2nd NN aluminium atom, its 3rd NN aluminium atom, up to the kth NN aluminium atom); the kNN distribution of a designated aluminium atom to other atoms of any type; the kNN distributions of a designated aluminium atom to other atoms of one type (magnesium or copper); and the kNN distribution of a designated aluminium atom to magnesium or copper atoms. The kNN distributions may be repeated for each aluminium atom, as well as repeated for each atom type; i.e. the kNN distributions of a designated magnesium or copper atom to other magnesium atoms, aluminium atoms, copper atoms, atoms of any type; atoms of one type or atoms of two types (aluminium and copper for the designated magnesium atom and aluminium and magnesium for the designated copper atom).

[0106] Figures 6(a) and 6(b) illustrate frequency histograms illustrating an exemplary set of kNN distributions 250, 260, 270 for an aluminium-copper-magnesium (Al-Cu-Mg)alloy, where the alloy is an AI-1.1Cu-1,7Mg (at. %) alloy aged for 60 seconds at 150°C, and k = 5 (i.e. 5th nearest neighbour or 5NN distributions). The frequency histogram in Figure 6(a) shows the 5NN distribution 250 for copper (i.e. a designated copper atom to other copper atoms), the 5NN distribution 260 for magnesium (i.e. a designated magnesium atom to other magnesium atoms) and the 5NN distribution 270 for both atoms (i.e. a designated atom, which can be magnesium or copper, to the other atoms). Each of the 5NN distribution curves are compared to random distributions of their respective atom-pairs (distribution 255 for copper-copper, distribution 265 for magnesium-magnesium and distribution 275 for atom-atom), showing the clustering of copper and magnesium atoms in these distributions are the result of a particular arrangement and are not simply randomly distributed. These NN distributions may be repeated for each NN for k = 1 up to a selected kth value. Figure 6(b) shows the cumulative frequency histogram for the 5NN distributions 250, 260, 270, showing the total number of atoms in each distribution fulfilling the threshold distance along the x- axis.

[0107] Referring to Figure 7A, an exemplary distribution of kNN distributions is shown where a holistic view or overview of the material can be observed from the distribution. Figure 7A(a) shows two atom maps for copper for two sets of data, one based on a computer simulated model and the other based on experimental data. The atom maps show the distribution of copper atoms in the material. Figure 7A(b) is a graph showing the SRO values for copper-copper pairs for the simulated model. The SRO values assist in filtering out Figure 7A(c) the distributions of kNN distributions for copper-copper pairs, with the distribution 280 of kNN distributions for the simulated model are in red, while the distribution 290 of the kNN distributions for the experimental data are in black. Both distributions use k values of 1 < k < 100. As shown in this Figure, the distribution 290 for the experimental data indicates that there is in fact a lower frequency of kNN distributions compared to the distribution 280 for the simulated model. The distribution 290 can be expanded to other atomic species or combinations of atomic species in the alloy. The distribution(s) 290 can thus create a three-dimensional picture or map of the kNN distributions for the material. From this distribution, concentrations or clustering of selected atomic species can be identified in various regions of the material. The distribution 290 is an example in which there can be an assessment of whether there is any concentration of atoms or grouping of arrangement of atoms (including atoms of more than one type) to indicate that a particular microstructure is present, and thus the exhibition of a particular property associated with that microstructure. For example, it isknown that the clustering of copper (Cu) and magnesium (Mg) atoms leads to the strengthening of Al-Cu-Mg 2xxx series alloys. The state of clustering is directly linked to the kNN distributions. Hence, by calculating the distribution of the kNN distributions of the atomic species, Cu and Mg, and to combinations of these atomic species, the clustering effect can be easily and quickly determined for the entire alloy. Consequently, the strength of the Al-Cu-Mg alloy may be easily assessed.

[0108] It has been found that producing multiple kNN distributions from 1 < k < -250 is sufficient to provide a distribution of kNN distributions to determine the microstructure of the material. However, it is possible to use a k value less than -250. It is preferred to use using all -250 of these kNN distributions as they provide a rich assessment of the solute (atom) distribution in the material. Taking the kNN distributions from 1 < k < -250 at different locations in the microstructure builds an atomistic NN mosaic distribution or function that can be weighted. For example, if a microstructure is thought to comprise of grains having the following microstructural constituents: (i) matrix or intragranular regions, (ii) grain boundaries, (iii) precipitates, (iv) defect structures of some type, and (v) other microstructural constituents, a weighted function of the, in this example, five separate kNN distributions from 1 < k < -250 (actually one thousand two hundred and fifty distributions) can be used to describe the microstructural state. There would be various ways to weight the five distributions, such as volume fraction of the various microstructural constituents, solute fraction at these microstructural constituents, etc.

[0109] A similar process may be used where a different mathematical function is chosen, such as SRO values or local composition probabilities. Short-range order (SRO) is used in crystallography as a quantitative measure of the relative tendency for the constituent elements in a material to deviate from a random distribution. Specifically, it is a measure of the tendency for certain atomic species to exhibit particular short-range NN relationships. These relationships may be either random 293, preferred ('clustering' 295), or non-preferred ('anti-clustering' 297), as shown in Figure 7B. The SRO value alpha (a) indicates how the atoms of a particular element (also called solutes) are distributed within a material. Generally, where a = 0, the solutes are distributed randomly. Where a > 0 the solutes have preferred interaction or “clustering” (tendency towards being grouped together) and when a < 0, the solutes tend not to interact or have an anticlustering effect. The SRO value a thus indicates how close or far apart the solutes are within a material, and enables a probability to be assigned to spatial relationship at a certain location in the material. The SRO values can be determined for different shells ofthe crystal. An example of a distribution of SRO values is shown in Figures 16(a) and 16(b), where the distribution of SRO values for various atomic species pairs (CoCo, CoCr, CoNi, etc.) have been taken over kNN distributions, where k values of 1 < k < 200 were used.

[0110] SRO values are not the same as kNN distributions as they are a probability of solutes being near or far from each other within a particular crystallographic shell, whereas kNN distributions involving the counting of atoms across defined neighbourhoods. Generally, kNN distributions are data rich but can be difficult to use due to the amount of data required to be processed. SRO values are simpler to process, being a single number, such as 0.00423, but are less data rich (and thus may be less accurate than kNN distributions).

[0111] The various kNN distributions (1 < k < -250) can be determined for individual atomic species in a multicomponent material (e.g. a five-component alloy comprising elements A-B-C-D-E) and then, as mentioned above, weights applied either to the distributions arising from the distribution from an individual k value, or ranges of k values for mathematical functions chosen that integrate the data. Other weights can be introduced to the kNN distributions from individual atomic species, or combinations of atomic species. For example, the kNN distributions from species ‘B’ in the above example might be given a different weighting from the kNN distributions of the species ‘C’, ‘D’ and ‘E’ or combinations thereof.

[0112] A similar process may be used where a different mathematical function is chosen to include SRO values from different atomic species with different weights assigned to each species. In the example above, the weights assigned to the SRO values can be tuned in a wide-ranging way. The SRO values of species ‘B’, can be assigned different weights to those from species ‘O’, ‘D’ and ‘E’. Similarly, the SRO values for species ‘B-C’, or ‘B-C-D’ or the SRO value for the species group ‘B-C-D-E’ could be assigned different weights from the SRO values calculated from other combinations of elements.

[0113] Table 1 below summarises the range of possible binary SRO values in the example of a five-component alloy comprising elements A-B-C-D-E. Table 1 represents only the binary SRO values. In fact, ternary, quaternary and quinary SRO values are also possible to calculate in a quinary alloy using combinatorial mathematics.Table 1 : Binary SRO values for a five-component alloy comprising elements A-B-C-D-E

[0114] For the avoidance of doubt, it is emphasised that the above discussion relates to the different weights that can be applied to the various kNN distributions or SRO values, respectively, from individual or combinatorial permutations of the species in the multicomponent system.

[0115] Local composition probabilities are based on local composition theory, where a mixture (or material) is assumed to have local regions have a specific composition of constituent atoms, so the properties of the mixture or material are determined by the local compositions. Local composition is expressed as a probability of a constituent atom being present at a local region of the material. For example, using the above example of an aluminium-magnesium-copper alloy, a particular area or region may have 40% aluminium, 30% magnesium and 30% copper. Based on these probabilities, the microstructure, and hence properties, of the material may be inferred.

[0116] Both of these alternative mathematical functions may be used for each localised region or area of the material to generate a set of mathematical functions for the entire material, from which a distribution of those mathematical functions are obtained.

[0117] As a result of performing the analysis method 100 on a material, it is possible to make correlations that provide a way of either broadly ranging or precisely determining determine its physical, mechanical, chemical or other properties. This provides a powerful tool for conducting research into materials, since the method 100 permits the multi-scale microstructural characterisation (including, explicitly, atomic-scale information about the atomistic arrangements as formulated through mosaics of kNN distributions or SRO values) coupled with local property measurements. For example, the physical, mechanical and chemical properties of a material, as determined by quantifying its microstructure, can be compared with a target microstructure of the material. This allows the material to be altered or modified in some way so that its microstructure will substantially match the target microstructure. This can achieved by varying how the material is to be created or formed (manufactured), or performing an additional process on the material post-formation to alter its microstructure

[0118] The analysis method 100 may also be used to detect defects in a material, since deviations in the actual microstructure (that corresponds or is the same as the detected microstructure) to the target microstructure will indicate some fault in the material. For example, such a deviation from the target microstructure in a particular location may indicate a defect or crack in the material, requiring remediation, reprocessing or discarding of the material.

[0119] The target microstructure can be a set of predetermined parameters or characteristics that are intended for the material to exhibit a set of physical, mechanical, chemical or other properties. The target microstructure can be generated from an initial set of data relating to the material. The initial set of data may be derived from theoretical values based on the assumed composition of the material or derived from computational modelling of the material, or based on an initial set of a parameters (such as the atomic components of the material) prior to creation or formation of the material. The initial set of data may be obtained from measurements made during the creation or formation of the material.

[0120] The analysis method 100 may also be employed in improving manufacturing methods using materials to make products of various types. For example, the distribution of kNN distributions enables control of the microstructure, and thus the properties of a material, through the manufacturing process. This control may be enhanced by coupling the distribution of kNN distributions with the grain structure or other microstructuralattributes of the material. Thus, these microstructural indicators can be directly determined and validated, serving to anchor the coupling between the manufacturing process and the properties of a material. As such, the capacity to quantify the microstructure provides critical capacity to calibrate and validate computationally generated microstructural information.

[0121] Hence, in another embodiment, there is provided a method 300 of manufacturing a product comprising at least a first material (the product could be composed entirely of the first material or of several compositions of which one is the first material), as best shown in Figure 8. The method 300 involves performing one or more manufacturing steps on the first material for producing the product having a target microstructure at step 310. At step 320, the analysis method 100 is then performed on the first material to obtain a detected microstructure of the material. The detected microstructure corresponds to the actual microstructure of the material. At step 330, the detected microstructure is compared to the target microstructure. At step 340, at least one of the manufacturing steps is adjusted in response to the detected microstructure being substantially different to the target microstructure.

[0122] The adjusting step 340 may involve one or more options, as indicated by box 350. In option 350, the adjusting step 340 involves one or more of the manufacturing steps being altered or changed to modify the detected microstructure of the first material to the target microstructure. This may involve modifying the how the manufacturing step is performed to modify the detected microstructure. For example, in a ceramic manufacturing process, the temperature and / or time in the firing oven may be varied to modify the microstructure of the first material.

[0123] In option 355, the adjusting step 340 comprises performing a second manufacturing step on the first material to modify the detected microstructure of the first material to the target microstructure. The second manufacturing step may be performed after stoppage or completion of a first manufacturing step.

[0124] In option 357, the adjusting step 340 comprises adjusting one or more design parameters of the product prior to repeating the manufacturing steps. This could involve changing the geometry of the product (in terms of its three-dimensional shape), the size dimensions of the product.

[0125] Each of the options 350, 355, 357 may be selected alone or in any combination when performing the adjusting step 340. Where the adjusting step 340 involves changing the manufacturing step(s) or the design parameter(s) under options 350 and 357, respectively, the method 300 may further comprise repeating the now adjusted manufacturing step(s) at step 310, as indicated by arrow 360. The material is again analysed at step 320 and the detected microstructure is then compared the target microstructure at step 330. Where the adjusting step 340 involves performing an additional manufacturing step under option 355, the method 300 may further comprise repeating the analysis at step 320 and comparing the detected microstructure to the target microstructure at step 330, as indicated by the arrow 370. This repetition or iteration of these steps may continue until the detected microstructure is substantially the same as the target microstructure.

[0126] In adapting the analysis method 100 to the manufacturing method 300, the atomic data may be obtained directly from the first material during the manufacturing step(s). Alternatively, a sample of the first material is taken during the manufacturing step(s) and the atomic data is obtained from the sample. As described above, this may be done using the APT microscopy method as illustrated in Figure 3.

[0127] The manufacturing method 300 may further comprise generating the target microstructure of the first material. As described above, the target microstructure is generated from an initial set of data relating to the first material, which may be derived in this case from theoretical values or from data acquired from the first material prior to performing the manufacturing step(s), or even during performance of the manufacturing step(s). The theoretical values may be obtained by computational modelling based on initial composition of the material.

[0128] Where the product comprises at least a second material in addition to the first material, the method 300 may also be performed in relation to the second material. That is, the manufacturing step(s) are performed on the second material for producing a second target microstructure, the analysis method 100 is performed in respect of the second material and the manufacturing step(s) are adjusted to modify the detected microstructure of the second material to the second target microstructure. In this case, the manufacturing step(s) are performed simultaneously on the first and second materials. Alternatively, the manufacturing step(s) are performed sequentially on the first and second materials.

[0129] It will also be appreciated that the material used in manufacturing the product may take many forms, as the method is applicable to many types of manufacturing. Consequently, the material may comprise a metal or metal alloy, a semiconductor in wafer or other from, or a ceramic material, as well as any other materials used in manufacturing products. One example of a metal alloy that may be used with the method 100, 300 are medium and high entropy alloys (M / HEAs) that can exhibit outstanding combinations of strength and ductility for engineering applications. Similarly, the range of possible products that can be manufactured is wide, and may comprise electronics components, a structural component, a machine or device component, a machine or device part or the entire machine or device.

[0130] Referring to Figure 9, a system 400 for manufacturing a product comprising at least a first material is shown, comprising a plurality of manufacturing machines 410 for performing one or more manufacturing steps on the first material to produce the product having a target microstructure. The first material is fed from an input 413 into the manufacturing machine(s) 410 and the product leaves as an output 417. A control unit 420 is configured to control the manufacturing machines 410 and a data retrieval unit 430 is provided for obtaining atomic data relating to the location of atoms within the first material. A processor 440 is configured to perform the analysis method 100 in respect of the first material, and compare the detected microstructure to the target microstructure.

[0131] The control unit 420 is further configured to adjust operation of the manufacturing machine(s) 410 in response to the detected microstructure being substantially different to the target microstructure. The control unit 420 may be in communication with each of the manufacturing machine(s) 410, wirelessly or through wired connections, to control the manufacturing machine(s). Thus, the control unit 420 is configured to adjust operation of the one or more manufacturing machines such that the detected microstructure of the first material is modified to the target microstructure. In some embodiments, there may be multiple control units 420, where a single control unit 420 controls a single manufacturing machine 410. In this case, there may be a master control unit (not shown) that controls each of the control units 420.

[0132] The data retrieval unit 430 is connected to the manufacturing machine(s) 410 to acquire the atomic data from the material. It will be appreciated that there may be multiple data retrieval units 430, one for each manufacturing machine 410. Alternatively,the data retrieval unit 430 is removably connected to each manufacturing machine 410 to obtain the atomic data from a selected manufacturing machine 410.

[0133] The data retrieval unit 430 may obtain the atomic data directly from the first material during operation of the manufacturing machine(s) 410. In other embodiments, as shown in Figure 9, the data retrieval unit 430 obtains the atomic data from a sample of the first material taken during operation of the manufacturing machine(s) 410. In this case, the data retrieval unit may comprise a sampling unit 450 and a data processing unit 460. The sampling unit 450 may be a FIB instrument. The sample is then sent to the data processing unit 460, which may be a microscopy instrument, such as a light- optical microscope, an electron microscope of some kind, an atomic force microscope (AFM), scanning tunnelling microscope, a photonic force microscope, recurrence tracking microscope, an atom probe or an X-ray microscope. The sampling unit 450 and the data processing unit 460 may be integrated into one unit. For example, the data retrieval unit 430 may comprise an instrument that selectively uses ion beams or electrons, enabling it to operate as a FIB instrument or as a SEM instrument.

[0134] The control unit 420, data retrieval unit 430 and processor 440 operate independently of each other in performing the method 300. That is, data retrieval unit 430 operates independently to obtain the atomic data. This atomic data is then sent to the processor 440 to perform the method 100. The result of the method 100 from the processor 440 is then used to operate the control unit 420 to modify operation of the manufacturing machines 410. This process reflects the fact that it may take some time for the processor 440 to perform the method 100 to determine the determined microstructure and make the comparison against the target microstructure.

[0135] However, it is contemplated that in other embodiments, the processor 440 may be placed in communication with the control unit 420 and the data retrieval unit 430, either wirelessly or through wired connections. In this way, the processor 440 is able to perform the analysis method 100 on the first material upon receipt of the atomic data from the data retrieval unit 420. It also enables the processor 440 to communicate with the control unit 420 to instruct the control unit 420 to modify operation of the manufacturing machine(s) 410 in response to the comparison of the detected microstructure to the target microstructure. That is, the control unit 420 may control the manufacturing machine(s) 410 to modifying its operation to modify a first manufacturing step and so modify the microstructure of the first material. This may involve themanufacturing machine(s) 410 performing a second or additional manufacturing step on the first material to modify the microstructure of the first material. The manufacturing machine(s) 410 may perform the second manufacturing step after stoppage or completion of the first manufacturing step.

[0136] The processor 440 may also be configured to generate the target microstructure from an initial set of data relating to the first material, as described above in relation to the method 300. It will also be appreciated that the processor 440 may comprise a computer, computer processing unit (CPU) or similar computational device.

[0137] Hence, the system 400 is able to perform the manufacturing method 300 of Figure 8. This also includes the iteration of the analysis step 320. That is, the data retrieval unit 430 obtains an additional set of the atomic data and the processor 440 performs the analysis method 100 on the additional set of the atomic data after the control unit 420 adjusts operation of the manufacturing machine(s) 420. The system 400 is configured so that the data retrieval unit 430 obtains the atomic data, the processor 440 performs the analysis method and the control unit 420 adjusts operation of the manufacturing machine(s) 410 iteratively until the detected microstructure is substantially the same as the target microstructure.

[0138] Where the product comprises at least a second material, wherein the system 400 is configured to perform the method 300 in relation to the second material. That is, the manufacturing machine(s) 410 perform the manufacturing step(s) on the second material for producing a second target microstructure, the data retrieval unit 430 obtains atomic data relating to the location of atoms in the second material, the processor 440 performs the analysis method 100 in relation to the second material and the control unit 420 adjusts operation of the manufacturing machine(s) in response to the detected microstructure of the second material being substantially different to the second target microstructure.

[0139] From the viewpoint of the final materials properties (e.g. the mechanical properties) exhibited by a material against a particular end-use application, the methods 100, 300 and system 400 may be used to provide a threshold requirement to determine whether a manufacturer should proceed with manufacturing the product using the material based on the current manufacturing steps. For example, where the mathematical functions are kNN distributions, there will be kNN distributions that can beclassified as nominal, marginal and unsatisfactory. Here, a “nominal” kNN distribution corresponds to good or satisfactory properties of the material, “marginal” corresponds to just meeting minimum property requirements of the material and thus the product, and “unsatisfactory” will not meet the minimum requirements. The notion of nominal, marginal and unsatisfactory may be considered as providing a tool for risk analysis in the manufacturing process according to the method 300 and system 400. For example, the parts of an engineering component or machine produced by a manufacturing process may need to be compliant with engineering performance standards that permit formal certification and qualification of that part. If the distribution of kNN distributions has most or all of its kNN distributions classified as nominal or marginal, then this would indicate that these requirements would be met by the manufacturing process. However, if the distribution of kNN distributions has most or all of its kNN distributions classified as unsatisfactory, then this would indicate that the requirements would not be met and thus modification of the manufacturing process is required. As noted above, in other embodiments, one or more representative kNN distributions may be selected for assessment as being nominal, marginal or unsatisfactory for this purpose, instead of viewing the overall distribution of kNN distributions. Similarly, nominal, marginal and unsatisfactory ranges of SRO values may be used.

[0140] A further embodiment of the disclosure provides an alternative method of analysis to the analysis method 100. As best shown in Figure 10, this method 500 has the same steps 110, 150 and 160. However, in step 120 the plurality of mathematical functions selected for the calculation is the plurality of kNN distributions (and relabelled as step 510). That is, step 510 involves performing a calculation on the atomic data to generate a plurality of kNN distributions according to one or more predefined parameters. In addition, step 130 is replaced by step 520 of calculating one or more Short Range Order (SRO) values from the plurality of kNN distributions. Step 140 is modified by step 530 where determining the microstructure of the material is based on the one or more SRO values where, again, a wide variety of species-specific SRO values may be calculated using combinatorial permutations of the individual components comprising the material system in question.

[0141] The calculation of SRO values in step 520 may involve selecting a representative kNN distribution from the plurality of kNN distributions and calculating the SRO values for that representative kNN distribution. For example, as shown in Figures 11(a) and (b), the SRO values were calculated for the 12thNN distribution (k = 12).Alternatively, the SRO values are calculated from some or all of the kNN distributions, such as illustrated in Figures 14(a) and 14(b) discussed below. As described above, the one or more predefined parameters may comprise atomic species or groupings of different atomic species. For example, in an Al-Cu-Mg alloy, there can be a kNN distribution (and hence SRO value) for Al atoms only, Cu atoms only or Mg atoms only (single atomic species); Al-Cu atom pairings, Al-Mg atom pairings, Cu-Mg atom pairings, and Al-Cu or Mg, Cu-AI or Mg and Mg-AI or Cu (groupings).

[0142] The calculation of SRO values may also comprise applying a correction or calibration factor to take into account variances occurring when the atomic data is obtained. The correction or calibration factor in one embodiment comprises assigning a true SRO value based on a theoretical value and dividing the true SRO value by the measured SRO value.

[0143] Hence, in this embodiment a distribution of the plurality of kNN distributions is not calculated, but instead the SRO values are calculated from the plurality of kNN distributions and used to determine the microstructure of the material. As discussed above, the SRO values provide an indication of the clustering (or anti-clustering) of atoms, and thus indicates whether a microstructure has formed that may exhibit certain properties (clustering) or fails to do so (random or anti-clustering). This approach offers an alternative to calculating the distribution of the mathematical functions in step 130 in order to determine the microstructure of the material. Aside from this different approach, the method 500 can be readily substituted for the method 100 in the manufacturing method 300 or system 400 described above. Consequently, a detailed discussion of implementing the method 500 into the manufacturing method 300 and system 400 will not be made to avoid repetition.Example

[0144] An example demonstrating the calculation of the SRO values from a plurality of kNN distributions will now be described, with reference to Figures 11 to 23. The present example relates to reliably and accurately measuring SRO values in multicomponent alloys like M / HEAs, using a CoCrNi alloy. The present example also shows SRO value changes in the CoCrNi alloy, induced by heat treatments. These species-specific SRO measurements enable the generation of computational simulations of atomic neighbourhood models that are equivalent to the experiment and can contribute to thefurther understanding and design of M / HEAs and other materials systems where SRO may occur. Accordingly, SRO values may be used as a state variable of the microstructure of a material that can enhance its properties, such as the mechanical properties in M / HEAs.

[0145] One difficulty with determining SRO values for multicomponent materials, such as alloys and M / HEAs, is separating background effects from SRO signal in the diffracted intensity. Diffuse scattered intensity and superlattice reflections are variously offered as evidence of periodic SRO (i.e. preferred interactions) in various X-ray, neutron or electron scattering experiments. However, it is not clear how superlattice reflections can detect non-periodic SRO, or how scattering based methods (like X-ray or neutron or electron-based scattering) could detect instances of anti-clustering (i.e. non-preferred interactions). Another factor is that a random atomic configuration of any alloy will inevitably contain local preferred solute interactions which can contribute diffraction effects. The diffracted intensity of these must be calibrated and separated from the experimental data to attain a measure of the net SRO. These all represent significant challenges in measuring SRO in the field.

[0146] It has been found that APT may be a suitable method for measuring SRO values. However, it is necessary to take into account two factors. One factor is the uncertainties in the true trajectories that the ions inevitably take as they detach from the specimen crystal via quantum mechanical interactions and take flight. While the overall projection function describing how the average ion transits from the specimen to the plane of the detector is well researched, uncertainties in the trajectory of any given individual ion remain. These uncertainties diminish the spatial resolution of the APT technique. Another factor is that the detectors in APT have finite efficiency, presenting a classic missing data problem. For example, -43% of atoms in instrument systems used in APT are not detected. Second order issues also present, such as the need for careful calibration of the reconstruction, and careful calibration and ranging of the mass spectrum. These factors are addressed in the example, where the SRO values in a CoCrNi MEA can be quantified under different heat treatment conditions, showing unequivocally that the SRO values can be engineered.Simulated SRO measurement

[0147] To evaluate the influence of detection loss and trajectory uncertainties on the measurement of the SRO value (a), a computational model of a face-centred cubic (FCC) CoCrNi M / HEA comprising -4 million atoms was created. Two model systems were generated such that the atomic sites were assigned to the Co, Cr, or Ni species by (i) random assignment (a = 0), and (ii) non-random assignments including certain pairwise interactions that were clustered (a > 0), and other pairwise interactions that were anti-clustered (a < 0) - see Figure 7B. The specific values of these imposed SRO parameters are summarised in Table 2 below. The computational technique for implementing these SRO values in the model system was a reverse Monte-Carlo approach.Table 2: Specific values of the imposed SRO parameters for Figure 7B and the related maximum 95% confidence levels (CL) of different SRO values.SRO (a) ~0.1 -0.075 -0.050 -0.025 -0.01 -0.00195% CL 0.00026 0.00019 0.00029 0.00026 0.00023 0.00018SRO (a) -0.1 -0.075 -0.050 -0.025 -0.01 -0.00195% CL 0.00026 0.00026 0.00028 0.00021 0.00028 0.00022

[0148] The influence of the APT detector efficiency was evaluated first by removing a proportion of the model atoms ranging from 0 to 90% by random selection and recalculating the SRO of the system. Increments of 5% detection efficiency were used and, for each value, the above process was repeated 100 times to build a statistical model. The algorithm for computing the SRO value is described in the Methods section and was the same for both the simulation and the experimental data. Figure 11(a) presents the average of 100 simulations and the corresponding 95% confidence intervals of the randomly assigned system at each value of detection efficiency sampled. The SRO values oscillate around a = 0 across the range of detector efficiencies. The vertical dashed lines in Figure 11(a) and 11 (b) represent various typical APT instruments in use around the world, and their approximate detection efficiencies. Inset to Figure 11(a) are the SRO values simulated near the detection efficiency of 57% (the value of the APT instrument that was used in the example). At the 95% level of confidence, for thisdetection efficiency, values |a| < 0.00022 must be considered random. Figure 11(b) presents the results for the non-random system, where the specific values of the 'true SRO' embedded in the model for the different pairwise permutations are given at the intercepts to the ordinate axis, corresponding to 100% detection efficiency (values are shown in Table 2 above). Figure 11(b) demonstrates that all the SRO values tend towards zero -linearly with increasing fraction of missing atoms. Nonetheless, the models do preserve the detection of a deviation from a random distribution (i.e. a 0) even when the fraction of the missing data is high (> 50%). Significantly, discerning whether SRO exists in a sample (a 0), and a capacity to follow the relative trend of the SRO values was retained. What was clearly lost was the precision of the measurement when compared to the true values embedded in the simulation, with a systematic underestimation observed. The simulations based on an equi-atomic alloy indicate that the measured value of SRO derived from APT instruments with limited detector efficiencies will underestimate the true value by a discrete, but determinable amount. Consequently, the APT instrument or the measured SRO value can be calibrated to take this underestimation into account.

[0149] To assess the effect of the trajectory uncertainties on atomic preferencing, Gaussian noise was added to the idealised atomic positions of the atomistic models. Recognising the well-known anisotropy in the spatial resolution of APT, different noise regimes were applied to the 'x-y plane', where the trajectory uncertainties are more manifest, to that in the 'z direction', (as shown in Figure 4), where the spatial resolution is better. Figures 11 (c) and 11 (d) provide the results of the measured |a| values for SRO mapped in a coordinate space defined by the spatial resolution in the lateral and in-depth directions. The spatial resolution was quantified as the standard deviation of the Gaussian noise filter, so that the origin point of these charts represents an ideal microscope with no uncertainty in the trajectory, resulting in atomic positions precisely as per those generated in the input model. Ranges were selected for the spatial resolution in the lateral and in-depth directions that correspond to values typical of the estimations conventionally produced in the technical field. Calculation increments were 0.1 nm for the lateral noise and 0.02 nm for the in-depth noise. For the randomly assigned system, Figure 11 (c), the SRO values fluctuate around 0 throughout the sampled range of spatial noise with |a| < 0.00016. Figure 11(d) summarises the results for the model generated with clear SRO using nonzero inputs for the a values. Specifically, this chart maps the measured |a| values for the Co-Ni pair and assigned an arbitrary pairwise SRO value of a(True) = 0.041 at kNN = 12 (the coordination number for an FCC lattice). This a valueand all |a| values investigated decrease towards 0 with increasing lateral spatial noise. These simulations are evidence that the measured SRO is influenced predominantly by the spatial noise, and most especially by the lateral spatial noise. Notwithstanding this, it remains the case that non-random values were detected even at high spatial noise levels, with the simulated range of SRO spanning 0.0000013 < a < 0.0437 for the noise parameter space simulated, where a(True) = 0.041.

[0150] A contour is mapped into Figure 11(d) (white dotted line) representing the conservative (larger) threshold value of |a| = 0.00022 determined in Figure 11(a), as the threshold for where random and non-random values are indistinguishable. Next, atomistic simulations were generated to assess the combined effect of both finite detection efficiency, set here at 57%, and trajectory uncertainties on the measured SRO values. Results for the model containing random assignments of the Co, Cr and Ni species are charted in Figure 11(e), where the SRO values remain close to 0 throughout, at |a| < 0.00022. Figure 11(f) charts the results from the same model as Figure 11(d), where the SRO for the Co-Ni pair was used at kNN = 7 to account for detection efficiency (since 0.57 x 12 ~ 7), in which case the non-random value of a(True) = 0.039. Inspection of the origin point of Figure 11(d) and Figure 11(f) reveals the effect of the 43% missing data without any diminishment in spatial resolution. In Figure 11(f) the SRO value was similar to the embedded value of a(True) = 0.041 used in Figure 11(d) where kNN = 12 and was a(True) = 0.039 (since kNN = 7). The diminished spatial resolution in the lateral and in-depth directions drive the measured SRO values further down, with lateral resolution again having the most acute impact. Non-random values of SRO were detected even at high spatial noise levels, with the recorded SRO ranged as 0.0000086 < a < 0.0390 for the noise parameter space simulated. The simulation in Figure 11 (f) is the most realistic and offers a potential map of the go / no-go region for where SRO values could be reasonably measured.

[0151] Using the threshold value of a = 0.00022, non-random values of SRO may be discerned to the left of the white dotted line (i.e.) requiring instrumental performance where the lateral noise was < 0.85 nm. This minimum lateral noise required was calculated for a range of SRO values (a(True)) between ~0.1 to 0 at 57% detection efficiency and the results are plotted in Figure 11(g). A 'go / no-go' region is thus mapped for different SRO values and x-y (lateral) spatial noise.

[0152] As the true SRO values (a(True)) decrease, the lateral spatial noise threshold for discerning non-random values also reduces — in other words, the instrumental performance thresholds become more demanding. Interestingly, the combined effect of spatial noise and detection loss do not artificially induce enhancements in the measure of the state of clustering or anti-clustering. Rather, they drive a — > 0. This diminishment of the SRO value to 0 to be a systematically linear relationship with both the fraction of the data loss, and the trajectory uncertainties. This monotonic relationship establishes a pathway to extrapolate back to the true SRO value in the material via data simulations.

[0153] The above analysis of the equi-atomic ternary alloy finds embedded relationships between the monotonic diminishment of a —> 0 as the spatial resolution and detector efficiency degrade.

[0154] An approach has been found to reconstitute the true value of the SRO from the (diminished) values measured experimentally, when it is possible to assign values for the spatial resolution and detector efficiency.

[0155] A CoCrNi alloy was arc melted using equal molar fractions of high purity Co, Cr and Ni in an argon atmosphere. The as-cast alloy was then homogenised at 1200°C for 24 hours followed by water quenching, and this sample was designated as the AH sample. A small piece of the AH sample was cut and measured using inductively coupled plasma atomic emission spectroscopy (ICP-AES) to obtain a statistical average of the alloy molar fraction, which confirmed near equi-atomic ratios of the constituent species, as shown in Table 3 below.Table 3: ICP-AES results for the CoCrNi ingot derived from weight percentages. at. % Cr Co Ni OthersIngot 32.51 33.75 33.32 0.26

[0156] 500°C was chosen as the temperature to induce SRO. Therefore, half of theAH sample was cut and placed in a salt bath at 500°C annealing temperature for 500 hours followed by a water quench (the sample at this condition is named the AN500 sample).

[0157] Samples for X-ray diffraction (XRD) and scanning electron microscopy (SEM) tests were cut into small pieces using Struers 50 diamond saw and then polished usingSiC sanding papers up to 4000-grit followed by electropolishing. The samples were polished to mirror like surfaces. The electropolishing was conducted using 10% perchloric acid in acetic acid at room temperature.

[0158] The XRD sample was analysed using a Stoe Stadi P X-ray diffractometer configured with molybdenum (Mo) source. The samples were tested from 15° to 50°. The electron backscatter diffraction detector (EBSD) and electron diffraction X-ray spectrometer (EDXS) were done using a Zeiss Ultra SEM equipped with the EDXS and the EBSD. Both AH and AN500 sample alloys were measured to have a single FCC using XRD and EBSD. The phase and lattice parameters for both samples were confirmed to be similar and no obvious differences in atomic local concentration distribution were found between two samples.

[0159] Figure 12(a) is an atom map across the x-y plane prepared after calibrating the APT reconstruction from AN500 sample and includes a zoomed-in image of the reconstructed {111} atomic planes along the z-axis. Figure 12(b) provides a 2D density map taken of the CoCrNi MEA (AN500 condition) experimental APT reconstruction across the xy-plane. A lower-density pole region corresponding to {111} is observed. The diagram below the map in Figure 12(b) shows the annular regions of interest used to measure in-depth spatial resolution in the corresponding reconstruction. The in-depth or z'- resolution across this region was estimated using spatial distribution maps (SDMs) generated from the annular regions close to the centre of the {111} pole.

[0160] Figures 12(c) to 12(e) are spatial distribution maps for the three regions at different distances from the {111} pole shown in Figure 12(b). The Gaussian noise values (az-) were determined to be 0.024 nm, 0.036 nm and 0.077 nm at annular regions 0 - 2 nm, 2 - 3 nm and 3 - 4 nm from the centre of the {111} pole, respectively (Figure 11(c)-(e)). On this basis, az- = 0.1 was selected for the in-depth resolution for the subsequent simulations, consistent with what would be expected based on previous studies on APT resolution. The lateral, or x-y resolution was estimated using values of ax,y- = 0.25. Second and third examples of arbitrary true SRO values with an in-depth resolution of az- = 0.1 and a lateral resolution of ax,y- = 0.5 (as best shown in Figure 14) and a lateral resolution of ax,y- = 1 (as best shown in Figure 15) were also calculated.

[0161] Figure 13 illustrates the reconstitution process to determine true SRO with different resolutions. Figure 13(a) shows measured SRO values (red) versus the “true” SRO values embedded in the simulated model of a CoCrNi MEA. This enables the determination of a correction factor, p, that accounts for the combined effects of the detection loss (57% detection rate) and the limited spatial resolution (ox.y= 0.50 nm, (oz= 0.1 nm) for each value of SRO for this alloy system (green). The SRO values for random simulations ranged |a| < 0.00022. This correction factor separated into two regimes: a sharp tendency for this quotient to tend -^-35 when there was little or no SRO, and a flat region where there exists a medium level of SRO, such that for a > 0.0016, -7.1 < p < -19.1. Figures 1(b), 13(c) and 13(d) show comparisons of the high true SRO values (black) (Figure 13(b)), medium true SRO values (black) (Figure 13(c)) and low input true SRO values (black) (Figure 13(d)) to the reconstituted SRO values (blue). The 95% confidence intervals are provided. 57% of the data is simulated 100 times using the random labelling method with around 4 million atoms and SRO is measured for kNN = 7 to range the random values (violet). Data are presented as the average of the reconstituted SRO value for each pair + / - their 95% confidence region. The fidelity of the reconstitution process was preserved for the high and medium input SRO values (See Figures 13(b) to 13(c)), but not for the low input values (See Figure 13(d)).

[0162] Figure 14 illustrates the reconstitution process to determine true SRO with different resolutions. Figure 14(a) shows measured SRO values (red) versus the true SRO values embedded in the simulated model of a CoCrNi MEA. This enables the determination of the correction factor, p, that accounts for the combined effects of the detection loss (57% detection rate) and the limited spatial resolution (ox.y= 1 nm, oz= 0.1 nm) for each value of SRO for this alloy system (green). Comparison of the high input true SRO values (black) to the reconstituted SRO values (blue) is shown in Figure 14(b). The 95% confidence intervals are provided. 57% of the data is simulated 100 times using the random labelling method with around 4 million atoms and SRO is measured for kNN = 7 to range the random values (violet). Data are presented as the average of the reconstituted SRO value for each pair + / - their 95% confidence region. The trend of SRO after the reconstitution process was preserved for the high input SRO values (Figure 14(bb)), but not for the medium or low input values.

[0163]

[0164] New CoCrNi MEA atomistic models containing ~4 million atoms were generated. Various pairwise SRO values ranging from ~0.1 to 0 were assigned to the nine possible different pairwise permutations, as shown in Table 4 below.Table 4: Data points corresponding to the pairwise permutations for Figure 15(a).

[0165] The resultant atomistic model was then subjected to a random removal of 43% of the atoms, and a random Gaussian noise of standard deviation ox,y-= 0.25 nm laterally, and oz-= 0.1 nm in-depth. The pairwise SRO values were then re-measured, recorded, and the process repeated 100 times. The results are charted in Figure 15(a), where the red curve compares directly the measured versus the true a values for this simulation regimen. A correction factor, p, is also charted in green on the alternate ordinate axis of Figure 15(a). This was determined by dividing the assigned true SRO value by the measured SRO value after the degradations from detection efficiency and trajectory uncertainties were applied to the initial atomistic model (i.e.): = a(True) I a(Measured)

[0166] This correction factor separated into two regimes: a sharp tendency for this quotient to tend p — > ~10 when there was little or no SRO, and a flat region where there exists a medium level of SRO, such that for a > 0.0014, ~3.7 < p < ~5.7. The low SRO range is enlarged in an inset in in Figure 15(a). Using the values calculated in Figure 11(g), it impossible to distinguish SRO values a(True) < 0.0048 when the spatial noise is 0.25 nm, and hence the go / no-go threshold is mapped accordingly.

[0167] These correction factors were validated using models embedded with three sets of arbitrary true SRO values that had 57% detector efficiency and values of spatial noise 0.25 nm laterally, and 0.1 nm in-depth applied 100 times. The three sets of input true SRO values are tabulated in Table 5 below.Table 5: Models embedded with arbitrary true SRO values for Figures 15(b)-(d).

[0168] These input true SRO values correspond notionally to high SRO (-0.01 < a <0.1, Figure 15(b)), medium SRO (~0.001<a<0.01, Figure 15(c)), and low SRO (-0.0001 < a <0.001, Figure 15(d)). The correction factors (P) determined from Figure 15(a) enable a system of equations to be used on the measured SRO values to reconstitute the true SRO values, so accounting for the monotonic degradations arising from finite detection efficiency and trajectory uncertainty. Using the threshold of |a| < 0.00022 for measured SRO values that must considered indistinguishable from random, it is demonstrated in Figure 15 that an APT with a detector efficiency > 57% and spatial noise within the thresholds used here will unequivocally return acceptable precision for high and medium input levels of SRO, Figures 15(b) and 15(c), but not for the low input levels of SRO, Figure 15(d). Figures 13 and 14 repeat this same simulation process for higher levels of lateral spatial noise. The standard deviation (ax,y~) of the random Gaussian noise was set to 0.50 nm, and 1 nm in Figures 13 and 14, respectively. The trend is that the minimum threshold value of SRO that can be detected is higher as the lateral noise increases.Experimental SRO measurement

[0169] As shown in Figure 12(a), the crystallographic planes were clearly resolved in the reconstructed APT data of the MEA, and the atomic mass-to-charge ratios in the MEAs are such as to enable a total differentiation between the Co, Cr and Ni species without any overlap in the mass spectrum. With these secondary considerations accounted for, the primary issues of spatial resolution and detector efficiency were addressed applying the reconstitution procedure described above.

[0170] Figures 16(a) and 16(b) present the results of calculating the cumulative SRO parameter from the first nearest neighbour (1 NN) to the 200th nearest neighbour (200NN) of the CoCrNi MEAs in the AH and AN500 conditions by using the entire dataset with at least 2 million atoms. Each SRO calculation considers all the atoms in a sphere out to the respective kNN value. After ~ 50NN, all pairwise SRO values in both conditions converged to a steady state, and the value at 200NN was used as the experimental SRO values between the different pairs. This result indicates that annealing has driven a clear departure from the random distribution apparent in the AH condition, with significant changes particularly for the Cr-Cr and Cr-Ni / Ni-Cr pairs.

[0171] These experimentally measured SRO values were then used as inputs to the reconstitution algorithm described above. Before and after reconstituted values are presented in Figures 16(c) and 16(d) for both the AH and AN500 samples of the CoCrNi MEA. The existence and conditions of SRO in the AN500 sample and the near random condition of AH sample has been further confirmed using TEM and APT spatial distribution methods discussed below.APT sample preparation and experiments

[0172] At least two APT specimens of each condition (i.e. , AH and AN500) were prepared using the lift-out method on a Thermo Fisher G4 Hydra Plasma FIB-SEM equipped with an Oxford instrument EBSD detector. The same crystal direction, {110} was arbitrarily chosen to be aligned to the z-axis or length of the tip specimen from both conditions by using correlative EBSD maps collected prior to lift-out and selecting grains with the same IPF-Z orientation. Annular milling was used on the lift out samples to reach a radius less than 100 nm APT tips. To evaluate the effects of pole orientations, studies have been conducted on both

[0100] and {111} orientations under varying conditions. The results are shown in Figure 22, discussed in more detail below.

[0173] APT experiments were carried out using a CAMECA LEAP 3 / 4000SL The running condition for samples was 20% pulse fraction, 200 kHz pulse rate, 50 K and detection rate of 0.2 %48. The data was reconstructed and analysed using the Interactive Visualization and Analysis Software (IVAS™) package (IVAS 3.8.4 and AP Suite 6.1) to achieve the calibrated position and mass-to-charge ratio of each species in a 3D space, as shown in Figure 17, where the content of impurity elements C, N, O, Fe, Al and Si are shown as being negligible. They do not change substantially between the AH and AN500 states and therefore do not significantly influence the SRO measurement. H is detectable in both conditions, most of the H is attributed to background H from the chamber and not from the material itself - hence it is having no influence on SRO. ICP- AES (Table 3) also found that impurity elements accounted for only 0.26 % in the original CoCrNi ingot.

[0174] After processing the APT data for both AH and AN500 conditions, the desorption maps were plotted. By using the density mapping technique in combination with the known grain orientation, at least two poles were identified. Image compression factor (ICF) and field factor (called kf) values were then calibrated for the APT data, as shown in Figure 21. Similar SRO trends were obtained from different tips for each condition.TEM sample preparation and experiments

[0175] Samples for TEM were sliced by diamond saw (Struers 50) and thinned by mechanical polishing to 70 pm foils. The foils were punched to disks with 3 mm in diameter. Electron transparent samples for TEM observation were prepared by twin-jet electro-polishing. This was carried out using a solution of 10% perchloric acid in methanal at -30 °C. The thin regions in the TEM specimen were used for TEM experiments. TEM samples of different heat treatments were used for observation. A JEOL 2200 microscope (200kV), equipped with an Omega energy filter, was used to take both diffraction patterns. By using energy filter, zero-loss peaks were selected to take the diffraction patterns.

[0176] Figure 18(a) displays the {110} orientation diffraction pattern for the AH sample with the intensity profile extracted from the rectangular region outlined, showing uniform intensity without significant fluctuations. Figure 18(b) shows the {110} orientation diffraction pattern for the AN500 sample with the intensity profile from the rectangularregion outlined, where the peaks indicated by arrows reveal periodic intensity variations, indicative of the presence of SRO. The rectangular regions in both Figures 18(a) and 18(b) are aligned parallel to the (200)* planes.

[0177] Figure 19(a) shows the FCC {111} diffraction pattern from the AH sample, with weak diffuse scattering evident, and Figure 19(c) provides an enlarged view highlighting this feature around the bright dots. Figure 19 (b) depicts the FCC {111} diffraction pattern for the AN500 sample, with strong diffuse scattering observed, which is further emphasized in the enlarged view in Figure 21(d). The fractional diffuse scattering in Figures 19(a) and 19(b) is marked by the {224 / 3} planes indicated by yellow arrows. The white arrows and dashed circles in Figure 19(d) indicate regions of pronounced diffuse intensity, characteristic of SRO.

[0178] Figure 20(a) shows the TEM image and diffraction pattern of the needle specimen fabricated so that the

[0111] direction coincides with the needle axis in the annealed sample. Figure 20(b) is a 2D desorption image showing central pole

[0111] , while Figure 20(c) is an atom map slice (5-nm thick) enlarged in the central pole region. Figure 20(d) are SDMs of Cr-Cr, Co-Co, and Ni-Ni along the

[0111] direction. Figures 20(e)-(g) present the AH sample results using the same SDM method, with peak correlations for Cr-Cr, Co-Co, and Ni-Ni pairs. Figures 20(h)-(j) depict the AN500 sample results. The black dashed lines in Figure 20(d) and red dashed lines in Figures 20(e) to (j) use the first peak as a reference to show the amplitude of the peaks.

[0179] The above described example shows that realistic atomistic models can be generated based on experimental APT data. These models can then serve as the starting point for computational materials simulations using density functional theory, and / or molecular dynamics. The described approach applies a data science technique to map the relationships between SRO values, detector efficiency and spatial noise in APT data. Moreover, the example demonstrates a reconstitution procedure that serves as a method to quantitatively measure the SRO in an equi-atomic CoCrNi MEA. When applied to homogenised CoCrNi samples (AH) and samples annealed at 500 °C for 500 h (AN500), clear changes in the SRO for the various elemental pairs were apparent, as shown in Figure 16. The Cr-Cr and Ni-Ni pairs were found to cluster while the Cr-Ni and Ni-Cr pairs were found to exhibit anti-clustering. Consequently, the present disclosure demonstrates that real-world atomistic data can be used in computational simulations to explore microstructural evolution and materials properties.Pairwise SRO formalism

[0180] The general theory behind SRO values will now be discussed. SRO is expressed as a dimensionless parameter referred to here as a, such that -1 < a < 1. When the atomic species under consideration are distributed randomly, a = 0. When these species are clustered together due to preferred interactions a > 0, and when anticlustering occurs, these species tend to be repelled and a < 0. The Warren-Cowley SRO (WC-SRO) formalism was originally derived for a dilute binary alloy system. To cover the more complicated situation that arises in M / HEAs alloys with compositional complexity, the expression for the SRO parameter, a, has been modified. The purpose of this revision was to simplify the mathematics for the M / HEAs type cases. The revised pairwise SRO parameter used here was a (mAB) as defined by the following equation: a(m) = (PAB- XB) / XB... (1)

[0181] The term a is the SRO parameter, m is the shell, XB is the concentration of the B atoms calculated from the entire atom probe dataset, PAB is the probability of finding atom B around a central atom A within certain nearest neighbour atom amounts. For the system of the example, A and B correspond to the pairwise instances of the Co, Cr, Ni atomic species.

[0182] The methodology in performing the SRO simulation will now be described below.The simulation of SRO

[0183] Step 1 : Build the model: A perfect face-centred cubic lattice containing ~ 4 million lattice sites with a lattice parameter a = 0.36 nm was generated. The lattice sites were randomly occupied by Co, Cr and Ni atoms in equal concentration. 616 This simulation was the basis for the a = 0 random case. The atomic positions were randomised 100 times using Monte Carlo simulations. The crystal structure and lattice parameters were assigned based on the XRD and EBSD experiment result above, as best shown in Figure 23. The simulation was then generated.

[0184] Step 2: Detector efficiency simulation: The three elements were randomly distributed in the model using a random labelling method (Figure 11(a)). Additionally,SRO-enriched models were built by forcing the atomic preference within kNN = 12 to various pairwise SRO values (0.1 to -0.1) within the extreme conditions for MEAs using reverse Monte Carlo simulations (Figure 11(b)). The influence of the detection efficiency on the SRO parameter for random and non-random simulations (Figure 11(a)-(b)) was simulated from 100% detection efficiency to 10% detection efficiency with a step size of - 5%. Each point was simulated one hundred times, and average values and 95% confidence level were plotted in Figures 11(a)-(b).

[0185] Step 3: Spatial noise simulation: Figures 11(c)-(d) were simulated using fixed SRO value pairs. For the random case, one random labelling model with a fixed random pair was used (Figure 11(c)). The lateral noise was simulated from 0 to 0.5 nm with a step size of 0.1 nm. The depth noise was from 0 to 0.1 nm with a step size of 0.02 nm. One hundred simulations were done, and the absolute value of the average SRO values was plotted. For the non-random case, models with the same pair were chosen. An SRO value of 0.041 at kNN = 12 was used in Figure 11(d). In Figure 11(d), both lateral noise and depth noise were simulated. This spatial noise is added by Gaussian noise characterized by a standard deviation (a) with a mean of zero. We added lateral noise (i.e., ox,y- ) ranging from 0-1.25 nm and depth noise (i.e., az-) from 0-0.1 nm to mimic the real APT resolutions. For example, given the nature of Gaussian distribution, with a mean of 0 nm, a a of 0.25 nm implies that 68% of the noise falls within this range, but 95% of the noise added corresponds to 2a, which is 0.5 nm. To maintain clarity, a values instead of claiming 95% at 0.5 nm. The method was tested under three conditions: 1. ax,y- = 0.25 to 2ax,y- = 0.5 nm; 2. ax,y- = 0.5 to 2ax,y- = 1 nm; and 3. ax,y- = 1.0 to 2ax,y- = 2.0 nm. For the first two conditions, the method remains effective (Figures 12 and 13), surpassing the standard material's tested resolution of < 0.28 nm to a worse condition of 1 nm, as best shown in Figure 24(c) where there is a sharpness in the peak distribution in the 1 D-SDM..

[0186] Step 4: The simulation of the detector and spatial noise: Combining the effect of detector efficiency and spatial noise, Figures 11(e)-(f) were simulated using fixed SRO value pairs but various kNN numbers. For the random case, one random labelling model with a fixed random pair was used (Figure 11(e)). In the beginning, 43% of the atoms are randomly removed. Then, the lateral noise was simulated from 0 to 0.5 nm with a step size of 0.1 nm. For the non-random case, models with the same pair were chosen. 43% randomly removed was applied, and an SRO value of 0.039 at kNN = 7 was used in Figure 11(f). The lateral noise was simulated from 0 to 1.25 nm. One hundred timesrandomly removed, and simulations were done, and the absolute value of the average SRO values was plotted.The determination of the spatial resolution

[0187] The spatial resolution of APT is instrument-based, highly anisotropic, and greatly dependent on the selection of experimental parameters and the material under analysis. The instrument was assessed using standard aluminium samples, as best shown in Figure 24. In Figure 24(a), the atom map is a three dimensional APT reconstruction of standard pure aluminium, while Figure 24(b) is a 2D SDM illustrating the lateral resolution capacity of APT to detect atomic distances smaller than 0.28 nm. Figure 24(c) also demonstrates the z-resolution capacity of APT, as indicated by the sharpness of the peak distribution in the 1 D-SDM. . Spatial resolution is higher in-depth than laterally by as much as order of magnitude. In-depth resolution is highest around crystallographic pole features where the evaporation sequence is highly ordered but these regions also have the lowest lateral resolution where local magnification effects brought about by trajectory uncertainties are more pronounced. Values were determined for the spatial resolution representative for the experimental data collected. The trajectory uncertainties were separated into two components: lateral resolution (x, y) and depth resolution (z). By considering the peak width of the central peak of a 1 D SDM generated along the normal direction to the {111} planes shown in Figure 12(b) to Figure 12(e), the standard deviation of in-depth noise (cz-) in this region was found to be 0.024 nm, 0.036 nm and 0.077 nm, respectively. These represent the highest in-depth resolution of the dataset. The in-depth resolution will degrade at regions further away from the (111) pole. A conservative value of az- = 0.1 nm for the in-depth resolution was used in the studies, consistent with existing literature on APT resolution studies including recent simulation studies that modelled the influence of changing evaporation fields in concentrated solid solutions or HEAs.

[0188] Lateral resolution could not be measured directly as the spatial noise was too high to resolve crystallographic information from a 2D SDM. However, based on estimates from previous studies, the lateral spatial noise is expected to have a standard deviation of approximately ax,y- = 0.25 nm. If it were much higher, any SRO within the analysed dataset below a ~ 0.0048. would not be detected as Figure 11(g) highlights. Yet Figure 14 clearly shows a measurable change in SRO between the experimentally derived AH and AN500 samples below these values.The simulation of the APT experiments

[0189] In SRO parameter calculations (as shown in Table 6 below), since the signal of the SRO values were only representing the clustering / ordering (plus sign) and anticlustering (negative sign) behaviours, the absolute value ( \PAB- XB| ) is showing the deviation from the concentration. Different true SRO values were embedded in the simulated models of a CoCrNi MEA. Gaussian noise with different standard deviation values (condition 1: x,y = 0.25 nm, and z = 0.1 nm; condition 2: x,y = 0.5 nm and z = 0.1 nm; condition 3: x,y = 1 nm and z = 0.1 nm) was added to the synthetic data and SRO parameters were calculated. This enables the determination of the correction factor, using Equation 1.Table 6: The relationship between different SRO parametersReconstitute and validate the SRO values

[0190] Nine pairs of a 4 million atoms CoCrNi dataset with perfect lattice was set to different true SRO values at kNN =12 with 100% atoms. The APT simulation (43% detection loss and x,y = 0.25 nm, x,y = 0.5 nm, x,y = 1 nm and z = 0.1 nm noise) was applied to the dataset 100 times for each pair. The measured SRO values after the degradations were reconstituted with the correction factors to get a distribution with the mean value and 95% confidence intervals, as shown in Figures 15(b)-(d).Experimental SRO calculation

[0191] The experimental SRO parameter was calculated using scripts run under Matlab®R2020. Based on Equation 1, three parameters were used during the calculation. First, XBis calculated from the dataset for each species. The number of B atoms in the whole dataset is taken and divided by the entire atoms in the dataset. XBis calculated for all three elements (Co, Cr and Ni).

[0192] Second, PAB, which is the probability of finding B around a central atom A within specific nearest atom amounts, is obtained. The nearest atom amounts (m) are set from 1 to 200, as shown in Figures 16(a) and 16(b). Then, Co, Cr and Ni are selected as the central atom A and find the Co, Cr and Ni atoms around the central atom and calculate the probability.

[0193] Third, the pairwise short-range ordering parameter is calculated after obtaining PABand XB. The numbers are saved and plotted as shown in Figures 16(a) and Figure 16(b). Random labelling tests were conducted to prove the exitance of SRO in the experimental results, as best shown in Figure 25. Figure 25(a) illustrates one instance of random labelling versus the experimental data, where the random labelling and the experimental data are relatively close in SRO values for kNN distributions in the range of around 40 < k < 200. Figure 25(b) expands this comparison to ten random cases with the experimental data (indicated by the arrow). The shaded area shows the regions of difference between the experimental results and the random cases, specifically for kNN distributions in the range of around 1 < k < 40 (i.e. the first 40 NN atoms).Pole assessment and extraction process

[0194] Samples were prepared from the {111} and {100} orientations for both AH and AN500 conditions of CoCrNi, using consistent parameters and methods across all orientations. The results, as shown in Figures 21 and 22, indicate that there are varying concentration changes around poles in different orientations, with the {111} orientation showing the most pronounced changes.

[0195] Figures 21(a) to 21(f) illustrate density hit maps and the pole identification process for the AH and AN500 samples under their heat treatment conditions. Figures 21(a) and 21(d) are the original hit maps for the AH and AN500 samples, respectively.Figures 21(b) and 21(e) are processed hit maps mapping the average distance between sequential detector events per pixel for the AH and AN500 samples, respectively. Figures 21(c) and 21(f) show the indexed poles from the processed figures for the AH and AN500 samples, respectively. Multiple poles can be clearly identified from Figures 21(c) and 21(f) for the reconstruction process.

[0196] Figure 22 show an APT analysis of elemental distribution in different crystallographic orientations. Figure 22(a) shows a three-dimensional reconstruction of an APT sample, with the atoms color-coded by element. Figure 22(b) displays 2D concentration maps for Cr, Co, and Ni in three different grain orientations: {111}, {100}, and {110}. Each row corresponds to a different orientation, as indicated, with the concentration of each element represented in colour scale. These maps reveal the spatial variation of element concentration within the grains, providing insight into the distributional homogeneity across the different crystallographic orientations.

[0197] Pole influence on concentration was reviewed. Figure 22 also indicates that Cr is more abundant in pole regions, while Ni / Co are less so. This is attributed to the differences in evaporation fields of these elements. Cr has the lowest evaporation field at 29 V / nm, while Co and Ni have higher fields at 37 V / nm and 36 V / nm, respectively. The concentration fluctuation varied with orientation is shown in Figures 20 and 21 : approximately 3 nm for the {110} direction (Figure 26(a)), around 5 nm for the {100} direction (Figure 26(b)) and about 7-8 nm for the {111} direction (Figure 26(c)).

[0198] The impact of size and concentration on pole extraction was examined, as best shown in Figure 26. Figure 26 shows an analysis of elemental concentration variations by APT with pole extraction from different crystallographic orientations. Figure 26(a) illustrates a lift-out from the {110} grain. Figure 26(a)(1) depicts the APT tip with a {111} pole; Figure 26(a)(2) shows the corresponding concentration map; and Figures 26(a)(3)- (6) represent concentration profiles for Ni, Co, and Cr at varying distances along the x axis with no extraction, and following 5 nm, 10 nm, and 15 nm pole extraction, respectively. Figure 26(b) shows a lift-out from the {100} grain. Figure 26(b)(1) illustrates the APT tip with a {100} pole; Figure 26(b)(2) shows the corresponding concentration map; and Figures 26(b)(3)-(6) display concentration profiles for Ni, Co, and Cr at varying distances along x axis with no extraction, and after 5 nm, 10 886 nm, and 15 nm pole extraction, respectively. Figure 26(c) shows a lift-out from the {111} grain. Figure 26(c)(1) demonstrates the APT tip with a {111} pole, and Figure 26(c)(2) provides the associatedconcentration map. Figures 26(c)(3)-(6) show concentration profiles for Ni, Co, and Cr at different distances along x axis with no extraction, and following 5 nm, 10 nm, and 15 nm pole extraction, respectively. After removing 10 nm in the {111} orientation, the concentration tended to be uniform, whereas a 5 nm extraction was sufficient for the {100} and {110} orientation. The {110} orientation's primary influence was found to be the {111} pole but at the edge. The concentration profiles highlight the influence of pole proximity and extraction size on the distribution of elements within the grains. The dashed line indicates the potential pole regions.

[0199] SRO results after pole extraction was considered. In the {110} orientation, the SRO results after extracting 10 nm were compared with those without pole extraction, as best shown in Figures 27(a) and 24(b). Figure 27(a) displays the SRO parameters for the AN500 sample without pole extraction while Figure 27(b) displays the SRO parameters for the AN500 sample after 10 nm pole extraction. The overall trend remained consistent, suggesting that preferential evaporation in APT, especially for the {110} grain, has a minimal impact after pole extraction. A comparative analysis of AH and AN500 was conducted following a 10 nm pole extraction, as shown in Figures 27(c) and 24(d). This comparison reveals a marked difference in the SRO trends between the two samples. Each graph plots the SRO parameter against kNN, illustrating the elemental pair correlations for Co-Co, Co-Cr, Co-Ni, Ni-Co, Ni-Cr, and Ni-Ni

[0200] A final pole extraction process was made. Concentration maps for Cr, Co, and Ni from the raw APT data were generated to check for the potential of segregation to crystallographic poles or other effects, as best shown in Figure 28. The concentration maps were calculated for both the AH (Figures 28(a)-(c)) and AN500 heat treatment conditions (Figures 28(d)-(f)). The maps showed evidence of preferential segregation of Cr near the {111} pole for the AN500 sample (Figure 28(d)), caused probably by evaporation. To eliminate the potential for this segregation to bias the SRO measurements, a cylinder of the data (10 mm radius in detector, as shown in Figures 28(g)-(i)) centred at the {111} pole was removed. The SRO algorithms were applied to the new, filtered data so as to remove any effects from segregation to poles.

[0201] It will further be appreciated that any of the features in the preferred embodiments of the disclosure can be combined together and are not necessarily applied in isolation from each other. For example, the method 300 and system 400 can be modified to selectively perform the analysis method 100 or 500. In another example,a combination of kNN distributions, SRO values and / or local composition parameters may be used in the analysis method 100. Similar combinations of two or more features from the above described embodiments or preferred forms of the disclosure can be readily made by one skilled in the art.

[0202] The above described embodiments provides methods of analysis and manufacturing, and a system, where determining a distribution of a plurality of mathematical functions relating to the spatial distribution of atoms in the material, like kNN distributions, enables determining of the microstructure of a material. Consequently, this detected microstructure can be linked to the process parameters used in the manufacture of a material, creating a feedback loop for rapid, iterative process design that achieves a targeted suite of materials properties. The above described embodiments may also be used generally in the assessment of the microstructure of materials, including the presence of any faults or defects, as well as enabling a go / no-go threshold to be established in the manufacturing process. As a consequence, these embodiments result in an improvement to the manufacturing process, reducing the consumption of material resources and time to manufacture a material or product exhibiting the correct or desired physical, mechanical and chemical properties. That is, as the material can be tested for their properties (via the detected microstructure) during the manufacturing process, this avoids the need to produce test specimens or prototypes for testing their properties after the manufacturing process has been performed. This in turn reduces the consumption of material and time in producing these test specimens, or at least reduce the number of test specimens required. Also, by being able to determine the properties of the material and final product during manufacture, the embodiments permit a quicker qualification or certification process that confirms whether a manufactured product will comply with any regulatory requirements, industry standards or contractual design requirements. Moreover, the embodiments enable an early assessment whether a designed product manufactured from the material is practically viable; that is, they can provide a threshold test to ensure whether the product exhibiting the required properties can be manufactured reliably. In all these respects, these disclosed embodiments represent a practical and commercially significant improvement over the prior art

Claims

Claims1. A method of analysing a material, comprising: obtaining atomic data relating to the location of atoms within the material; performing a calculation on the atomic data to generate a plurality of mathematical functions relating to the spatial distribution of the atoms according to one or more predefined parameters; calculating a statistical distribution of the generated mathematical functions; and determining a detected microstructure of the material based on the statistical distribution.

2. The method of claim 1, wherein determining the microstructure comprises determining the concentration of atoms according to the one or more predefined parameters from the statistical distribution; and the concentration of the atoms according to the one or more predefined parameters indicates a clustering effect of the atoms to exhibit the one or more properties of the material.

3. The method of claim 1 or 2, wherein the plurality of mathematical functions comprises k-Nearest Neighbour (kNN) distributions.

4. The method of claim 1 or 2, wherein the plurality of mathematical functions comprises Short Range Order (SRO) values.

5. The method of claim 1 or 2, wherein the plurality of mathematical functions comprises probability functions representing local composition parameters.

6. The method of any one of the preceding claims, comprising assigning weights to one or more of the mathematical functions and calculating the statistical distribution based on the weighted mathematical functions.

7. The method of any one of the preceding claims, comprising obtaining the atomic data using a microscopy method comprising one or more of transmission electron microscopy (TEM), atom probe microscopy (APM), X-ray synchrotron and neutron scattering.

8. The method of any one of the preceding claims, comprising generating a target microstructure of the material and comparing the detected microstructure to the target microstructure.

9. The method of any one of the preceding claims, wherein the one or more predefined parameters comprises atomic elements and / or distances between a designated atom from one or more other atoms.

10. A method of manufacturing a product comprising at least a first material, comprising: performing one or more manufacturing steps on the first material for producing the product having a target microstructure; performing the method of analysis of the first material, wherein the analysis method is in accordance with any one of the preceding claims; comparing the detected microstructure to the target microstructure; and adjusting at least one of the manufacturing steps in response to the detected microstructure being substantially different to the target microstructure.

11. The method of claim 10, wherein the adjusting step comprises at least one of: changing one of the manufacturing steps to modify the detected microstructure of the first material to the target microstructure; performing a second manufacturing step on the first material to modify the detected microstructure of the first material to the target microstructure, after stoppage or completion of a first manufacturing step; and adjusting one or more design parameters of the product prior to repeating the one or more manufacturing steps.

12. The method of claim 10 or 11, wherein the obtaining, analysis and adjusting steps are repeated until the detected microstructure is substantially the same as the target microstructure.

13. A system for manufacturing a product comprising at least a first material, comprising: one or more manufacturing machines for performing one or more manufacturing steps on the first material to produce the product having a target microstructure; a control unit configured to control the one or more manufacturing machines;a data retrieval unit for obtaining atomic data relating to the location of atoms within the first material; and a processor configured to perform an analysis method of the first material, wherein the analysis method comprises: performing a calculation on the atomic data to generate a plurality of mathematical functions relating to the spatial distribution of the atoms according to one or more predefined parameters; calculating a statistical distribution of the generated mathematical functions; determining a detected microstructure of the first material based on the statistical distribution; and comparing the detected microstructure to the target microstructure; wherein the control unit is configured to adjust operation of the one or more manufacturing machines in response to the detected microstructure being substantially different to the target microstructure.

14. The system of claim 13, wherein the control unit is configured to adjust operation of the one or more manufacturing machines such that the detected microstructure of the first material is modified to the target microstructure.

15. The system of claim 13 or 14, wherein: the system is configured so that the data retrieval unit obtains the atomic data, the processor performs the analysis method and the control unit adjusts operation of the one or more manufacturing machines iteratively until the detected microstructure is substantially the same as the target microstructure; and / or the data retrieval unit comprises one or more of light-optical microscope, electron microscope, atomic force microscope (AFM), scanning tunnelling microscope, the photonic force microscope, recurrence tracking microscope, atom probe, X-ray microscope or other microscopy instrument.

16. A method of analysing a material, comprising: obtaining atomic data relating to the location of atoms within the material; performing a calculation on the atomic data to generate a plurality of k-Nearest Neighbour (kNN) distributions according to one or more predefined parameters; calculating one or more Short Range Order (SRO) values from the plurality of kNN distributions; anddetermining the microstructure of the material based on the one or more SRO values.

17. The method of claim 16, further comprising determining one or more properties of the material from the detected microstructure and / or wherein determining the microstructure comprises using the one or more SRO values to determine whether the atoms have a clustering or anti-clustering effect to cause the material to exhibit the one or more properties of the material.

18. The method of claim 16 or 17, wherein the calculation of SRO values comprises: selecting a representative kNN distribution from the plurality of kNN distributions and calculating the SRO values for that representative kNN distribution; or calculating the SRO values from some or all of the kNN distributions.

19. The method of any one of claims 16 to 18, wherein: the calculation of SRO values comprises applying a calibration factor to take into account variances occurring when the atomic data is obtained; and the calibration factor comprises assigning a true SRO value based on a theoretical value and dividing the true SRO value by the measured SRO value.

20. A method of manufacturing a product comprising at least a first material, comprising: performing one or more manufacturing steps on the first material for producing the product having a target microstructure; performing a method of analysis of the first material, wherein the analysis method is in accordance with any one of claims 16 to 19; comparing the detected microstructure to the target microstructure; and adjusting at least one of the manufacturing steps in response to the detected microstructure being substantially different to the target microstructure.

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