The thermodynamics of mixed crystals of ammonium chloride and ammonium bromide. II. An analysis of the heat capacity of ammonium chloride, ammonium bromide, and an approximately equimolar solid solution of these salts

Abstract

The heat capacity C p of ammonium chloride, ammonium bromide and the mixed crystal NH 4 Br 0.55 Cl 0.45 has been analysed, for temperatures in the range 0-500 K, on the assumption that can be expressed as the sum of the terms ( C p — C v ), C (lat.), C (lib.), C (int.) and C (extra); C (lat.), C (lib.) and C (int.) are respectively, the contributions from the lattice vibrations (phonons), and the librations (torsional oscillations) and internal vibrations of the ammonium ions. C (extra) is the contribution from order-disorder changes or any other ‘abnormal’ sources. The analysis requires a knowledge of certain thermodynamic and spectroscopic properties of the crystals, and current information on these has been surveyed. The ‘normal ’ or ‘baseline’ heat capacity C´ p for the three solids has been estimated; C´ p is the molar heat capacity to be expected from the progressive excitation of the lattice vibrations, torsional oscillations and internal vibration of the cations, and from the expansion of the lattice. By comparing C´ p and the observed heat capacity C p , C (extra) has been evaluated, making it possible to examine the development with rising temperature of the configurational or otherwise ‘extra’ entropy. The main results emerging from this are the following, ( a ) For all three solids, the entropy gain at the λ-transition (or at the two lower transitions, taken together, in ammonium bromide) is not about R ln 2, as has often been stated, but is roughly 50 % larger. The excess over R ln 2 is to be attributed to changes in the phonon spectrum and to a reduction in the frequency of the torsional oscillations of the ammonium ions, ( b ) The heat capacity of the β-phase of all three solids is abnormally large. Possible reasons for this are briefly discussed, but a definitive explanation is lacking. ( c ) The overall entropy gain for all three solids when the high-temperature face-centred a-phase has been formed is considerably greater than R In 6, the configurational contribution to be expected from the structural evidence that each ammonium ion in this phase has access to six distinguishable orientations. The balance is believed to be due to enhanced freedom of torsional movement of the ammonium ions, which must be a complex motion. However, from its observable thermodynamic consequences, this motion is still far from true free rotation.