As much as both titanates are miscible in each other, the peak shift is linear and continuous between the extreme compositions; that is, it follows Vegard's law. However, the presence of the metastable tetragonal phase is possible due to the presence of oxygen vacancies [11,12].
Composition values x were obtained by considering that that peak shift follows Vegard's law with the extreme values corresponding to those of SrTi[O.sub.3] (x = 0) and BaTi[O.sub.3] (x = 1).
Points were fitted with a straight line corresponding to Vegard's Law:
Table 4 presents the A, B, and [R.sup.2] values, which indicate a linear relation of the composition of the cubic BST-SS with Vegard's law as observed in Figure 5(a).
For this case, Vegard's law has been applied, which states that the lattice parameters of an alloy will vary linearly between the end members.
where [c.sub.AlInN] and [a.sub.AlInN] are the measured lattice parameters (which take into account strain), [c.sub.o] and [a.sub.o] are the relaxed parameters predicted by Vegard's law, and [C.sub.13](x) and [C.sub.33](x) are elastic constants linearly interpolated from the binary values.
The inplane and out-of-plane strain components can be defined as [[epsilon].sub.xx] = [[a.sub.meas] - [a.sub.0]/flo] and [[epsilon].sub.zz] = [[c.sub.meas]/[c.sub.0] - where [a.sub.meas] and [c.sub.meas] are the measured lattice parameters, while [a.sub.0] and [c.sub.0] are the relaxed parameters given by Vegard's law [31, 33].
TABLE 1: The In content (x), lattice parameters [a.sub.meas] and [c.sub.meas] and the strain components [[epsilon].sub.zz] and [[epsilon].sub.xx] of the AlInN epilayers, calculated from the RSM measurements and the relaxed lattice parameters [c.sub.0] and [a.sub.0] of the AlInN epilayers calculated by using Vegard's law are given in column 4 and 5, respectively.
Their fundamental structural properties (type of crystal lattice, Vegard's law, Kufala equation: the dependence of the band gap on the composition, etc.) are similar to [Al.sub.x][Ga.sub.1 - x]As solid solutions.
Thereby, Vegard's law for solid solutions [([Al.sub.x][Ga.sub.1-x] [As.sub.1-y][P.sub.y]).sub.1-z][Si.sub.z] can be written in general form as follows:
Assuming that Vegard's law is obeyed for the obtained [([Al.sub.x][Ga.sub.1 - x][As.sub.1 - y][P.sub.y]).sub.1 - z][Si.sub.z] solid solutions, we specified the concentrations of the elements (see Table 3) analyzing expressions (1)-(3) and calculation of the lattice parameters and data from microanalysis.
Based on the above linear interpolation for Vegard's law we can similarly use the relation between the band gap and the atomic concentration for five-component [([Al.sub.x][Ga.sub.1 - x][As.sub.1 - y][P.sub.y]).sub.1 - z][Si.sub.z] solid solutions.