In this paper, the effect of Rh content on the mechanical properties of Ir–Rh alloys was investigated based on first-principles density functional theory. The calculated results show that when the Rh content is small, the three elastic moduli (elastic modulus (B), shear modulus (G), and Young’s modulus (E)) of Ir–Rh alloy increase rapidly with the increase of Rh content. They reach a maximum value at Ir–10Rh and then decrease, before rising slowly at Ir–40Rh and then gradually decreasing again. This shows that adding a small amount of rhodium to iridium can effectively improve the strength and hardness of iridium. Among all the components of the selected Ir–Rh alloys, Ir–10Rh has the highest hardness and strength. The addition of Rh can cause the embrittlement of Ir–Rh alloys, and its brittleness first increases and then decreases with the increase of Rh content, and reaches the highest at Ir–50Rh. Considering the results obtained from theoretical calculations and experiments, Ir–20Rh was selected as the alloy composition for the study of hot isostatic pressing technology. The effects of mixing time, whether to mix powder with balls, and degassing temperature on the properties of metal powders were studied to find the best mixing and degassing process parameters. In the experiment of mixing powder for the iridium and rhodium alloy, it is found that the time required for mixing powder with balls to reach uniformity was shorter than that without balls. The oxygen content of the final mixed powder obtained by the two processes is the same. The nitrogen content of the metal powder mixed with the ball is slightly higher than that without the ball, but it can be reduced to below 0.001% after the degassing process. During the sintering process, with the increase in temperature, the mutual diffusion speed between iridium powder and rhodium powder increases, the sintering neck grows, the internal pores decrease, and the density of the sintered body increases. Therefore, the final decision process is to select mixing with balls for 10 h, degas at 1200 °C for 2 h, and then raise the temperature to 1800 °C for sintering. With the increase of hot isostatic pressing temperature and pressure, the density of the alloy increases. When the highest temperature (1300 °C) and highest pressure (140 MPa) are used for hot isostatic pressing for 2 h, the density can reach 95.7% of the theoretical density.
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