Legend has it that the feathers of the zhen bird are extremely poisonous.
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history
饮鸩止渴 (yǐnzhènzhǐkě, 'drink poison to quench thirst') is the canonical chengyu, recorded in 《后汉书·霍谞传》 (Hòu Hàn Shū). It describes solving an immediate problem with a method that guarantees later disaster.
memory
The character is 鸟 (bird) on the right + 冘 phonetic on the left. Royal poisonings throughout Chinese history were often described as being 'gifted a cup of wine', meaning 鸩酒 (poisoned wine).
鸟 is the bird radical, here in simplified form. It places 鸩 in the bird family alongside 鸡鸭鹅鹰, all 鸟-headed characters for fowl. Specifically marks 鸩 as a particular legendary species, not a general avian term.
冘 supplies the sound (yín drifted to zhèn). The same phonetic powers 沉枕耽. A faint air of dim, sinking flavor fits the legend: 鸩 was a black bird whose plumage carried a slow, undetectable poison.