Electric dipole waves and vibration motion of protons in hydrogen-bonded crystalline KH2PO4at low temperatures

On the basis of a model that was proposed to explain a large isotope effect on the temperature (T c ) of the transition from a ferroelectric phase to a paraelectric phase in KH 2 PO 4 (KDP), the motion of electric dipole moments is examined in the framework of the harmonic approximation; it is concluded that, in the ferroelectric phase, there are electric dipole waves, by which the vibration motion of a proton is induced along the direction of an oxygen-hydrogen-oxygen (O-O) bond. Scattering of thermal neutrons induced by this motion of protons (deuterons) is also examined.