To explain the large isotope effect on the transition temperature in KH2P04, the tunnel­ ing motion of the protons in hydrogen bonds is considered and a theory of the phase transi­ tion is developed under the assumption that the ferroelectric behavior of this substance is due to cooperation of the ionic displacements, the interactions between ions and protons and the tunneling motion of protons. The relation between the present theory and the Slater model or the Blinc model is discussed. § I. Introduction In spite of the considerable amount of investigation made from the theo­ retical as well as the experimental side, the microscopic mechanism of the phase transition in KH2P04 and isomorphous crystals does not seem to be clearly un­ derstood. If . we classify the ferroelectric substances roughly into two groups, displacive and order-disorder type ferroelectrics, then KH2P04 will certainly belong to the latter group. However, the experimental data accumulated so far do not really give us a definite molecular picture of the phase transition, but sometimes reveals obvious inconsistencies among observed quantities. The main object of the present paper and a forthcoming one is to organize the somewhat divergent observed facts from the theoretical point of view and to suggest some experiments which might be helpful in attaining a full understanding of the phenomena. The crystal structure of KH2P04 (which will be abbreviated as KDP here­ after) is the so-called tetragonal diamond type. A characteristic feature of this structure is the existence of hydrogen bonds connecting two P04 tetrahedra, which run almost perpendicularly to the direction of the ferroelectric c axis. In the ferroelectric phase, the magnitude of the saturated polarization Ps is well accounted for by making use of the observed values for the displacements of ions K+I, p+ 5 and o- 2 along the c axis relative to their symmetric positions. 2 ),s) Therefore the hydrogen bonds do not contribute any appreciable dipole moments to the saturated polarization, and hence the essential unit of the dielectric prop­ erties in this crystal is the dipole moment of the complex [K-P04] as shown in Fig. 1. If KDP is of an " order-disorder " type of ferroelectric, that is, if the phase transition is caused by order-disorder arrangements of the dipole moments, the two configurations of the complex [K-P04] denoted as (A) and

Theory of Ferroelectric Phase Transition in KHzP04 Type Crystals. I

Structure and Vibrational Spectrum ofβ-Cs3(HSO4)2[H2−x(P1−x, Sx)O4] (x∼0.5), a New Superprotonic Conductor, and a Comparison withα-Cs3(HSO4)2(H2PO4)

Structure analysis of K 3 H(SO 4 ) 2 was performed by X-ray diffraction experiments at various temperatures down to 27 K in order to investigate the hydrogen bond character in connection with the geometrical isotope effect. The hydrogen bond length R OO monotonically decreases with decreasing temperature, accompanied by the contraction of lattice parameters, and it crosses the critical bond length r c ( H) at about 100 K. Simultaneously, the double site feature of hydrogen atoms changes into the single site state at the center of the hydrogen bond. This behavior explains why K 3 H(SO 4 ) 2 has no phase transition in spite of the existence of the disordered character at room temperature.

Temperature Dependence of Hydrogen Bond Nature in K3H(SO4)2

Na 3 H(SO 4 ) 2 , K 3 H(SO 4 ) 2 and Rb 3 H(SO 4 ) 2 crystals are composed of (SO 4 HSO 4 ) −3 dimers linked by rather strong hydrogen bonds ( R O…O =2.43 A for Na 3 H(SO 4 ) 2 , R O…O =2.48 A for Rb 3 H(SO 4 ) 2 and R O…O =2.49 A for K 3 H(SO 4 ) 2 ). Crystallographic data of the salts at room temperature indicate either asymmetric (Na 3 H(SO 4 ) 2 ) or symmetric (K 3 H(SO 4 ) 2 and Rb 3 H(SO 4 ) 2 ) hydrogen bonds. Inelastic neutron scattering (INS), infrared and Raman spectra of crystal powders at 20 K are reported for these three compounds. The OH bending modes, which give large INS intensities, appear only weakly in the infrared. The two bending modes are degenerate in Na 3 H(SO 4 ) 2 which has the shortest hydrogen bond but are well separated in K 3 H(SO 4 ) 2 and Rb 3 H(SO 4 ) 2 . The OH stretching band profiles in INS are also quite different from those in the infrared. Strong INS bands at 57 and 44 cm −1 for K 3 H(SO 4 ) 2 and Rb 3 H(SO 4 ) 2 , respectively, are assigned to 0→1 transitions in quasi-symmetric double-minimum potentials for the OH stretching coordinates. For K 3 H(SO 4 ) 2 the frequency is unaffected by temperature between 2 and 100 K. Potential functions are calculated and the dynamics of the proton transfer are discussed. Infrared spectra are thus dominated by OH stretching transitions in asymmetric double-minimum potentials with low barriers, with relative intensities indicating a large electrical anharmonicity.

Proton transfer dynamics in the hydrogen bond. Inelastic neutron scattering, infrared and Raman spectra of Na3H(SO4)2, K3H(SO4)2 and Rb3H(SO4)2

Superprotonic and ferroelastic phase transition in K3H(SO4)2

Structure analysis of K 3 H(SO 4 ) 2 was performed by X-ray diffraction experiments in order to study the hydrogen bond character in connection with the geometrical isotope effect. Crystal data at room temperature were obtained as a=9.777(1)A, b=5.674(1)A, c=14.667(4)A, β=102.97(2)° and the space group A 2/ a , Z =4. The hydrogen bond length R OO determined from the positional parameters was 2.493(1)A which was close to but still longer than the so called critical bond length r c . The electron density of split hydrogen atoms was observed on a differential Fourier map. It is concluded that the hydrogen atoms take the disordered state at room temperature and the distance between hydrogen atoms R HH is approximately 0.65 A. The possibilities for the existence both of the low temperature phase and the high temperature prototype phase are discussed.

Koumei Kafuku

Papers

Structure Analysis and Hydrogen Bond Character of K3H(SO4)2