A mathematical model was created in this article, which consists of a thermoelastic, unified, and isotropic rigid sphere subjected to thermal diffusion. Thermal and chemical potential shocks of a diffusive substance have loaded the sphere's bounding structure. The governing equations were established in the form of a theory of generalized thermoelastic diffusion with mechanical damage taken into account. The temperature increment, concentration, pressure, displacement, stress, and chemical potential numerical effects have been expressed in figures with different values of the mechanical damage parameter, thermal relaxation time, and diffusional relaxation time. All the studied functions are significantly affected by the mechanical damage parameter, radial distance, time, thermal, and diffusional relaxation times. In the Lord-Shulman model, heat, diffusion, and mechanical waves spread at finite speeds on the thermoelastic solid sphere.