Components having coating systems comprising mud cracks and methods for forming the coating systems

A component comprising:

• a substrate comprising silicon nitride;
• and
• a coating system on a surface of the substrate, wherein the coating system includes:
• a first layer of a first coating material on the substrate, wherein the first coating material includes a rare earth silicate and has a first thickness measured in a direction perpendicular to the surface of the substrate;
• and
• a second layer of a second coating material on the first layer, wherein the second coating material includes a rare earth silicate and has a second thickness that is greater than the first thickness of the first layer, wherein the second layer includes mud cracks that extend from an exterior surface thereof toward the substrate, wherein the mud cracks have widths in a range of about 50 to 200 micrometers.

A vehicle comprising a component that includes:

• a substrate comprising silicon nitride;
• and
• a coating system on a surface of the substrate, wherein the coating system includes:
• a first layer of a first coating material on the substrate, wherein the first coating material includes a rare earth silicate and has a first thickness measured in a direction perpendicular to the surface of the substrate;
• and
• a second layer of a second coating material on the first layer, wherein the second coating material includes a rare earth silicate and has a second thickness that is greater than the first thickness of the first layer, wherein the second layer includes mud cracks that extend from an exterior surface thereof toward the substrate, wherein the mud cracks have widths in a range of about 75 to 125 micrometers, wherein the second thickness is in a range of 6 to 12 micrometers, wherein the mud cracks have inner surfaces that have a smooth or rounded profile.