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Materials made from thermodynamically stable carbon compounds
I am still considering whether wood should be included under a modified definition as it is a short term sink but not thermodynamically stable. It burns! CO2 stored underground is reactive. It will react eventually.
The need for a new and very large sink can be appreciated by considering the balance sheet of global carbon in the crust after Ziock, H. J. and D. P. Harrison depicted below.
According to Ziock, H. J. and D. P. Harrison "The size of natural carbon sinks or pools compared to fossil fuels reserves and to potential emissions in the new century. For emissions we show four blocks of 600 Gt each. 600 Gt would be the result of 100 years of constant emissions at the current rate. If the last century is any guide, the output could be five to six times larger. In the emission column below the zero line we show the far smaller total emissions of the 20th century, which in turn dwarfed the emissions of the 19th century. Individual blocks below the zero line represent 100 years of emission at the rate of 1900. The easily accessible carbon reservoirs with the exception of the ocean are comparable in size to the expected emissions of the next century. However, one would be hard pressed to actually double the existing biomass without substantively changing the environment. The ocean reservoir, at 39,000 Gt of carbon, is far larger, but its ability to take up carbon without environmental change is limited. Above the zero line, we are showing the amount of carbon that when dissolved in the ocean in the form of CO2 would change its pH from top to bottom by 0.3. .....The resource columns show that available fossil energy exceeds all likely demand for at least a century or two."
See also our page Carbon Cycles and Sinks - The Case for Man Made Carbonate 
 John Harrison. So long ago I can't remember!
 Modified from Figure 2 in Ziock, H. J. and D. P. Harrison. "Zero Emission Coal Power, a New Concept." from http://www.netl.doe.gov/publications/proceedings/01/carbon_seq/2b2.pdf. by the inclusion of a bar to represent sedimentary sinks.