(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">BAl</mml:mi></mml:mrow><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>)Cs:mA cluster-assembled solid

First-principles calculations on the geometry and stability of ${\mathrm{Al}}_{\mathrm{n}}$${\mathrm{B}}_{\mathrm{m}}$ clusters have been carried out to examine the effect of size, composition, and electronic-shell filling on their relative stability. It is shown that although Al and B are both trivalent, a ${\mathrm{BAl}}_{12}$ cluster is more stable than an ${\mathrm{Al}}_{13}$ by 3.4 eV. The enhanced stability is shown to arise due to the relaxation of surface strain in the Al cage when the central Al is replaced by a smaller B atom. Replacement of an additional Al by B to produce ${\mathrm{B}}_{2}$${\mathrm{Al}}_{11}$ results in deformation of the icosahedral ${\mathrm{BAl}}_{12}$ cage and reduces the stability. The possibility of forming crystals using ${\mathrm{BAl}}_{12}$ and Cs is examined via total-energy calculations. It is shown that a solid with icosahedral or cuboctahedral ${\mathrm{BAl}}_{12}$ and Cs and having the CsCl structure is metastable and could be synthesized.