Surfaces (see Howe Chapters 3 and 4)
In this short description one of the key things I want to bring out is the similarity between
surfaces and other bulk defects, as well as the interplay between different energy terms
which is important throughout this course.
The simplest type of planar boundary (or the most complicated) is the solidgas or solid
vacuum boundary. (Some of these ideas also apply to interfaces.) Some basic definitions:
1x1 Surface: Take the bulk material, cut it on a particular plane, separate.
Lowindex surface: result of this cut produces a specific lowenergy plane, e.g. (111)
Vicinal surface: results produces a stepped surface, e.g. (776)
Energy: surface free energy (similar to interface term)
Surface Stress (similar to interface term)
Surface Entropy
A surface is thermodynamically stable if it is a stable facet on a Wulff construction; if it
is not it will (if the kinetics allow) transform
Broken bond model (primitive, but useful). For an fcc material each atom has 12
neighbours (6 in plane, 3 above, 3 below). Suppose that the heat of atomization is 12C.
(Definition: heat of atomization = energy to convert to isolated atoms, often easier to
handle than free energies at STP.)
Example: fcc material
(111) surface,3 bonds less, area sqrt(3)/2
surface free energy = 2*sqrt(3)C = 3.46C
(100) surface, 4 bonds less, area 1,
surface free energy = 4C
= 4C
(110) surface, 6 bonds less, area sqrt(2)
surface free energy = 6/sqrt(2)C = 4.24C
Approximate model is not so bad, for instance energies relative to the (111) energy for
some simple fcc metals:
(100)
(110)
Pt
1.14
1.23
Au
1.14
1.23
Cu
1.16
1.20
Ag
1.13
1.25
BB Model
1.15
1.22
As the temperature goes to the melting point the entropy terms become more important
and the surface free energy tends towards a constant value independent of direction.
Values for the surface entropy are not as well understood as surface free energies, and
even the later are not always that well measured. Part of the reason is that if you have a
chemical species on the surface, this changes all the energy terms by large factors – so
extreme experimental care is needed.
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The 1x1 surface is not always the most stable structure (ignoring faceting). A simplistic
(naive) explanation is to say that the surface has many broken bonds and the material will
reconstruct to increase the number of bonds. We refer to a reconstructed surface in one of
two ways:
a) Woods notation: by two numbers plus (if needed) a rotation where the numbers
correspond to the relative size of the surface cell w.r.t. the bulk, for instance a 2x1 or a
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 Winter '10
 MatSci
 Energy, Entropy, Surface, Crystallographic defect

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