Unstable growth phase

The air-mass thunderstorm is the least severe of all thunderstorms. In its simplest form, an air-mass thunderstorm grows as a single cell when solar radiation heats the surface air in an unstable atmosphere. Its life cycle lasts around 30 minutes. Towering cumulus clouds are formed as in-cloud updrafts push moisture upward. The tower may reach a height about five times the diameter of the cloud base in the growth phase. 

Limits on the unstable growth rate are obtained from a modified version of the so-called semicircle theorem, developed by researchers J. Miles and L. Howard in 1%1. This significant global theorem states that the complex phase speed c = c, + ic (where c, is the growth rate divided by the zonal wavenumber k) must satisfy the relationship... 

Note that Ap- 0 and Aa-> -2 as 0. The spectrum of Ap may be called the phaselike branch, and that of Aa the amplitudelike branch, since they are associated, respectively, with phase fluctuations and amplitude fluctuations in the limit of vanishing q. We may say that the instability of the uniform oscillation is related to the unstable growth of some phaselike fluctuations. 

With condition 6 G ix 76(p <0 (within the spinodal region), the system is unstable to small fluctuations of concentration. The supersaturated solution starts decomposing through the entire volume simultaneously, without generation of nuclei. The spinodal separation is a kinetic process of a spontaneous formation and continuous growth of another phase in an unstable parent phase,caused by the origination of low-amplitude fluctuations of the composition. As a result, the rapid growth of the second phase proceeds with charac-... 

As theoretical models were proposed to give an account for the spinodal decomposition for unstable one-phase compositions (4-6) and for the nucleation and growth mechanism for metastable one-phase compositions (7), the necessity arose for information on the earliest stages of phase separation. It is the reason why additional techniques including neutron scattering (8, 9), N.M.R. spectroscopy (10, 11) and fluorescence emission were used with the aim to delect the phase separation on a molecular scale. 

Phase Diagram in the Temperature vs. composition plane. Below the binodal the mixture is stable and only one phase exists. Above the binodal the mixture phase separates. Phase separation occurs via nucleation and growth if the mixture is initially in the metastable region. If it begins in the unstable region phase separation occurs by spinodal decoposition. 

The study of ultra-thin Fe thin films on Cu(OOl) substrate has attracted a lot of interest in the past. This is due to the abundance of interesting phenomena associated with this system. Due to the small epitaxial misfit a good layer by layer growth is expected stabilizing the film in a structure related to the fee phase of bulk Fe which is otherwise unstable at low temperatures It also become a test system for magnetic measurements. 

Low-temperature solid-state synthesis is preferred in most cases, where appropriate, for obvious reasons such as energy and cost economy and process safety or for critical concerns regarding the accessibility of compounds that are stable only at low temperatures or non-equilibrium phases, i.e., compounds thermodynamically unstable with respect to the obtained phase (e.g., a ternary instead of binary phase). The use of low-temperature eutectics as solvents for the reactants, hydrothermal growth... 

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