Linear calcite

In the calculation results (Fig. 14.6), increasing the CO2 fugacity decreases the pH to about 6, causing calcite to dissolve into the fluid. The fugacity increase drives CO2 from the buffer into the fluid, and most of the CO2 (Fig. 14.7) becomes C02(aq). The nearly linear relationship between the concentration of C02(aq) and the fugacity of C02(g) results from the reaction... 

Trace elements are useful tracers of geochemical processes mostly because they are dilute their behavior depends primarily on the trace element-matrix interaction (e.g., Rb-host feldspar, Sr-calcite) and very little on the trace-trace interaction (e.g., Rb-Rb, Sr-Sr). Consequently, the distribution of trace elements among natural phases largely obeys the linear Henry s law. The modeling of trace elements in various geological environments (magmas, hydrothermal fluids, seawater,...) relies on three different aspects... 

Because one mole of calcite reacts with one mole of quartz, the molar reaction rates of phase A and B are identical, which equals the molar growth rate of wollastonite (D). Therefore, the linear reaction rate and u are related as follows ... 

For the calculations, averages of the results of the two 5. -equilibrium models of Ca2+ = 35 p.p.m., Mg2+ = 7 p.p.m., and alkalinity = 1.55 X 10 3 equiv./liter are used. Solubility data of Larson and Buswell (11), carbon dioxide solubility data of Hamed and Davies (2), and the carbonate ionization data of Hamed and Hammer (3) and Hamed and Scholes (4) are used. Linear interpolations are made for dolomite between pK(soly) = 16.3(5°C.) and 17.0(25°C.). Equations outlining the calcite and dolomite calculations are ... 

Figure 15.8 Equilibrium constant for the solubility of calcite [reaction (15.25)] as a function of temperature obtained from Line 1 Measured solubility (fitting equation assumes ACp is linear in temperature). Line 2 Thermodynamic data assuming ACp equals zero. Line 3 Thermodynamic data assuming ACp is constant. Line 4 Thermodynamic data assuming ACp is constant with corrected CP(CO2-).

Unfortunately, there is generally a large scatter in the values obtained for these partition coefficients. A possible reason for this scatter, as shown by the study of Lorens (1981), is probably the major effect of precipitation rate on the values of the partition coefficients. It is interesting to note that the partition coefficients for the transition and heavy metals in calcite, studied by Lorens (Cd2+, Mn2+, Co2+), have a negative linear log partition coefficient- log precipitation rate relation, whereas Sr2+ has a positive relation. This behavior may be explained by the fact that the transition metal carbonates are isostructural with calcite, whereas strontium carbonate is isostructural with aragonite. Also, as precipitation rates increase, partition coefficients tend towards unity. 

Chave et al. (1962) limited their measurements to changes of pH during the dissolution reaction, and estimated the pH at infinite time by extrapolation of plots of pH versus the reciprocal of the square root of time. These plots were chosen empirically, because they usually yield linear plots as infinite time is approached when calcite, aragonite, or other simple carbonate minerals are used (Garrets et al., 1960). Chave et al. claimed that in the case of magnesian calcites, however, only... 

Chave (1952) reported a linear relationship between the position of the 1014 diffraction peak of skeletal calcites and their Mg concentrations, as determined by wet chemical techniques, over the range 0-18 mole % MgC03. At higher Mg concentrations, the relationship was observed to be nonlinear. He concluded "that Mg was replacing Ca in the calcite lattice, shrinking it, and forming a solid solution between calcite and dolomite" (Chave, 1981). 

E.T. Malus discovered that images of objects viewed through calcite crystals appeared to become doubled [3]. This phenomenon of double refraction was ultimately ascribed to linear birefringence, where the indices of refraction along the axes of the anisotropic crystal were unequal. A beam of... 

An approximate relationship between the degree of undersaturation of seawater with respect to calcite and the extent of dissolution can be established by comparing the saturation state at the various sediment marker levels with estimates of the amount of dissolution required to produce these levels. In Figure 9 the "distance from equilibrium (1 - 2) has been plotted against the estimated percent dissolution of the calcitic sediment fraction. Within the large uncertainties that exist in the amount of dissolution required to produce the FL and Rq levels, a linear relation between the degree of undersaturation and extent of dissolution can be established. The intercept of the linear plot with the FL and Rq levels indicates that approximately 15 percent more material has been lost than Berger s (12) minimum loss estimate of 50% and 10%, respectively. 

Both Peterson (41) and Berger (42) found that dissolution started at approximately 0.5 km water depth and the rate of dissolution increased slowly with increasing water depth until a depth of approximately 3.8 km was reached. Below this depth the rate of dissolution rapidly increased with increasing water depth. The change in the saturation state of seawater, with respect to calcite, in the deep water of this region is close to linear with depth (43). Consequently, the results of these experiments indicated that the rate of dissolution was not simply related to saturation state. Edmond (44) proposed that the rapid increase in dissolution rate could be attributed to a change in water velocity. Morse and Berner (45) pointed out that this could be true only if the rate of dissolution was transport controlled. Their calculations indicated that the rate of dissolution measured by Peterson (41) was over 20 times too slow for diffusion controlled dissolution, this being the slowest transport process. 

Using the pH-stat technique, Morse and Berner (45) found that the dissolution rate of synthetic and pelagic biogenic calcite did not increase linearly with increasing undersaturation. Beyond a critical undersaturation a very rapid increase in the rate of... 

Clearly, there are real differences in ki between experiments. The highest value of ki is estimated from the data of Weyl (9 )y who directed a jet of CO2-saturated water (pH = 3.9) onto the surface of calcite. Weyl found that the rate of solution varied with the jet velocity. His rates imply that kj varies from 0.11 to 0.23 when velocity of the jet increases from 18 to 35 m sec The smallest value of k (.0073) is derived from the data of Tomlnaga et al. (10). These authors rotated a disk of marble in HCl solutions (0.1750 - 0.5317N) at 485 rpm. Rate of dissolution was followed by the volume of CO2 evolved. After an initial period for saturation of the acid with CO2, rate of gas evolved becomes linear in the cumulative amount of CO2 produced. Because the acid concentration decreased as calcite dissolved, we extrapolated the observed linear relation in CO2 production back to the initial condition to estimate Initial rates under known acid concentrations. Correction to pH via the Davies equation leads to the rates shown for these authors in Figure 6. 

Rate expressions of this form were derived for calcite precipitation with = 1 (Nancollas and Reddy, 1971 Reddy and Nancollas, 1971), and with mj = 0 and = 0.5 (Sjoberg, 1976 Kazmierczak et al, 1982 Rickard and Sjoberg, 1983 Sjoberg and Rickard, 1983). Rate equations such as (57) wherein rates are linearly proportional to AG close to equilibrium have been attributed to adsorption-controlled growth (Nielsen, 1983 Shiraki and Brantley, 1995). Such rate models have been used by some researchers to model dissolution and precipitation of quartz over a wide range in temperature and pressure (Rimstidt and Barnes, 1980) however, it has been pointed out that this has only been confirmed with experiments at high temperature (Dove, 1995). 

If it is assumed that calcite, dolomite, gypsum, and carbon dioxide are the phases to be considered, mass balance can be described by four linear equations of the form given by Equation (9). Simultaneous solution of these four equations for water chemistry changes between unmineralized rainwater to the water composition of Polk City yields the mass balance ... 

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