Neutron Diffraction Residual Strain Measurements of Molybdenum Carbide-Based Solid Oxide Fuel Cell Anode Layers with Metal Oxides on Hastelloy X

Three composite feedstock powders (Mo-Mo₂C/Al₂O₃, Mo-Mo₂C/ZrO₂, Mo-Mo₂C/TiO₂) were fabricated from carbide of molybdenum powder catalyst (Mo-Mo₂C) and three metal oxides (e.g. Al₂O₃, ZrO₂, TiO₂, each favourable for catalyst stability). The powders were subsequently employed to fabricate three diverse anodes [36]. Each of the adjusted composition anode feedstock powders was comprised of 80% Mo-Mo₂C and 20% metal oxides (i.e. Al₂O₃, ZrO₂, TiO₂). It is noteworthy that a lower bound weight metal oxide was selected for this study to enable it to act as a catalyst with the molybdenum carbide powder. Nonetheless, research on the effects of varied weight composition can be part of an upcoming enquiry.

The selected substrates (Hastelloy®X, 20 mm diameter and 4.7 mm thick) were provided by Haynes International Limited, Manchester, UK. As a metallic matrix with carbide, the Mo with Mo₂C (i.e. Mo-Mo₂C, melting point was 2620 °C) feedstock powder material (Fig. 1(a, b)) was an agglomerated and sintered spheroidal powder designed for coating applications using atmospheric plasma spray (APS). The powder material (Metco 64, nominal particle size distribution −90 + 38 μm, provided by Sulzer Metco, Germany) had an elemental composition consisting of 97.3% Mo, 2.1% C, 0.1% O and 1% others. It is important to note that a “+” sign before the sieve mesh indicates the particles are retained by the sieve, whereas, a “-” sign before the sieve mesh indicates the particles pass through the sieve, and typically, 90% or more of the particles will lie within the indicated range. For example, if the particle size of Mo-Mo₂C is described as −90 + 38 mesh, then 90% or more of the material will pass through a 90-mesh sieve and be retained by a 38-mesh sieve.

The titanium oxide (TiO₂, melting point of 1843 °C) feedstock powder material was available in a wide variety of colours and shapes ranging from dark grey to black, fused and crushed or agglomerated and sintered, and sizes with angular, blocky or spheroidal morphology, respectively. This agglomerated/sintered and spheroidal powder material (METCO-6231A) was supplied by Sulzer Metco, Germany and had elemental composition incorporating TiO₂ (balance wt.%), Al₂O₃ (<0.1 wt.%), Fe₂O₃ (<0.1 wt.%), SiO₂ (<0.1 wt.%) and others (<0.5 wt.%); the normal particle size distribution was −105 + 32 μm.

The white alumina (Al₂O₃, melting point of 2054 °C) feedstock powder material (METCO-105SFP supplied by Sulzer Metco, Germany) was fused and crushed with resulting in a random angular morphology (Fig. 1(c)). The elemental composition of the powder material (particle size distribution −31 + 3.9 μm) consisted of Al₂O₃ (99.5 wt.%), Fe₂O₃ (0.03 wt.%), Na₂O (0.15 wt.%), SiO₂ (0.01 wt.%) and CaO (0.01 wt.%). The Zirconia (ZrO₂, melting point of 2700 °C) feedstock powder material which was available in a wide variety of shapes and sizes, Fig. 1(d) was supplied by Alfa Aesar (40453), UK and consisted of Zirconium(IV) oxide, calcia stabilized, 99.4% (metals basis excluding Hf). The powder material elemental composition encompassed 96% ZrO2 and 4% CaO, whereas, the normal particle size distribution was −100 + 325 μm.

The powders were sprayed on to the grit blasted Hastelloy®X substrate and no bond coating was used. Air plasma spray (APS) deposition was carried out at an industrial thermal spray facility (Monitor Coating Limited, UK), using a spray system (Table 1). Trials were directed to define the operational range of the process parameters. The range of controllable factors were identified specifically feed rate, current, hydrogen flow, spray distance and spray angle. To determine the limits of the investigational factors, a key criterion was assumed that the anode layer must have high porosity. Additionally, the alteration in melting temperatures of the main feed-stock powder Mo-Mo₂C (2620 °C) and precursors [Al₂O₃ (2054 °C), ZrO₂ (2700 °C), TiO₂ (1843 °C)] can present a challenge for plasma spray deposition. Though, an optimised process parameter was chosen for each of the anode layers (Table 1 ).

The surface characterisation of materials included scanning electron microscope (SEM) imaging using Karl Zeiss EVO LS10 and JEOL JSM 6010 LA, whereas, the X-ray diffraction (XRD) analysis using Empyrean diffractometer (PANalytical, NL) with Copper kα radiation (1.54 Å) was employed to reveal the crystalline phase composition of the coatings. The geometry employed was a standard Bragg - Brentano reflectance geometry (ω - 2θ) in conjunction with a sample stage designed for solid objects. Patterns were acquired over the range (2θ = 10–75°) with a step size of 0.026° and a total collection time of 30 min.

The total porosity of coating surface (using a thresholding at 65% in the image processing software) was evaluated as the average of five area-normalized regions each from optical microscope and image analysis (IA) software (release 6.3, Lumenera Corporation). This measures all open, closed, connected elongated porosity and cannot distinguish the type, and are easily detected by image analysis due to the high degree of contrast between the dark pores (voids) and the more highly reflective coating material. It is important to note that the cross-sectional image analysis for porosity quantification is not ideal method as polished sample (intrusive method) could smear cross-section with impaired (not true representative) porosity.

Nanoindentation trials for hardness and elastic modulus (at 30 mN load, instrument chamber temperature 300 K) of the anode and substrate cross-sections were performed using a calibrated NanoTest™ system (Micromaterials Limited, UK) with a diamond Berkovich tip. The nanoindentation techniques were programmed as three sections of a trapezoidal shape; the first segment increased the capacity to a maximum value at a loading rate of 10 mN/s, followed by a 30-s holding section at the maximum load, and the third segment retrieved the indenter tip from the sample at an unloading rate of 10 mN/s.

Overall twenty-five assessments were done on each coating cross-section, which were dispersed in five lines of 5 measurement points each, at a specific space from the boundary, (i.e. coating surface). Depressions were spaced 22 μm apart, to circumvent any interaction of adjacent indentations. By the same token, the 10 measurements spread in two lines of 5 measurement points apiece were accomplished on each substrate cross section near the interface, at a specific distance from the interface. The force-displacement contours were examined by means of typical approaches with the area function for the Berkovich indenter whereas the modulus and hardness were investigated according to the Oliver and Pharr scheme [36]. The elastic modulus (E _i ) and Poisson’s ratio (ν _i ) of the diamond indenter were taken as 1140 GPa and 0.07 at room temperature, whereas to calculate the elastic modulus (E _s ) of the specimen, the Poisson ratio for the anode layer (ν _s ) was assumed as 0.30 (Mo [37, 38]) and for the substrate (ν _s ) was presumed to be 0.32 (Hastelloy [39]). Post-test residual impressions were mapped by means of an SEM.

Neutron diffraction strain measurements were implemented at the UK’s Science and Technology Facilities Council’s (STFC) laboratory, by means of the ENGIN-X strain diffractometer at ISIS facility [32‐34]. These tests were completed at room temperature on three anode coatings (Mo-Mo₂C/Al₂O₃, Mo-Mo₂C/ZrO₂, Mo-Mo₂C/TiO₂) put down by air plasma spray (APS). The trials were conducted in a vertical scan mode with a slit gap of 200 μm in order to determine the through thickness residual strain profile of the anode-substrate system. To achieve a through-thickness residual strain profile with high resolution, a partially-submerged beam was used for measurements near the coating surface, as well as a beam submerged in the coating and substrate materials near the coating-substrate interface. A gauge volume of 0.2 × 8 × 4 mm was employed [34]. Strain checks were executed at the geometric centre of the specimen. Specifics of the vertical scan technique are described in previous work [32‐34].

It has been argued that if the incident beam is scanned vertically out of a horizontal surface, there is no change in diffraction angle and, hence, no pseudo-strains generated as the gauge volume moves out of the surface. It is important to note that the specimen positioner has three orthogonal linear motor drives (with nominal accuracy of 5 μm): X and Y (horizontal), and Z (vertical). The coated specimen was moved up or down in the Z-direction by at least 50 μm for depth profiling of strain in the coating and by at least 25 μm for depth profiling of strain in substrate materials (i.e. closer to interface). The incident beam was passed through a vertical and horizontal slit assembly to give a beam height at the slits of 0.2 mm. Partially submerging the gauge volume allowed the strain in the coated material (Mo-Mo₂C/Al₂O₃ with coating thickness 250 μm), Mo-Mo₂C/TiO₂ with coating thickness 300 μm and Mo-Mo₂C/ZrO₂ with coating thickness: 220 μm) to be measured, whereas the substrate strain was mostly measured using a fully submerged gauge volume. Longer measurement times were therefore required as many measurements as necessary for strain measurement in the coating material and near interface in substrate (3 h per vertical depth).

The peaks selected for the strain examination within each anode material were such that there was minimal overlap with other crests. The strain was obtained from the shift in individual points for the anode and substrate materials using a single peak fitting routine [40, 41]. The strain free lattice parameter (\( {d}_{hkl}^0 \)) for the coating material was found from originally mixed powder (i.e. Mo-Mo₂C/Al₂O₃, Mo-Mo₂C/ZrO₂ and Mo-Mo₂C/TiO₂). These powders were then put in a vanadium tube and their lattice factors determined. The strain free lattice parameter for the Hastelloy®X was assessed at the surface of the uncoated substrate disc. The direct elastic strain in the material in the measured path was calculated as (equation (1)):

where d _hkl is the measured interplanar spacing and \( {d}_{hkl}^0 \) is the stress-free interplanar spacing for the given material. The elastic stress values were determined from the strain values by means of the appropriate elastic modulus (i.e. values at appropriate depth measured with a nanoindentation technique) ("Nanoindentation Tests For Hardness and Elasticity" section).

The porosity was controlled by a selection of APS process parameters (Table 1) devoid of the need for adding a pore-forming material. The anode surfaces showed final splat structures presumably resulting from the impact of molten and semi or partially molten particles during APS thermal spraying. Additionally, SEM images of anode surfaces and cross-sections are presented in Fig. 2. In the image in Fig. 2(I), the occurrence of high density surface connected porosity was observed for all three specimens. The current study found that the anode layers had a volumetric porosity as high as 19 ± 1% for both Mo-Mo₂C/Al₂O₃ (coating thickness: 250 μm) and Mo-Mo₂C/TiO₂ (coating thickness: 300 μm) and around 16 ± 1% for Mo-Mo₂C/ZrO₂ (coating thickness: 220 μm).

Substantial surface coarseness was seen in all three anodes. Furthermore, anode layer cross-sections of the samples (Fig. 2(II)) showed more detailed features which suggest the presence of relatively high porosity for Mo-Mo₂C/Al₂O₃ and Mo-Mo₂C/TiO₂. The observed structures included very distinct alternate layers ranging from light to dark grey in Mo-Mo₂C/Al₂O₃ and Mo-Mo₂C/TiO₂ anode layers and relatively less distinct layers in the case of Mo-Mo₂C/ZrO₂. Micro-cracks were also observed on the surface (Fig. 2(I) (a)).

The XRD spectrum of the anode surface showed the presence of dominant phase (Fig. 3). It is important to note that the infinite orientations criterion of powder diffraction may not be satisfied and so there may be pronounced textural effects observed in the XRD data; therefore, relative intensities of peaks may not match reference data and it is possible that some peaks of a phase are missing entirely due to their orientation. However, all major peaks have been clearly identified using the International Centre for Diffraction Data (ICDD) software Powder Diffraction File™ (PDF) number (00-004-0809 for Mo, 00-011-0680 for Mo₂C, 00-036-0863 for Mo_0.42C_0.58, 00-030-0029 for Al₂Mo₃C, 01-078-1070 for MoO₂, 00–049-1642 for ZrO₂, 01-083-2242 for TiO₂) used in this analysis. The Mo peak for all powders is clearly identified in Fig. 3, which was the main peak used for the strain measurements (Neutron Diffraction Measurements section). XRD analysis of anode layers in Fig. 3 indicates that Mo-Mo₂C undergoes some oxidation and decarburisation forming MoO₂ and Mo_0.42 C_0.58, because of high temperature and oxygen environment during APS spraying process. This phenomenon is also frequently reported for other carbides e.g. WC-Co where oxidation and decarburisation occurs during thermal spraying process [42‐44]. For specimen with blend of Mo-Mo₂C and Al₂O₃, there was some evidence of limited formation of intermetallic compound (Al₂Mo₃C). Formation of these compounds is possible due to high temperature in plasma stream, however as the dwell time (time powder spends in the heating zone) is very short, there is very little time for the formation of intermetallics. Formation of nano-crystals or amorphous phases can however result due to high temperatures and very high heating and cooling rates in plasma spraying, which normally lead to broadening of XRD peaks. However, these changes were minimal in the current study. The configuration was dominated by three strong reflections corresponding to metallic molybdenum. The segments identified in the Mo-Mo₂C/Al₂O₃ anode layer included Mo, Mo₂C, Mo_0.42C_0.58, Al₂Mo₃C and MoO₂ (Fig. 3(A)). The phases recognized in the Mo-Mo₂C/ZrO₂ anode layer encompassed Mo, MoO₂, Mo₂C, Mo_0.42C_0.58 and ZrO₂ (Fig. 3(B)). The phases identified in the Mo-Mo₂C/TiO₂ anode layer involved Mo, MoO₂ and TiO₂ (Fig. 3(C)). Also, shown in Fig. 3(C) for the Mo-Mo₂C/TiO₂ anode layer, the main phase by a considerable margin was metallic molybdenum (Mo). Unlike the previous two samples (Mo-Mo₂C/Al₂O₃ and Mo-Mo₂C/ZrO₂), there were no species of molybdenum carbide (Mo₂C) detected.

The hardness results (Fig. 4(a)) principally showed that the upper layers of the coatings had higher average values than the lower subsurface layers, with significantly high standard deviations in coating zones (e.g. Mo-Mo₂C/TiO₂) and low standard deviations in substrate zones. Each data point represented an average of 5 tests. The measurements of the elastic modulus of sample, E _s (Fig. 4(b)) indicated that overall the values were very similar for each coating with significantly higher standard deviations in coating zones (e.g. Mo-Mo₂C/TiO₂) and lower standard deviations in substrate zones.

The Fig. 5 presents neutron diffraction patterns near the anode-substrate interface in the anode layer (also includes hkl peaks which were identified and analysed) for Mo-Mo₂C/Al₂O₃, Mo-Mo₂C/ZrO₂, and Mo-Mo₂C/TiO₂, and in the substrate Hastelloy®X of the anode Mo-Mo₂C/Al₂O₃ layer. It is important to note that the (hkl) peaks identified and analysed include four molybdenum (Mo) peaks (body-centred cubic or bcc) for each anode layers [(110), (200), (211) and (220)] and five Ni (gamma phase, is a face-centred cubic or fcc) peaks for each Hastelloy®X substrates [(111), (200), (220), (311) and (222)].

As shown in Fig. 6, the residual strain measurements were performed through thickness of specimens using a fully submerged gauge volume for deeper beam penetration and a partially submerged volume for near surface analysis [32‐34]. Individual diffraction peaks corresponding to crystallographic planes (110), (200), (211) and (220) were employed to measure the average residual strain in each of the three anode layers, whereas, diffraction peaks corresponding to crystallographic planes (111), (200), (220), (311) and (222) were used to measure the average residual strain in the Hastelloy®X substrate. The x-axis of these plots was analysed on a logarithmic scale to highlight the variation in the anode-substrate strain.

The trends of residual strain in each of the three anode layers for diffraction peaks corresponding to crystallographic planes (110), (200), (211) and (220) were largely tensile with some compression near the interface (e.g. in Mo-Mo₂C/TiO₂) for planes (211) and (200). The trends of residual strain in each of the three Hastelloy®X substrates for diffraction peaks corresponding to crystallographic planes (111), (200), (220), (311) and (222) were highly compressive stress at the interface (except for plane (200) in Hastelloy®X substrates with Mo-Mo₂C/Al₂O₃, Mo-Mo₂C/ZrO₂ anode layers), including some relatively high tensile residual strain away from the interface in the Hastelloy®X substrate for plane (222).

While analysing the residual strain results obtained from an average of individual diffraction peaks, it can be seen that the trends of residual strain in each of the three anode layers for diffraction peaks corresponding to crystallographic planes (110), (200), (211) and (220) were mainly tensile (Fig. 7(a)). Results indicated that the average trends of residual strain in each of the three Hastelloy®X substrates for diffraction peaks corresponding to crystallographic planes (111), (200), (220), (311) and (222) were compressive at the interface, including some high tensile average residual strain away from the interface in the substrate, for example, for the Mo-Mo₂C/Al₂O₃ anode substrate. To convert the through thickness residual strain data to analyse the corresponding residual stress distribution (Fig. 7(b)), an average value of measured elastic modulus (Fig. 4) was utilized where measurement depth location of residual strain and elastic modulus did not match. This portion of the investigation indicated that the anode and substrate individual peaks or average residual strain/stress varied significantly with the anode coating conditions.

As mentioned earlier, anode layers of 200 μm to 300 μm thicknesses and with a volumetric porosity as high as 20% could be produced by selecting the proper atmospheric plasma spray (APS) process parameters without the need for the addition of a pore-forming material. For example, Fig. 2(I) showed the coating’s surface, which was mainly composed of splats with some semi- or partially-molten granules, including surface connected macro-pores and cracks in splats (but very little in Mo-Mo₂C/Al₂O₃, Fig. 2(I) (a). This suggests that the pores formed as a result of reduced bonding between adjacent splats, while micro-cracking arose from contraction of the splat in the course of quenching and succeeding differential thermal contraction between substrate and coating. This confirms previous related results from our investigations [32‐35]. For the anode cross-section surfaces (Fig. 2(II)), the splat thickness and features within appeared more or less very similar for all three anode layers (Mo-Mo₂C/Al₂O₃, Mo-Mo₂C/TiO₂ and Mo-Mo₂C/ZrO₂) with distinct layer gaps between splats (i.e. the splat does not appear to have dissolved). It can be argued that the slight variance in splat structures may be due to dissimilar powder shape and sizes.

In the XRD pattern, though the main phase was metallic molybdenum (Mo), considering some unique phase, as shown in Fig. 3 for the Mo-Mo₂C/Al₂O₃ anode layer, there was a small amount of aluminium-molybdenum-carbide (Al₂Mo₃C). Al₂Mo₃C is known to be a superconductor at a specific temperature as mentioned by Weil [45]. One can speculate that one possible area for further study is an SOFC coating as a superconductor.

Overall hardness results indicated that the upper layers of the anode surface have higher average values than the subsurface layers in the anode layer with some effect of APS high temperature deposition on the substrate (i.e. higher bound at the interface for each specimens). The average hardness measured using nanoindentation technique for the anode layer cross-section surface (Fig. 4(a)) in the current investigation was found to lie within the range 5 GPa to 9 GPa (for Mo-Mo₂C/Al₂O₃ anode layer), 5 GPa and 10 GPa (for Mo-Mo₂C/ZrO₂ anode layer), 7 GPa and 14 GPa (for Mo-Mo₂C/TiO₂ anode layer), with a significantly high standard deviation within coating and low standard deviation in the substrate (Hastelloy®X). The small differences in the average hardness can be attributed to the lower degree of phase transformation in APS during deposition of Mo-Mo₂C/ZrO₂ and Mo-Mo₂C/TiO₂. This could also lead to potential differences between the measured elastic values. Other factors, such as inter-splat bonding, residual stress and porosity may also contribute to the differences in the elastic modulus of the three anode layer coatings. In addition, high standard deviations in through thickness nanoindentation measurements (i.e. hardness, elastic modulus) also suggest an important effect of the compound anode morphology (Fig. 4(b)). For example, the average elastic modulus measured for anode layer cross-section surface ranged between 283 GPa to 305 GPa (for Mo-Mo₂C/Al₂O₃ anode layer), 134 GPa and 244 GPa (for Mo-Mo₂C/ZrO₂ anode layer), 171 GPa and 275 GPa (for Mo-Mo₂C/TiO₂ anode layer), with a significantly high standard deviation in the coating zones and a low standard deviation in the substrate (Hastelloy®X) zones.

The complex anode coating cross-sectional morphology is best expressed in Fig. 8 which presents an example of Berkovich nanoindentation at 30 mN load for the anode cross-section in Mo-Mo₂C/TiO₂. Here the indent line shown in the Hastelloy®X substrate cross-section (i.e. 100 μm away from the coating-substrate interface in substrate, Fig. 8(a)), suggests a moderately uniform microstructure, leading to a low standard deviation in the substrate (Hastelloy®X) zones, as seen in Fig. 4. For the indent mark presented for the anode cross-section in Mo-Mo₂C/TiO₂ (220 μm away from the coating-substrate interface in coating, Fig. 8(b)), showing indentation of non-uniform microstructure (surface), leading to high standard deviation in anode zones, seen in Fig. 4. The Fig. 8(c) presents the corresponding P-h profiles for the anode cross-section in Mo-Mo₂C/TiO₂ including the inbox in P-h profiles which indicate that each anode coating forms distinct alternating layers of the two materials (identifiable largely by light grey and also by dark grey lamellar structures) in each anode coatings (e.g. Fig. 8(d, e) for Mo-Mo₂C/TiO₂). Also, evident from XRD pattern in Fig. 3 for Mo-Mo₂C/TiO₂ anode layer, the main phase by a considerable margin was lighter grey metallic molybdenum (Mo) including the high temperature polymorph of darker grey titania (TiO₂, rutile) was present. The Fig. 8(d) shows a zoomed view of Berkovich indentation for indent 5 (on darker phase with hardness (7.6 GPa), reduced elastic modulus (128 GPa)), and for a zoomed view of Berkovich indentation for indent 4 (on darker phase with impaired indenter landing). The indent 1 (on lighter grey phase) suggests higher hardness (9.6 GPa) and reduced elastic modulus (218 GPa) compared to the darker grey phase. The values for indent 4 (hardness = 2.1 GPa; reduced elastic modulus = 42 GPa) is much low possibly because it landed on the edge.

In the current investigation, the Poisson ratio for the anode layer was taken as 0.30 (Mo [37], due to dominant phase observed in X-ray and neutron diffraction), however, the elastic modulus values can be influenced by the Poison’s ratio (ν _s ) of the specimen. Some references recommended a Poisson’s ratio value as high as 0.32 for Mo [38]. From the present investigation, a sensitivity analysis indicated that the average modulus will change (i.e. decrease) by about 1.36% if a higher Poisson’s ratio value of 0.32 is used. Considering the sensitivity of Mo₂C, Nino et al. [39] suggested a value of 0.28, which is very similar to the Poisson ratio for the Hastelloy [39], the average modulus will change (i.e. increase) by about 1.08%.

The APS spraying conditions appeared to have only a slight effect on the average modulus (Fig. 4(b)). Also, the higher magnification images of the Hastelloy®X substrate near the interface indicated negligible differences in the microstructure. The hardness did not show substantial differences between the near-interface hardness of the Hastelloy®X between the anode materials, indicating that microstructural transformation was not substantial, which was consistent with the observed microstructure (Fig. 4(b)). Hence, it was difficult to relate this small change in modulus and no change in hardness of near coating-substrate interface modulus of Hastelloy®X on possible microstructural transformations in Hastelloy®X during APS coating deposition. As shown in Fig. 4(c), it possible that near interface nanoindentation may land in the gaps (non in this case) or either on the substrate or coatings and hence some results may have been related to coating and other to the substrate.

The residual strain and stress results (presented in Fig. 7) indicated that, with all other factors constant, the measured strain is dependent upon the depth of measurement. This in turn is suggestive of the combined effect of thermal mismatch based on the difference in the coefficient of thermal expansion (α _CTE ) of the anode coating and substrate system, the role of quenching stress in individual lamellae, and the effect of phase transformations [32‐34]. Furthermore, residual stress measurement of the molybdenum (bcc) structure in Mo-Mo₂C/Al₂O₃ anode layer (for planes: (110), (220), (211), (220)) indicated largely tensile residual strains, whereas planes ((111), (200), (220), (311), (222)) in Hastelloy®X substrate which are Ni (gamma, are face-centred cubic or fcc) peaks indicating compressive strain values at the interface for all measured planes except (200) which was tensile strain throughout the substrate thickness. This dependency of measured values on the plane is not unusual on the basis of volume conservation and Poisson’s ratio. However, it does indicate that when a single peak fitting analysis is used (e.g. in the sin²ψ technique in X-ray measurements), the results will be sensitive to the designated peak, and hence reported stress values are not uncommon, indicating not only the difficulty of residual strain measurement in these complex materials but also that the multiple peak through thickness analysis via neutron diffraction provides a more detailed strain analysis.

As summarised above in “Assessing Neutron Diffraction Residual Strain” section, the strain was obtained from the shift in individual peaks for the coating and substrate materials obtained using a single-peak fitting. Single-peak fits use a peak profile consisting of the convolution of a truncated exponential with a pseudo-Voigt function (note: pseudo-Voigt part is a convolution of Gaussian and Lorentzian curves) shown in Fig. 5(a) routine. The quality of single peak fitting to the neutron diffraction is shown in the zoomed window for the Mo (110 bcc) peak in Fig. 5(a) which has resulted in standard deviations of strain measurements (Fig. 7) which are consistent with previous studies on thermal spray coatings [e.g. 32–35].

In general, for simple crystal structures Rietveld refinement analysis can be applied which considers multiple peaks in the spectra to evaluate lattice parameters. However, Rietveld refinement can be difficult to apply where the spectra has overlapping peaks. In the current study overlapping peaks are possible due to submergence of the beam in both coating and substrate materials and formation of other compounds, which reduces the reliability of Rietveld refinement. As the Mo peak in the current study had no overlapping peaks (Figs. 3 and 5), a single peak fitting refinement was used, which is consistent with previous studies of thermal spray coatings [32‐35]. At Engin-X neutron scattering facility, peak positions can be precisely determined by “least-squares” refinement of the peaks, with a typical sensitivity of 50 με (1 με = 10⁻⁶). Least-squares means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. Each diffraction peak provides information from only a small fraction of the crystallites within the sampled volume, i.e. those oriented to fulfil the Bragg condition. As summarised by Santisteban et al. [46], a good approximation to the macroscopic (engineering) elastic strain is usually given by a weighted average of several single-peak strains (ε _hkl ). In such time-of-flight (TOF) based neutron scattering instruments, the engineering strain can also be approximated from the change in the average lattice parameters from Rietveld or Pawley refinements of the complete diffraction spectrum.

The neutron scattering for strain measurement is conceptually very simple but its practical application can be time-consuming. Very long counting times are required when small gauge volumes and large penetration depths are involved [46]. In the current investigation, large counting times for coatings and in substrate near interface (3 h per vertical depth) and short counting times for substrates away from interface (1 h per vertical depth) were used to ensure data quality.

Surface properties (e.g. texture) in thermal spray coatings can originate from quenching of lamellae and plastic deformation of un-molten coating particles [32, 47]. Thermo-mechanical characteristics of anode particles during deposition therefore control the degree of texturing in thermal spray coatings. The analysis of multiple peaks presented in this investigation (Fig. 6(a)) therefore highlights this dependency of texture, which can form during coating formation in APS, on residual strain. This anode texturing and its influence on residual strain will also influence its thermo-mechanical performance, which will improve in grains that are oriented such that they carry a compressive residual strain near anode layer/substrate interface.

For bulk (macro) mechanical property evaluations, an averaged value of strain, e.g. as indicated in Fig. 7 can be used to interpret the macro-strain in the anode specimens. Such detailed strain analysis is currently not possible using other techniques e.g. sin²ψ where a single peak is measured or hole-drilling or curvature techniques where an averaged stress is estimated. Even for neutron based residual strain measurements, complications do arise. For example, the gauge volume contains diffraction peaks from both the coating and substrate materials, which overlap and reduce the accuracy of Rietveld peak refinement [32‐34].

As was seen in Fig. 7, the measurements of the average residual strain/stress profile in the anode layer varied significantly with the coating conditions. The average residual strain and residual stress in the Mo-Mo₂C/Al₂O₃ anode layer and Mo-Mo₂C/TiO₂ anode layer changed from tensile near the surface to compressive at the interface, whereas the average residual strain/stress in the Mo-Mo₂C/ZrO₂ anode layer was slightly tensile. These residual strain values revealed the collective outcome of a thermal mismatch founded on the dissimilarity in the coefficient of thermal expansion (α _CTE ) of the anode layer/substrate system, the role of quenching stress in specific lamellae, and the influence of phase changes [32‐34]. These factors have been discussed in detail by Ahmed et al. [32] on the basis of physical mechanisms dictating the residual stress behaviour. Additionally, residual stresses within a coating can disturb the coating bond on a substrate, predominantly for cyclical temperature operation [48], especially in SOFC. It can be argued that the reduction of the residual stress and enhanced bonding between the anode layers should diminish the trend to delaminate, especially during thermal cycling in fuel cell operation.