considered as Ge dots in Si host. The large dm/dP observed in our NCs (in SiO2 host) can be explained if we assume that the effective pressure acting on the NCs is different from the applied pressure. This effect has been observed by Haselhoff et al. [46] for CuCl NCs in alkali-halide matrices. However, in their model the strain at the interface between the NCs and the matrix was not taken into account.
As shown in Figure 12.13, we have performed the pressure dependence study of the Ge-Ge modes of the NCs for one pressure cycle and there is no hysteresis observed. This confirms that the pressure-induced strain in the NCs is reversible. With this elastic behavior of our Ge/SiO2 NCs-matrix system, we assume both the NCs and the matrix as isotropic elastic continua [46]. We modeled the NC as a sphere of radius r1 in a spherical SiO2 matrix of radius r2, where r2 > r1. The system is subjected to a hydrostatic pressure P. Using spherical co-ordinates with the origin at the center of the NC sphere, our system has a spherical symmetry where the displacement vector u is everywhere radial and can be written as u = ar + b/r2. The components of the strain tensor are urr = a - 2b/r3 and ugg = u^ = a + b/r3. The constants a and b are determined from the boundary conditions. At the interface between the NC and the matrix, the interface strain is given as 8 = u\g - ule, where ul66 and u2ee are the strain tensor of the NC and the matrix, respectively. From the boundary conditions at r1 = r2, the effective pressure PNC at the NC is given by [47]
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