Nanoscale mechanical surface properties of single crystalline martensitic Ni–Mn–Ga ferromagnetic shape memory alloys

Located beyond the resolution limit of nanoindentation, contact resonance atomic force microscopy (CR-AFM) is employed for nano-mechanical surface characterization of single crystalline 14M modulated martensitic Ni–Mn–Ga (NMG) thin films grown by magnetron sputter deposition on (001) MgO substrates. Comparing experimental indentation moduli—obtained with CR-AFM—with theoretical predictions based on density functional theory (DFT) indicates the central role of pseudo plasticity and inter-martensitic phase transitions. Spatially highly resolved mechanical imaging enables the visualization of twin boundaries and allows for the assessment of their impact on mechanical behavior at the nanoscale. The CR-AFM technique is also briefly reviewed. Its advantages and drawbacks are carefully addressed.


Introduction
Yielding magnetically switchable strains of up to 10% in the 14M modulated martensitic phase by magnetically induced reorientation of variants, Ni-Mn-Ga (NMG)-based ferromagnetic shape memory alloys (FSMA) have attracted much interest since their discovery towards the end of the last millennium [1][2][3]. While active bulk single crystals are well established-and even commercially available within actuators-at this point 5 , miniaturization as functional thin films remains an unresolved challenge. Prerequisites for technically meaningful films with maximum attainable strains are (i) a 14M modulated martensitic phase at room temperature, (ii) single crystallinity, (iii) highly mobile twin boundaries and (iv) the absence of external (i.e. substrate) constraints. It was demonstrated recently that epitaxy on an MgO (001) substrate from a magnetron sputtering source can successfully be employed to cope with challenges (i) and (ii) [4], whereas freestanding films can readily be obtained by subsequent lift-off approaches [5,6] (as a remedy for (iv)). However, the understanding of deformation mechanics during reorientation of martensite variants as well as austenite-martensite transition (AMT) in the presence of open surfaces or reduced dimensionality is far from complete. While it is basically well established that the motion of twin boundaries (TBs) mediates the macroscopics of AMT (see, e.g., [7] and reference therein for a review on macroscopics), a quantitative experimental characterization from a nanomechanical point of view is still lacking. Since it might be tempting to consider nanoindentation as the technique of choice within this scope, there is a need to stress that with tip radii and indentation depths of the order of a tenth of a micron, resolution clearly proves to be insufficient. Inspired by early suggestions [8,9], the capability of CR-AFM to assess mechanical response at the nanoscale on FSM materials was explored and demonstrated to be perfectly suitable to quantify nanomechanical properties at surfaces [10] in the present work. Based on cross-sectional high-resolution transmission electron microscopy (HRTEM) investigations and x-ray diffraction [4], it was already shown that sputter deposited single-crystalline NMG films on MgO (001) substrates reside in an orthorhombic 14M modulated martensitic phase with lattice parameters a = 0.612, b = 0.578 and c = 0.554 nm at room temperature (see section 3 for sample preparation details). The surface morphology is characterized by micro-scale domains with a regular twin variant pattern (see figure 1(a)). A representative lamella cut along a (110) plane of the MgO substrate (or equivalently the (010) plane of austenitic NMG) is exemplarily shown in figure 1(c). As summarized in figure 1(d), twinning generally can occur on {110} planes, while only one of the latter is observed within each domain. Residing in a 45 • angle with two of the {100} planes and being normal to the other, the intradomain stripe pattern under 45 • to the surface (as shown in the cross-sectional TEM image in figure 1(c)) is readily understood. Morphology on the surface (figure 1(b)) thus reflects a cross section of the twin variant structure. The intravariant structure, on the other hand, was always determined to be 14M martensite in HRTEM, while the b-axis of the orthorhombic cell proved to be directed in plane with the surface and twinning planes-as sketched in figure 1(b). Also shown is the orientation of the TB (red line). Within the present context it is important to emphasize that, on both sides of a surface stripe, an asymmetry in material properties can thus arise (i) for crystallographic reasons (orientation of the aor c-axis normal to the surface) and (ii) because of the inclination of the TB with respect to both variants. [11] based on total energy calculations is performed to predict mechanical properties of the 14M modulated Ni 2 MnGa martensite phase. Electronic structure calculations employed ultrasoft pseudopotentials [12][13][14] with nonlinear core corrections [15] based on the atomic reference configurations [Ar] 3d 9 4s 1 , [Ar] 3d 5 4s 2 and [Ar] 3d 1 04s 2 4p 1 for Ni, Mn and Ga, respectively 6 , and a plane-wave basis set, as implemented in the pwscf code [16]. The effects of exchange and correlation are treated according to the Perdew-Burke-Ernzerhof functional [17] with spinpolarized generalized gradient correction. Brillouin zone integration (using 10 × 8 × 4 up to 20 × 16 × 8 Monkhorst-Pack grids [18]) using the Methfessel-Paxton smearing [19] (0.27 eV), as well as the energy cut-off of the plane-wave basis set (612 eV) and augmentation charges (6123 eV) were optimized to obtain energy and stress convergence better than 0.5 meV atom −1 and 2%, respectively, after structural relaxation runs. Taking the unit cell of the 14M modulated Ni 2 MnGa martensite phase proposed by Zayak et al [20] as the starting point, the present DFT study first relaxed the lattice vectors and basis towards equilibrium for the currently employed conditions. As the resulting reference cell agrees to within less than 1% with the suggestion of Zayak et al [20], this corroborates the accuracy of both treatments-in particular because they can be considered to be methodologically independent. Within the present study, ionic and cell relaxations are always realized with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) scheme as implemented in pwscf. For the sake of comparison with experiments, it is desirable to determine the tensor of elasticity C i j (given in the Voigt notation in the following) within the   (1)). As a double check, the tensor of elasticity was also calculated from the ground-state energy as a function of strain, which after fitting to the Murnaghan equation of state yielded identical results within the error bars. However, the experimental approach based on the CR-AFM technique yields an indentation modulus M, since a cantilever tip is applied on the sample surface. The resulting elastic response is thus determined by an interplay of elastic constants given in C i j and additionally depends on the tip shape as well as indentation direction. The theory behind calculating the M of mechanically anisotropic solids is challenging but has been revealed and discussed intensively ( [21,22] and references therein).

Density functional theory (DFT) predictions of elastic properties. DFT
Based on the work of Vlassak et al [21], M was calculated numerically from C i j for different indentation directions, assuming a spherical tip shape. The results are listed in table 2 and will be consulted for a comparison with experimental data (see section 4).

The contact resonance atomic force microscopy (CR-AFM) technique
CR-AFM is a dynamic mechanical spectroscopy method, utilizing cantilever eigenfrequencies during material contact to get information about mechanical surface properties. Therefore, a cantilever is applied to the sample surface with a defined static load F L (figure 2(a)). Additionally, an ultrasound transducer feeds wide band longitudinal acoustic waves into the sample and thus excites the cantilever to vibrate. In order to get a correlation between the cantilever's contact resonance frequency (CRF) and the sample's indentation modulus, a model of beam bending dynamics needs to be connected to a contact mechanics theory. The fundamentals are briefly reviewed here. A deeper insight into this topic can be found in [23,24].

Beam bending model.
An AFM cantilever possesses a set of individual eigenfrequencies f i,res (i ∈ N), which are determined by a bending model based on the beam bending differential equation and proper boundary conditions. Flexural undamped modes of a beam with length l, cross sectional area A = b d and mass density ρ are given by where E is the elastic modulus and I describes the area moment of inertia, which is calculated by b d 3 /12 for an ideal rectangular-shaped beam. The boundary conditions n = 0, 1, 2, 3 ensure a one-sided clamping of the beam at x = 0. For small vibration amplitudes around the cantilever's static equilibrium deflection, the repulsive tip-surface interaction can be described by a linear force approach according to F = −ku(x)| x=l , with 'contact stiffness' k. Compared to a free cantilever, boundary conditions n = 2, 3 are modified and resonance frequencies f i,res will shift in the presence of k = 0. Equation (2) has been studied intensively and the f versus k dependence is discussed considering a wide range of influences such as the tilt angle of cantilever, tip height, lateral forces, etc. However, equation (2) cannot be solved analytically for non-ideal rectangular-shaped beams consisting of elastic anisotrope materials, which is excited cantilever typically the case for commercial AFM cantilevers. A powerful numerical approach consists in finite-element modelling (FEM) as already shown in [25]. Figure 2(b) illustrates the dispersion relation f versus k for the first two eigenmodes f 1,res and f 2,res , calculated by FEM 7 of a Bruker MPP130 cantilever ( f 1,free = 116 kHz, f 2,free = 726 kHz). Obviously, the dispersion curves can be separated in a region with nearly linear slope (d f i,res /d k = 0), resulting in high sensitivity to surface stiffness, as well as a region where the curve saturates (not suitable for CR-AFM imaging). It is also noticeable that sensitive regions shift to higher values for higher-order eigenmodes. Depending on influences such as tip dimensions, cantilever stiffness and surface rigidity, a proper eigenmode for optimum sensitivity needs to be selected.

2.2.2.
Tip-surface contact model. The beam bending model was applied to link the cantilever-eigenmodes f i,res to the contact stiffness k. In a second step, k is associated with the material-specific indentation modulus M. Based on the Hertzian contact theory for anisotropic materials [26] and according to Vlassak and Nix [27], one defines 7 FEM calculations used COMSOL Multiphysics 3.5a.
Mn Ga 48 ± 1 31 ± 1 21 ± 0.5 400 ± 10 7.6 ± 0.05 303 ± 1 307 ± 1 363 ± 1 whereas A describes the tip-surface contact area and M includes indentation moduli of tip-and surface-material according to In the more general case of elastic anisotropic materials, the middle part of equation (3) still holds as long as a threefold or fourfold rotational symmetry, perpendicular to the surface plane, is ensured [27]. Finally, by combining equation (3) and the dispersion relation of the bending model (figure 2(b)), a correlation between the experimentally observable CRF f i,res and the sample's indentation modulus M sample is established. One should note that the tip radius R is just an equivalent of the tip-curvature rather than the lateral tip size, which means that even small tips (of several nm in size) might have high radii (e.g. a flat punch yields R = ∞).

Sample preparation
As described in [4], almost perfect Ni 49 Mn 32 Ga 19 single crystals were grown on MgO (001) substrate 8 by magnetron sputter deposition from a multicompound target 9 . Prior to film deposition, the chamber was baked overnight to ensure a base pressure at least within the high-vacuum (HV) regime and to dehydrate the MgO substrate. After 300 s of presputtering, preparation of 400 nm thick films was performed at 600 • C substrate temperature and a deposition rate of 0.19 nm s −1 . The latter was realized by using an Ar pressure of 3 × 10 −3 mbar and a nominal sputtering power of 50 W (dc). After deposition, samples were routinely checked for their chemical composition using energy dispersive x-ray spectroscopy (EDX), for crystal structure by means of x-ray diffraction analysis (XRD) and for surface topography by scanning electron microscopy (SEM). Furthermore, temperature-dependent electrical resistivity measurements were used to gain the martensite transition temperature T M and the Curietemperature T C (table 1) [28].

The CR-AFM setup
The current setup is based on a programmable Asylum Research MFP-3D SA AFM 10 , which is additionally equipped with an ultrasound transducer directly underneath the sample.  A segmented photodiode is sensitive to angular changes of the reflected laser spot caused by cantilever displacements. The digitized signal is split, filtered and post-processed in order to gain CRF f i,res as well as topographic information. An exemplary CR-AFM image shows rectangular Ti patterns (t ≈ 100 nm) on the Si substrate. The overlaid f 1,res colormap clearly reveals differing elastic properties of both domains.
As indicated in figure 3, the cantilever deflection is read out optically, whereby a laser spot is reflected from the cantilever's back side and detected by a photodiode. Finally, the AFM's 5 MHz ADC digitizes the signal. The low-frequency signal parts yield information about surface topography, whereas the high-frequency part contains contact resonance spectra. Two fast digital lock-in amplifiers, integrated in the AFM's field programmable gate array (FPGA), allow the identification of CRFs out of the high-frequency spectra. The whole acquisition process is carried out dynamically at each point (pixel) during an image scan. Besides this continuous image-scan mode, where the cantilever is kept engaged to the surface, the setup also allows point-map acquisition. In this mode, the tip only touches the surface at discrete points within a predefined m × n array to acquire f i,res . Since there is no lateral movement during contact, tip wear is low compared to image-scanning. This advantage is at the expense of significantly increased measuring duration due to continual engage-withdraw processes. It is preferable to use the point-map method if absolute quantitative information about the elastic surface modulus is of more interest than knowledge of spatially resolved elastic variations. Two Bruker MPP130 cantilevers (denoted as MPP130-1 and MPP130-2) were used for the measurements discussed here. Effective stiffnesses of k 130−1 = 13 N m −1 and k 130−2 = 11.5 N m −1 were determined via FEM modelling and experimentally confirmed by the thermal noise method [29]. The first two free bending modes amount to f 1,130−1 = 121 kHz, , f 2,130−1 = 755 kHz and f 1,130−2 = 116 kHz, , f 2,130−2 = 726 kHz, respectively.

Data acquisition and analysis
Since CR-AFM is not a standard-less measuring method, quantitative determination of elastic surface properties call for proper reference samples with known indentation moduli. As is 9 usual in CR-AFM analysis, [001]-grown single-crystalline silicon (M Si = 165 GPa) and fused silica (M FS = 75 GPa) were utilized. In the following, a short overview about identifying the indentation modulus M sample of an unknown sample is given. A procedure typically applied in the CR-AFM community [30] is therefore followed here.
The measuring series consists in acquiring a 6 × 4 point-map on every sample to gain the corresponding average second CRF f 2,res . The scanned area extended to 1 µm 2 in size. Those measuring series were performed several times on different sample regions in order to avoid flawed data due to tip wear (change in tip radius R) and surface artifacts, respectively. This measuring process was repeated at two different applied loads F L . For the sake of reproducibility, the whole procedure was carried out again utilizing a second MPP130 cantilever possessing a significantly more blunted tip. All measurements were realized at room temperature. Once f 2,res is known for each sample, the contact stiffness k can be associated using the dispersion relation figure 2(b). The next step consists in calculating the effective tip indentation modulus M tip by means of known M Si and M FS . For this purpose, one solves the ratio k 1 /k 2 by substituting equation (4) into equation (3): Finally, equation (5) can be used again to calculate M sample .

Elastic properties: DFT versus CR-AFM
Following the analytical approach described in the previous section, the indentation modulus M NMG was measured along the [001] direction of the sample NMG-1, which remained attached to the MgO substrate throughout the experiments. Force-distance measurements, previously acquired for the sample, revealed that adhesion forces can be neglected. Together with numerical data of DFT calculations, experimental results are listed in table 2. Indentation moduli M NMG were calculated assuming a flat and a spherical tip, respectively-yielding very similar results. It can be seen that the absolute error of f 2,res (standard deviation σ ) for NMG-14M is higher than that of the reference samples, which could have its origin in the characteristic surface structure (see figure 1(a)). This fact will be discussed in the next section. One more aspect is conspicuous-compared to DFT results, experimentally observed indentation moduli are significantly reduced. Conceivable explanations for this discrepancy can be given considering pseudoplasticity and elasticity due to inter-martensitic phase transformation characteristics in NMG, respectively. As for pseudoplasticity, a schematic stress-strain diagram upon loading is sketched in figure 4(a): starting with single variant martensite, region I describes stress-strain dependence according to linear elasticity. Beyond a critical stress σ c (viz the 'twinning stress') pseudoplastic deformation occurs while tetragonal unit cells successively reorient (TB motion). This process is marked as region II. Once all unit cells are reoriented, the material again shows a linear elastic behavior (region III) at moderate further deformations. The magnitude of σ c for inducing TB motion substantially depends on parameters such as the straining direction and sample temperature, as well as intrinsic stress fields (e.g. lattice defects due to off-stoichiometry and other impurities). In the case of martensite NMG, it was shown that σ c ≈ 2-200 MPa is sufficient to cause pseudoplastic behavior [31,32]. It is necessary to emphasize that pseudoplasticity implies an irreversibility, viz a remaining strain or, deformation upon unloading.
Martynov and Kokorin [32] proposed that pseudoplastic deformation, induced by external stresses, can be accompanied by pseudoelasticity due to inter-martensitic phase transitions (10M→14M→non-modulated), whereas each martensite phase remains stable within a certain temperature interval. Conversely, at constant temperature, increasing shear stresses will favor phases/modulations with increasing tetragonality (i.e. non-modulated martensite), as described by the Clausius-Clapyron equation. The loading curve under these conditions follows a shape qualitatively akin to figure 4(a), while unloading is fully reversible with a hysteresis. Since visible plastic deformations-as observed in pseudoplasticity-are absent from the present CR-AFM measurements, this particularly favors the occurrence of inter-martensitic pseudoelasticity as the more probable mechanism. Due to the employed boundary conditions, very limited size of the simulation cell and rather moderate applied stresses in the calculation of the tensor of elasticity, twin boundary motion or phase transformation is intrinsically excluded in the present DFT calculations. In other words, the stress-strain relation assessed in DFT currently corresponds to the pure elastic region I (red line in figure 4(a)). As can be seen in table 2  In both cases, the very low stress regime is characterized by elastic deformation (region I), typically followed by a plateau (region II) dominated by the 'resistivity' of twinning dislocation motion (leading to variant reorientation or inter-martensite phase transformation in the case of pseudo plasticity and elasticity, respectively). Upon completion of reorientation or transformation (regime III), elastic response is again observed. (b) Distributions of the uniaxial vertical stress σ zz , uniaxial in-plane stress σ xx and principal shear stress τ = |σ zz − σ x x |/2 along the z-axis for a spherical and a flat indenter calculated according to Johnson [37]. A Poisson ratio of ν = 0.3 was assumed. (c, d) Contour plots of the uniaxial vertical stress σ zz and the radial stress σ r , respectively, for a spherical tip (ν = 0.3).
Nevertheless, the stress distribution in solids induced by indenters is complex and needs to be considered. Figures 4(c)-(d) show uniaxial stress distributions σ zz ( to 001 ) and (σ r ) (⊥ to the surface plane), induced by a spherical indenter (normalized to p m , the polar coordinates in surface plane). Referring to these stress distributions, the question arises as to whether they can conform to the assumption of stress-induced pseudoplastic deformation and intermartensitic transition. From a quantitative point of view, σ zz and σ r are large enough near the central region of the indentation spot to overcome σ c . Moreover, shear forces arising due to lateral and depth gradients of both stress states can cause plane shuffling and consequently transitions between different martensitic phases. Existing shear stresses within the material additionally need to be taken into account, as they might interfere with the nano indentation process. A generalized Clausius-Clapeyron approach can describe a shift of the martensite transition temperature T M due to thermal stresses within a film (dσ c /dT M = 2.2 MPa K −1 [33][34][35]). Sources of shear stresses include (i) thermal stresses by differences in thermal expansions of film and substrate, (ii) epitaxy misfit stresses and (iii) lattice defects. With the known chemical composition and T M (table 1) of NMG-1 as well as the phase diagram given in [36] and thermal expansion coefficients of film and MgO substrate, one can calculate the inplane biaxial thermal tensile stress as σ Th = 10-110 MPa. This rough estimation is due to the uncertainty of chemical composition in NMG-1 obtained by EDX measurements (see table 1). The orientation of σ Th , however, results in a constructive superposition with σ r since both are characterized by in-plane tensile straining the sample surface. Thermal stresses should thus not hinder possible pseudoplasticity as well as inter-martensitic transition provoked by the loaded cantilever tip. However, it was not possible for us to give a comparable quantitative estimation of stresses corresponding to (ii) and (iii) since the influence of substrate and related fixation of TB is poorly understood. Referring to the presence of different twin variants-with twin boundaries in between-the question arises how twin variants in figure 1(b) (variant 1: long a-axis out of the surface plane, variant 2: short c-axis out of the surface plane) differ in their mechanical properties. As will be shown in the next section, no recognizable differences between both crystal orientations were measured with CR-AFM. This finding clearly cannot be explained by a sole elastic response, since DFT predicts significantly different values for M [100] and M [001] .
As an additional confirmation of this picture, temperature-dependent CR-AFM measurements are currently carried out on as-deposited and lift-off films.

CR-AFM imaging: surface artifacts and twin boundaries
Since tip-surface contact at the nanoscale is a complex phenomenon influenced by various interaction mechanisms, AFM-based imaging techniques 11 often need to deal with disturbed data which complicate subsequent analysis. Regarding CR-AFM measurements presented here, surface roughness in particular strongly affects the contact area-resulting in CRF shifts that do not correspond to real mechanical characteristics. This key problem requires an even more critical review when surface features are of a similar lateral size to the scanning probe tip. The increased error of indentation modulus for NMG-1, mentioned in the previous section, can be assigned to that interplay, as illustrated in figure 5. The overlaid CRF colormap suggests asymmetric elastic properties of twin patterns. Considering schematic 1(b), one first tends to conclude that this behavior could be addressed to different orientations of orthorhombic unit cells (interchange of the a and c axes) on both sides of the pattern. This argument can be checked by rotating the whole sample around 180 • and repeating the measurement. Pure mechanical influences would also cause a rotation of the CRF colormap. The experiment, however, does not confirm this initial guess (see figure 5), indicating artifacts due to topography and nonaxis symmetric tip shape. This is confirmed by measurements with a more blunted tip and 11 For example, magnetic force microscopy (MFM) and piezo force microscopy (PFM). a shape closer to rotational symmetry. The CRF color-contrast for that tip is symmetrically distributed over the twin pattern, whereas elevated regions appear 'softer' than lower ones (not shown here) because of varying interaction area. However, a precise decomposition of CR-AFM contrast in real mechanical fluctuations, on the one hand, and surface artifacts, on the other hand, is non-trivial. Consequently, an elimination of twin structure surface features by changing the lattice orientation is helpful. One further NiMnGa sample (NMG-2) was produced with modified processing parameters. A lateral temperature gradient within the substrate was sustained during deposition. The chemical composition of NMG-2 is nearly identical to that of NMG-1. Besides the typical twin pattern (according to figure 1(a)) the sample additionally yields microscopic domains with a flat non-patterned surface ( h RMS ≈ 0.3 nm). A CR-AFM image utilizing a cantilever MPP130-1 was performed near the boundary of two domains (see figure 6). As can be seen, the non-patterned region clearly reveals a periodic mechanical contrast ('stripes') not corresponding to surface features. The in-plane angle of these stripes compared to the patterned twin domain amounts to exactly 45 • . This can be understood considering constraints of epitaxial growth on MgO and figure 6. Non-patterned regions are characterized by a change of crystallographic orientation, where the aand c-axis now lie in the surface plane (b-axis out of plane). Pure mechanical variations are thus only caused by highly ordered TB and amount to M ≈ ±4 GPa, which is about one third lower than the error of M for NMG-1 (see table 2). From this comparison it can be seen that even slight surface features such as periodic twin structure can disturb CR-AFM data. One should remember that no surface damage is caused by CR-AFM imaging, as can be seen by comparing figures 5 and 1(a). It is also noticeable that these TB are highly ordered plane-like (viz two-dimensional) defects with an orientation perpendicular to the sample surface (see scheme (b) in figure 6) but drop M roughly about 8 GPa in total. Considering that the indentation modulus M is an average value over the tip-surface contact area of A = π a 2 c,sphere with a c,sphere 15 nm, one can conclude that the presence of TB significantly affects local mechanical characteristics. This finding perfectly agrees with the generally accepted notion that macroscopic deformation by reorientation of martensite variants at existing TB (movement of TB) is preferred to generating new TB within a martensite variant.

Conclusions
Elastic properties-i.e. elastic constants C i j and corresponding indentation moduli M DFT -of 14M modulated martensite Ni-Mn-Ga were calculated for the first time by a DFT approach.
Considering DFT calculations of [38] for austenite, 5M modulated and non-modulated martensite Ni-Mn-Ga, the present data set gives suitable predictions regarding elastic behavior of 14M modulated Ni-Mn-Ga. These results were compared to an experimental indentation modulus M exp of epitaxial grown 14M modulated Ni-Mn-Ga thin films, obtained with CR-AFM-a recent promising technique for non-destructive investigation of mechanical surface properties with nanoscale resolution. It was found that M exp is about three times lower than M DFT . Based on the results published in [32] and a consideration of stress distributions induced by an indenting cantilever tip, it is assumed that pseudoplastic deformation as well as pseudo elastic inter-martensite phase transitions could explain these findings. Complementary studies to verify these suggestions will be undertaken in the future. In particular, temperature-dependent CR-AFM measurements and comparisons to lift-off Ni-Mn-Ga thin films need to be carried out. Furthermore, limitations of CR-AFM were carefully investigated within the present work. In particular, highly periodic topographic features with lateral dimensions comparable to tip radii disturb experimental results and call for attentive data analysis. It was shown for the first time that lateral highly resolved CR-AFM mechanical contrast imaging enables the visualization of twin boundaries due to their characteristic influence on nanomechanical material properties. M exp decreases about 13% at such highly ordered lattice defects for the utilized tip.