We demonstrate direct evidence that the strain variation induced by local lattice distortion exists in the surface layers of SnO2 nanowires by coupled scanning transmission electron microscopy and digital image correlation techniques. First-principles calculations suggest that surface reduction and subsurface oxygen vacancies account for such vigorous wavelike strain. Our study revealed that the localized change of surface atomistic configuration was responsible for the observed reduction of elastic modulus and hardness of SnO2 nanowires, as well as the superior sensing properties of SnO2 nanowire network.

It has proven that surface atomistic structure plays a critical role in properties of nanostructures. Numerous models have been developed to correlate the nano-properties with surface features. For mechanical properties, surface tension,1 surface relaxation,2 surface stress,3 and surface energy density gain4 have been proposed to be responsible for the size-effect. For metal oxides, surface atomistic structure has an even stronger influence due to mixed ionic and covalent bonds. Most of the previous studies focused on theoretical calculations while direct and detailed experimental evidence of the surface atomistic structure correlating to unique nano-properties is yet lacking to fully address its importance.

Recently, surface reconstruction induced change in surface stress was used to explain stiffening in ZnO nanobelts with the aid of high resolution transmission electron microscopy (HRTEM),5 which showed great potential for probing the surface effects of nanostructures.6 Such findings raised questions on some assumptions made in classic surface analysis, e.g., distortion of unit cells concentrates on only a few outermost layers if not considering additional adsorbed molecules.7 In this study, we focus on elucidating how the surface atomistic strain field in nanowires can be mapped with coupled scanning transmission electron microscopy (STEM) and digital image correlation (DIC) techniques. Furthermore, how such results yield information on local surface structure, thereby better explaining the unique mechanical and sensing properties of nanowires.

Our subject is rutile-SnO2, a wide band gap (3.6 eV) semiconductor desirable in various applications including sensors, lithium-ion batteries, solar cells, and supercapacitors.8,9 A rich family of 1D SnO2 nanostructures has been synthesized in the past decade.10,11

In this letter, SnO2 nanowires were synthesized at 880 °C.12 As indicated by Figs. 1(a) and 1(b), the as-synthesized products varied extensively in thickness-to-width ratio. Vapor-solid (VS) route is the governing growth mechanism due to absence of catalyst particles on nanowire tips. Single phase of the final product is indicated by X-ray diffraction (XRD) spectrum in Fig. 1(c). No traceable impurities can be found from X-ray photoelectron spectroscopy (XPS) or energy-dispersive X-ray (EDX) near surfaces of nanowires.12 HRTEM analysis in Fig. 1(d) unveils a dominant growth direction of [101], similar to the literature.10 

FIG. 1.

Typical morphology of SnO2 nanowires under (a) SEM (cross-section shape and high purity of the nanowires are indicated by the high magnification image and EDS spectrum in the inset) and (b) TEM. (c) XRD pattern of as-synthesized nanowires shows SnO2 peaks exclusively. (d) HRTEM demonstrates a growth direction of [101].

FIG. 1.

Typical morphology of SnO2 nanowires under (a) SEM (cross-section shape and high purity of the nanowires are indicated by the high magnification image and EDS spectrum in the inset) and (b) TEM. (c) XRD pattern of as-synthesized nanowires shows SnO2 peaks exclusively. (d) HRTEM demonstrates a growth direction of [101].

Close modal

Nanoindentation was used to analyze their deformation behavior.12 Most examined nanowires have a rectangular cross section, as illustrated in Figs. 2(a) and 2(b), with width ranging between 100 and 250 nm. Forces ranging from 50 to 200 μN were elaborately picked to minimize substrate and sample size effects.13–15 The contact radii were controlled <30% of the nanowire width as in Fig. 2(c). Oliver-Pharr method16 was applied on unloading curves represented in Fig. 2(d), during which a Poisson's ratio of 0.29 was assumed for SnO2. As shown in Fig. 2(e), the averaged elastic modulus (E) and hardness (H) were 66.43 ± 9.03 GPa and 6.98 ± 0.85 GPa, respectively, comparable to the previous reports.17–19 Despite differences between the methods, all results acquired are critically lower than the bulk modulus (∼212 GPa)20 with 70% reduction in our case. We know such unusual decrease attributes to special surface status, but what exactly happened?

FIG. 2.

AFM images display (a) a SnO2 nanowire, (b) its cross-sectional profile, and (c) an indent mark on top-surface. (d) Typical loading-unloading curve with the loading-segment profile and (e) modulus/hardness values summarized.

FIG. 2.

AFM images display (a) a SnO2 nanowire, (b) its cross-sectional profile, and (c) an indent mark on top-surface. (d) Typical loading-unloading curve with the loading-segment profile and (e) modulus/hardness values summarized.

Close modal

To answer this question, the cross-sectional morphology and surface atomistic structure of the nanowires were further studied with HRTEM. A dark-field STEM detector was used to collect electrons scattering between 50 and 285 mrad. Typical imaging beam current was 10 pA. Figs. 3(a) and 3(b) demonstrate a cross-section, close to a square, prepared by microtome. Due to the symmetric shape of the cross-section, plastic deformation during sectioning was ruled out. According to the diffraction pattern, the nanowire grew with an axial (201¯) growth plane (or along [101¯] direction) and was enclosed by ±(010) and ±(101) facets. HRTEM further discloses that each corner of the cross-section is composed of small (101) and (110) facets. Such configuration is understandable due to similar surface energies of these low-index planes.21 Additionally, stacking faults and steps were found abundant on the surface (Fig. 3(c)).

FIG. 3.

(a) HRTEM unveils a rectangular cross-section enclosed by (101) and (010) surfaces. (b) Atomistic details of the noted areas in (a) showing (101) surface and minute facets on each corner. (c) Surface defects, i.e., stacking faults and step sites. The atomistic simulation was simulated by EDM package. (d) Slab model for DFT calculations representing bulk-terminated (upper) and reduced (bottom) (101) surface of rutile-SnO2. (e) Line profile of inter-layer distance measured near surface imaged by STEM. (f) DIC conceived radial strain (εyy) map on the identical image.

FIG. 3.

(a) HRTEM unveils a rectangular cross-section enclosed by (101) and (010) surfaces. (b) Atomistic details of the noted areas in (a) showing (101) surface and minute facets on each corner. (c) Surface defects, i.e., stacking faults and step sites. The atomistic simulation was simulated by EDM package. (d) Slab model for DFT calculations representing bulk-terminated (upper) and reduced (bottom) (101) surface of rutile-SnO2. (e) Line profile of inter-layer distance measured near surface imaged by STEM. (f) DIC conceived radial strain (εyy) map on the identical image.

Close modal

For surface structure, we focus on the (101) surface since it is dominant according to HRTEM and previous literature6,17 and is of particular interest for sensing.22,23 STEM was applied due to its superior atomic-number related contrast which ensured accurate imaging of Sn atoms alone, making the atomic-scale profile imaging more explicit. One has to keep in mind that two extra layers of O are located between consecutive Sn layers, as sketched in Fig. 3(d). In the STEM images, the inter-Sn layer distance, h, can be considered as an indicator for lattice parameter (a) change, or even for the modulation in bond length. In this case, hasin55.97° according to density functional theory (DFT) calculated parameters. According to our observation, the line-profile of h along radial direction of the nanowire has a wavelike characteristic as shown in Fig. 3(e), indicating the existence of alternative strains deep into the surface, similar to recent observations5,6 and contradicting classic models. However, can single line profile(s) be representative for the overall strain status? A “strain map” is ideal to resolve such controversy.

Due to the excellent contrast and resolution of STEM, one can realize such a “map” on a large scale through DIC by comparing the true atomistic arrangement with ideal cells.12 It should be noted that all the discussions below are based on the radial direction (εyy), since the strain on the axial direction (εxx) is exceedingly small and uniform.12 In Fig. 3(f), an area of 50 atoms by 60 layers is analyzed. DIC yields an average εyy of 0.4% and a maximum strain of approximately ±15%. The most notable feature unveiled by the map is that large, oscillatory strains (tensile strain is dominant) exist among the first few layers.

Similar features were detected in other nanowires as well,12 proving that such result is representative for the superficial status. Moreover, DIC reveals a much stabilized strain near the center of nanowires.12 Statistical study on over 800 layers from more than 10 HRTEM images also confirmed that strains near nanowire surface can be ∼22%, which obviously cannot be explained alone by experimental noise.12 Accordingly, it is obvious that the observation in Fig. 3(f) was not attributed to noise fluctuation during STEM imaging.

Why are such oscillatory strains present near the nanowire surface? It is well-known that the (101) surface can be terminated either by O (stoichiometric composition) or by threefold-coordinated Sn (reduced composition), as shown in Fig. 3(d), since Sn can be easily reduced due to its dual valency and stability against reconstruction.24 DFT calculations indicate that energy to convert a bulk-terminated surface to an oxygen-resolved surface is 1.80 eV/O atom,12 a value easily fulfilled by the synthesis temperature. Details of the slab model can be found in supplementary material. There are four layers of Sn atoms and eight layers of O atoms in our slab supercell. At each surface layer, there are two atoms. We also used a thicker slab containing 6 Sn layers 12 O layers. Increasing the thickness only caused negligible changes to the surface formation energy and the strain.12 Thereby, it is highly likely that our nanowires possess dominant reduced (101) surfaces, which is also supported by other reports.6 However, surface reduction alone cannot lead to the considerable strains observed since relaxation of most stable surfaces is often the weakest. A detailed DFT examination on how the surface reduction changes the distance between the neighboring Sn layers proved such trend.12 

Then, what else can lead to such strains? A highly reduced surface could be considered low-energy sites for adsorbing oxygen atoms, hence facilitating the formation of subsurface oxygen vacancies (OVs).25 While quantitatively analyzing EDX and XPS results, the atomic ratio Sn:O was found to be 1:1.80–1:1.96,12 indicating presence of such OVs. Such hypothesis is confirmed by our DFT calculation. It notes that the OVs in n-type SnO2 crystal are stable in a neutral (0) charge state.26 As demonstrated in Fig. 4(a), oxygen deficit reduced surface (with 4% subsurface OVs in the reduced surface) was predicted to have even lower surface energy than the simple reduced surface at synthesis temperature.

FIG. 4.

(a) Formation energy of bulk-terminated, reduced, and oxygen deficit reduced (101) surface as a function of oxygen chemical potential. (b) Variation of the energy per surface area of reduced (101) surface slabs as a function of applied strain along [101¯]. (c) Influence of bond length expansion on E of a single lattice cell.

FIG. 4.

(a) Formation energy of bulk-terminated, reduced, and oxygen deficit reduced (101) surface as a function of oxygen chemical potential. (b) Variation of the energy per surface area of reduced (101) surface slabs as a function of applied strain along [101¯]. (c) Influence of bond length expansion on E of a single lattice cell.

Close modal

Different types and concentration ratios of OVs have a fundamental impact on physical properties of SnO2.27,28 Nevertheless, the relaxation led by such OVs has not been considered before. Accordingly, we removed monolayers of O in between consecutive Sn layers in the (101) reduced surface in DFT. After fully relaxing the ionic positions, significant strains between the Sn layers were found in different cases as listed in Table I, well consistent with the maximum strain identified in Fig. 3(f). Consequently, DIC and DFT results concur to define a strongly reduced surface with high oxygen deficiency level. The formation of OV clusters below the surface induces large, oscillatory strain near the surface.

TABLE I.

Energy to remove monolayer of O from a reduced (101) surface and the resulting strains, i.e., the change in h between consecutive Sn-atom layers near the surface (labeled as Sn1, Sn2, and Sn3) as compared to the bulk crystal.

PositionFormation energy (eV/O)Strain between Sn1 and Sn2 (%)Strain between Sn2 and Sn3 (%)
First layer 4.31 −6.7 +0.7 
Second layer 3.83 +22.1 +0.5 
Third layer 4.05 +2.0 +6.0 
Fourth layer 4.03 −1.4 +13.2 
PositionFormation energy (eV/O)Strain between Sn1 and Sn2 (%)Strain between Sn2 and Sn3 (%)
First layer 4.31 −6.7 +0.7 
Second layer 3.83 +22.1 +0.5 
Third layer 4.05 +2.0 +6.0 
Fourth layer 4.03 −1.4 +13.2 

Current finding can help understanding some overlooked details on the “actual surfaces” of nanostructures and their profound impact on nano-properties. First, the characteristic length defining the surface was only a few angstroms in the previous continuum and quantum mechanics schemes.29,30 Our results indicate a different story for complex system, as intensive radial strain can be even identified a few nanometers down into the free-surface, likely led by defect formation. One can be amazed how a few nanometers can make a huge difference.

Take mechanical properties for an example, we inferred the mechanical behavior with different surface configurations from the stretching tests of the (101) surface slabs with DFT method. The results reveal that the bulk-terminated surface would decrease its potential energy under (axial) compressive strain up to 2.5%,12 whereas the reduced surface would decrease energy under tensile strain up to 1.5% (Fig. 4(b)). We have elaborated that the Young's modulus of the nanowire would be lower than bulk value if the external surface favors expansion,3,31 just as the case of the reduced (101). On the contrary, the bulk-terminated surface should lead to higher modulus.

DIC results further unveiled another reduction mechanism led by subsurface defects.32 The origin of elastic modulus is the second derivative of the net potential between two neighboring atoms. Introducing defects into the cell will change the equilibrium distance (bond length), thus altering the cell parameter and modulus. As mentioned earlier, inter-layer distance (h) is an indicator of the cell parameter. The modulus of a cell with defects can be expressed as a function of h as12,33

E=(a0a0*)qE*=(h0h)qE*,
(1)

where E* is the elastic modulus for stoichiometric configuration, a0 and a0* are the cell parameters in vacancy-introduced and stoichiometric configurations, respectively, and h0 is the distance between two Sn-layers in stoichiometric lattices. For ceramics (mixed ionic and covalent bonds), constant q lies between 4 and 15.33 A simple fitting in Fig. 4(c) illustrates that E of a lattice cell can easily decrease 70% with the strain level in the DIC results. Since nanoindentation is extremely sensitive to local features, we believe that the dramatic decrease in E is led by complexity of the surface configuration, i.e., reduced surface and OVs.

In a more general sense, E of 1D nanostructures could be simplified with a rule of mixture between surface and core.34 In classic schemes, depth of “surface” was about 10 Å, which is feasible for defect free, perfectly relaxed surfaces. However, in current case, our results extend such depth to a few nanometers. Clearly, one might have yet underrated the surface effects in nano-mechanics.

The decreased indentation hardness value of the nanowires is also noticed without obvious indentation size effect (ISE). The reduction is comparatively mild as the bulk hardness is 10–12 GPa.35 Aside from the common sources of errors in nanoindentation,36 which were attentively taken care of, the localized subsurface defects might also contribute extensively to such deviation: OV-clusters can be considered pre-existing dislocations, which reduce energy for dislocation initiation and propagation, thus facilitating local plastic deformation and decreasing hardness.

Apart from the deformation behavior, we also tried to get a deeper understanding of another surface-related event, gas sensing mechanism. Measurements were performed on SnO2 nanowire networks grown on stainless-steel substrates. Such networks can detect down to 1 ppm of NO2 gas with a response of ∼92.5% and work stably under elevated temperature (200 °C) as illustrated in Fig. 5. The response of the sensor is defined as the ratio of the electrical resistance in NO2 (Rg) to that in air (Ra).

FIG. 5.

Response of SnO2 nanowire network exposed to NO2 under (a) room temperature and (b) 200 °C. (c) Optimized structure of NO2 molecule adsorbed on a reduced (101) surface.

FIG. 5.

Response of SnO2 nanowire network exposed to NO2 under (a) room temperature and (b) 200 °C. (c) Optimized structure of NO2 molecule adsorbed on a reduced (101) surface.

Close modal

Although drop in conductance for SnO2 nanoribbons on stoichiometric (101) surface was explained,22 reduced, even defective surface condition has not been considered. Subsurface OVs act like low-energy sites for absorbents and can n-dope SnO2.37 Accordingly, details in surface configuration of the nanowires can alter local energy gap, leading to tuning of sensing capability.

We used DFT to simulate the absorption of NO2 on reduced (101) surfaces. It was found that NO2 would favorably adsorb on top of Sn atoms as shown in Fig. 5(c), with a low adsorption energy of −0.63 eV. O atoms in NO2 molecule would form two Sn-O bonds (bond lengths of 2.65 and 2.41 Å). Bader charge analysis38 showed that 0.81 electron would transfer from the surface to the adatom with this configuration, much higher than that of the possible configurations on a stoichiometric surface.12 Thus, the adsorbed NO2 molecules would trap most electron charges on a reduced (101) surface, leading to the high sensitivity of as-synthesized nanowire networks.

In summary, by coupling STEM and DIC techniques, atomic-scale imaging correlation mapped local strain induced by lattice distortion in the surface layers of SnO2 nanowires. With the help of DFT, a reduced surface configuration with subsurface oxygen vacancies was unraveled. The vacancies were found responsible for the large and vigorously alternating strains identified by DIC. Such configuration better explains the size effect on mechanical properties measured by nanoindentation, unveiling a mixed effect from surface energy and expanded bond length due to vacancy formation. Such configuration also better explains the superior gas sensing capabilities of nanowire networks.

Financial support for this study was provided by the U.S. National Science Foundation (CMMI-1418696, CMMI-1358673, and CMMI-0824728) and the U.S. Army Research Office under Agreement/Grant No. W911NF-08-0299. G.W. also acknowledges Grant No. DE-FG02-09ER16093 from Department of Energy. The authors thank the University of South Carolina EM Center staff members for SEM support.

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Supplementary Material