ABSTRACT

The atomic surface of graphite was examined using a Scanning Tunneling Microscope. The lattice structure of graphite was observed to be hexagonal layers, confirming that predicted by theory and experiment. The atomic radius of carbon was measured to be 1.45Å, a 5.84% deviation from the accepted value.

BACKGROUND

The resolution of the naked eye—that is, the smallest detail it can discern—is about 1x10⁶Å (1x10^-4m)— i.e., an eyelash. The resolution of the best optical microscope is about 1x10³ Å (1x10^-7 m)—i.e., a cell. And now, with the advent of quantum mechanics, the Scanning Tunneling Microscope (STM) has extended man’s eyesight to resolutions on the order of 1 Å (1x10^-10m)—i.e., atoms.

THEORY:

Whereas the resolution of ordinary microscopes is limited by the wavelength of the waves that are used to view the sample, the STM takes advantage of quantum mechanical principles which govern the behavior of electrons. One of the assertions of quantum mechanics is that electrons possess a wave nature in addition to their particle characteristics, so rather than viewing an electrons as a particle bouncing around inside a metal, it is depicted as a wave composed of an electron cloud. When this wave hits barrier of the material, part will reflect and part will transmit, depending on the energy of the wave and the energy of the barrier (determined by the spacing and potential between the two metals). If the wave encounters a "thick" barrier—that is, an energy gap an electron must overcome to move from one material to another—it will mostly be reflected. The little that does get through will exponentially decay to zero.

When the tip approaches the sample in the diagram above, the barrier between materials becomes thinner and thinner. According to classical Newtonian mechanics, electrons will not pass from one material to the other until there is contact between the metals, resulting in conduction. Quantum mechanics however allows electrons to pass from one metal to the other before contact occurs. If the barrier is thin enough, electrons are able to "tunnel" across the barrier into the other material. Note they do not move through the gap separating the materials as would occur in sparking, but instead, by the powers of quantum mechanics, vanish from one metal then immediately reappear in the other¹.

In order to produce a detectable current, the metals must only be 10Ź apart. The closer the two metals are brought together, the greater the tunneling current that flows.

This distance dependence of the tunneling current is the governing principle behind the STM. A metal tip scans the surface of a conductive material while recording the tunneling. This allows current, or height, to be plotted as a function of position, rendering a 3D map of the surface.

The STM derives its high resolution from a sharp, atomic sized probing tip.
 

 

The fine point of the tip focuses the tunneling current to a sharp point where ideally one atom will be closer to the surface than any other. This forces all tunneling to occur through one atom, resulting a resolution that is literally atomic.

To achieve a surface image over an area of atoms, in addition to atomic resolution one also needs atomic movement for the tip to scan with. This is accomplished with piezoelectrics placed strategically around the tip. When a current is passed through a piezoelectric, it will contract in the direction of the electric field and expand in the direction perpendicular to it. With a sensitivity of about 1Å/10mV, both lateral and vertical atomic movements can be achieved.
 

PROCEDURE:

In order to expose a smooth surface of graphite, the sample was prepared by pressing a piece of tape to the graphite and then slowly peeling away the tape. In doing so, a layer of graphite was stripped away onto the tape leaving a freshly exposed graphite surface.

To eliminate vibrations, the STM was placed on top of a two inch thick iron plate which sat on about a foot high on rubber tubing.

The sample was then placed in position, the tip approached, and scanning commenced.

DATA

RESULTS

As the theoretical models predict, the crystal structure of graphite takes the shape of a hexagonal lattice.

The atom in the center of the ring is an atom from a lattice layer below the plane of the ring shown above. A birds-eye-view of two hexagonal lattice layers looks like staggered rows of atoms:

The black solid circles represent atoms from both layers which are vertically in line with each other while outlined circles represent atoms from both layers which do not sit above (or below) atoms from the other layer.

A side view of these hexagonal lattice layers looks as follows:

Although we were not able to measure the vertical separation between the layers, the surface scan of the STM did reveal the size of the atomic radii of the carbon atoms. Measurements of these distances reveal the following data:

Average:           1.45

Accepted³:       1.54
 
Percent Error:   5.84%
 

Ironically, the very obscurity of quantum mechanics is responsible for the illumination of the crevices of matter. The vindication of quantum mechanics has delivered the ever sought visual evidence to both the eager theorist and hard nosed skeptic. For when all’s said and done, one adage will always remain true: seeing is believing.

BIBLIOGRAPHY

1.  Miller, Dwayne R.J., Mizes, H.A., A.Samsaver. Instructional Scanning Tunneling Microscope Workbook. New York: Burleigh, 1992.
2.  Freedman, Roger A., Paul K. Hansma. "The Scanning Tunneling Microscope." Physicists for Scientists and Engineers. pp: 1204-1211.
3.  Weast, Robet C.  Handbook of Chemistry and Physics.  Ohio: The Chemical Rubber Co., 1968.