Analysis of the Raman frequencies of a lattice mode in NH 4 Cl close to the tricritical and second order phase transitions H. Yurtseven * , M.H. Tu ¨ mkaya Department of Physics, Middle East Technical University, 06531 Ankara-Turkey Received 30 March 2005; accepted 5 October 2005 Available online 15 November 2005 Abstract We analyze here our observed Raman frequencies of the m 5 (174 cm 1 ) mode in NH 4 Cl close to its tricritical (P = 1.6 kbar) and the second order (P = 2.8 kbar) phase transitions. The critical behavior of the frequency shifts 1/m (om/oT) P for this optical mode is described by a power-law with the critical exponent a. Our values of a = 0.01 (T < T C ) and a = 0.11 (T > T C ) for P = 1.6 kbar in NH 4 Cl are close to the values of 0.066 (=1/16) below T C and 0.125 (=1/8) above T C for the specific heat C P due to a three-dimensional Ising model. Our value of a = 0.18 (T < T C ) for P = 2.8 kbar in NH 4 Cl is also close to the Ising value (1/16), whereas our value of a = 0.64 (T > T C ) is far from the Ising value (1/8), which can be reasonably compared with those obtained by previous workers, for the thermal expansivity a P and the specific heat C P in this crystalline system. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Raman Frequencies; Lattice Mode; NH 4 Cl 1. Introduction NH 4 Cl exhibits k-type of phase transition at T = 241 K from the disordered b phase to the ferro-ordered d phase. This order–disorder type of phase transition is due to reori- entation of the NH þ 4 ions [1,2]. In the disordered b phase the NH þ 4 ions are randomly distributed between two ener- getically equivalent states, whereas in the ferro-ordered d phase all the NH þ 4 ions have the same orientation. The dis- ordered b phase has the CsCl structure with the O 1 h symme- try (space group Pm3m) and the ferro-ordered d phase has the cubic structure with the T 1 d symmetry (space group P43m). The k phase transition in NH 4 Cl that occurs at atmo- spheric pressure (T = 241 K) is regarded as a first order (weakly first order or nearly second order) phase transition. This discontinuous behavior changes toward a continuous one at about 1.6 kbar (T = 257 K), which can be classified as a tricritical phase transition as has been observed exper- imentally [3]. As the pressure increases further, the phase transition becomes a second order type at 2.8 kbar (T C = 267 K). Thus, the NH 4 Cl system exhibits all the three types of phase transitions, namely, first order (P = 0), tricritical (P = 1.6 kbar) and second order (P = 2.8 kbar). The phase diagrams containing the disordered b and the ferro-ordered d phases in NH 4 Cl, have been reported in the literature. The experimental P–T phase diagram [4] and its modified version [5] in ammonium halides, have been given in earlier studies. A general P–T phase diagram in ammo- nium and deutero-ammonium halides has been obtained experimentally [6]. There have been some experimental studies to obtain T–X phase diagrams for a mixed crystal- line system of NH 4 Br x Cl 1  x [7–10]. Apart from those experimental studies regarding the phase diagrams in ammonium halides, some theoretical phase diagrams in these crystalline systems have been obtained [11–13]. We have also obtained using the mean field theory P–T phase diagram of ammonium halides [14] and T–X Br phase dia- gram of NH 4 Br x Cl 1  x system [15]. 0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.10.015 * Corresponding author. Tel.: +90 312 210 5056; fax: +90 312 210 1281. E-mail address: karacali@newton.physics.metu.edu.tr (H. Yurtseven). www.elsevier.com/locate/chemphys Chemical Physics 323 (2006) 574–578