In this paper, investigations were carried out on the effects of simultaneous partial substitution of Tl at the Hg site on the physical properties of an Hg_1-xTl_xBa₂Ca₂Cu₃O_8+δ cuprate superconductor with x= 0, 0.1, 0.2, 0.3 and 0.4. Two steps of the solid state reaction method were used to prepare samples in capsule. The results showed that the optimum sintering temperature was equal to 850 ^ᵒC and the sintering time was equal to 20 h for the prepared samples.  

    The best conditions for constitution and stabilization of the high T_c phase-1223 were obtained by investigating the effects of Tl substitution on Hg site and oxygen content (δ) on the superconducting properties.

         Structural investigation revealed that all the samples have a tetragonal structure with two phases, namely an Hg-1223 high T_c phase as a main phase and an Hg-1212 low T_c phase. Besides, some impurity phases like CuO and CaHgO₂ were found. The increase of Tl content in Hg_1-xTl_xBa₂Ca₂Cu₃O_8+δ compound from 0 to 0.4 caused a change in the lattice parameter, density of the unit cell (ρ_m), and c/a values.

        HgBa₂Ca₂Cu₃O_8+δ compound exhibited a critical transition temperature that is equal to 115 K. On the other side, the results showed that the highest T_c was 119 K for Hg_0.8Tl_0.2 Ba₂Ca₂Cu₃O_8+δ. The oxygen content (δ= 0.46) was expected to be the optimum hole doping for Hg_0.8Tl_0.2 Ba₂Ca₂Cu₃O_8+δ compound, which  means in our opinion that  δ plays a remarkable role in the assessment of T_c.