This course deals with the branch of solid state physics called surface physics. The first part of the course concerns defining the meaning of surfaces and some of the techniques that are used to study them. The purpose of this to familiarize students with what is known about surfaces and interfaces before beginning the second part of the course dealing with contact mechanics. The second part is largely mathematical and abstract. This is why the first part is so important. We should never lose sight of what real surfaces are when we are dealing in the simplified, abstract realm of contact mechanics. Part I: Surfaces and Surface Characterization
1. Definition of a Surface
We live in the physical world. We all know about three-dimensional objects. They have insides and outsides. We know what is part of an object and what is not part of an object. The surface then is the boundary between what is a given object and what is not. The mathematical definition of surface is the locus of points in space that are that boundary. Of course, mathematical points have no physical size; and a mathematical surface has no thickness.
Surface physics is considered a branch of solid state physics, but most of solid state physics ignores the surface. The reason for this is that if you are dealing with solids with atomic densities on the order of 1023 atoms/cm3, the number of atoms at the surface is small and becomes negligible. Also, treating a crystalline solid by taking advantage of an infinite translational periodicity simplifies mathematical treatment considerably. This works reasonably well when one wants to derive the macroscopic (bulk) properties of the solid. This also works well for spectroscopic probes of the material such as X-rays and neutrons.
In the study of surfaces in the physical world, we are forced to describe the surface with reference to the scale on which an observation is made. If we are simply looking at an object, such as a tabletop, we notice its color and perhaps its texture (smooth or rough on the large scale). We might even decide what the object is made of based on its facial appearance. But then again, we have always been told that you cannot judge a book by its cover. Looking at the tabletop, we might be fooled into thinking it was made of wood when in reality it is simply a plastic facade with a wood grain appearance. So we have to look closer with all of the tools at our disposal such as microscopes, particle beams, contact probes, spectroscopies, etc. to really begin to learn about surfaces. Figure 1 is an example [1]. It shows the head of a pin under increasing magnification.
Figure 1. The head of a pin is machined to be very sharp. The initial magnification on the left shows the machining marks. Note that the tip is truncated. The center image shows a closer view of the tip which has some ridges remaining from the machining process. The yellow blobs are bacteria clusters. Upon greater magnification, we see that even the surface of each of the bacteria has some structure.
It turns out that physics in the two dimensional realm of surfaces can be very different than that well-known to us in three dimensions. We know that in crystalline solids, atoms are ordered with a periodicity that can be either long- or short-range. In an ideal, perfect crystalline solid, the periodicity extends throughout the solid until the surface. Within the solid, the atoms are constrained by neighboring bonds, but at the surface, the atoms are not constrained in the same manner. They are said to be relaxed. Figure 2 shows the relaxation of the surface atoms in a GaAs (110) surface [2]. Any dangling bonds of the surface atoms are then available for chemical reactions with other entities outside the crystalline solid. This forms the basis for the branch of chemistry known as surface chemistry.
Figure 2. Reconstruction of the GaAs (110) surface. The solid lines represent the ideal arrangement of the atoms. The blue, dashed lines represent the relaxed atoms at the surface as a result of the lack of constraining bonds from outside the material.
Here are two useful definitions:
Morphology
A macroscopic property of materials that represents the form or shape of a surface.
Structure
This term is used to describe materials at the atomic level in terms of the arrangement of atoms in space.
The use of these terms is clear when one is working at the atomic level or when one is working at the large scale (such as naked eye observation), but less clear in the intermediate realm. Also, what goes on at the structural level certainly determines morphology. In this field we are often confronted by the use and choice of scale; and we tend to work at length scales ranging from 0.1 nm to 0.1 mm.
2. A Solid-Vapor Interface
Let's now take a detailed look at a surface issue. Figure 3 is a schematic representation [3] of a solid-vapor interface of area Aand thickness d. This solid-vapor system is in equilibrium, but physical properties, such as density, vary substantially between those of the bulk material and those of the vapor within the interface. This system can be analyzed using thermodynamics; and the thermodynamic properties (T, P, S,etc.) are well-defined within each region (solid, interface, and vapor). Unlike the case of the homogeneous regions (solid and vapor), the pressure P,force per unit area, is not isotropic.
Consider a plane that lies perpendicular to the surface of the solid and extends across the interfacial region. According to the figure, the area of that plane is the product of band d. Since the pressure is not uniform in the interface, the force on that plane will vary. Let's assume that the force on the plane is(1)
F = Pbd - gbwhere g is often referred to as the surface tension, but it is more correctly referred to as a surface stress. To get a better understanding about this, let's take a side-trip into the concept of surface tension before we continue with solids.
Figure 3. A Schematic Representation of a Solid-Vapor Interface
3. Surface Tension (Liquids) - The Young Model
In this course we are primarily interested in solids, but to understand solid surfaces we must borrow what is known about other phases as well. Technically, solid surfaces do not exhibit surface tension, but rather a surface stress which is similar to the concept of surface tension. The Young Model [2] of interfaces was developed in the study of mechanical equilibrium in capillaries. The model assumes that the interfacial region in Figure 3 can be replaced with a thin elastic membrane, called the tension surface, of infinitesimal thickness. This surface exists between two fluid (not solid) phases. Figure 4 will be used to develop our concept of surface tension. An arbitrary interface is cut with a plane labeled ABCDin the figure. To maintain equilibrium, the sum of the forces and the sum of the torques existing along the length of the interfacial curve must be zero. The force existing along a unit length dlis the surface tension g; and an appropriate unit for it is N/m.
Figure 4. A Schematic Representation of a Solid-Vapor Interface
Figure 5 shows an interface, s,of thickness d between two fluids, aand b. The x-zplane passes through pointsA, A', B, and B'where A'and B'are on the curves betweenthe respective fluids and the interface. The arrows represent the pressureat each value of zdirected at the plane within each fluid. The pressureon the plane is uniform within each fluid, but Pamaynot equal Pb. The left sideof the figure (a) represents a real system while the right side (b) representsthe Young model. In (a), the pressure distribution t(z)varies continuously,but in an indeterminable way. In the model, an infinitesimally thin interfaceis located at zs. The surfacetension g acts at the interface.
Figure 5. An Application of the Young Model illustrating the Forces, Pressures, and Surface Tension of (a) a real system and (b) the Young Model Interface
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