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This question might be a bit silly, but I have to ask since I am very curious and I did not find any good answer. I visited two places, where quartz crystals (var. smoky quartz) occurs - and both sites are pretty similar and could host the same formation process.

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My question is - could you explain how exactly these crystals of quartz could form in calcite veins in limestone ? Hydrothermal fluids ? What does it mean, could it be easily described ? Where did the SiO2 come from ? Was there any radiation, too ?

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Your question is

How does quartz form in calcite veins?

But maybe a more appropriate question will be

How does quartz not form in calcite veins?

Quartz is one of the most common vein material in Earth's crust, and for a reason. SiO2 is not a particularly soluble compound at the surface, but once you get deeper it becomes extremely soluble (source):

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The solubility of SiO2 is almost 0 at at 1 bar and 25 °C, but increases strongly with pressure and temperature. For example, at 200 °C and 2000 bar (2 kbar, 0.2 GPa, about 5–6 km depth), conditions that are reasonable for an unmetamorphosed but deeply buried limestone, you can fit about 500 mg of SiO2 in 1 kg of H2O. At atmospheric pressure that's one litre of water, but it's much less voluminous at depth. That is a lot of SiO2! Once the fluid goes up towards the surface, it depressurises and cools, causing precipitation of quartz.

There is no shortage of sources for SiO2. It is the most common chemical component in the crust. Even in seemingly pure limestone there are more than enough impurities of silicates to provide a source for SiO2.

The fact that quartz and calcite occur together in a vein is no problem at all. You might expect them to react, but they actually do not. Here's a diagram to show it (source):

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Calcite and quartz can peacefully coexist, unless it's extremely hot and then they react to form wollastonite (a Ca-silicate). This is the kind of stuff you find in high grade metamorphosed marbles, for example.

As an aside, another question that may be asked is why only calcite and quartz? If hot dense water are so good in dissolving stuff? Where's the rest of the periodic table? Well, most of the elements are readily soluble in acidic fluids. In this case, the abundant calcite buffers the pH of the water to rather basic conditions, which are not that great in dissolving stuff.

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Vein mineralization occurs when percolating groundwaters exceed saturation with respect to the mineral being precipitated. The saturation index for each mineral, defined as log(IAP/KT) may be negative-undersaturated (mineral dissolves), positive-oversaturated (mineral precipitates), or zero (nothing happens). It is a function of thermodynamic equilibrium with respect to each mineral in which the mineral chemistry has dissolved components in the groundwater. It is a bit complicated, but if you measure the redox potential, pH, temperature, and full chemical analysis of the groundwater, then you can feed the results into an open access programme such as PHREEQE or WATEQ4F, and it will tell you which minerals are oversaturated. There is also the matter of reaction kinetics, such that some minerals may be over-saturated but so sluggish to precipitate that you won't find it in the vein.

Calcite and quartz are both common, almost ubiquitous in limestone veins. Obviously, the calcite is re-precipitated limestone. The groundwater chemistry undergoes cycles according to recharge characteristics, temperature, pressure and partial pressure of CO2, so sometimes it dissolves and re-precipitates the same carbonate several times, discernible by subtle changes in dissolved Mg and Sr and isotopic composition. All limestones have differing degrees of impurities, typically from about 0.5 to 10%, of which silica is a ubiquitous component. Groundwaters typically carry dissolved silica, as silicic acid, in the concentration range of about 5 to 50 mg/litre. Under normal temperature-pressure conditions silica / quartz precipitates or dissolves extremely slowly, but at higher pressures and temperatures the kinetics of crystallization are dramatically accelerated. So precipitation of quartz and calcite is actually quite common.

Radiation is not normally a feature unless there also happens to be dissolved uranium or high levels of potassium in the environment. Radiation does not change the basic thermodynamic controls over precipitation.

PS: IAP is the 'ion activity product', K is a characteristic constant unique to each phase change, and T is the temperature in degrees Kelvin.

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