PHYSICAL REVIE%' A VOLUME 28, NUMBER 1 JULY 1983 Amplitude combinations in the critical binary fluid nitrobenzene and n-hexane G. Zalczer, A. Bourgou, * and D. Beysens Service de Physique du Solide et de Resonance Magnetique CEK-Saclay, N191 Gif sur -Yve-tte Cedex, France (Received 14 June 1982) We have determined experimentally the amplitudes of the correlation length and suscep- tibility along the three principal trajectories: critical isochore, coexistence curve, and, for the first time in a critical mixture, critical isotherm. We have also determined the ampli- tude of the coexistence curve and that of the specific heat along the critical isochore. These amplitudes allowed us to compute several universal amplitude combinations, which are all in agreement with current theoretical predictions, except C+/C which agrees better with the renormalization-group value than with the high-temperature-series one. Moreover, linewidth measurements allowed us to determine the dynamic constant R, found to be close to unity. I. INTRODUCTION The hypothesis of universality has played a cen- tral role in the study of phase transitions. It arises from the fact that characteristic lengths near a criti- cal point are much larger than the microscopic in- teraction scale. Therefore, these details are forgot- ten and most of the observed quantities depend only on the dimensionalities of the space (d) and of the order parameter (n). For instance, the three- dimensional Ising model and the fluid and binary mixtures transitions belong to the same class of universality d=3, n= 1. At the present state of the theory, the exponents are universal and related by the so-called scaling laws, while the microscopic na- ture of the system is reflected through two indepen- dent amplitudes, at least asymptotically close to the critical point. The other amplitudes can then be de- duced using universal amplitude combinations. While the exponents and the relations between them have been subjects of experiments for a long time, the amplitudes received attention only recent- ly. The reason for that is that their study requires the gathering of results of different kinds of experi- ments and therefore the knowledge of many param- eters, including the critical exponents themselves. These exponents are now well known and the theoretical methods which have therefore proved their reliability can be used to calculate these new constants. A complete check of the theory, however, re- quires experimental deterrainations of these com- binations. The purpose of the present paper is to determine some of these constants for the mixture of nitrobenzene and n-hexane. The different tech- niques involved are static and dynamic light scatter- ing (self-beating spectroscopy and Fabry-Perot in- terferometry), interferometry, refractometry, and volumetry. However, the measurements have been perforrrted using the very same cell whenever possi- ble. Although the theory predicts the behavior of a system along the three basic trajectories (critical iso- chore, critical isotherm, and coexistence curve), most of the experiments so far have been limited to the critical isochore. However, in this paper, all these three trajectories will be studied. II. THEORETICAL BACKGROUND A. General According to the standard teriiiinology, we shall call M the order parameter, H the conjugate field, T, the critical temperature, and t =( T — T, )/T, the reduced temperature. Along the critical isochore (t ~ O, M =H =0) the following quantities will behave as follows: susceptibility specific heat kit + CX 1983 The American Physical Society