# Energy cost of material transportation spell

For my universe I am designing a spell that transports material from one item O to another A, for example for repairs. I envision it as taking material uniformly from the Volume of O.

Now, the question is: what is the minimal energy required? I am thinking, we could find the energy needed to free one atom from the lattice (or other atom configuration) of O. Then multiply by the Avogadro constant to find an estimate for one mol. Then transform to grams.

But how much is the energy needed for removal from the lattice? Is it the energy needed to make the desired fraction of O boil? Or could it be significantly less, if I am not rendering most of the atoms of O weakly bound (as in boiling)?

Obviously, the value depends on material. I want to know how and starting from what (table,…) I should compute the estimate.

1. The energy required for breaking the bonds which bond the atoms or molecules of a solid is not related to boiling, but to melting.

2. The "desired fraction" of bonds which need to be broken is tiny -- as small as thin you can make your blade. In the limit, the energy required is very small -- all you have to do is break those relatively few bonds that fall along the plane of separation.

Example: Consider how much energy is required to break a pane of glass (very little) compared to how much energy is required to melt it (lots). Or how much energy is required to cut a steel wire compared with how much energy is required to melt it.

• So, should one say, the absolute lower limit, that can never be avoided is something of the order of melting a layer of atoms one atom wide (which I can translate to grams by learning about the lattice of at least the materials which have one and then use heat capacity, melting point, etc)? Or are there actually significant interactions with more than 2 other layers? Obviously I am only among for a very rough order of magnitude...
– Ludi
Sep 23, 2020 at 12:58
• In the limit, you will have an infinitely thin (= magical) blade which will break bonds along an infinitely thin plane. The point being that adding up the energy required to break those bonds will result in a very small number. Which is how we know that infinitely thin blades are magical... Sep 23, 2020 at 13:09
• Yes. But what energy would that blade need (order). Would it be the order of melting one layer of atoms of O or something completely different (because f.e. thermal energy is inefficient at this)?
– Ludi
Sep 23, 2020 at 13:14
• For a first order approximation, yes, you can take a surface equal to the section of the object, assume a thickness of one atom/molecule, and compute how much energy would be needed to melt it. Sep 23, 2020 at 13:17

how much is the energy needed for removal from the lattice?

There is no single value valid for all materials. Each lattice has its own value. You can get an estimate by looking at the melting temperature of each material: roughly speaking, the higher the temperature, the more energy is needed to set an atom/molecule from the reticle where it belongs.

Gallium, melting in your hands, has a much lower energy request than Tungsten.