# VII IVays and Packing

A one-dimensional phase-boundary line between two coexisting phases is always rough i.e., its mean position does not lock into the lattice but can fluctuate freely in thermodynamical equilibrium. A physical representation of such a phase boundary line between two phases would be the edge or the step of a terrace on a crystal surface, where on one side of the step there is one additional atomic layer deposited on the crystal surface. The step follows the atomic structure of the lattice in atomically sharp turns or kinks. A single kink represents a sideways displacement of an originally straight step by one lattice unit. A slip of the kink along the step, in consequence, moves the average position of the step in the normal direction virtually continuously. The mean width w of the step increases due to the existence of kinks along the step as a function of the length L of the step (in the sense of random fluctuations around the average) as iv /T. Therefore, the width of the fluctuating step diverges when the length L of the step goes to infinity (see Sec. IIIF 1). [c.859]

Therefore, we can obtain that (iiyV) = 0, i.e. W G K, and pass to a lower limit in the following inequality [c.162]

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**VII IVays and Packing**:

**[c.33] [c.494] [c.2399] [c.86] [c.165] [c.165] [c.195] [c.232] [c.1151] [c.129] [c.134] [c.449] [c.449] [c.1224] [c.145]**

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** Surface production operations Ч.2
-> VII IVays and Packing
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