  We consider the evolution of the phase transition from the parent hexagonal
phase $P6_{3}/mmc$ to the orthorhombic phase $Pmcn$ that occurs in several
compounds 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 threshold
value 1.26 the direct first-order transition $Pmcn-P6_{3}/mmc$ is characterized
by 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 intermediate
incommensurate $(Inc)$ phase. DSC measurements were performed in $Rb_{2}WO_{4}$
to characterize the thermodynamics of the $Pmcn-Inc-P6_{3}/mmc$ transitions. It
was 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 $A'A''BX_{4}$ compounds
reveal an unusual Lifshitz point where three first order transition lines meet.
We propose the coupling of crystal elasticity with $BX_{4}$ tetrahedra
orientation as a possible source of the transitions discontinuity.
