Stable Speckle Patterns for Nano-scale Strain Mapping up to 700 °C

The TiAl alloy, Ti-45Al-2Nb-2Mn(at%)-0.8 vol% TiB₂, was received in a nearly lamellar condition following casting and HIPping. A more refined lamellar structure was produced by air cooling after 2 h at 1350 °C, and then heating for 8 h at 850 °C, with samples wrapped in Ta foil and encapsulated in quartz glass tubes in 0.15 atm Ar. Samples were electro-discharge machined and ground to 4000 grit, then polished by vibratory polishing (Vibromet 2, Buehler, Germany) in colloidal silica.

The sample was coated with Au (or Pt, Ag or Pb) using a sputter coater (Emitech K550, Quorum Technologies, UK) and then moved to the apparatus described in [1] for vapour remodelling at 300 °C. Since only a partial reconstruction was obtained, a series of heat treatments were conducted in air, or with the sample wrapped in Ta foil and encapsulated as above to avoid surface oxidation. The description of such heat treatments and their effect on the size, morphology and distribution of the speckles is given in the Results section.

To characterise the stability of the speckle patterns to extended thermal exposure, image correlation of pre- and post-exposure scanning electron microscopy (SEM) images was employed, using commercially available DIC software (DaVis 8, LaVision, Germany). The images were acquired on a dual beam FIB/SEM (Helios NanoLab, FEI, USA). Atomic force microscopy, AFM (Veeco Dimension 3100, Bruker, US), with ultra-sharp tips (TESP-SS, Bruker, US) was used to study the morphology of the speckles.

There are many measures for pattern quality; such expressions may be classed as local or global. Local indicators evaluate the variability of greyscale values in a subset, a few examples are ones based on intensity gradients from DIC error theory (sum of squares of subset intensity gradient (SSSIG) [35], mean intensity gradient [36], mean intensity of the second derivative [37] and the mean subset fluctuation [38]), and others that consider the entropic variability of subsets [39]. Global indicators provide a single value to instead account for the average pattern quality across a potentially non-uniformly speckled area using particle morphology distribution, or entropic methods (Shannon entropy [40]).

In the current study the suitability of a pattern for image correlation was evaluated using the mean subset fluctuation, (MSF) [38]; a clear benefit of the mean subset fluctuation is its computational ease for an indicator that evaluates the local pixel intensity variations across the whole pattern. It is given by the expression S _f:where at point p, a _ij is the grey value, \( \overline{a} \) the mean of a _ij for the 3 × 3 pixel subset centred on p, and F is the image of the speckle pattern considered, of area H × V. This indicator represents the difference of the pixel intensities in each 3 × 3 subset to the subset average intensity in order to produce a single indicator of image quality describing the average extent of local intensity variations. For comparability between patterns, the MSF is normally calculated from 8-bit greyscale images.

For higher MSF values there must be large variations, and hence steep gradients, between immediate pixel neighbours. However this is not a sufficient condition for successful strain mapping. Indeed, the regular pixel arrays with binary 8-bit intensities in Fig. 2(a–d) generate very high MSF values, ~10 times higher than those of the experimental patterns in the present or other studies [38], despite lacking the randomness required for a unique strain mapping solution [30]. Further, the combined effect of image resolution and intended subset size is not effectively accounted for by the MSF. Noise levels in strain maps are strongly dependent on the minimum subset size [1]. If two cases are considered, both resulting in the same strain mapping resolution at the same magnification and dwell time, where one employs a 1024 × 884 pixel image and an 8 × 8 minimum subset size, Fig. 2(e), whilst the other is at 4096 × 3536 pixels and a 32 × 32 minimum subset, Fig. 2(f), the latter case is found to present a worse MSF value, by a factor of 2 to 3, despite a nominally increased accuracy of strain mapping and lower noise [30]. This disconsiders effects like increased sample drift for longer image capture times. Additionally, the lower resolution image is likely to suffer from pixel locking [41].

Recently, interest has been in dynamic subset selection [42] where the correlation algorithm is capable of selecting the most appropriate subset size locally, varying this as necessary across the pattern, and hence generating a spatially varying resolution of the calculated displacement field.

With these considerations in mind, a second pattern quality indicator, the subset size dependent mean subset fluctuation (SSDMSF), is proposed here as an adaptation to the MSF equation of Hua et al. [38]. The SSDMSF accounts for a destined DIC subset size in determining its pattern quality value, as follows:for a square subset of size n × n pixel²; all other notation is as above. The SSDMSF sums intensity differences to the mean subset intensity across the whole subset size rather than the 3 × 3 nearest neighbour consideration of the normal MSF, followed by normalisation by the number of pixels in the subset (A _subset).

Cuboids for compression testing 4 × 4 × 8 mm³ in size were electro-discharge machined and ground on all faces to 4000 grit, with one large face vibratory polished in colloidal silica. Compression testing was carried out ex situ on a 25 kN screw machine (Tinius Olsen, U.K.) at a strain rate of 10⁻³ s⁻¹, to several strain increments. Samples were heated in air by a halogen lamp hoop heater (Heraeus Noblelight GmbH, Germany) stable to ±0.5 °C of the setpoint, placed around the cuboid, with a type K thermocouple junction for PID control spot welded to the middle of another side face.

Fatigue samples had a 2 × 2 × 8 mm³ square cross-section gauge prepared equivalently to the compression cuboids. HCF testing at 50 Hz in tension, R = 0.1 and load-controlled, was performed on a 100 kN servo-hydraulic machine (Mayes, UK).

Between all mechanical testing and SEM imaging steps, the testpieces were handled in air, using polyacetal tweezers. A custom built sample holder for the test specimens ensured mechanical clamping of the testpiece for SEM imaging of the speckle pattern; this noticeably reduced temporal drift compared to alternatives such as silver dag fixation or, worse, carbon tape. Imaging was carried out as an up to 10 × 10 grid on the dual beam FIB/SEM in high contrast backscatter mode, to be stitched after correlation [43].

Image correlation of pre- and post-deformation SEM images was performed on DaVis as above to characterize the performance of the applied speckle pattern.

Digital image correlation of repeatedly imaged regions of the high temperature speckle pattern gave a noise level in the maximum shear strain, Fig. 6(a–c), well below 1%, resulting from SEM scanning imperfections, for a subset size of 8 × 8 and hence a resolution of ~60 × 60 nm². The island arrays generated by reconstruction may coarsen over time by coalescence due to island mobility [44]. To demonstrate the suitability of the pattern for use at high temperature, the same region was exposed for 1 h to successively higher temperatures, with electron imaging of the same region between heating steps, Fig. 7. Correlation of such images relative to the initial state revealed no deterioration of the backscatter imaged speckle pattern, Fig. 7(a–e) beyond the standard noise level. This occurred until the temperature reached 740 °C, despite considerable oxide growth between speckles, visibly obscuring the secondary electron images, Fig. 7(f–j). For monotonic loading tests, thermal stability for an hour was sufficient. However high cycle fatigue experiments required a pattern that was thermally stable for over 6 h. The long term stability of the pattern was therefore also investigated, Fig. 8. The pattern was found to coarsen exclusively on the α₂-Ti₃Al phase and the boride particles after 12 h, whereas Au speckles on γ-TiAl were stable for over 72 h. To further demonstrate the robustness of the reconstructed Au speckle pattern, a speckled sample was placed in an ultrasound bath of acetone for 20 min. Recorrelation of the same region, Fig. 6(d), showed no consequential change in the speckle pattern. Equivalent robustness of the room temperature-suitable speckle with regards to ultrasound cleaning was observed, Fig. 6(e).

Regions ~250 × 200 μm² of the gauge sections of monotonic testing specimens underwent strain mapping. Equivalent tensile high cycle fatigue testing ensued. In order to achieve the desired spatial resolution, SEM imaging at 4000× magnification was necessary; backscatter imaging of the speckle with suitable low brightness, high contrast conditions, Fig. 4(a), produced sufficient compositional contrast of the gold to overcome contrast usually observed between α₂-Ti₃Al and γ-TiAl phases. With individual image widths of 32 μm, at 4096 × 3536 px² resolution, 10 μs dwell and no integration, a 9 × 8 image array was required to cover the region of interest, with ~10% image overlap. Hence pattern imaging after each compression step could take several hours. In order to produce multiple strain maps for different testing conditions and stages of compression, automation of the imaging was necessary, and was performed using a custom script once low sample drift had been achieved and the sample carefully positioned to match the locations imaged before testing. Image correlation was performed in one user operation by loading the full list of images into DaVis, with sequential pairs undergoing correlation. Up to 30 passes per step were required, finishing with 25% subset overlap and normalised cross correlation for the final stage; image stitching ensued. A suitable minimum subset size for the patterns in the present study was determined by considering both the noise level of correlation of repeatedly imaged regions, Fig. 6(c), and the minimum spacing of shear bands within the material investigated. From this an 8 × 8 px² subset was selected giving a resolution of ~60 × 60 nm².

The TiAl alloy was tested in two microstructural conditions, both nearly fully lamellar, but with different mean lamellar thicknesses of 1.2 μm and 150 nm for the γ-TiAl layers. Strain mapping of the thinner lamellae condition using the speckle pattern and ~60 × 60 nm² resolution presented above is shown in Fig. 9(a). The importance of such high resolution in identifying individual shear bands in a refined material is clear if compared to Fig. 9(b) for which the spatial resolution is a sub-micron ~0.25 × 0.25 μm². Individual shear bands are now poorly distinguished. Other deformation features such as plasticity surrounding hard TiB₂ particles were well resolved; this required both high accuracy and low noise of image correlation to resolve compound deformation components from the displacement fields such as the rotation of the underlying lattice [16]. However, for the coarser speckle pattern produced on boride particles, a 32 × 32 subset was most suitable, Fig. 9(b), to reduce noise from poor correlation of unsuitably small subsets.

Compression of TiAl was performed in multiple steps, with the present example undergoing testing to strains of 1, 3, 8 and 14%. For the 72 images captured at each step, the MSF values were calculated, see Fig. 10. A first observation is that in all cases the MSF reduces from the top left, where imaging was initiated, to the bottom right, final image. No trend is observed between successive stages of compression.

Contrast and brightness degradation was not found to be an issue when testing at room temperature; that is to say, the Au speckle suffered no noticeable fine-scale damage as a result of electron imaging or general handling between testing steps. For the speckle tested at high temperature, the identical brightness and contrast conditions generally remained suitable between steps. Only after several cumulative hours (> 5 h) at temperature, owing to the requirement for cooling then reheating and stabilising between testing steps to allow for pattern imaging, was sufficient oxide found to have accumulated around the Au islands for slight manual adjustments in the brightness and contrast conditions of imaging to be necessary before initiation of automated imaging. Such small changes aimed to maintain similar speckle appearances to the initial state.

To overcome the issue of Au island coarsening at 740 °C and above, Fig. 7, Pt was sputter coated onto the OPS vibratory polished TiAl surface. Reconstruction was achieved by the same approach as that for Au. An example of a remodelled Pt speckle pattern suitable for nDIC strain mapping is given in Fig. 11(a). The Pt speckle pattern was found to be stable up to 800 °C, at which point the oxidation of the current TiAl alloy became too excessive for surface strain mapping in air.

Alternatives to Au were also sought that might reconstruct at lower temperatures than 750 °C. Ag and Pb were both successfully remodelled to produce nano-scale island patterns in Fig. 11(c, d), after holding for short periods at 650 °C and 185 °C respectively.

The use of heat treatments alone to reconstruct the Au thin film for DIC use has not been described before. Vapour-assisted remodelling has been used on various substrate materials such as glass [4], stainless steel [1, 45] and an Al-Si alloy [46], but was insufficient for reconstruction alone on TiAl for a sample temperature up to 300 °C. Within the context of thin film and device materials, extensive studies [47, 48] have investigated the effects of film thickness, temperature and time on island formation, as has the field of surface-enhanced Raman scattering [34]. The different reconstruction techniques also produce dissimilar Au particle morphologies; indeed, Luo et al. [34] reported globular, closely packed, Au particles following water vapour-assisted reconstruction, whereas in the present work the islands appear crystallographically facetted for those reconstructed in air, and globular but well-spaced for those reconstructed in vacuo. Such faceting reflects the exposure of specific crystallographic planes, and hence the islands achieving a more stable, low energy state, in a comparable manner to island growth during thin film deposition processes [49]. With respect to imaging of the speckle, the bimodal distribution of pixel intensities achieved is characteristic of successful speckle patterns identified elsewhere [38].

The robustness of speckle patterns is of significant practical importance, especially when mechanical tests are carried out ex situ and at high temperatures where contact lubricant may disperse across the sample surface. From the acetone ultrasound tests, the benefit of Au thin film reconstruction is clear, compared to other additive speckle methods such as SiO₂ or Al₂O₃ colloid deposition where some speckle detachment upon such cleaning is immediate.

It is well reported that for colloidal SiO₂ and metal nanoparticle deposited speckle patterns for SEM DIC strain mapping, the pattern is significantly non uniform across the specimen surface, displaying regions with much higher or lower densities of particles [15], with closely spaced, non-agglomerated spheres being desirable [2]. In contrast, no noticeable non-uniformities were observed for the speckle patterns presented in the current work across specimens multiple centimetres in size. This is undoubtedly a result of the uniformity of the initial Au sputter deposition preceding island reconstruction.

To achieve high resolution strain maps without phase bias in a multi-phase material, uniformity in speckle size and spacing is required in order for the same minimum subset size to be appropriate for all phases. Considering that Au film reconstruction conditions differ according to the substrate [4], achieving similar coarsening means finding the overlap in island growth parameter space on each phase, if it indeed exists. The detrimental effect of variable island coarsening on DIC is illustrated in Ti4522XD here: whilst an equivalent distribution, and hence strain mapping resolution, is achieved on both γ-TiAl and α₂-Ti₃Al, the minimum subset size required for TiB₂ particles is to the detriment of the highest resolution necessary for shear band mapping in the refined lamellae condition, Fig. 9(b).

Though the aim of the current work was to generate a speckle pattern with suitable thermal stability for extended time periods for DIC strain mapping upon ex situ mechanical testing in fatigue, the pattern described here could also be used for in situ high temperature mechanical testing experiments. Furthermore, if use of a backscattered electron detector at high temperature is possible with the setup, then the compositional contrast of the pattern may exclude from the image surface oxides growing during the experiment. This is achievable by strongly negatively biasing the Faraday cage of an Everhart-Thornley detector to repel thermal electrons.

The spalling of the oxide layer intergrown between Au islands upon room temperature testing of the pattern generated in air, and hence loss of the speckle pattern, is consistent with observations [29] that TiAl forms an oxide that is ductile at high temperature, but brittle at room temperature. Au thin film reconstruction by in vacuo heat treatment is also new and gives a nearly oxide-free surface speckle. Preliminary high temperature tests at 700 °C with this pattern indicate it to be a promising alternative to the oxidised reconstructed Au speckle pattern, if mechanical testing is carried out in vacuo.

The quality of the patterns produced here, as evaluated using the MSF, indicates highly suitable speckle designs, with values consistently above maxima reported elsewhere [38]. The ~60 × 60 nm² resolution (8 × 8 px² subset) and corresponding noise level was found to be well adapted according to the SSDMSF and necessary to the identification of deformation features in the refined microstructure of the nearly lamellar TiAl alloy tested. The diminishing MSF as sequential imaging progresses is due to the loss of focus from slight inclination of the sample surface. Initial focussing in the centre of the region of interest before initiating automated imaging has effectively reduced the extent of such deterioration in the MSF value. The role of the experimentalist in obtaining a high MSF upon imaging is additionally seen in Fig. 10, where the brightness/contrast conditions selected to best overcome topographical effects in BSE imaging as deformation progresses cause the MSF values to vary non-uniformly between testing steps.

The speckle patterning method developed in the current study, employing a maximum heat treatment temperature of 750 °C, has enabled the deformation mechanisms in TiAl between room temperature and 700 °C to be studied. In some cases, this heat treatment temperature for thin film reconstruction may be prohibitive to the use of Au; for example, in deformation studies on shape memory alloys, such a thermal cycle may significantly change the distribution of crystallographic variants initially present, whilst overaging of precipitates in 2000 and 7000 series aluminium alloy test-pieces may similarly occur [50]. It was apparent from the speckle development process that in the absence of vapour assistance, reconstruction should take place at a temperature above that of testing to ensure the stability of the pattern so that undue coarsening of the metal islands does not occur during testing. At a given temperature, the self-diffusion of pure metals varies inversely to the melting temperature [51]. Accounting for this, along with previous reconstructed thin film work [4] and the benefit of employing heavy speckling elements for high backscatter electron contrast, alternative speckling elements with lower melting points than Au, such as Ag or Pb, could be sought which will reconstruct at temperatures as low as 185 °C. This may be below the studied substrate material’s limiting temperature.

The progressively higher isothermal holds for 1 h in air of an Au speckled sample, Fig. 7, identified the limit of use of the Au speckle pattern produced in the present study to be below 740 °C. Strain mapping at temperatures above 700 °C was achieved with a reconstructed thin film of higher melting point Pt and was stable up to at least 800 °C.

In short, the use of alternative speckling elements enables the range of materials and test temperatures accessible to nDIC strain mapping to be extended relative to the limits of the Au speckle.

Beyond speckle application, the actual DIC method employed in the current study to generate high resolution, accurate strain maps combines recently established references by DIC pioneers such as SEM BSE imaging [52] and post-correlation stitching [43] in order to achieve a mapped area of ~250 × 200 μm² covered by ~6500 × 5000 individual displacement vectors. The use of industry standard DIC software, along with a refined speckle pattern was vital if unambiguous measurements of local strain were to be obtained: as well as uniaxial strain along the image axes, ε _xx and ε _yy, relatively noise-free maximum shear strain, max(ε _xy), and in-plane rotation maps have been obtained. The latter are most relevant to identifying the underlying deformation micro-mechanisms such as slip bands and lattice rotation features, respectively [16].