Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Different parameters obtained from XRD diffractograms_
| Zinc contents (x) | Lattice parameter (Å) | Crystallite size (nm) | Particle size (nm) | Bulk density d(g/cm3) | X-Ray density r(gm/cm3) | Energy Band gap (eV) |
|---|---|---|---|---|---|---|
| 0 | 8.3523 | 68.11 | 400 | 2.02 | 1.45 | 2.49 |
| 0.2 | 8.3523 | 67.07 | 380 | 2.23 | 1.68 | 2.64 |
| 0.4 | 8.3532 | 61.40 | 295 | 2.32 | 1.78 | 2.66 |
| 0.6 | 8.3544 | 56.62 | 230 | 2.36 | 1.89 | 2.67 |
| 0.8 | 8.3559 | 58.92 | 190 | 2.37 | 1.78 | 2.66 |
| 1.0 | 8.3578 | 56.62 | 175 | 2. | 2.09 | 2.68 |
Inter atomic distance between the cations “Me–Me” and cations and anions “Me–O”_
| x | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
|---|---|---|---|---|---|---|
| b | 3.6166 | 2.9530 | 2.9533 | 2.9537 | 2.9541 | 2.9549 |
| c | 3.4626 | 3.4627 | 3.4630 | 3.4635 | 3.4644 | 3.4649 |
| d | 3.6165 | 3.6167 | 3.6170 | 3.6175 | 3.6182 | 3.6190 |
| e | 5.4249 | 5.4252 | 5.4255 | 5.4263 | 5.4273 | 5.4285 |
| f | 5.1147 | 5.1148 | 5.1152 | 5.1160 | 5.1169 | 5.1180 |
| p | 1.0440 | 1.0441 | 1.0442 | 1.0443 | 1.0444 | 1.0447 |
| q | 3.6165 | 3.6166 | 3.6169 | 3.6174 | 3.6181 | 3.6189 |
| r | 3.4578 | 3.4579 | 3.4583 | 3.4587 | 3.4593 | 3.4601 |
| s | 4.2039 | 4.2040 | 4.2044 | 4.2050 | 4.2067 | 4.2071 |
Magnetization data for ZnxCo1−xCr0_5Fe2O4_
| Zn contents (x) | MS (emu/g) | Mr (emu/g) × 10−2 | Mr/Ms × 10−2 | μB (obs) bohr magneton × 10−2 | μB (cal) bohr magneton | Coercivity kOe |
|---|---|---|---|---|---|---|
| 0 | 4.366 | 3.88 | 0.88 | 3.056 | 3.0 | 102.30 |
| 0.2 | 3.370 | 3.80 | 1.12 | 2.461 | 2.7 | 37.27 |
| 0.4 | 1.464 | 2.57 | 1.75 | 1.114 | 2.0 | 2.781 |
| 0.6 | 0.4317 | 2.24 | 5.19 | 0.342 | 1.3 | 0.821 |
| 0.8 | 0.4249 | 0.493 | 1.16 | 0.349 | 0.6 | 0.404 |
| 1.0 | 0.2930 | 0.387 | 1.32 | 0.250 | 0.5 | 0.412 |
Stiffness constant bulk modulus, young's modulus and rigidity modulus of Co1−xZnxCr0_5Fe1_5O4_
| x | Stiffness constant | Young's modulus (E) | Rigidity modulus (G) | Bulk modulus (K) | |
|---|---|---|---|---|---|
| C11 | C12 | ||||
| 0 | 1.840 | 0.881 | 5.11 | 3.10 | 3.46 |
| 0.2 | 1.846 | 0.884 | 5.14 | 3.11 | 2.29 |
| 0.4 | 1.792 | 0.852 | 4.86 | 2.94 | 2.08 |
| 0.6 | 1.723 | 0.825 | 4.48 | 2.91 | 2.14 |
| 0.8 | 1.722 | 0.825 | 4.47 | 2.71 | 1.88 |
| 1.0 | 1.721 | 0.824 | 4.42 | 2.68 | 1.84 |
Structural parameters obtained from Eqs (7)–(14)_
| Zinc | Mean radii ionic (nm) | USystem (nm) | Bond length (nm) | Packing factor | |||
|---|---|---|---|---|---|---|---|
| X | rA | rB | RA | RB | PA | PB | |
| 0 | 3.6165 | 0.3828 | 0.482 | 3.723 | 1,932 | 0.990 | 4.467 |
| 0.2 | 3.6166 | 0.3842 | 0.429 | 3.873 | 1.959 | 1.032 | 4.738 |
| 0.4 | 3.6169 | 0.3842 | 0.418 | 3.989 | 1.975 | 1.064 | 4.780 |
| 0.6 | 3.6174 | 0.3843 | 0.401 | 4.234 | 2.163 | 1.132 | 5.273 |
| 0.8 | 3.6181 | 0.3843 | 0.393 | 4.392 | 2.195 | 1.176 | 5.3535 |
| 1.0 | 3.6189 | 0.3844 | 0.331 | 4.751 | 2.229 | 1.275 | 5.473 |
FTIR analysis of Co1-xZnxCr0_5Fe2O4_
| Zn (x) | ν2 (cm−1) | ν1 (cm−1) | K1 (N/m) | K2 (N/m) | LA (Å) | LB (Å) |
|---|---|---|---|---|---|---|
| 0 | 487 | 612 | 16.12 | 14.62 | 3.7905 | 3.0950 |
| 0.2 | 487 | 612 | 16.10 | 14.74 | 3.7909 | 3.0948 |
| 0.4 | 483 | 604 | 15.73 | 14.21 | 3.7968 | 3.0997 |
| 0.6 | 475 | 600 | 15.56 | 13.44 | 3.7977 | 3.1004 |
| 0.8 | 471 | 597 | 15.49 | 13.32 | 3.7982 | 3.1009 |
| 1.0 | 455 | 608 | 15.70 | 13.10 | 3.7994 | 3.1018 |
Estimated cationic distribution from XRD_
| X | Tetrahedral site | Octahedral site |
|---|---|---|
| 0.0 | Co0.25Fe0.75 | Co0.75Cr0.5Fe0.75 |
| 0.2 | Co0.2Zn0.05Fe0.75 | Co0.6Zn0.15Cr0.5Fe0.75 |
| 0.4 | Co0.15Zn0.04Cr0.05Fe0.76 | Co0.45Zn0.36Cr0.45Fe0.74 |
| 0.6 | Co0.14Zn0.03Cr0.06Fe0.77 | Co0.26Zn0.57Cr0.44Fe0.73 |
| 0.8 | Co0.13Zn0.02Cr0.07Fe0.78 | Co0.07Zn0.78Cr0.43Fe0.72 |
| 1.0 | Zn0.01Cr0.08Fe0.0.91 | Zn0.99Cr0.42Fe0.59 |