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At ambient conditions SrAl$_4$ adopts the BaAl$_4$ structure type with spacegroup $I4/mmm$. It undergoes a charge-density-wave (CDW) transition at$T_{CDW}$ = 243 K, followed by a structural transition at $T_{S}$ = 87 K.Temperature-dependent single-crystal X-ray diffraction (SXRD) leads to theobservation of incommensurate superlattice reflections at $\mathbf{q} =\sigma\,\mathbf{c}^{*}$ with $\sigma = 0.1116$ at 200 K. The CDW hasorthorhombic symmetry with the superspace group $Fmmm(0\,0\,\sigma)s00$, where$Fmmm$ is a subgroup of $I4/mmm$ of index 2. Atomic displacements represent atransverse wave, and they are mainly along one of the diagonal directions ofthe $I$-centered unit cell. The orthorhombic phase realized in SrAl$_4$ isanalogous to that found in EuAl$_4$, albeit with the presence of higher ordersatellite reflections (up to $m = 3$) and a shorter modulation wave vector.Electronic structure calculations and phonon calculations by density functionaltheory (DFT) have failed to reveal the mechanism of CDW formation. SrAl$_4$remains incommensurately modulated at the structural transition, where thesymmetry lowers from orthorhombic to $\mathbf{b}$-unique monoclinic. Thepresent work draws a comparison on the modulated structures of non-magneticSrAl$_4$ and magnetic EuAl$_4$ elucidating their similarities and differences,and firmly establishing that although substitution of Eu to Sr plays little tono role in the structure, the transition temperatures are affected by theatomic sizes. We have identified a simple criterion, that correlates thepresence of a phase transition with the interatomic distances. Only thosecompounds $X$Al$_{4-x}$Ga$_x$ ($X$ = Ba, Eu, Sr, Ca; $0 < x <4$) undergo phasetransitions, for which the ratio $c/a$ falls within the narrow range $2.51 <c/a < 2.54$.

Transverse structural modulation in SrAl$_4$ and elucidation of its origin in the BaAl$_4$ family of compounds