Disordering versus ordering experiments

In any kinetic experiment, a natural or synthetic starting material must have been partially or completely pre-equilibrated at a certain temperature T0, here called the initial temperature. At such a temperature, a cation gains its initial site occupancies

1400 1200 - ordering T (K) 1000 ■ 800 ■ 600

initial pre-equilibration temperature A , :723 K ^ A2: 773 K A3: 823 K B , : 923 K B2: 973 K B3: 1023 K B4: 1273 K T= 873 K x Fe = 0.515 disordering

x|7x?

ordering and disordering 7 = 8 7 3 K x Fe = 0.515 kf | = 0.0000495 k = 0.0000169 0.335 - 0.305 - 0.275 6 A ill ill l l 0.245 - 0.215 40000 60000 80000 100000 20000

Fig. 2-7. Effect of initial equilibrium site occupancies on ordering and disordering experiments. (A) Starting samples for the ordering (Bj to B4) and disordering (Aj to A3) experiments are supposed to have gained equilibrium site occupancies at different temperatures before the kinetic experiments are conducted at 873 K. Values of T- XFe(M2)/XFe (M i) are calculated from experimental results for the orthopyroxene sample TZ of Besancon (1981). (B) Kinetic site occupancies are strongly dependent on the initial site occupancies of the samples, showing an increase for disordering experiments A \ to A3, in contrast to a decrease for ordering experiments Bi to B4.

0.33 0.31 - 0.29 - 0.27 - 0.25 - 0.23 - 0.21 0.32 0.30 0.28 ■ 0.26 0.24 • 0.22 ordering at 773 K initial condition: pre-equilibrated at 1273 K rFe. time (s) '0 = 0 100000 t 2 = 200000 f3 = 360000 f4 = 600000 1000000 infinite 'e 500000 1000000 1500000 2000000 t (s) disordering at 873 K □ r0 * • <1 20000 40000 60000 80000 t (s)

Fig. 2-8. Influence of initial kinetic site occupancies upon ordering and disordering experiments. (A) Starting samples (e.g., orthopyroxene) first gain equilibrium site occupancies at to = 0 and T = 1273 K, then obtain kinetic site occupancies at different times corresponding to t\ to t5 at 773 K, and finally reach equilibrium at t = t£ - infinite and T = 773 K. The initial conditions and kinetic coefficients are calculated from the orthopyroxene sample TZ of Besancon (1981). (B) Different initial kinetic site occupancies strongly affect the kinetic behaviour of a cation as illustrated by the disordering of Fe2+ at Mj at 873 K in the orthopyroxene, giving different kinetic curves.

(either equilibrium or kinetic) either by geological processes or laboratory heating before a kinetic experiment is conducted at a different temperature T. If T > T 0, this experiment is usually called a disordering experiment; on the other hand, if T <T0, it is referred to as an ordering experiment since most cations usually become more disordered with increasing temperatures.

Initial equilibrium site occupancies for a fixed total composition o f a mineral will affect the kinetic behaviour o f the cation, leading to different kinetic curves o f the ordering experiments from the disordering experiments at the same temperature and pressure. In order to illustrate this, let us consider an example: an orthopyroxene with a total composition X Fe =0.515, which is the sample TZ o f Besancon (1981). Based on experimental data (Besancon, 1981) and nonlinear parameterisation, we get the following Arrhenius relations for kinetic coefficients with temperature:

LnkF2 = (17.15 ± 1.23) + (-23630 ± 1180) / T (2-29)

Lnkji = (17.94 ± 0.88) + (-25257 ± 846) / T. (2-30)

Now suppose that a series of kinetic experiments were conducted on this sample at the same temperature, 873 K, and that all conditions for the kinetic experiments are exactly the same except for initial pre-equilibration temperatures.

In Fig. 2-7A, samples A i, A2 and A3 are assumed to have been pre-equilibrated at three different temperatures, 723 K, 773 K and 823 K, and they represent disordering kinetic experiments since the kinetic experimental temperature (873 K) is higher than the

initial pre-equilibration temperatures. Similarly, samples B i, B2, B3 and B4 are

supposed to have been pre-equilibrated at 923 K, 973 K, 1023 K and 1273 K respectively, and they correspond to ordering kinetic experiments. Combining Equations 2-5 and 2-20 with Equations 2-29 and 2-30, we can get the initial equilibrium site occupancy data, for example, x Fe =0.218 and x Fe = 0.811 at 773 K, and x Fe = 0.302 and x Fe =0.728 at 973 K. Fig. 2-7B clearly demonstrates that the site occupancies o f Fe2+ at Mj for the ordering kinetic experiments are very different from those o f the disordering experiments. In this example, the disordering experiments are monotonously increasing functions, but the ordering experiments correspond to monotonously decreasing

functions. Fe2+ at M2 and Mg2+ at both sites show similar behaviour.

On the other hand, the kinetic history o f the samples also has strong influence on the site occupancies o f the cation in any kinetic experiments. Let us consider the following example. We assume that an orthopyroxene sample (e.g., sample TZ) has been equilibrated at 1273 K, and then becomes partially ordered at different times at 773 K. In Fig. 2-8A, points t\ to are a series o f partly equilibrated or ordered samples at 773 K, whereas points to and t£ represent the samples which are completely equilibrated at 1273 K and 773 K respectively. Using these samples as starting materials, different

kinetic curves corresponding to these points have been calculated at 873 K (Fig. 2-8B). Clearly, samples with varying degrees of order yield different kinetic curves. From these two examples, it can be observed that

(1) Initial equilibrium concentrations of a cation and the kinetic history of the samples have significant effects on the kinetic site occupancies of the cation in any experiments. In other words, it is impossible to replicate a kinetic experiment or reproduce the experimental data at a given temperature and pressure for a sample with exactly the same composition, without knowing the initial kinetic or equilibrium site occupancy data.

(2) Equilibrium site occupancies and kinetic coefficients of a cation are independent of initial site occupancies (equilibrium or kinetic). All different curves in Figs. 2-7B and 2-8B give the same kinetic coefficients and yield the same equilibrium site occupancies for the cation. This can be easily proven from Equations 2-18 and 2-19. The best way to repeat or duplicate an experiment (especially natural samples), therefore, might be to test whether the kinetic coefficients and equilibrium site occupancies are the same, rather than the kinetic site occupancies.

Chapter 3

A kinetic model for three-site intracrystalline