The electronic band structure and pressure-temperature-dependent structural evolution of ${\mathrm{BaAl}}_2{\mathrm{Si}}_2$ were investigated using ab initio calculations based on density functional theory (free energies and vibrational spectra) combined with room-temperature synchrotron powder x-ray diffraction under high pressure. The resulting $P-T$ phase diagram delineates transformation boundaries among polymorphs, structural metastability, and irreversibility. These features are rationalized by the baric/thermal response of the three-dimensional ${\mathrm{AlSi}}_4$ rigid-tetrahedral framework, Ba-intercalation-induced steric strain, and the activation-barrier landscape. This framework also accounts for the structural evolution across the $A{\mathrm{Al}}_2{\mathrm{Si}}_2$ series ($A$ = Ca, Sr, Ba) under complete cation substitution. Finally, electronic-structure calculations reveal subtle differences in Fermi-surface topology between the main ${\mathrm{BaAl}}_2{\mathrm{Si}}_2$ polymorphs and their Ca/Sr counterparts, consistent with electrical transport.

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• Compressive strength
• Electrical conductivity
• Intercalation
• Phase transitions
• Pressure effects
• Structural properties
• Crystal structures
• Layered crystals
• Polycrystalline materials
• Density functional calculations
• Pressure techniques
• Resistivity measurements