THERMODYNAMICS AND KINETICS IN CONDENSED MATTER

In condensed matter (liquids and solids) order can manifest itself in the position of the atoms (this is the case in crystals) or in the ori entation of the molecules or of the magnetizations. The forces involve d act only over atomic distances. If the order in question is stable, free energy is at an absolute minimum. Besides its stable state, howev er, the system can exhibit a secondary minimum in its free energy, whi ch often corresponds to a metastable phase. A perturbation (whether th ermal or an external constraint) can cause the system to change from t he metastable phase to the stable phase. The fatter initially develops like a seed which must grow and exceed a critical size related to the interfacial tension. When the system has a large number of metastable states, the stable state is difficult to reach (for example in solid friction, ferromagnetism or spin glasses). The kinetic order departs f rom the thermodynamic equilibrium conditions. During crystal growth fl at faces grow less quickly than rough faces. Flat dense faces develop as growth proceeds. If the liquid contains impurities, these can becom e concentrated at the interface, car? dissolve in the crystal and can create dislocation walls in it. Turbulent hydrodynamic flows also exhi bit characteristic regularities, this is the case with Benard's instab ilities in which arrays of vortices are formed. If the instability is increased the vortex order can become intermittent and can then lead t o chaos.