Origin of carbonate sediments
Calcium carbonate occurs dissolved in seawater and fresh waters. Calcium derives from the weathering of Ca-bearing minerals in rocks, like plagioclase, and it is present in water as Ca²⁺ ions. Atmospheric CO₂ dissolves in water producing H₂CO₃ (carbonic acid), a weak acid, following the reaction:

CO₂(gas) + H₂O(liquid) ⇌ H₂CO₃

H₂CO₃ dissociates in water as carbonate [CO₃^2-] and bicarbonate [HCO₃^–] ions:

H₂CO₃ ⇌ H⁺ + HCO₃^–
HCO₃^– ⇌ H⁺ + CO₃^2-

The precipitation of calcium carbonate [CaCO₃] from water is, hence, balanced by the reaction:

Ca²⁺ + 2HCO₃^– ⇌ CaCO₃ + H₂CO₃

The precipitation of dolomite [CaMg(CO₃)₂]from a water solution is controlled by a similar reaction. Magnesium is another common ion in water, which, like calcium, derives from the alteration of minerals like olivine:

Ca²⁺ + Mg²⁺ + 4HCO₃^– ⇌ CaMg(CO₃)₂ + 2H₂CO₃

The dissolution of calcite and dolomite is, hence, controlled by how acidic water is, or, in other words, how much atmospheric CO₂ is dissolved in water: the more carbonic acid, the more aggressive water is to carbonates. CO₂ is a gas, so its solubility in water is favored by low temperature (CO₂ molecules move slower and are more easily dissolved in water), high pressure (promoting the dissolution of the gas phase to water), or simply because there is more atmospheric CO₂ (which is why tropical carbonate reefs are struggling due to CO₂ emissions). Consequently, the dissolution of carbonates is favored by low temperature, high pressure, or high amounts of CO₂ dissolved in water. On the other hand, high temperatures, low pressures, or any process leading to a decrease of dissolved CO₂ favor the precipitation of carbonates from water. In nature, the balance between dissolution and precipitation is controlled both by inorganic and organic processes. In particular, many marine life forms are responsible for the formation of the vast majority of carbonate rocks, since organisms either produce shells and other skeletal parts of carbonates or cause the precipitation of carbonate as a byproduct of their activities.

Organic precipitation of carbonates
Carbonates are common in seawater and marine organisms have learned to use calcium carbonate to produce shells and other skeletal parts. Invertebrates like bivalves, gastropods, cephalopods, brachiopods (“sea shells”), echinids (sea urchins), crinoids (sea lilies), asteroids, ophiurids (starfishes), anellids (segmented worms), and many other taxa produce hard parts of one or both polymorphs of calcium carbonate (calcite or aragonite), but most marine carbonates are produced by microorganisms with carbonate tests (nanoplankton), like foraminifera and coccolithophores. Reefs are constructions of carbonate rocks produced by reef-building organisms like corals, bryozoans, and cyanobacteria (stromatolites). Carbonate precipitation is favored in hot waters and, for this reason, reefs occur in tropical and subtropical seas nowadays. The details of how organisms manage to cause the precipitation of carbonates are not well understood, but they use a wide range of proteins capable of favoring the nucleation of calcite and aragonite crystals in specific orientations.

Carbonate sand with abundant fragments of corals, echinoids, molluscs, and pink foraminifera. Deposits of carbonate sand transform into carbonate rocks during burial and diagenesis. Field of view: 32 mm. Photo © Siim Sepp.

Photosynthesis
Photosynthetic organisms living in water use sunlight to convert dissolved CO₂ to organic compounds, releasing oxygen (O₂) in the process. The decrease of dissolved CO₂ causes the precipitation of carbonates that end up encrusting photosynthetic organisms like algae, plants, and cyanobacteria. The progressive encrustation of colonies of cyanobacteria (microbial mats) produces layered limestone formations known as stromatolites and also rounded concretions known as oncolites. These organisms also trap carbonate particles coming from the surroundings as they grow.

Inorganic precipitation (and dissolution) of carbonates
Ooids
The white sands of tropical beaches, like the Bahamas or the Maldives, consists of ooids, spherical concretions of calcium carbonate with a maximum diameter of 2 mm. In tropical areas, waters are commonly saturated with calcium carbonate. Ooids nucleate around a small core, which may consist of any small solid object, like the fragment of a shell or a quartz grain. When the nucleus of the ooid is transported by waves, the instantaneous drop in pressure causes the precipitation of calcium carbonate, typically in the form of aragonite which can hence recrystallize as calcite. The process is repeated by wave action, leading to the formation of several, concentric layers around the original core. When ooids are about 2 mm wide, waves are no longer able to transport them in suspension, and the process halts.

Pisoids
Pisoids are similar to ooids but are much bigger: they are concentric carbonate concretions that can reach several centimeters in diameter. Their formation is caused by periodic changes in the surface of groundwater saturated in calcium carbonate within a sediment. Each time the water table changes, it deposits a thin layer of calcium carbonate over the grains of a sediment. The process is seasonal and can continue forever, until the porosity of the sediment is eventually sutured by the growth of pisoids. Another ambient where pisoids form are caves, where concretion of carbonates can deposit on grains transported by water or on karst breccias.

Karst and caves
Karstic environments occur anywhere there are outcrops of carbonate rocks exposed on the surface and are a great example of how subtle the equilibrium between dissolution and precipitation of carbonates is at ambient conditions. Rainwater that falls on carbonates contains atmospheric CO₂ that progressively attacks carbonate rocks. The dissolution of carbonates is a selective process which runs faster where water is stagnant, as in small pools, or where it can infiltrate rocks, as along fractures. The infiltration of aggressive water in fractured carbonates progressively enlarges the fractures, enhancing the infiltration of acidic waters at depth, ultimately leading to the formation of cave systems. Once water reaches caves, carbonate precipitation can occur, producing cave formations like stalactites and stalagmites. Stalactites and stalagmites form from water droplets dripping in the cave that release CO₂ when they fall and when they hit the ground, due to the instantaneous drop in pressure, causing the precipitation of carbonate from water, droplet after droplet.

Travertines
Travertines are carbonate rocks produced by the inorganic precipitation of carbonate from hot springs and fresh waters. Hot springs derive from deep waters that are released by geothermal systems (or from other sources) and may contain large amounts of dissolved CO₂ (which may be released for example by cooling igneous intrusions). When these waters reach the atmosphere, they rapidly release most of the dissolved CO₂ ,causing the rapid precipitation of carbonates from water. Travertine deposits encrust the surrounding rocks, soil, and can trap organisms and produce molds of fossils, commonly leaves.