Effect of cooling rate on eutectoid transformation of β phase in copper-beryllium alloy

The copper (Cu)-beryllium (Be) alloy is a critical material for high-performance photomultiplier cathodes. The microstructure evolution of the β phase in the Cu-2.8Be alloy subjected to cooling rate ranging from 0.5 to 80 °C/s after heat treatment. The non-isothermal phase transformation kinetics equation of the alloy was derived. At a cooling rate of 0.5 °C/s, the β phase completely transformed into the α phase and γ phase through a eutectoid reaction (β → α + γ). The γ phase preferentially precipitates at locations with higher free energy, such as grain boundaries and defects in the parent phase. The orientation relationship between the α phase and the γ phase follows the Kurdjumov-Sachs (K–S) relationship (${\left[110\right]}_{\alpha }\parallel {\left[111\right]}_{\gamma }$; ${\left(1\bar{1}\bar{1}\right)}_{\alpha }\parallel {\left(0\bar{1}1\right)}_{\gamma }$), and the α phase nucleates and grows with a twin relationship to the Cu matrix. As the cooling rate increases, the transformation fraction of the β phase decreases. The critical cooling rate at which the β phase eutectoid reaction is completely suppressed is 80 °C/s. A non-isothermal phase transformation kinetics equation for the β phase eutectoid transformation was established: $f\left(r\right)=1-\exp \left\{-{\left\{34.703r^{-1.062}\left[\exp \left(-{0.9107}^r\right)-0.3575\right]\right\}}^{2.2}\right\}$, elucidating the relationship between the phase transformation fraction and the cooling rate, which provides a theoretical basis for controlling the microstructure of Cu–Be alloy through heat treatment. Validated by the Cu-3.3Be alloy, this equation demonstrates excellent universality.