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We consider the evolution of the phase transition from the parent hexagonalphase $P6_{3}/mmc$ to the orthorhombic phase $Pmcn$ that occurs in severalcompounds of $A'A''BX_{4}$ family as a function of the hcp lattice parameter$c/a$. For compounds of $K_{2}SO_{4}$ type with $c/a$ larger than the thresholdvalue 1.26 the direct first-order transition $Pmcn-P6_{3}/mmc$ is characterizedby the large entropy jump $Rln2$. For compounds $Rb_{2}WO_{4}$, $K_{2}MoO_{4}$,$K_{2}WO_{4}$ with $c/a<1.26$ this transition occurs via an intermediateincommensurate $(Inc)$ phase. DSC measurements were performed in $Rb_{2}WO_{4}$to characterize the thermodynamics of the $Pmcn-Inc-P6_{3}/mmc$ transitions. Itwas found that both transitions are again of the first order with entropy jumps$0.2Rln2 and $0.3Rln2$. Therefore, at $c/a ~ 1.26$ the $A'A''BX_{4}$ compoundsreveal an unusual Lifshitz point where three first order transition lines meet.We propose the coupling of crystal elasticity with $BX_{4}$ tetrahedraorientation as a possible source of the transitions discontinuity.Comment: 13 pages,1 Postscript figure. Submitted as Brief Report to Phys. Rev.  B, this paper reports a new work in Theory and Experiment, directed to  Structural Phase Transition

physical review. b, condensed matter

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Thermodynamics of the incommensurate state inRb2WO4:The Lifshitz point in