Elastic and anelastic properties of a ceramic sample of elasticoluminescent SrAl 2 O 4 : Eu have been characterized as a function of temperature by resonant ultrasound spectroscopy. Both the bulk ͑K͒ and shear ͑G͒ moduli show changes attributable to the influence of the P6 3 22→ P6 3 ͑ ͱ 3A͒ → P2 1 sequence of structural phase transitions. Softening of K and stiffening of G at the P6 3 22 → P6 3 ͑ ͱ 3A͒ transition ͑T c Ϸ 1135 K͒ is consistent with weak strain/order parameter coupling and

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... ical character. In marked contrast, the first order P6 3 ͑ ͱ 3A͒ → P2 1 transition near 930 K is accompanied by stiffening such that G is ϳ50% larger at room temperature than the value for a P6 3 22 structure extrapolated directly from high temperatures and K is ϳ15% larger. Softening of G at high temperatures is consistent with the existence of a soft acoustic mode. Both the P6 3 ͑ ͱ 3A͒ and P6 3 22 phases show an increasing acoustic dissipation with increasing temperature and there is an additional peak in the dissipation behavior below ϳ650 K. Landau theory has been used to analyze the overall strain and elastic behavior of SrAl 2 O 4 : Eu. The stability of the P2 1 structure is considered in terms of coupling between order parameters with ⌫ 6 and M 2 symmetry, though it could also be stabilized by pairwise coupling of order parameters corresponding to irreps ⌫ 4 +M 2 , ⌫ 4 +M 3 , ⌫ 6 +M 3 , and M 2 +M 3 . Twin walls in this material should have interesting properties, which are quite distinct from those of the bulk material and could contribute differently to the elasticoluminescent properties.