A method for coating a substrate includes spraying a combination of powders. The combination of powders includes: Hf.sub.0.5Si.sub.0.5O.sub.2; Zr.sub.0.5Si.sub.0.5O.sub.2; and, optionally, at least one of HfO.sub.2 and ZrO.sub.2. A molar ratio of said Hf.sub.0.5Si.sub.0.5O.sub.2 and HfO.sub.2 combined to said Zr.sub.0.5Si.sub.0.5O.sub.2 and ZrO.sub.2 combined is from 2:1 to 4:1. A molar ratio of said Hf.sub.0.5Si.sub.0.5O.sub.2 to said HfO.sub.2 is at least 1:3.

A thermal barrier coating includes a highly porous layer and a dense layer. The highly porous layer is formed on a heat-resistant base, is made of ceramic, has pores, has a layer thickness of equal to or larger than 0.3 mm and equal to or smaller than 1.0 mm, and has a pore ratio of equal to or higher than 1 vol % and equal to or lower than 30 vol %. The dense layer is formed on the highly porous layer, is made of ceramic, has a pore ratio of equal to or lower than 0.9 vol % that is equal to or lower than the pore ratio of the highly porous layer, and has a layer thickness of equal to or smaller than 0.05 mm.

An article includes a substrate, a bond coat on the substrate, and a multilayer environmental barrier coating (EBC) on the bond coat. The multilayer EBC includes a first EBC layer defining a first thickness and a second EBC layer defining a second thickness. The first EBC layer includes a first rare earth disilicate and a first concentration of a sintering aid that includes alumina. The second EBC layer includes a second rare earth disilicate and a second concentration of the sintering aid that includes alumina, less than the first concentration of the sintering aid.

A ceramic membrane filter includes a porous substrate including cells through which a fluid flows, an intermediate membrane formed on the porous substrate, and a separation membrane formed on the intermediate membrane. In this ceramic membrane filter, the percentage of the number of cells having cracks with a size of 4 ?m or less relative to the total number of cells is 9% or less.

An article that includes a substrate; a first layer including yttria and zirconia or hafnia, where the first layer has a columnar microstructure and includes predominately the zirconia or hafnia; a second layer on the first layer, the second layer including zirconia or hafnia, ytterbia, samaria, and at least one of lutetia, scandia, ceria, neodymia, europia, and gadolinia, where the second layer includes predominately zirconia or hafnia, and where the second layer has a columnar microstructure; and a third layer on the second layer, the third layer including zirconia or hafnia, ytterbia, samaria, and a rare earth oxide including at least one of lutetia, scandia, ceria, neodymia, europia, and gadolinia, where the third layer has a dense microstructure and has a lower porosity than the second layer.

An article that includes a substrate; a first layer including yttria and zirconia or hafnia, where the first layer has a columnar microstructure and includes predominately the zirconia or hafnia; a second layer on the first layer, the second layer including zirconia or hafnia, ytterbia, samaria, and at least one of lutetia, scandia, ceria, neodymia, europia, and gadolinia, where the second layer includes predominately zirconia or hafnia, and where the second layer has a columnar microstructure; and a third layer on the second layer, the third layer including zirconia or hafnia, ytterbia, samaria, and a rare earth oxide including at least one of lutetia, scandia, ceria, neodymia, europia, and gadolinia, where the third layer has a dense microstructure and has a lower porosity than the second layer.

A thin-film thermocouple for measuring the temperature of a ceramic matrix composite (CMC) component includes a first thermocouple leg and a second thermocouple leg deposited on a surface of a CMC component, where each of the first and second thermocouple legs has a length extending from a reference end to a working end thereof. The working ends of the first and second thermocouple legs are joined at a junction region on the surface. At least one of the first thermocouple leg and the second thermocouple leg comprises silicon carbide.

A thin-film thermocouple for measuring the temperature of a ceramic matrix composite (CMC) component includes a first thermocouple leg and a second thermocouple leg deposited on a surface of a CMC component, where each of the first and second thermocouple legs has a length extending from a reference end to a working end thereof. The working ends of the first and second thermocouple legs are joined at a junction region on the surface. At least one of the first thermocouple leg and the second thermocouple leg comprises silicon carbide.

Coating systems on a surface of a CMC component, such as a CMC shroud, are provided. The coating system can include an environmental barrier coating on the surface of the CMC component and an abradable coating on the environmental barrier coating and defining an external surface opposite of the environmental barrier coating. The abradable coating includes a compound having the formula: Ln.sub.2ABO.sub.8, where Ln comprises scandium, yttrium, lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, or mixtures thereof; A comprises Si, Ti, Ge, or a combination thereof; and B comprises Mo, W, or a combination thereof. In one embodiment, the abradable coating has a first coefficient of thermal expansion at an interface with the environmental barrier coating that changes to a second coefficient of thermal expansion at its external surface. Methods are also provided for applying an abradable coating onto a CMC component.

Coating systems on a surface of a CMC component, such as a CMC shroud, are provided. The coating system can include an environmental barrier coating on the surface of the CMC component and an abradable coating on the environmental barrier coating and defining an external surface opposite of the environmental barrier coating. The abradable coating includes a compound having the formula: Ln.sub.2ABO.sub.8, where Ln comprises scandium, yttrium, lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, or mixtures thereof; A comprises Si, Ti, Ge, or a combination thereof; and B comprises Mo, W, or a combination thereof. In one embodiment, the abradable coating has a first coefficient of thermal expansion at an interface with the environmental barrier coating that changes to a second coefficient of thermal expansion at its external surface. Methods are also provided for applying an abradable coating onto a CMC component.