Above are some TEM images from the paper In Situ TEM Investigation of Congruent Phase Transition and Structural Evolution of Nanostructured Silicon/Carbon Anode for Lithium Ion Batteries. They show a hollow, conductive fiber with a layer of silicon (Si) around the outside. On the right are some electron diffraction images, taken where the red circles indicate.
What the researchers found is that as more and more lithium (Li) ions enter the Si, the Si layer remains amorphous (order-less) until the composition reaches the level of Li15 Si4. At this atomic composition, the layer attains a crystalline order. A way to think of that is like freezing. Ice is like water with a crystalline order imposed. In this case both the amorphous and crystalline phases are solid, but you sort of freeze to go from one to the other.
The way the researchers could tell this happened is from the electron diffraction images. The dots in the bottom image are caused by crystalline order. The electrons bounce off the regular faces of the crystals and interfere with each other, giving dots.








