Measuring Residual Strain and Stress in Thermal Spray Coatings Using Neutron Diffractometers

During thermal spray coating, residual strain (or stress) is formed within the coating and substrates due to many processes (quenching stress, peening effect, deposition temperature, lamella structure) and micro-structural phase changes. It is also known that the residual stress values of thermally sprayed coatings are dependent upon the measurement method. Neutron diffraction technique can provide a non-destructive through-thickness residual strain analysis in thermally sprayed components with a level of detail not normally achievable by other techniques. Despite this advantage, the number of studies involving neutron diffraction analysis in thermal spray coatings remain limited, partly due to the limited number of neutron diffraction strain measurement facilities globally, and partly due to the difficulty is applying neutron diffraction analysis to measure residual strain in the complex thermal spray coating micro-structure. This paper provides a comprehensive guide to researchers planning to use this technique for thermal spray coatings, and reviews some of these studies. ENGIN-X at the ISIS spallation source in the UK is a neutron diffractometer (time-of-flight) dedicated to materials science and engineering with high resolution and versatile capabilities. The focus is on the procedure of using ENGIN-X diffractometer for thermal spray coatings with a view that it can potentially be translated to other neutron diffractometers. Neutron sources worldwide (e.g. Africa, Asia, Australia, Europe, and North America) have been used to measure strains in various materials, and here, we present few examples where thermal spray coatings have been characterized at various neutron sources worldwide, to study the residual strains and micro-structures.


Introduction
This paper presents test methodologies for experimentally determining residual strain (and stress) in thermal spray coatings neutron diffraction technique with emphasis on ENGIN-X diffractometer at the ISIS neutron source in the UK [1]. The techniques presented here can potentially be applied to other neutron diffractometers, available globally, for the measurement of residual strain in thermal spray coatings. Although the physics of neutron diffraction remains the same, the availability of strain measurement instrumentation at different neutron diffractometers varies globally and requires adjustments for a comprehensive strain analysis. Nevertheless, the high resolution of through-thickness non-destructive residual strain analysis, if planned and performed carefully using neutron diffraction, is not normally achievable by other experimental techniques. This guide can apply to all thermal spray coating and substrate systems and intended to measure through-thickness microscopic residual strain that uses the measurement of the positions of the diffracted neutron spectra peaks to determine changes in the lattice spacing.
Thermal spray coating processes involve the build-up of a layer of partially molten splats which are heated and propelled by a spray (a flame or plasma, see Fig.   1(a)) towards a substrate. Difference between coatings obtained through a single pass and multiple passes is shown in Fig. 1(b). The relevant differences are: (a) thicker substrate, (b) higher temperature seen on the substrate, and (c) the substrate is of a different material. Thermal spray processes are characterized by residual strain (or stress) within the coating and substrates due to different physical phenomena (quenching stress, peening effect, deposition temperature, lamella structure) and phase transformations [2][3][4][5][6], Fig. 1(c). That residual stresses dictate the quality and performance (e.g. adhesion, fatigue, tribological behaviour [3]) of the coating substrate system (with coating thicknesses ranging from 50-500 m) is a well-established fact.
Measurement of residual stress is therefore crucial to evaluate and quantify coatings quality.
The measurement method dictates the residual stress measured within a thermally sprayed coating (or any other material). Non-destructive (laboratory X-ray, synchrotron X-ray, neutron (e.g. Fig. 2), Raman spectroscopy, digital image correlation, photoluminescence piezospectroscopy), semi-destructive (hole-drilling & ring-coring, layer removal, focused ion beam milling, indentation), and miscellaneous other (curvature, modified layer removal, material removal, diametral compression) approaches have been adapted to experimentally evaluate the residual stress fields in thermal spray coatings. The lifetime of the coating system is very much dependent on the residual stress and this is dependent on the measurement method. This dependency on the measurement method directly influences the verification of numerical and Electronic copy available at: https://ssrn.com/abstract=3711244 experimental models used to predict the residual stress evolution within the coating systems. Hence what is important and is lacking within the existing literature is the comparative study of the various destructive and non-destructive methods of through thickness residual stress measurement, though studies exist on the use of a single method [4].
Non-destructive measurement of these strain (or stress) fields in relatively thin thermal spray coatings is also technologically challenging, because techniques such as deep hole drilling, laboratory X-ray, synchrotron X-ray and beam curvature methods are either destructive and/or provide only a sub-surface strain measurement. Where the very-near surface residual stresses play a critical role, e.g. surface crack initiation due to wear, surface roughness effects complicate the surface residual stress measurements.
Particularly in the case of thermal spray coatings, techniques such as X-ray and synchrotron X-ray can only provide a through thickness residual stress measurement through a destructive process (layer-removal process). Accordingly, recent investigations have concentrated on the use of various non-destructive techniques (e.g. diffraction, optical spectroscopy) for such strain analysis.
In this work, a practical example of the test method at room temperature and unloaded condition was presented with some of the recent findings of through-thickness residual strain measurements in as-sprayed coatings via the ENGIN-X neutron diffraction instrument. We also present few examples where thermal spray coatings have been characterised at various neutron sources worldwide to study the residual strains and microstructures.

Origin of residual stresses in thermal spray coating
Residual stresses occur in the material or components at the removal of any external loads (e.g. applied force, displacement, thermal) during manufacturing or service loading [7][8]. These stresses are locked inside the material and are superimposed on stresses subsequent service loading or manufacturing. Residual stresses in thermal spray coatings can have different magnitude and distribution, depending on the combination of coating and substrate materials and processing conditions. These stresses can also be altered due to service loading and/or thermal heat-treatment of the coating substrate system. A certain level of compressive residual stress in the coating material is always desirable to resist crack initiation/propagation and coating degradation during service loading. Very high compressive residual stress in coating is however not desired [9][10][11][12][13][14].
As the coating performance during service loading depends on the structureproperty relationships, such as microstructural phases, hardness, fracture toughness, anisotropy and other microstructural features, it is not always possible to design the optimum residual stress profile in the given coating substrate system. Functional grading Electronic copy available at: https://ssrn.com/abstract=3711244 of the coating, where the composition of coating microstructure is varied through thickness, either uniformly, or by depositing layers of different materials can sometimes be used to improve the residual stress profile to combat coating delamination. Formation of residual stress is inherent to the nature of thermal spray coating process. These stresses can be caused by quenching stress, peening effect, deposition temperature and phase transformations. Based on physical and metallurgical phenomena dictating the residual strain behaviour, through thickness residual strain profile of thermal spray coating is influenced by the following four major factors [6]: (a) Role of quenching stress: The quenching stresses, which appear within individual splats, are caused due to the constriction of the contraction of the individual splat by the lamellae lying underneath that are created due to the preceding spray pass. The degree of constrained contraction is a function of the individual splat temperature and the size of powder particles. Quenching stresses are always tensile as the contraction of splat or lamella during its rapid cooling is constrained by the underlying deposit at relatively lower temperature, means deposited splats thermal contraction after solidification is constrained by the underlying solid splats. Hence the magnitude of quenching stress is a function of ratio of the deposition temperature of the powder particle and its melting point.
(b) Peening effect: The high particle velocity seen in thermal spray processes is known to have a peening effect which results in compressive residual stresses in the coating. Hence the peening stress is a function of the momentum of the powder particle during thermal spraying, i.e. the deposition velocity and the mass of the powder particle and the temperature-dependent plasticity of the underlying deposit. The mechanism is like the shot-peening of gears and shafts as an engineering practice to induced compressive residual stress to combat fatigue and fracture. Hence, thermal spray coating processes such as the high velocity oxyfuel (HVOF) process, with relatively high particle velocities are understood to cause relatively high compressive residual stresses in the coatings.
(c) Role of deposition temperature: Macro residual stress occurs due to the differences in the coefficient of thermal expansion (CTE) of coating and substrate materials. These stresses can be compressive or tensile depending upon the mismatch of the CTE of the coating and substrate materials, e.g. if > , the stress in the coating will be tensile as its contraction is constrained.
(d) Phase transformation: The cooling of impacting powder particle or lamella occurs in a matter of few micro-seconds from a near-molten temperature to form a solid deposit. This can lead to amorphous phases in the coating material depending upon the temperature of the impacting lamella. There is not enough time for Electronic copy available at: https://ssrn.com/abstract=3711244 crystal structures to form in a fully molten powder particle, so it is desirable to control the heating of powder particle to near-melting point but not above it.
There is also a possibility of oxidation of powder materials in some cases leading to further phase transformations. Some of these phase transformations can lead to a small volume change in the crystal structure. This change in volume can provide an accommodation mechanism at inter-splat boundaries for the coatings, leading to residual strain.
Overall, the residual stress in thermal spray coatings is a function firstly of the distribution of temperature and velocity of individual powder particles in the spray stream. Not all sprayed powder particles have the same temperature or velocity, which is a function of the location of the powder particle within the spray-stream during thermal spraying. Secondly, the residual formation is a function of the thermomechanical properties of the coating-substrate system, the most important being the temperature-dependent CTE characteristics and temperature-dependent elastic-plastic behaviour. Although, it is possible to model crudely the evolution of residual stress generation during thermal spraying using numerical modelling, but these numerical techniques are unable to accurately comprehend the variation of stress or account for phase transformations [15]. Multiscale modelling to combat some of these limitations makes the modelling approach computationally expensive. Hence, non-destructive experimental residual stress measurement remains critical for the evaluation of coating quality and predicting the service life of components.

Principle of neutron diffraction
Neutrons interact directly with the nucleus of the atom in a given material [16][17][18][19] instead of the electron cloud which significantly increases the penetration depth of neutrons for strain measurements. Since neutron of all energies is produced in a short pulse, the de Broglie's relation given momentum ( ) and hence neutron speed ( ) is given by [16]: where, is neutron mass, is Planck's constant. Since = 1.67 × 10 -27 ℎ = 6.63 × 10 -34 neutron travels down the flight path ( ) (e.g. 10 m to 100 m), to separate neutrons in time, therefore, time ( ) of arrival at the detector is given by [16]: Neutron diffraction method, as with X-ray diffraction methods, measures the Bragg angle of scatter radiation using the equation (Fig. 3) [16]: Electronic copy available at: https://ssrn.com/abstract=3711244 where is a positive integer, is the wavelength of the incident wave, is the interℎ planar spacing, ( ) is the Miller indices, is one half of the angle through which the ℎ ℎ incident beam is diffracted by planes, which is related to the spacing between crystallographic planes. Hence, peaks are measured at times ( ) given after the initial pulse given by [16]: Each peak corresponds to an (hkl) family of lattice planes is given by Bragg's law.
Like the X-ray diffraction method, the accuracy of the neutron diffraction method is dependent on the knowledge of spacing of the unstressed lattice of the crystallographic planes. This is because the stress is tri-axial at depth [19]. Similar to the synchrotron Xray method, spacing at the measurement point in an unstressed lattice should be known but is not easy to measure. The neutron diffraction method shows a smaller range of scattering than X-ray diffraction which is another contributing factor to why it can penetrate deeper. A typical wavelength for neutron diffraction will range between 0.7 Å and 3 Å, and can measure the elastic strains caused residual stress by component thickness varying between 0.1 m and 1.5 m to less than 1 mm. This means the bulk residual stress within the component can be examined in a non-destructive manner.
Neutron diffraction strain measurements at the UK ISIS Facility utilises ENGIN-X strain measurement diffractometer, which is a pulsed neutron diffractometer equipped with slits and collimators to achieve small gauge volumes [17]. At ENGIN-X, the residual strain in the coating and substrate materials can be obtained from the shift in individual peaks (e.g. scheme shown in Fig. 3(b)) using a single or multiple peak fitting routine.
Peaks with little to no overlap with others can be chosen for the strain analysis. The feedstock powder material or the powder obtained by carefully removing the coating from the substrate and crushing it can be used to measure the strain-free lattice parameter ( ) for the coating material. This powder can then be put in a vanadium 0 ℎ tube (which is transparent to neutrons) and its lattice parameter measured. The substrate strain free lattice parameter can then be measured at the free surface. The direct elastic strain (average) in the material at the measured direction can be calculated from the following [17]: is the measured interplanar lattice spacing and is the stress-free ℎ 0 ℎ interplanar spacing for the material. The strain is measured in the direction of the scattering vector (Fig. 3). The elastic stress can be calculated from these strain values using the through-thickness (coating and substrate) elastic modulus values or Hooke's law: Electronic copy available at: https://ssrn.com/abstract=3711244 is stress calculated for a particular direction, is the elastic coefficient for ℎ ℎ plane, and is Poisson's ratio for . The practical example of the residual strain test at ENGIN-X neutron diffraction instrument at room temperature and unloaded condition presented here is for air plasma sprayed (APS) Mo-Mo 2 C/Al 2 O 3 coatings on to Hastelloy-X ® substrate [5]. An example of a diffraction peak (scattered by polycrystalline materials [5,22]) from a monochromatic instrument is shown in Fig. 4. Time-of-flight (TOF) diffractometers are typically used at pulsed sources (e.g. at ENGIN-X), where each pulse provides a diffraction profile across a large range of lattice spacings. The ENGIN-X instrument has a large flight path from the source to the sample (50 m) providing good resolution [17][18].

Test preparation
Electronic copy available at: https://ssrn.com/abstract=3711244 Before carrying neutron strain measurements at ENGIN-X, the preparation involves several steps, as careful planning as possible can help to minimize the losses of beamtime hours or days involved. These include preparation in view of understanding the coating and substrate crystal structure, planning neutron scanning, gauge volume and calibration of the instrument.

Microstructure assessment and plan for neutron scanning
Apart from size and shape of the specimen, it is important to know the material properties and microstructure before neutron scanning using some analytical instruments, such as X-ray diffraction (XRD) for phase analysis, energy dispersive in such cases, the some of the diffraction peaks might be missing completely and so may not match the reference peaks [5]. However, all major peaks can be identified using the International Centre for Diffraction Data (ICDD) software Powder Diffraction File™ (PDF) [23] numbers in the analysis.
Microstructure analysis using SEM for both coating surface and cross-section helps to identify the splat orientation or crack and residual defect within the coating layer, including any prior delamination of the coating at the interface. Some understanding of these features (coating layer) and comparison of associated residual strain measurement at ENGIN-X facility may help plan the full experiment with confidence [2][3]. The cross-sectional analysis may also provide exact coating thickness and information about bonding quality between coating and substrate at the interface. If the coating layer has a significantly high number of vertical cracks with layered pores (e.g. normally observed in some YSZ thermal barrier coatings [24]) or the bonding quality between coating and substrate at the interface has already been compromised Electronic copy available at: https://ssrn.com/abstract=3711244 (i.e. delamination leading to stress relaxation), the residual strain measurement values may not be a true representation of the as-coated and as-received sample.

Sample gauge volume and counting times
Two important practical considerations are the gauge volume and the counting time for a given sample. How small should be the sample gauge volume for coating part, especially when the coating thickness is typically about 50 μm to 500 μm? This is the volume defined as a cuboid of sides ( ). In neutron strain experiments, the diffracted ∆ = ∆ .∆ .∆ signal is obtained from a defined volume [25] in space that contains part of the specimen material. Typically, some understanding of the structure and size of original sprayed powder (e.g. conventional, nanostructured) and through-thickness splat size can help define the gauge volume. The simplified sketch in Fig. 5 presents how a sampling volume is defined through apertures (e.g. slits) placed in the incident and diffracted beams. The intersection of the incident and diffracted beams defined by slits and collimators defines the gauge volume [17]. Usually, the largest gauge volume can minimise the counting times (useful for bulk or large volume of material testing).
However, different coating and substrate materials will require different counting times depending on the sample geometry, dimensions, and measurement point positions due to the neutron path lengths. Larger gauge volumes can be used to reduce counting times, but it needs to be optimised between counting time and measurement spatial resolution. The diffracted signal recorded on the detector (e.g. at Bank 1, Bank 2; centred at ±90° to the incident beam) in neutron strain and stress measurements originates from this volume [3]. In thermally sprayed coating sample testing, the gauge volume can be rastered across the sample through thickness (or vertical scan mode [2][3][4][5]), e.g. Fig. 6(a,b), as the divergence perpendicular to the diffraction plane, does not affect the resolution. ENGIN-X uses a few sets of removable radial collimators, such as 0.5 mm, 1 mm, 2 mm, 3 mm, and 4 mm gauge width [7].
As demonstrated in previous work [5,22], the scattering trials can be conducted Electronic copy available at: https://ssrn.com/abstract=3711244 is necessary to ensure that the data point collection strategy is optimised for the beam time available.
Strain checks can be executed at the geometric centre of the specimen. To overcome the generation of pseudo-strains as the gauge volume moves out of the surface, it has been argued that the incident beam be scanned vertically out of a horizontal surface, as there would not be any change in the diffraction angle. [6]. The specimen position can be adjusted through the use of three orthogonal motors along the three co-ordinate axis (X,Y -Horizontal, Z -Vertical). The specimens can be moved along the Z-axis along steps of 50µm within the coating and in steps of 25µm within the substrate material (i.e. closer to the interface). A beam height of 0.2mm can be achieved by passing the beam through an assembly of horizontal and vertical slits.
Partially submerging the gauge volume allowed the strain in the coated material with coating thickness 250 µm ( Fig. 6(b)), whereas, a fully submerged beam can be used t measure the substrate strain. To measure the strain within the coating and substrate, different measurement times will be necessary (3 to 4 hours per vertical step along coating depth and coating-substrate interface), and fully in substrate (30-45 minutes per vertical step along substrate depth) [2][3][4][5][6].

Calibration of a neutron diffractometer
The calibration of the neutron diffractometer and associated instruments must be tested prior to scanning (normally carried by instrument scientist) using the procedure that has been verified according to practices at ENGIN-X. A sample configuration that produces statistically determinate strain in the sample must be used. The procedure must be repeated to ensure reproducibility of the measurement data and the repeatability must be examined. Calibration of the ENGIN-X neutron diffraction instrument is done through the determination of the wavelength of the incident neutron beam and the angular response of the neutron detector accurately [18]. At a TOF (e.g. ENGIN-X) source, isotropic neutron scatterers (e.g. vanadium) with very weak or no diffraction peaks of their own are used to perform the necessary calibration of the detector efficiency as a function of wavelength. [26].

Strain testing
Strain testing includes experiment preparation in view of sample mounting, reference point, fast scanning, full scanning of sample, and scanning for d 0 -spacing ( ). Mounting System [27]. If the experiment requires testing at a given temperature and external mechanical loading conditions, the servo-hydraulic stress rig and environmental test chamber (e.g. furnace or cryogenic, which can be varied at different rates) within the normal atmosphere or under inert gas, can be useful. The test samples could be mounted in loading fixtures (with a pre-stress) for sequential loading through a range of force and temperature as mentioned above. The change in interplanar d-spacing can then be measured for each force and temperature conditions [1,26].

Reference point and fast scanning
These are a time-consuming but important step for the strain measurements. It is good practice to position the centroid of the gauge volume at the reference point. The ENGIN-X instrument reference axis and neutron beam reference height must be aligned at the centre of the instrument gauge volume (IGV) [18]. This is to refer to the position of the test sample. One practical method is to first centre a vertical pin on the table (ENGIN-X positioner, top tier) so that pin tip defines the reference point. The centring of the pin tip can be done by viewing the tip through a theodolite, which is an optical apparatus for measuring coordinates of visible points. The centring of the pin tip can also be done by using a micrometre contact gauge and adjusting the position of the translator. Following the centring steps, the gauge volume is arranged to have the reference point as its centre by positioning the apertures in the horizontal and vertical planes [18]. Once the sample has been mounted on the stage or table (ENGIN-X positioner, top tier), the necessary step in performing neutron diffraction of the effective position in the sample at which the strain is measured is important. This is typically done through fast scanning (using vertical scan mode, through-thickness of the coated sample) of thermally sprayed coatings (e.g. Fig. 8). The registration of diffracted neutron spectra, both at the start and end of the scan where scattering volume is partially filled, can give an abnormal peak shift which can be incorrectly interpreted as strain. These steps (reference point, fast scanning) can be adjusted to ensure that the centre of the neutron spectra intensity Electronic copy available at: https://ssrn.com/abstract=3711244 profile versus the vertical position of the translator is in the encoder values corresponding to the reference axis position [18].

Scanning of coated sample for d-spacing
The experiments are typically conducted in vertical scan mode (Fig. 6) to measure the through-thickness residual strain profile of the coating-substrate system. Several samples can be assembled on a holder as shown in Fig. 9(a). The details of the vertical scan method are described elsewhere for thermal spray coatings [2][3][4][5][6]. Strain measurements are typically performed at the centre of the specimen (at p 1 ) but can be performed at other locations as well (e.g. at a radial distance, r = 5 mm (at p 2 ) from the centre [3]), as shown schematically in Fig. 5(c). Although the measurement locations in the specimen can be changed, the distance to the detectors (Bank 1 and Bank 2) is always the same. A partially submerged beam can be used at the coating surface and a beam submerged partially in the coating and the substrate can be used at the coatingsubstrate interface to obtain a high resolution profile of the through thickness residual stress distribution. Measurement of the residual strain at a volume smaller than the gauge volume using a partially submerged beam can be understood from other studies [17]. The coating-surface interface and the coating surface can be located within a resolution of 50m with the help of fast vertical scans and careful location of the specimen using theolodites.

Scanning of materials for d 0 -spacing
Though there is not a requirement to measure the stress free lattice spacing [18], the either removing the coating from the substrate and crushing to create the coating powder or direct measurement of the feedstock powder can be carried out to measure the strain-free lattice parameter ( ) [2][3][4][5][6], as shown in Fig. 9(b). This powder can 0 ℎ then be put in a vanadium tube and its lattice parameter measured, as shown in Fig.   9(c). The strain-free lattice parameter for the substrate can be measured at the suitable area of the uncoated substrate sample where has been verified to be independent of 0 ℎ position and direction at that region in the materials [18] (or unsprayed substrate can also be used). In case dedicated reference samples are needed; these should be prepared in advance before visiting ENGIN-X lab for experiments or while other measurements are ongoing.

Pre-processing steps
Neutron spectrum are characterised by several parameters that can be analysed, e.g.
position/shape/amplitude/width of the peak in the spectra, however, the positions and Electronic copy available at: https://ssrn.com/abstract=3711244 widths of the spectra are important parameters which can be related to the strain field in the sample [18]. Typical steps after neutron diffraction testing of coated samples include plotting spectra (neutron counts v/s d-spacing; neutron counts v/s TOF; e.g. Fig. 4, and as an example, a set of experimental data and analysis is provided in Appendix A, using ISIS ENGIN-X software Open genie) for both banks (detectors) for each location. It is highly recommended to carry few preliminary analyses as soon the first few neutron spectra data is available during the experimentation. This can assist in the identification of neutron spectra peaks (corresponding to each planes known, or identified through ℎ X-ray diffraction carried for test preparation) in both banks, and in locating depth where they had no or minimal overlap with other peaks. If one single or several nonoverlapping peaks are measured, their spectra parameters are analysed for each peak separately, however, the analysis of the whole spectrum can be performed using Rietveld methods. diffraction peaks for the coating and substrate materials is possible either (or both) using the Rietveld refinement method or individual peak method. Use of the Rietveld refinement method may be easy, however, in the individual peak method, the listing of and spacing needs to be done for each identified peak for peak-by-peak analysis. The peak-by-peak analysis can help in analysing the strain for each hkl planes.

Post-processing steps
Evaluation of the lattice parameters in the case of simple crystal structures can be carried out through the Rietveld refinement analysis which considers multiple peaks in the spectra. However, where the spectra has overlapping peaks, e.g. coating to substrate and substrate to coating, this method can be challenging to apply. . At each measurement location, the neutron spectra recorded by the individual detectors are time focused using the computer code GSAS [28]. Using a library of common engineering materials, this software automatically refines the single-peak and full-spectra within the diffraction spectra [17]. To ensure the convergence of the refinement, single-peak refinement of the most intense peak is performed to speculate the lattice parameters initially.

Strain calculations 7.3.1 Rietveld profile refinement
Electronic copy available at: https://ssrn.com/abstract=3711244 The standard method of analysing the neutron diffraction experimental results is the Rietveld profile refinement method. In this, the intensity measured as a function of the scattering angle is fit with the parameters of a model. The strain can be obtained from the shift in diffraction peaks for the coating and substrate materials using Rietveld refinement. The Rietveld method allows analysis of spectra with strongly overlapping lines and patterns from multiphase materials. A change in in d-spacing or in the lattice spacing due to internal strains will result in a shift of a Bragg peak position (typically in the range of 0.005° to 0.2°) when a single wavelength is used [18]. The General Structure Analysis System (GSAS) software [28] can be used in the data analysis. The fitting parameters of the refinement, confirming good fit to the diffracting pattern.

Individual peak fitting
The strain can also be obtained from the shift in 'individual' diffraction peaks for the coating and substrate materials using a single peak fitting routine [21] using GSAS software. The fitting parameters of the refinement, confirming good fit to the diffracting pattern (shown in Fig. 4(b)). The peaks chosen for the strain analysis should be such that they had no or minimal overlap with other peaks. As an example, a set of experimental data and analysis is provided in Appendix A (for RB1510238 [5,22]).

Strain calculations
After analysing individual diffraction peaks results, residual strain ( results in ℎ = ℎ -0 ℎ 0 ℎ ) coatings and substrate can be analysed using individual peak method or Rietveld (using Equation 5). Figure 10 shows an example of residual strain measurement (plotted using single peak fitting routine analysis). The averaging of strain across the various identified crystallographic planes can also give similar results to the Rietveld refinement.

Stress calculations
The average coating and substrate residual strain (and stress) can vary significantly with the coating conditions. From the measured strain, the residual stresses can be determined using the elastic constant (Hooke's law, Equation 6) for material types, where bulk elastic modulus values of materials are typically used from literature or through standard mechanical testing of samples (e.g. bending/tensile tests). However, as shown in Fig. 11(a), number of nanoindentation based elastic modulus measurement for stress measurement ( ) can be done on each coating-substrate cross-section, = which can be dispersed in five lines of 5 measurement points each, at a specific space from the boundary (i.e. coating surface). Indentations can be spaced by several microns Electronic copy available at: https://ssrn.com/abstract=3711244 apart, to avoid any interaction of adjacent indentations. By the same method, some 10 measurements can be spread in two lines of 5 measurement points apiece on each substrate cross-section near the interface, at a specific distance from the interface. To convert the through-thickness residual strain data to analyse the corresponding residual stress distribution, an average value of measured elastic modulus can be utilized where the measurement depth location of residual strain and elastic modulus did not match. As an example, a set of experimental data and analysis is provided in Fig. 11(b), and analysis is provided in Appendix A.
If required, the stresses can then be normalised by dividing by the yield stress data ( ) of the coating and substrate materials, respectively. In the example shown ( Fig. 12), the yield stress of the Hastelloy-X ® substrate is taken as 385 MPa and for Mo-Mo 2 C/Al 2 O 3 it is taken as 770 MPa (at zero plastic strain) [30]. As shown, both for coating and substrate parts, the normalised stress . < 1

Precision and bias
Neutron scattering allows the atomic positions in the structure to be determined with high precision. At ENGIN-X, the precision of neutron diffraction instrument alignment within 50 µε can be achieved [17]. The accuracy of this method is considered to be absolute, however, the error or uncertainties can be related to various factors, such as Using MPISI instrument at NECSA and KOWARI instrument at ANSTO, Venter et al. [33] studied 200 µm thick HVOF sprayed coatings (e.g. WC-12wt%Co, WC-10wt%VC-12wt%Co) deposited on to 4 mm thick mild steel substrate. The residual strains were investigated in the erosion wear scar regions. While using the test protocols of MPISI instrument [34], the focus was to study the strain behaviours in the substrates by employing through-thickness fine measurement, and by doing so, the stress in the coating could be determined by imposing strain balance in the sample. While using the test protocols of KOWARI instrument [35], with diffracted beam slit at a width of 0.3 mm, and positioning the gauge volume in the centre of the 200 µm thick coating, the strains were measured directly in the coatings [33]. It was proposed that it is almost impossible to provide unstressed reference material (due to thin layer of coatings) and used equal-biaxial stress approach. Overall, the neutron scattering results indicated that the erosion impact angles influenced the residual strains and the coating composition.
Using KOWARI instrument at ANSTO, Luzin et al. [36] studied through thickness residual stresses in three coating materials sprayed using HVOF (JP 5000, DJ2700 was also measured using the same method to address possible pre-coating stress within the substrate. The stress profiles were then subtracted from the stress profiles of the coated samples so that the reported stress profiles are only associated with the spraying process only. Two methods for the residual stress measurement were used (i.e. before and after subjection of coated samples to a partial loading regime via cantilever bend fatigue). It was observed that the distribution of the residual stresses within a coatingsubstrate system can be influenced by the application of external mechanical loading stresses into the system. The effect of increased compressive residual stress within the coating surface during cantilever fatigue loading was also observed, due to the geometry and test configurations.
Using KOWARI instrument at ANSTO, Saleh, Luzin and Spencer [40]  Electronic copy available at: https://ssrn.com/abstract=3711244 The coating was assumed to be in a bi-axial stress state with the stress in the direction normal to the surface assumed to be zero for thin coatings. Kim et al. [42] suggested that the existence of zero stress condition in the direction normal to the thickness is a valid assumption for the coating with the thickness of up to 2mm but not for the substrate with much higher thickness. This assumption is still valid for the substrate till a distance of 2mm from the interface. coating thickness (i.e. 1 mm to 2.5 mm) did not modify through-thickness residual stress in coatings, and overall compressive stress was achieved both in coating and substrate at the interface, but the difference in stress amplitude at the interface seems to significantly decrease when coating thickness was increased.
Using POLDI instrument at SINQ, Kovářík et al. [45]  normal stress was approximated, however, the through-thickness measurement was possible, including two measurements per measurement point were suggested to be sufficient. For thick coating (t>5 mm), the assumption of normal stress (to be zero) was suggested. For thick coating, to resolve the three principal stress components, the knowledge of atleast three independent measurements and the stress free spacing ( ) 0 ℎ is required. It was proposed that owing to their high penetration, neutrons allows stress profiling through the coating thickness, and multiphase materials can be studied, including the effect of other surface treatments, such as shot peening, and laser peening.
Using BT8 instrument at NIST, Li et al. [47] investigated residual strains of single splats as well as 380 µm thick coatings of plasma sprayed molybdenum deposited onto 1040 steel (2.4 mm thick). From the measured strain, the residual stresses were determined using the elastic constant (Hooke's law) for material types (analysed by Electronic copy available at: https://ssrn.com/abstract=3711244 selecting the most intense peak of the spectra). Though no apparent residual stress was found in the 380 μm coating, a single splat layer exhibited a high residual stress due to the high degree of bonding of the first splat layer and stress relaxation within the coating due to the large number of defects.
Using the BT8 instrument at NIST, Luzin et al. [48] in continuation of Choi et al.
[31] work related to cold spray Al coatings, investigated surface and in-plane stresses in Cu and Al cold sprayed coatings. Cold sprayed Cu (onto Cu and Al substrates) and Al (onto Cu and Al substrates) samples were about 3 mm thick. The Cu substrates were 3.1 mm thick, whereas the Al substrates were 2.6 mm thick [48]. A gauge volume 0.5 x 0.5 x 18 mm 3 was used. The internal stress in the freestanding substrates were measured before the cold spraying, and this internal stress was subtracted to isolate stresses induced by the cold spray process. From the measured strain, the residual stresses were determined using the using the assumption of a balanced biaxial plane stress state [31].
It was observed that the kinetic parameters of the cold spray process, the deformation behaviour of the particles and the feedstock material properties dictate the residual stress within the coating [48]. Compared to Al coatings, the mechanical properties of the Cu coating were closer to bulk properties. The higher plastic strain the Cu coatings resulted in higher residual stress in the Cu coatings and higher compaction [48].
Using the BT8 instrument at NIST, Luzin et al. [32] investigated residual stresses in low-pressure cold sprayed coatings (e.g. Al-Al 2 O 3 metal matrix composite) of 1 mm thickness onto 3 mm thick A16061 aluminium substrate. A gauge volume 0.5 x 0.5 x 20 mm 3 was used and applied equal-biaxial stress approach to obtain residual stresses. In the example shown, it was observed that the overall residual stress in the coating was compressive. Also, due to the elevated spray temperature characteristic of low-pressure cold sprayed coatings (dynamic metallization), thermal stresses were also present, and because of the multi-phase composition and thermal mismatch between the metal and ceramic components of the metal matrix composite (MMCs), inter-phase micro-stresses also accumulated, leading to overall compressive residual stresses [32].
Using DIANE instrument at LLB, Ceretti et al. [49] investigated residual strain profile from the coating surface to the material through the interface in a ferritic steel cylinder having 78 mm diameter. The elastic constant (Hooke's law) related to the most intense peak of the spectra were measured with respect to the three principal directions.

Other analysis
Small-angle neutron scattering (SANS) techniques [50] helps analyse the total specific surface area of the voids (size up to about 100 nm), whereas, multiple small-angle neutron scattering (MSANS) technique can help analyse average pore size and orientational distribution. Using SANS and MSANS techniques at NIST, Keller et al. [51] Electronic copy available at: https://ssrn.com/abstract=3711244 properties of materials, reflects the thermomechanical history including recrystallisation, particle rotation and phase transformation. In addition, the bulk texture of a polycrystalline material constitutes the orientation distribution function of the crystallographic orientation with respect to the sample coordinate system [54]. The texture analysis of the coated surface showed [53] that selective grain growth likely caused considerable change in the texture at high temperatures. Also, Takajo et al. [53] suggested that Zr coating showed a preferential orientation and correlated with the initial texture of the uncoated U-10Mo.
Using D20 instrument at ILL, Jakani et al. [55] investigated crystallinity of plasma sprayed hydroxyapatite coatings (feedstock was micro and nano-sized particles) deposited onto a Ti-6Al-4V substrate. The sample was heat-treated (2 hours at 600 °C) to reduce amorphous fractions. Using the neutron spectra of samples (feedstock powder and coatings), Jakani et al. [55] observed that the deposited coating showed retention of the nano-meter crystallite and no secondary phases were identified. This meant that the nano-coating will have nucleation cites to the reconstituted bone, which will allow stabilisation of the implant in the bone.
Using HB-2B instrument at ORNL, Liu et al. [56] investigated the plastic deformation in a series of low-pressure cold sprayed Al-Cu coatings (on Al-Cu-Mg-Mn alloy (AA2024) substrate) using dislocation density as an indicator. for The copper content ranged from 2 mass% to 5 mass%. Analysing the neutron diffraction peaks, it was observed that the increase in the copper alloy additions (from 2 mass% to 5 mass%)increased the breadths of full width at half maximum (FWHM) of the cold Electronic copy available at: https://ssrn.com/abstract=3711244 sprayed coatings increased, meaning the dislocation density in the Al-Cu coatings systematically increased with increasing Cu alloy content . Liu et al. [56] also showed that the peak breadth (FWHM) changes from the substrate to the coating and through the coating, and this change throughout the coating was accounted for by the fact that a the regions near the coating-substrate interface saw a larger number of repetitive impacts from subsequent particles than the rest of the areas towards the top surface of the coatings.
Using the powder diffractometer ECHIDNA at ANSTO OPAL (wavelength of 1.622 A˚), Luzin et al. [48] investigated oxide volume fraction of Cu and Al feedstock powder materials for cold sprayed coatings. The analysis was carried to compare it against the feedstock powder, and to confirm the chemical purity of the feedstock powders. It was experienced that the usage of neutron powder diffractometer is better compared to Xray diffraction, because the X-ray diffraction could only provide surface properties and not the subsurface, whereas the neutron diffractometer provides a better average measurement.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.