Can chemicals change crystal structure by only touching?
No, there is no "exact mimic" crystal, but the crystal habit can alter the crystal form. Consider that the environment in the uniform inside of a substance is different from that along its boundaries; growing on a different surface can alter the shape of the crystal. 

The semiconductor industry, in particular, is often faced with difficulties in growing crystalline semiconductors with layers of varying composition (epitaxy). There is often strain, leading to defects, unless an intermediate layer can smooth the transition.