That's a very specific question. I'm not an expert in this field, but I can try to give you some general information based on the web results.
Density is a measure of how much mass is contained in a given unit volume. Relative density is the ratio of the density of a substance to the density of a reference substance, usually water or air. Unit cell is the smallest repeating unit of a crystal structure. Grain size is the average diameter of the grains in a polycrystalline material.
According to ², Ba0.95Ca0.05SnxTi1-xO3 (BCST) is a lead-free piezoceramic material that has a perovskite structure with ABO3 formula. The A site is occupied by Ba and Ca, and the B site is occupied by Ti and Sn. The x value represents the Sn content, which can vary from 0 to 0.2.
The web results suggest that changing the x value or adding other elements such as Zr or Na can affect the phase structure, microstructure, dielectric and piezoelectric properties of BCST ceramics ⁴⁵⁶. For example, ⁴ reports that adding Zr can improve the density and piezoelectric activity of BCST ceramics, and ⁵ reports that adding Na can induce a ferroelectric relaxor behavior.
However, I could not find any direct answer to your question about the relationship between density, relative density, unit cell and grain size for BCST ceramics with different Sn content. You may need to consult more specialized sources or experts for that. I hope this helps a bit.
(1) Crystal structure, unit cell parameters, grain size, and relative .... https://www.researchgate.net/figure/Crystal-structure-unit-cell-parameters-grain-size-and-relative-density-of-the-three_tbl1_322510965.
(2) Studies on structural, dielectric and optical properties of (Ba0.95Ca0 .... https://pubs.rsc.org/en/content/articlepdf/2021/ra/d1ra00952d.
(4) Structure, energy storage properties and dielectric responses of Ba0 .... https://www.researchgate.net/publication/337871524_Structure_energy_storage_properties_and_dielectric_responses_of_Ba095Ca005ZrxTi1-xO3_ceramics_prepared_by_a_citrate_method.
(5) 12.1: Crystal Lattices and Unit Cells - Chemistry LibreTexts. https://chem.libretexts.org/Courses/University_of_Arkansas_Little_Rock/Chem_1403%3A_General_Chemistry_2/Text/12%3A_Solids/12.01%3A_Crystal_Lattices_and_Unit_Cells.
(6) What is the relationship between the density, the relative density .... https://www.researchgate.net/post/What_is_the_relationship_between_the_density_the_relative_density_unit_cell_grain_size.