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Monazite, as a source of raw materials, plays a significant role in the development and applications of green technologies, including medicine and energy production. It contains nuclear materials, which are challenging to extract by convectional cracking processes. However, a new method (thermal plasma cracking) has been proposed for processing monazite. The first principles calculation approach was used to investigate the theoretical structure and mechanical properties of monazite-systems to gain deeper understanding of monazite's thermodynamics and mechanical structure. The calculated lattice parameters were found to correlate well with obtained experimental values and that these monazite type systems are exceptionally mechanically stable. The results also show that there are imaginary soft modes in dispersion curves which may correspond to negative elastic constant C35 indicating vibrational instability.

C43H34NO8PS2Re2, monoclinic, P21/c (no. 14), a = 12.165(8) Å, b = 19.027(11) Å, c = 18.848(14) Å, β = 108.735(2)°, V = 4131(5) Å3, Z = 4, Rgt(F) = 0.0308, wRref(F2) = 0.0683, T = 100(2) K.

C36H28Co1N6O4, triclinic, P1̄ (no. 2), a = 6.3166(4) Å, b = 8.5454(5) Å, c = 14.8075(9) Å, α = 105.157(2)°, β = 94.494(3)°, γ = 101.890(2)°, V = 747.5(2) Å3, Z = 1, Rgt(F) = 0.0332, wRref(F2) = 0.0790, T = 100(2) K.

C7H4NO4Rh, monoclinic, P21/c (no. 14), a = 3.5780(12) Å, b = 10.932(4) Å, c = 20.866(7) Å, β = 94.792(11)°, V = 813.3(12) Å3, Z = 4, Rgt(F) = 0.0345, wRref(F2) = 0.0712, T = 100 K.

C24H19NO3PRh, triclinic, P1̅ (no. 2), a = 9.1734(16) Å, b = 9.5433(18) Å, c = 12.342(2) Å, α = 92.400(6)°, β = 105.460(5)°, γ = 99.472(5)°, V = 1023 Å3, Z = 2, Rgt(F) = 0.0236, wRref(F2) = 0.0597, T = 100 K.

C25H20AsN2O3Rh, triclinic, P-1 (no. 1), a = 9.2781(15) Å, b = 10.1405(15) Å, c = 13.303(2) Å, α = 99.789(5)°, β = 107.971(5)°, γ = 94.089(5)°, V = 1162.9(3) Å3, Z = 2, Rgt(F) = 0.0578, wRref(F2) = 0.1833, T = 100(2) K.

C8H20Cl6N1Ta1, monoclinic, P21/n (no. 14), a = 7.1550(4) Å, b = 10.0090(6) Å, c = 11.6290(4) Å, β = 98.487(5)°, V = 823.7(8) Å3, Z = 2, Rgt(F) = 0.0207, wRref(F2) = 0.0531, T = 100(2) K.

C21H14ClN, orthorhombic, Pca21 (No. 29), a = 7.6860(5) Å, b = 10.1610(5) Å, c = 19.8990(5) Å, V = 1554.1(13) Å3, Z = 4, Rgt(F) = 0.0318, wRref(F2) = 0.0783, T = 100(2) K.