X-ray phase analysis was used to analyse the composition of Pb8Na(2±x)(PO4)6 (lead-sodium apatite structure) with different X values (X values refer to changes in the excess or lack of sodium (2±X) in the apatite structure): -0.15, -0.10, -0.05, 0.00, +0.05, +0.10, and +0.15. The ceramic method (solid-state reaction) was used to synthesize all samples at a temperature of 800 °C. Many programs, such as match software (v.3), PDF-4 database (ICCD), and database PDF-4 (ASTM), were used to study the single phases. The least-squares method was used to calculate the unit cell parameters. Results have shown that the following compositions: Pb8Na2(PO4)6, Pb8Na1.95(PO4)6, Pb8Na1.90(PO4)6, and Pb8Na1.85(PO4)6 contain only the pure phase of lead sodium apatite structure. On the other hand, the compositions of Pb8Na2.05(PO4)6, Pb8Na2.10(PO4)6, and Pb8Na2.15(PO4)6 showed other phases besides the phases of lead sodium apatite structure.
The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve
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