Disorder, reaction

Both ordered and normal spinels should disorder at high temperature, since the entropy of the random spinel is larger. The disordering reaction for a normal spinel can be described by a quasi-chemical reaction... 

The previous sections have largely concentrated on the relative accuracy with which a given order-disorder reaction can be described and the associated computing time. However, one of the ultimate tests is to see whether these procedures can be integrated into calculations for real, rather than model, systems. 

Chemical reactions in a mineral. One example is the Mg-Fe order-disorder reaction in an orthopyroxene (opx) crystal ... 

There are many other order-disorder reactions in minerals, for example,... 

Example 1.2 The following data are from Besancon (1981) for Fe-Mg disordering reaction between Ml and M2 sites of an orthopyroxene. The errors are estimated from the number of experimental data points for each determination and whether there are enough points between the initial state and the final equilibrium state. 

The above methods of investigating the order of the reaction with respect to each species independently, although simple and practical for many reactions (such as atmospheric reactions and aqueous reactions) studied by chemists and geochemists, is often difficult to apply to homogeneous reactions in a silicate melt or mineral because the concentration of each species may not be varied freely and independently. This will become clear later when the kinetics for the Fe-Mg order-disorder reaction in orthopyroxene and the interconversion reaction between molecular H2O and OH groups in silicate melt are discussed. 

Consider a homogeneous reaction such as Fe-Mg order-disorder reaction in an... 

Figure 1-19 Schematic diagram showing how Ku for the Fe-Mg order-disorder reaction varies during cooling. The arrow indicates the progression of time. The thin dashed curve shows how the equilibrium iCo varies with temperature as the system cools. The solid curve shows how iCo varies with temperature during rapid quench in a volcanic rock. The thick and long dashed curve shows how Kj) varies during slow cooling in a plutonic rock.

Only two high-temperature homogeneous reactions have been investigated in detail for their kinetics by geochemists. One is the Fe-Mg order-disorder reaction in orthopyroxene, and the other is the hydrous species interconversion reaction in rhyolitic melt. The two reactions have been applied as geospeedometers in various geochemical and meteoritic problems. Because they are often encountered in geochemical kinetics literature, the two reactions are discussed in depth below. 

Some other intracrystalline exchange reactions have also been investigated to some extent, such as Fe, Ni, and Mg exchange between Ml and M2 sites in olivine (Ottonello et al., 1990 Henderson et al., 1996 Redfem et al., 1996 Heinemann et al., 1999 Merli et al., 2001), Fe and Mg exchange between Ml + M2 + M3 and M4 sites in amphibole (Ghiorso et al., 1995), order-disorder reaction for Mg and Al, or for Mg and Fe +, between the tetrahedral and octahedral sites (O Neill, 1994 Harrison and Putnis, 1999 Andreozzi and Princivalle, 2002), and... 

Figure 2-4 Kjj values for the Fe-Mg order-disorder reaction in orthopyroxene as a function of temperature for selected compositions. The line is a fit to the data for Xps = 0.011 and 0.162 (Equation 2-57). Data sources are as follows = 0.011and0.162 (Wang et al.,...

In the literature on intracrystalline reactions, another formulation, which is more general than that shown in Table 2-1, has been advanced to treat the kinetics of order-disorder reactions (Mueller, 1969 Ganguly, 1982). The method is outlined below to help readers follow the literature. Those who are not interested in such details may jump to Section 2.1.5. 

Ganguly s treatment of the kinetics of order-disorder reactions... 

The following are some real experimental data for the Fe-Mg order-disorder reaction in orthopyroxene at 600°C (Wang et al., 2005) ... 

This section focuses on how the Fe-Mg order-disorder reaction (Section 2.1.4) is applied as a geospeedometer. The equilibrium and kinetics of the reaction are discussed in Section 2.1.4 and only a brief review is provided here. Although there is some complexity in the kinetics of this reaction (e.g.. Figure 2-5), it is minor, and is hence usually ignored so that the forward and backward reactions are treated as elementary reactions. The rate coefficient for the forward reaction of this reaction (Reaction 2-55)... 

Seifert F. and Virgo D. (1975) Kinetics of Fe +-Mg order-disorder reaction in anthophyl-lites quantitative cooling rates. Science 188, 1107-1109. 

Sykes-Nord J.A. and Molin G.M. (1993) Mg-Fe order-disorder reaction in Fe-rich orthopyroxene stmctural variations and kinetics. Am. Mineral. 78, 921-931. 

Post-Traumatic Stress Disorder Reaction Index for Children Private, via author, A.M. La Greca, Ph.D., Department of Psychology, 4100 Malaga Ave, Miami, FL 33133-6325... 

In this case, the number of zinc ions in interstitial positions and the number of free electrons will be decreased by an increase in the partial pressure of oxygen. These disorder reactions result in a dependence of the electrical conductivity on the oxygen pressure. This effect is a well known phenomenon in the field of semiconductors (1). Complicated relations, however, will occur at lower temperatures, at which no equilibrium can be attained between the gas phase and the lattice defects in the whole... 

Most chemical reactions occur by a change in the configurational order (AS 0). Compared to fluids, crystalline reactants already have a low entropy and thus solid state reactions are normally exothermic In this sense, order-disorder reactions are in no way special, except that they occur in homophase crystals. 

Since the above disorder reaction is restricted to the silver sublattice we can condense Eq. (2) to the even more concise form ... 

Let us explicitly consider an oxide MO and assume that only oxygen defects can be formed to a perceptible extent, then we have to consider the set of internal and external equations given by Table 1. (Note that one disorder reaction is redundant in Table 1.) The free parameters are obviously (i) the temperature which enters the mass action constants (see Table 1) and (ii) the partial pressure Px2 which... 

---