analysis of (6b) shows that for a 4-0, a continuous displacive transition will occur at some X c (a) with X c (a) an increasing function of a. An interesting feature of this instability-driven transition is that the transition becomes increasingly sharp as a -0. Thus, if this were used to model a real physical system, a case could occur in which it would be impossible experimentally to determine that the transition was not first order. The results for (6b) are as shown in Table I. In conclusion, a clearer picture of the transition found in Ref. 4 is now available. In the absence of a symmetry-breaking term there should be no transition. In the presence of one (which could be implicitly introduced through the MFA), there should be a second-order transition. These results are for an idealized model. In a real, physical system, there should be at least a weak symmetry-breaking term. Then, since the transition is of the instability-driven type (with the instability of the Coulomb lattice providing an effective "hump" for the TO mode) there would be a sharp second-order transition with almost a first-order character. If this were accompanied by, for example, a lattice distortion, the transition could be a real, first-order transition.Cosmogenic radionuclides having very long half-lives can be useful dating tools in a number of astrophysical, geophysical, and cosmochemical problems. One of the most prominent of such species is the nuclide 10 Be, which has significant applications in studying the history of cosmic rays, 1 meteorites, 2 lunar samples, 3 marine sediments, 4 and polar deposits. 5 The generally accepted 6 half-life of 10 Be is (2.7 ±0.4)xi0 6 yr, a value based on two separate experiments carried out more than 20 years ago. 7, 8 We have become interested in the question of the accuracy of this number because of its importance in trying to "date" cosmic-ray ages. 1 Although we had no reason to suspect a large error Thus, the first-order character of either the MFA or SPA treatment of the instability-driven transition should not be considered spurious, but rather a strong indication of the inherent instability of the system.We are especially appreciative of a critical examination of our results by W. J. Camp.Any quartic Hamiltonian with a single degree of freedom can be scaled to the form (6). This is also the region where k B T is of the order of the depth of one of the minima of the effective doublewell potential associated with the long-wave length optic mode.in the accepted value, we felt its widespread use warranted an attempt to reduce the error limits. While we have not yet succeeded in that goal, we have found a value which is in strong disagreement with the older number, and which should have important implications in a number of fields of study.The two essential quantities in the determination of any half-life which is too long to be followed directly are the decay rate and the number of atoms of the decaying species, Usually the former can be measured directly, while the latter is obtained by a ma...