Reconstructive transformations in layered silicates need a high temperature in order to be observed. However, very recently, some systems have been found where transformation can be studied at temperatures 600 degrees C below the lowest experimental results previously reported, including sol-gel methods. We explore the possible relation with the existence of intrinsic localized modes, known as discrete breathers. We construct a model for nonlinear vibrations within the cation layer, obtain their parameters, and calculate them numerically, obtaining their energies. Their statistics show that, although there are far less breathers than phonons, there are much more above the activation energy, making them good candidates to explain the reconstructive transformations at low temperatures.