Order-disorder reaction

Various modes of ordering are feasible. In systems with amphoteric cations ( .., Al34-), the fraction of Al3+ in tetrahedral or octahedral sites is a possible order parameter. Strain may lead to a bending of Si-O bonds. Periodic distributions of the components in space, along with elastic and/or electrostatic interactions, indicate spinodal ordering (demixing). Some examples will illustrate these general features. 

T 1300°C. Thus, a real understanding of the transition and ordering mechanism has still not been achieved [A. Putnis (1986)]. 

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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,... 

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. 

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. 

This analysis breaks down if c(X, r) is not strictly constant. For example, the cell dimensions may change during the experiment due to thermal expansion, or the crystal may move very slightly, or the x-ray spectrum may vary due to fluctuations in the source or optics. The likelihood of these experimental artefacts and the magnitude of the errors they would introduce if present must be carefully evaluated in an individual experiment. Indeed, the entire experiment may fail if an order-disorder reaction occurs that leads to transient loss of the x-ray diffraction pattern [37],... 

R. M. Hazen and A. Navrotsky. Effects of pressure on order-disorder reactions. Am. Mineral., 81 1021-1035, 1996. 

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