Growth reactivity

Support preparation Nucleation and growth Reactivity Structure, morphology and characterization of metal clusters of the metal clusters... 

All reactive flow models require as a minimum two equations of state, one for the unreacted explosive and one for its reaction products a reaction rate law for the conversion of explosive to products and a mixture rule to calculate partially reacted states in which both explosive and products are present. The Ignition and Growth reactive flow model [60] uses two Jones-Wilkins-Lee (JWL) equations of state, one for the unreacted explosive and another one for the reaction products, in the temperature dependent form ... 

Vapor transport solids are transported through the gas phase in a closed vessel using a reactive gas that is not consumed in the process. This method is used for crystal growth, reactive sintering, and synthesis of solids. 

For the reaction between massive solids, from the experimental knowledge of the kinetic law, it is theoretically possible to deduce the specific nucleation frequency and the growth reactivity, with the condition of having modeled the space function. 

Determine the morphologic model (what steps and zone where they occur) of this reactioa Deduce the growth reactivity. 

In order to choose the rate-determining step for growth. Give the possible expressions of growth reactivity as a function of water pressure knowing that the protons ensure the electric neutrality at any point of the layer of metakaolinite. Compute the values of the model parameter at temperature 450°C. 

Give the expression of growth reactivity as a function of temperature. Compute the values of the model parameter at pressure 2.5 hPa. 

Table 19.13. Growth reactivity of the metakaolinite versus pressure and temperature...

Confidence intervals for the growth reactivity and the specific frequency of nucleation. 

Evaluate the error obtained on and Bit. Give a value of A and t for each pressure. Calculate the growth reactivity and nucleation specific frequency at each pressure and their error. 

Calcirlate the growth reactivity at each pressure for each possible prrre mode. Which step do you retain as rate-determining step for growth ... 

We note a very high error on nucleation specific frequency that is much more important than that on growth reactivity. 

Starting from the values thus calculated, we can plot the curves in Figure 19.14a and b, giving the variations of growth reactivity and specific frequency of nucleation with carbon dioxide pressure. 

Table 19.19. Growth reactivity for the various pure modes...

Look at the differences between the obtained results for the two models. What model do you accept eventually Deduce the growth reactivity. 

We deduce that the model with instantaneous surface diffusion is the one to retain. According to the slope of the line, we calculate the growth reactivity (relation [19.82]) ... 

We consider three crystallographic axes of initial solid (not necessarily perpendicular). In the general case, each direction is characterized by its own growth reactivity. Take xft, z), X2(t, i), and xft, t) as Mor lengths reached at time t by the solid phase formed at the time r. Irrdicate by and the respective reactivities in the three directions. 

It will be noted that it is not possible, starting from such a law, to deduce nucleation frequency and growth reactivity however, if we are able to determine the variations of growth reactivity with intensive properties (by the switch method), we can deduce the ones of nucleation frequency, starting from experiments carried out for various values of a property (e.g. temperature) using the product (fy. 

This expression, which does not depend on the reactivity of growth, makes it possible to recognize such a law, and thus, the calculation of the nucleation constant g. deduction of growth reactivity while substituting into [A9.19] or [A9.20],... 

We notice that expressions [A.9.25] and [A.9.26] do not depend on the nucleation constant and should thus allow calculating growth reactivity directly. It will be noted, however, that this is realizable only if the approximation applies for short times (large under the terms of Remark 2 of section A.9.1.2. 

We thus obtain power in time laws with powers on the rate different from 3. It will be noted that these laws do not make it possible to separately calculate the growth reactivity and the nucleation constant starting from the experiment. On the other hand, we can determine q, which gives indications on the structure of the mechanism of nucleatioa... 

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