Possess a silicon core that is coated with one hundred nm of nitrogen doped conductive diamond. The standard tip curvature radius is 100 nm, and the cantilever’s spring continual is between two.five and 10 Nm.SCIentIFIC REPORTS | (2018) 8:422 | DOI:ten.1038s41598-017-18843-www.nature.comscientificreportsFigure 1. (a) Illustration of the laboratory reference method “attached” to the cantilever, as well as the directions of your corresponding converse piezoelectric displacements induced by the electric field Ez in the tip. (b) Schematic of your relation of the piezoelectric surfaces plus the polarization vector with respect to the measurement path. The orientation in the polarization vector has to be varied to simultaneously match dzz, dzx and dzy onto the piezoelectric surface.Measurement procedure.As talked about above, for vector PFM 1 out-of-plane and two in-plane measurements are necessary for any full reconstruction in the polarization orientation. The two in-plane components need to be measured for two independent directions. Practically this implies that the sample has physically to be rotated by 90 Soon after rotation a relocation of the probe to the very same location is needed, which may be rather challenging. Here, the rotation and relocation was performed manually and required additional overview scans so that you can find the right location once again. So that you can facilitate the identification from the same measurement area, regions have been preselected that showed distinct surface functions like pores or scratches which acted as orientation marks. Initially, 80 80 topography overview scans were recorded in the preselected places. Within these areas, the final 10 10 areas for inspection were defined. The very first two measurements which are one VPFM and one particular LPFM measurement for the out-of-plane and one particular in-plane component can conveniently be measured with no moving the sample. For the second in-plane measurement, the sample rotation must be carried out. The complete vector PFM data then includes 6 data sets which are the X-, and Y-LIA data for the three components of piezoresponse in x, y, and z.Data evaluation. The theoretical background for quantitative vector PFM has been elaborated within a series of papers22,273. The theoretical Fmoc-Gly-Gly-OH Protocol successful piezo-coefficients of tetragonal material (point group four mm) “as observed in the tip” in x-, y-, and z-direction is usually expressed as30:dzx = – (d 31 – d 33 + (d15 + d 31 – d 33) cos(2 )) cos sindzy = – (d 31 – d 33 + (d15 + d 31 – d 33) cos(2 )) sin sindzz = (d15 + d 31) sin2 cos+ d 33 cos3(1a) (1b) (1c)Right here, and will be the Euler angles describing the transformation involving the crystal coordinate method plus the coordinate program defined by the AFM cantilever (see Fig. 1a). Within this case, denotes the angle among the path of your electric field (surface normal) plus the [001] crystallographic axis on the grain below test. Note that because of the tetragonal symmetry only two Euler angles are required to get a description rather than three as for the general case. In our case, we’ve got defined our laboratory coordinate method like indicated in Fig. 1a. Once the displacements (truly, their relative magnitude to each other) as well as the piezo-coefficients dij are known, the relative orientation with the nearby polarization vector can in principle be reconstructed together with the support on the method of Eq. 1a . On the other hand, Equ. 1 is overdetermined, hence it could only be solved approximatively. Ideally, it could be enough to solve only two in the equations, and also the t.