Taking Mo-Si compounds as model systems, we show that the coefficients of t
hermal expansion (CTEs) of complex structures can be calculated precisely f
rom first principles by incorporating the Debye model for acoustic response
. Specifically, we obtain a nearly isotropic CTE in MoSi2 but a highly anis
otropic CTE in Mo5Si3. The CTE anisotropy in Mo5Si3 is due to an elasticall
y more rigid basal plane and a higher anharmonicity along the c axis. As th
e structure of 5-3 compounds is modified from D8(m) to D8(l) by boron subst
itutions (Mo5SiB2), we predict a significant decrease in the CTE anisotropy
, which is confirmed by experiments.