Diffusion thermal bath

A system well-adapted to the analysis of these concepts is a diffusing particle in contact with an environment, which itself may be in equilibrium (thermal bath) or out of equilibrium (aging medium). 

To begin with, we summarize some results about the (possibly anomalous) diffusion of a particle in a thermal bath. 

One usually studies diffusion in a thermal bath by writing two fluctuation-dissipation theorems, generally referred to as the first and second FDTs (using the Kubo terminology [30,31]). As recalled for instance in Ref. 57, the first FDT expresses a necessary condition for a thermometer in contact solely with the system to register the temperature of the bath. As for the second FDT, it expresses the fact that the bath itself is in equilibrium. 

Formula (164) shows that, when diffusion takes place in a thermal bath, the velocity correlation function is characterized by the same law as is the average velocity. This result constitutes the regression theorem, valid at equilibrium for any y(co). 

For a particle evolving in a thermal bath, we focused our interest on the particle displacement, a dynamic variable which does not equilibrate with the bath, even at large times. As far as this variable is concerned, the equilibrium FDT does not hold. We showed how one can instead write a modified FDT relating the displacement response and correlation functions, provided that one introduces an effective temperature, associated with this dynamical variable. Except in the classical limit, the effective temperature is not simply proportional to the bath temperature, so that the FDT violation cannot be reduced to a simple rescaling of the latter. In the classical limit and at large times, the fluctuation-dissipation ratio T/Teff, which is equal to 1 /2 for standard Brownian motion, is a self-similar function of the ratio of the observation time to the waiting time when the diffusion is anomalous. 

Each type of metallic coating process has some sort of hazard, whether it is thermal energy, the reactivity of molten salt or metal baths, particulates in the air from spray processes, poisonous gases from pack cementation and diffusion, or electrical hazards associated with arc spray or ion implantation. 

The onset of thermal diffusion depends on the gas concentrations, the sample surface area, the rate at which the sample cools to bath temperature, and the packing efficiency of the powder. In many instances, using a conventional sample cell, surface areas less than 0.1 m can be accurately measured on well-packed samples that exhibit small interparticle void volume. The use of the micro cell (Fig. 15.10b) is predicated on the latter of these observations. Presumably, by decreasing the available volume into which the lighter gas can settle, the effects of thermal diffusion can be minimized. Although small sample quantities are used with a micro cell, thermal conductivity detectors are sufficiently sensitive to give ample signal. 

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