SEM image of the ZnO nanowires. The inset is the magnified SEM images of the ZnO nanowires.
(a) A typical SEM image for the fixed GaN nanowires on a Si substrate by Pt deposition; (b) the corresponding SFM contour image scanned by a Berkovich indenter .
(a) A SEM image of a fixed GaN nanowire on a Si substrate by Pt deposition; (b) the corresponding SFM contour image scanned by a Berkovich indenter; (c) the topographic profile corresponding to the black line in (b), which is consistent with the shape of a Berkovich indenter as in Fig. 4(c).
(a) The top-view schematic of a blunt tip scanning a nanowire with a radius; (b) the calculated scanning profile of the nanowire along the dashed line in (a) for a blunt cube-corner indenter with a tip radius; (c) the calculated scanning profile of the nanowire along the dashed line in (a) for a blunt Berkovich indenter with a tip radius; (d) a contour image of a nanowire with a radius scanned by a Berkovich indenter [the scanning direction is not exactly as the dash line in (a)]; (e) the topographical profile corresponding to the black line in (d).
The schematic of the indentation of a nanowire on a substrate (half-space). For very small indentation depths, the indenter can be modeled as a spherical indenter.
The plot of and vs . is also plotted as a dashed line.
The schematic of receding contact for an unbonded elastic layer with thickness equal to or an unbonded cylinder with a diameter equal to on a frictionless elastic half-space.
vs for the plane strain and axisymmetric problems with an applied concentrated force .
The relation between and for various values of for evenly distributed forces.
for various for fixed . All forces are evenly distributed except the data with the triangular symbol.
versus for the plane strain and axisymmetric problems.
The contact zone for an unbonded cylinder pressed against a rigid half-space by evenly distributed concentrated forces on the top of the cylinder. (This graph is extracted from Ref. 34).
The flow chart for calculating the lower bound of the hardness of a nanowire using the nanoindentation data. (The upper bound of the hardness can be obtained using a similar procedure, except that Eq. (6) is replaced by Eq. (8) and that in Eq. (2a) is replaced by .)
Central sections of the elastic modulus surfaces for GaN and ZnO calculated from the elastic constants in Table I.
(a) Two typical curves for GaN and ZnO nanowires; (b) the curves for GaN and ZnO nanowires, where there are two sets of data for GaN and there are three sets of data for ZnO; the solid lines are polynomial fits of the corresponding data.
(a) The SFM contour image of a GaN nanowire before indentations [/contour for (a)–(c)]; (b) the image after a indentation; (c) the image after another indentation as in Fig. 15(a); (d) the topographical profiles along the black lines in (a)–(c).
The original and computed data for nanoindentations of a ZnO nanowire and a GaN nanowire : the stiffnesses vs the load in (a) and (b); the displacements vs in (c) and (d). The meaning of subscripts are as follows: 1 the values for the contact between nanowires and the indenter, 2 the values for the contact between nanowires and the substrate, and the elastic components. This meaning of subscripts is also applied in Figs. 18 and 19.
The computed contact dimensions for nanoindentations of the nanowires: the contact lengths vs in (a) and (b); the contact widths vs in (c) and (d).
The computed hardness for nanoindentations of the nanowires, where can be treated as the hardness of the nanowire. Here, (c) and (d) are the results in the valid range by considering the requirements in this section. The meaning of the extra subscripts are as follows: the values calculated using the standard Oliver-Pharr method (Ref. 13); the values calculated using the Joslin-Oliver method [see Eq. (12)] (see Ref. 46).
The comparison of the calculated Oliver-Pharr moduli with the bulk values for the two nanowires. Here, the subscript “bulk” stands for the bulk values as shown in Table I.
The elastic constants and some related values. [ and are the hardness and Young’s modulus for bulk single crystals measured using nanoindentation (Refs. 37 and 39–43). The elastic constants are referred to Refs. 37 and 39–44. and are Hill’s averages for Young’s modulus and Poission’s ratio of single phase polycrystalline materials (Ref. 37). and are anisotropy factors for hexagonal crystals45 (for cubic crystal is 1.0 automatically), and they are 1.0 for isotropic materials. is defined in Eq. (4) and calculated using and .]
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