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## Main Question or Discussion Point

I've got several thoughts, but none of them is complete.

A general explanation is that when a few atoms form a structure with lowest energy, then when the interfacial energy is low, these independent small groups of particles tend to gather together and form periodic structure.

But why are the interfacial energy always small?

A theoretical explanation is that we believe that the atoms tends to preserve as many symmetries as possible. The competition of the two kind of interaction gives a characteristic length, therefore the continuous transverse symmetry should be broken, but the discrete transverse symmetry can be preserved. Then nature chooses to preserve it.

But this explanation is too theoretical. How can we understand it in physical picture.

Another way to understand the ques is that we consider how a crystal, say ice, is formed. It grows from a kernel, the competition of culom interaction and Pauli interaction determine the atoms form around the kernel. In every step, it seeks a energy-favor form, so it's easy to see that solid should have a special structure.

But why the structure is periodic?

Actually, it can form ice which is periodic, it can also form flake which is fractal. Then why in each case?

A general explanation is that when a few atoms form a structure with lowest energy, then when the interfacial energy is low, these independent small groups of particles tend to gather together and form periodic structure.

But why are the interfacial energy always small?

A theoretical explanation is that we believe that the atoms tends to preserve as many symmetries as possible. The competition of the two kind of interaction gives a characteristic length, therefore the continuous transverse symmetry should be broken, but the discrete transverse symmetry can be preserved. Then nature chooses to preserve it.

But this explanation is too theoretical. How can we understand it in physical picture.

Another way to understand the ques is that we consider how a crystal, say ice, is formed. It grows from a kernel, the competition of culom interaction and Pauli interaction determine the atoms form around the kernel. In every step, it seeks a energy-favor form, so it's easy to see that solid should have a special structure.

But why the structure is periodic?

Actually, it can form ice which is periodic, it can also form flake which is fractal. Then why in each case?