Rotational disorder phase transition

As mentioned above, polymorphs may also be related by order-disorder transitions, e.g. the onset of free rotation of a group of atoms, or local tumbling in semi-plastic or plastic phases. This may be due to random orientation of the molecules or ions, but is also diagnostic of the onset of a reorientational motion. Roughly spherical molecules and ions are likely to show order-disorder phase transitions to a plastic state. In the cases of co-crystals or of crystalline salts this process may affect only one of the components, leading to semi-plastic crystals (an example will be discussed below). Order-disorder phase transitions have often... 

Solid-state nuclear magnetic resonance (NMR) has been extensively used to assess structural properties, electronic parameters and diffusion behavior of the hydride phases of numerous metals and alloys using mostly transient NMR techniques or low-resolution spectroscopy [3]. The NMR relaxation times are extremely useful to assess various diffusion processes over very wide ranges of hydrogen mobility in crystalline and amorphous phases [3]. In addition, several borohydrides [4-6] and alanates [7-11] have also been characterized by these conventional solid-state NMR methods over the years where most attention was on rotation dynamics of the BHT, A1H4, and AlHe anions detection of order-disorder phase transitions or thermal decomposition. There has been little indication of fast long-range diffusion behavior in any complex hydride studied by NMR to date [4-11]. 

Fig. 9.4 An example of order-disorder phase transition. Molecules are rotating in the high-temperature form of octafluoronaphthalene (left) but are stationary in the low-temperature phase (right). (Adapted with permission from [35]. Copyright 2010 American Chemical Society)...

In molecular solids the molecules cannot move around freely, but they are trapped in relatively deep potential wells, caused by the intermolecular potential. In these wells they can vibrate and since the vibrations of individual molecules are coupled, again by the intermolecular potential, one obtains collective vibrations of all the molecules in the solid, called lattice vibrations or phonons. Phonons associated with the center of mass motions of the molecules are called translational phonons, phonons associated with their hindered rotations or librations are called librons. The degree of hindrance of the rotations may vary. If the molecules have well-defined equilibrium orientations and perform small amplitude librations about these, one speaks about ordered phases. If the molecular rotations are nearly free or if the molecules can oscillate in several orientational pockets and easily jump between these pockets, then the solid is called orientationally disordered or plastic. Several molecular solids may occur in each of these phases, depending on the temperature and pressure they undergo order/disorder phase transitions. Also the intramolecular vibrations are coupled by the intermolecular potential, via its dependence on the internal coordinates. The excitations of the solid associated with such vibrations are called vibrational excitons or vibrons. 

More interesting are the simulations of fullerene derivatives, which, in virtue of their nearly spherical shape, can enjoy rotational freedom in the solid state. The occurrence of an orientational order-disorder phase transition in Cgo at 260 K has been described with different simulation methods. MC simulations based on an atomistic model, complemented with additional interaction sites placed at the... 

FIG. 14 Phase diagram of the quantum APR model in the Q -T plane. The solid curve shows the line of continuous phase transitions from an ordered phase at low temperatures and small rotational constants to a disordered phase according to the mean-field approximation. The symbols show the transitions found by the finite-size scaling analysis of the path integral Monte Carlo data. The dashed line connecting these data is for visual help only. (Reprinted with permission from Ref. 328, Fig. 2. 1997, American Physical Society.)... 

A second-order phase transition is one in which the enthalpy and first derivatives are continuous, but the second derivatives are discontinuous. The Cp versus T curve is often shaped like the Greek letter X. Hence, these transitions are also called -transitions (Figure 2-15b Thompson and Perkins, 1981). The structure change is minor in second-order phase transitions, such as the rotation of bonds and order-disorder of some ions. Examples include melt to glass transition, X-transition in fayalite, and magnetic transitions. Second-order phase transitions often do not require nucleation and are rapid. On some characteristics, these transitions may be viewed as a homogeneous reaction or many simultaneous homogeneous reactions. 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

Tunneling rotation of three-dimensional coupled rotors in solid methane is dealt with in many experimental and theoretical studies. The phase transition at 20.4 K turns this species from orientationally disordered phase I to partially oriented phase II. According to neutron... 

---