Abstract
High-entropy pyrosilicate element selection is relatively blind, and the thermal expansion coefficient (CTE) of traditional β-type pyrosilicate is not adjustable, making it difficult to meet the requirements of various types of ceramic matrix composites (CMCs). The following study aimed to develop a universal rule for high-entropy pyrosilicate element selection and to achieve directional control of the thermal expansion coefficient of high-entropy pyrosilicate. The current study investigates a high-entropy design method for obtaining pyrosilicates with stable β-phase and γ-phase by introducing various rare-earth (RE) cations. The solid-phase method was used to create 12 different types of high-entropy pyrosilicates with 4–6 components. The high-entropy pyrosilicates gradually transformed from β-phase to γ-phase with an increase in the average radius of RE<sup>3+</sup> ions (<inline-formula> <math display="inline" id="MA1"><mrow><mover accent="true"><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><msup><mrow><mtext>RE</mtext></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math></inline-formula>). The nine pyrosilicates with a small <inline-formula> <math display="inline" id="MA2"><mrow><mover accent="true"><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><msup><mrow><mtext>RE</mtext></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math></inline-formula> preserve β-phase or γ-phase stability at room temperature to the maximum of 1400 ℃. The intrinsic relationship between the thermal expansion coefficient, phase structure, and RE–O bond length has also been found. This study provides the theoretical background for designing high-entropy pyrosilicates from the perspective of <inline-formula> <math display="inline" id="MA3"><mrow><mover accent="true"><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><msup><mrow><mtext>RE</mtext></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math></inline-formula>. The theoretical guidance makes it easier to synthesize high-entropy pyrosilicates with stable β-phase or γ-phase for the use in environmental barrier coatings (EBCs). The thermal expansion coefficient of γ-type high-entropy pyrosilicate can be altered through component design to match various types of CMCs.
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