In the acoustic coupling performance experiment element
Lattice spacing as a function of the Cr3+ concentration shows the Gaussian-type behaviour as presented in Fig. 2. As mentioned above, at the lower mol%, the increase in lattice spacing is attributed to the substitution of Al3+ by the Cr3+ BMH-21 at the octahedral sites as shown on the inset in Fig. 2. However, as the Cr3+ mol% was increased further, the increase in lattice spacing reached a critical point at 0.065±0.002% Cr3+ and then started to decrease as the Cr3+ mol% was increased further. It is important to note that we have observed similar kind of behaviour departing from the Virgard?s law in our recent results  and the ref therein. Our previous results  have indicated that for some materials such as ZnAl2O4, the Vergard?s law can be obeyed and disobeyed but that depends on the dopant concentration. In the current results, it is concluded that the decrease in lattice spacing above the critical point was certainly due to the substitution of the Zn2+ by the Cr3+ ions as well (see insert in Fig. 2). Therefore, in such cases the Cr3+ ions occupies the tetrahedral site in the host matrix. Without any doubt this results suggest that, depending on the mol%, Cr3+ ions can occupy either the octahedral or tetrahedral sites in the ZnAl2O4 host matrix, which is in good agreement with Dong et al.  results. Their results  showed special senses the luminescence properties of Cr3+ ions depend strongly on their coordination, crystal field and lattice imperfections. For an example, when Cr3+ ions occupy sites with strong or intermediate crystal field, the lowest excited state is the 2Eg level, which will be responsible for the narrow band phosphorescence with a characteristic lifetime of tens of ms. While in the case where Cr3+ ions lie at sites with weak crystal field, the lowest excited state will be the 4T2g level, which will be responsible for the broad band fluorescence with a characteristic lifetime of tens of ms . Different Cr3+ environment or locations in the host matrix is anticipated to have dissimilar crystal field strength and, as a results, diverse emission on the PL results are expected  and . The average lattice spacing was estimated to be 0.243 nm, which corresponds with the (311) lattice spacing of the ZnAl2O4 reported in our recent results  and by Zawadzki et al. .