CMAS-resistant barrier coatings

A method comprising:

• predicting a composition of active components of calcium-magnesium-aluminum-silicate (CMAS) to be encountered by a high temperature mechanical system during use of the high temperature mechanical system, wherein the composition of active components of CMAS comprises a relative molar composition of at least two of calcium oxide, magnesium oxide, aluminum oxide, or silicon oxide;
• and
• selecting a composition of a CMAS-resistant barrier coating layer based at least in part on the predicted composition of active components of CMAS, wherein, prior to exposure of the barrier coating to an operating environment of the high temperature mechanical system, the CMAS-resistant barrier coating layer comprises:
• a base composition comprising at least one of a rare earth monosilicate or a rare earth disilicate;
• at least one secondary oxide selected based on the predicted composition of active components of CMAS to reduce, compared to the base composition alone, at least one of:
• a diffusion gradient of the active components of CMAS into the CMAS-resistant barrier coating layer;
• or
• a reaction gradient of the active components of CMAS with the base composition of the CMAS-resistant barrier coating layer,
• wherein the at least one secondary oxide comprises at least one of an oxide of a divalent element, an oxide of a trivalent element, or an oxide of a tetravalent element,
• wherein the CMAS-resistant barrier coating layer comprises greater than 0 mol. % and less than about 7 mol. % of the at least one secondary oxide, and
• wherein the at least one secondary oxide includes at least one of calcium oxide, barium oxide, magnesium oxide, aluminum oxide, or silicon oxide.