I cannot find a quiet place to study.句中to study是做定语还是状语?

to study 在这里是做 目的状语
目的状语的逻辑主语是句子的主语
例如：I have bought this notebook to write my diary.
I-主语,have bought-谓语,this notebook-宾语,to write my diary-目的状语（逻辑主语是I)