[The company] says it has made Portland cement from silicate rocks like basalt—at the lab scale. Basalt contains a mix of minerals that include calcium, aluminum, iron, magnesium, sodium, silicon, and oxygen. (Note the absence of carbon from that list.) The basic idea is that you don’t need limestone to get calcium oxide.

The process of freeing these components from basalt looks more like a refining or recycling process than the toss-it-in-the-oven simplicity of the limestone process. Acid can be used to leach elements like calcium out, then a chemical or energetic process precipitates that calcium as calcium hydroxide. Toss that in a kiln with additives of your choice, and with less heating than you need for limestone, you’ve got Portland cement, with only water vapor released.