The Earth's accretion process is accompanied by a large number of collisions. It is widely accepted that collisions dominate the Earth's late accretion stage. Among all these collisions, there is a special type of collision called Core-merging giant impact (CMGI), in which much or most the impactor's core merges directly with the proto-Earth's core. This core-merging scenario plays an important role in the Earth's accretion process and deeply affects the formation of the Earth's core and mantle. However, because CMGI is a small probability event, it has not been fully studied. Here we use the SPH method to comprehensively study all possible CMGIs in the Earth's accretion history. We find that CMGI only occurs in the initial conditions with small impact angle, small impact velocity and big impactor. We further discuss the implications of CMGI. We are confident that CMGI inevitably causes the chemical disequilibrium of the Earth's core and mantle. The CMGI process also brings many light elements into the Earth's core. In particular, if the Moon-forming giant impact is a CMGI, then CMGI can also explain the abnormal content of HSEs in the Earth's current mantle.

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