Calcite theory

We say then that a crystal is satisfactory for purposes of chemical analysis if the beam it reflects is monochromatic within the limits established by the collimating system. As theory shows,15 some broadening is to be expected on Bragg reflection even from perfect crystals, but this broadening is so small (not over 0.001°) that we need not consider it. Relatively few crystals, notably some diamonds and calcites, approach perfection. Sodium chloride, more useful in x-ray spectrog-raphy, broadens monochromatic x-rays appreciably, but the. total broadening can be smaller than 0.30°,16 the collimator a perture. See Figure 4-9. 

Berner, R.A. Morse, J.M. 1974. Dissolution kinetics of calcium carbonate in seawater. IV. Theory of calcite dissolution, American Journal of Science, 274,108-134. 

Thus, larger solid/water ratios such as are encountered in pore waters of sediments lead to smaller MgC(>3 contents in the equilibrium magnesian calcites although in either case the magnesium content of the solid increases. Wollast and Reinhard-Derie presented data to support the theory from the standpoint of dissolution and some of our results for the precipitation case... 

The other reason why the average salinity of seawater is 35%o lies in the fundamental chemistry of major ions. For example, the sevenfold increase in the Na /K ratio between river water and seawater (Table 21.8) reflects the lower affinity of marine rocks for sodium as compared to potassium. In other words, the sodium sink is not as effective as the one for potassium. Thus, more sodium remains in seawater, with its upper limit, in theory, being controlled by the solubility of halite. Likewise, the Ca /Mg ° ratio in seawater is 12-fold lower than that of river water due to the highly effective removal of calcium through the formation of biogenic calcite. 

In the context of transition-state theory, for ions and molecules in the liquid to attach to the crystal, they must first become an activated complex. The same is true for detachment (Figure 4-5). For clarity of discussion, use calcite (Cc), assumed to be pure CaCOs, growth from an aqueous solution as an example. The reaction is... 

Carlson W.D. (1983) Aragonite-calcite nucleation kinetics an application and extension of Avrami transformation theory. /. Geol. 91, 57-71. 

A third problem with the mitochondrial theory of biomineralization is that many mineralized tissues contain carbonate rather than phosphate. Since bicarbonate ions do not pass across mitochondrial membranes with any ease, it has now been shown that in phosphate-free buffers, calcium will enter mitochondria if dissolved carbon dioxide is available. It appears that some mitochondria possess carbonic an-hydrase activity on the inner membrane or in the mitochondrial matrix and are thus able to synthesize bicarbonate within the organelle. In such cases, inhibitors of carbonic anhydrase block the accumulation of calcium and carbonate ions622) since crystals of calcite have been identified in the mitochondria of earthworms calci-ferous glands623. These cells freqently showed spherical granules in the cytoplasm and lumen of the glands during phases of mineral secretion and it was suggested that they were aspects of cellular breakdown which occurred at these times. 

The activities of Mg++ and Ca++ obtained from the model of sea water proposed by Garrels and Thompson have recently been confirmed by use of specific Ca++ and Mg++ ion electrodes, and for Mg++ by solubility techniques and ultrasonic absorption studies of synthetic and natural sea water. The importance of ion activities to the chemistry of sea water is amply demonstrated by consideration of CaC03 (calcite) in sea water. The total molality of Ca++ in surface sea water is about 10 and that of COf is 3.7 x 1C-4 therefore the ion product is 3.7 x 10 . This value is nearly 600 times greater than the equilibrium ion activity product of CaCO of 4.6 x 10-g at 25°C and one atmosphere total pressure. However, the activities of the free 10ns Ca++ and COj = in surface sea water are about 2.3 x 10-3 and 7.4 x 10-S, respectively thus the ion activity product is 17 x 10 which is only 3,7 rimes greater than the equilibrium ion activity product of calcite. Thus, by considering activities of sea water constituents rather than concentrations, we are better able to evaluate chemical equilibria in sea water an obvious restatement of simple chemical theory but an often neglected concept in sea water chemistry. 

McKean 182> considered the matrix shifts and lattice contributions from a classical electrostatic point of view, using a multipole expansion of the electrostatic energy to represent the vibrating molecule and applied this to the XY4 molecules trapped in noble-gas matrices. Mann and Horrocks 183) discussed the environmental effects on the IR frequencies of polyatomic molecules, using the Buckingham potential 184>, and applied it to HCN in various liquid solvents. Decius, 8S) analyzed the problem of dipolar vibrational coupling in crystals composed of molecules or molecular ions, and applied the derived theory to anisotropic Bravais lattices the case of calcite (which introduces extra complications) is treated separately. Freedman, Shalom and Kimel, 86) discussed the problem of the rotation-translation levels of a tetrahedral molecule in an octahedral cell. 

Griffin and Jurinak (1974) calculated pseudothermodynamic parameters for phosphate interactions with calcite using reaction-rate theory. Gonzalez et al. (1982) applied reaction-rate theory to a treatment of adsorption-desorption processes on an Fe-selica gel system. In 1981, Sparks and Jardine applied reaction-rate theory to kinetics of potassium adsorption and desorption in soil systems for the first time (Table 2.5). 

It is instructive to pursue the interpretation of the calcite rhomb experiment beyond the simple Huyghenian construction to learn something about the polarization of the transmitted light. The electromagnetic theory of light requires that the electric vector shall be contained in the plane of the wave front. The ordinary disturbances vibrate perpendicular to a principal section. Also the extraordinary disturbance must vibrate in the principal section plane. 

One of the most controversial topics in the recent literature, with regard to partition coefficients in carbonates, has been the effect of precipitation rates on values of the partition coefficients. The fact that partition coefficients can be substantially influenced by crystal growth rates has been well established for years in the chemical literature, and interesting models have been produced to explain experimental observations (e.g., for a simple summary see Ohara and Reid, 1973). The two basic modes of control postulated involve mass transport properties and surface reaction kinetics. Without getting into detailed theory, it is perhaps sufficient to point out that kinetic influences can cause both increases and decreases in partition coefficients. At high rates of precipitation, there is even a chance for the physical process of occlusion of adsorbates to occur. In summary, there is no reason to expect that partition coefficients in calcite should not be precipitation rate dependent. Two major questions are (1) how sensitive to reaction rate are the partition coefficients of interest and (2) will this variation of partition coefficients with rate be of significance to important natural processes Unless the first question is acceptably answered, it will obviously be difficult to deal with the second question. 

Winograd, I.J., Szabo, B.J., Coplen, T.B. and Riggs, A.C., 1988, A 250,000-year climatic record from Great Basin vein calcite Implications for Milankovitch theory. Science 242 1275-1280. 

In theory, it should also be possible to use C-isotope variations in speleothems as a monitor of past climate change in a manner analogous to 0-isotopes. The carbon isotopic signal in speleothem calcite arises from the ratio of dissolved inorganic carbon... 

Hiickel theory [or the Giintelberg or Davies equation (Table 3.3)] may be used to convert the solubility equilibrium constant given at infinite dilution or at a specified / to an operational constant, valid for the ionic strength of interest. In seawater solubility equilibrium constants, experimentally determined in seawater, may be used. For example, the CaC03 calcite solubility in seawater of specified salinity may be defined by = [Ca " ] [CO f ], where [Caj ] and [C03f ] are the total concentrations of calcium and carbonate ions, for example,... 

Many natural aquatic systems have a chemical composition close to saturation with respect to calcite or even dolomite. This is the case, for instance, for seawater, which is usually slightly oversaturated in the upper part of the water column and slightly undersaturated at greater depths. Under these conditions, the rates of both precipitation and dissolution contribute significantly to the overall rate of reaction. Even though the reaction paths may be very complex, there is a very direct and important link between the kinetic rate constants, according to which the rates of forward and reverse microscopic processes are equal for every elementary reaction. The fundamental aspect of this principle forms the essential aspect of the theory of irreversible thermodynamics (Frigogine, 1967). 

A given set of experimental data may be explainable by different models. For example, Reddy et al. (31) measured the growth rate of calcite and fit the data to a rate law model proposed by Plummer et al. (32). It was later shown (22) that a very simple "transition state theory" rate law, quite different in form, fit the data about as well (neither model fit the data perfectly). One should keep in mind that such models may extrapolate differently. 

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