The results of the direct quasistatic calculations

The results of the direct, quasistatic calculations of the bulk value of the Young׳s modulus in step (2) are summarized in Table 2. k-points for the tetragonal and orthorhombic unit Tubastatin A were also chosen according to the Monkhorst–Pack scheme. In Table 2 the number of divisions n, however, refers to an approximately equivalent (n, n, n) k-point mesh for the conventional 4-atom cubic unit cell with lattice constant a. The lattice vectors of the tetragonal and orthorhombic unit cells have lengths of , and . Thus, in the actual calculation divisions of , and of the corresponding reciprocal basis vector, rounded to the next larger integer number, were used. For a Gaussian smearing of σ=0.015Ry the SOEC were well converged for a k-point density of 28 and 24 (see Fig. 1). For this σ-value and the k-point mesh with n=28, however, the Young׳s modulus calculated by quasistatic tensile test still deviates by 1.8GPa from the analytic value calculated from the SOEC (see Table 2). For a better agreement between direct calculation and analytic result from SOEC for , σ has to be lowered to 0.010Ry and the k-point density has to be increased to n=32. With the settings of σ=0.015Ry and the k-point mesh of n=28 the error margin of the DFT calculations is more than 1GPa, for σ=0.010Ry and the k-point mesh with n=32 the numerical uncertainty is reduced to about 0.3GPa. In Table 3 the calculated Young׳s moduli for the orthorhombic unit cells with twin boundaries are compared to their corresponding values for the defect-free bulk. For the calculations with σ=0.015Ry and the k-point mesh with n=28 the results for for cells with and without twin boundaries are within our estimated error margin. For these settings the unit cells with twin boundaries were also strained in [112]-direction, which is the actual orientation of the nanowires in the experiments of Ref. [1], but no significant difference between and is observed. For the more accurate settings with σ=0.010Ry and a k-point mesh with n=32, the Young׳s modulus is systematically smaller for cells with twin boundaries than the bulk value, and decreases systematically with increasing twin boundary density. However, even for the highest density of twin boundaries, in which twin boundaries are separated by only 3 atomic planes, the change in is less than 2% compared to the bulk. This can be taken as an upper limit for the modification of Young׳s modulus due to twin boundaries in Ag.
Acknowledgments This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) via the Cluster of Excellence EXC 315 “Engineering of Advanced Materials”.
Materials and methods Synthetic benchmarks were an alternative to the real measurements at the middle stage of the Neurochem project, when the main sensor array of the project was under development [2]. The realization of the synthetic experiments required a model of an array of gas sensors. That model needed to capture the main features shown by polymer sensors (the reference data set was measured with an array of conducting polymer sensors) and be simple enough so that it could be included in the system software. The model was implemented in the data simulation tool (the R package chemosensors) [1,3]. The synthetic benchmarks produced for the three scenarios classification, segmentation and sensor damage possess a particular feature of the large number of sensors (1020). This feature will particularly suit for examination of the role of diversity and redundancy among the sensors at large scale. Recent examples of the data analysis based on real large sensor arrays include an array of 96 metal-oxide sensors combined with 10 different sensor families modulated in temperature [5], and an array of 16,384 conducting polymer sensors based on 24 different kinds of polymer materials [6] (both arrays are products of the Neurochem project).