We report ferrielectricity in a single-phase crystal, TSCC -- tris-sarcosine calcium chloride [(CH3NHCH2COOH)3CaCl2]. Ferrielectricity is well known in smectic liquid crystals but almost unknown in true crystalline solids. Pulvari reported it in 1960 in mixtures of ferroelectrics and antiferroelectrics, but only at high fields. TSCC exhibits a second-order displacive phase transition near Tc = 130 K that can be lowered to a Quantum Critical Point at zero Kelvin via Br- or I-substitution, and phases predicted to be antiferroelectric at high pressure and low temperatures. Unusually, the size of the primitive unit cell does not increase. We measure hysteresis loops and polarization below T = 64 K and clear Raman evidence for this transition, as well of another transition near 47-50 K. X-ray and neutron studies below Tc = 130K show there is an antiferroelectric displacement out of plane of two sarcosine groups; but these are antiparallel displacements are of different magnitude, leading to a bias voltage that grows with decreasing T. A monoclinic subgroup C2 may be possible at the lowest temperatures (T<64K or T<48K), but no direct evidence exists for a crystal class lower than orthorhombic.
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