Glassy Crystals Low-frequency and Low-temperature Properties a

Glasses are amorphous like liquids, but are rigid like crystals. To a chemist, this may seem natural: silicon dioxide, when covalently bonded into a well-relaxed random network, should resist deformations as an elastic solid just as it would in a crystalline network. To a theoretical physicist, this is more mysterious. What broken symmetry’ causes the rigidity‘! Of course, the chemist may in the end be right-the observed rigidity may be due purely to short-range order. I f so, glasses must flow like a (very viscous) liquid on sufficiently long time scales. Even though it is not favorable for any individual bond to break, rearrangements of sufficiently large clusters of atoms will allow the energy to decrease or remain the same. (If the order is short range with a range R, a cluster of size larger than R will typically allow such an internal rearrangement.) At any finite temperature, these rearrangements will proceed by thermal activation at a slow but nonzero rate. Any external stress applied to the system will produce a bias in these rearrangements, producing in the end the finite shear rate characteristic of a liquid. If the glass is truly solid, it must have some sort of long-range order to produce infinite barriers to rearrangements. The study of the glass transition is the study of the phase boundary between the fluid liquid and the rigid glass. This subject is controversial, and has recently seen several interesting developments. In this paper we will not discuss the glass transition. We will deal partly with the universal low-temperature2 properties of glasses, which are not as controversial; indeed, in many ways they are quite well understood. The tunneling center t h e ~ r y ~ , ~ explained why glasses have specific heats proportional to temperature and thermal conductivities proportional to T 2 , in contrast to insulating crystals where both properties are proportional to T 3 for low temperatures T. I t predicted correctly that glasses would have a saturable ultrasonic attenuation and a “time-dependent” specific heat; the experimental specific heat varies logarithmically with the measuring time. We will also deal with the low-frequency response of glassy materials. In the experimental phenomenology, there are two kinds of low-frequency response in glasses, with quite different signatures, which often (or always) coexist. There has been much study of the a-relaxation processes because of their relationship to the glass transition. The a-relaxations typically are observed in the supercooled liquid, and have a