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Of Friction And 'The Da Vinci Code'

August 26, 2005
Lawrence Berkeley National Laboratory
Half a millenium ago Leonardo Da Vinci made fundamental discoveries about the role of geometric profiles in the strength of friction between materials. Researchers at Lawrence Berkeley National Laboratory and Ames Laboratory have examined periodicity in friction at the atomic scale using quasicrystals -- materials with amusing (and eerie) echoes in Dan Brown's "The Da Vinci Code," as in the Fibonnaci spacing of rows of some quasicrystal atoms.

Atoms are spaced periodically in one direction on a surface perpendicular to a quasicrystal's 10-fold rotational axis. But at right angles they are spaced in a Fibonacci sequence, in which the ratio of short to long spacings is an irrational number like that of the Golden Mean. Friction is eight times greater in the periodic direction than in the aperiodic direction.
Credit: Image courtesy of DOE/Lawrence Berkeley National Laboratory

BERKELEY, CA – The Da Vinci Code, the best selling novel andsoon-to-be-blockbuster film, may also be linked some day to the solvingof a scientific mystery as old as Leonardo Da Vinci himself — friction.A collaboration of scientists from Lawrence Berkeley NationalLaboratory (Berkeley Lab) and the Ames Laboratory at Iowa StateUniversity have used Da Vinci's principles of friction and thegeometric oddities known as quasicrystals to open a new pathway towardsa better understanding of friction at the atomic level.

In apaper published in the August 26 issue of the journal Science, aresearch collaboration led by Miquel Salmeron, a physicist withBerkeley Lab's Materials Sciences Division, reports on the first studyto measure the frictional effects of periodicity in a crystallinelattice. Using a combined Atomic Force Microscope (AFM) and ScanningTunneling Microscope (STM), the researchers showed that friction alongthe surface of a quasicrystal in the direction of a periodic geometricconfiguration is about eight times greater than in the direction wherethe geometric configuration is aperiodic (without regularity).

Geometricperiodicity was confirmed via rows of atoms that formed a Fibonaccisequence, a numerical pattern often observed in quasicrystals — andwhich was one of the clues to solving the Da Vinci code in the novel byDan Brown.

"That we can get such a large difference in frictionalforce just by scratching the surface of a material in a differentdirection was a major surprise," says Salmeron. "Our results reveal astrong connection between interface atomic structure and the mechanismsby which frictional energy is dissipated."

Collaborating on theScience paper with Salmeron were Berkeley Lab's Jeong Young Park andFrank Ogletree, and Raquel Ribeiro, Paul Canfield, Cynthia Jenks, andPatricia Thiel of the Ames Laboratory at Iowa State University.

Theprinciples of friction, as described by Leonardo Da Vinci some 500years ago, work fine for macroscale mechanics like keeping the movingparts in the engine of your car lubricated with oil. However, asmechanical devices shrink to nanosized scales (measured in billionthsof a meter), a far better understanding of friction at the molecularlevel becomes crucial.

"Friction is difficult to characterizebecause there are so many different factors involved," says Park."Scientific studies of frictional force were in limbo for such a longperiod of time because we simply didn't have the tools we needed tostudy it at the atomic level."

The key tool deployed in thisstudy was the combined AFM and STM. Both microscopes utilize a probethat tapers to a single atom at its tip. This tip is scanned across thesurface of the sample to be studied, revealing atomic-levelinformation. In the AFM mode, the tip actually touches the sample'ssurface atoms like a phonograph needle making contact with a record —but with so little force that none of the scanned atoms are dislodged.In the STM mode, the tip never quite touches the sample atoms but isbrought close enough that electrons begin to "tunnel" across the gap,generating an electrical current.

"We first used the STM mode toproduce topographical images of our quasicrystals and ascertain whichdirection was periodic and which was aperiodic," says Salmeron. "Wethen switched to the AFM mode and gently scratched the crystals in eachdirection to measure and compare the frictional force."

At theatomic level, when two surfaces come in contact, the chemical bonds andclouds of electrons in their respective atoms create frictional forceand cause energy to be dissipated. From Da Vinci's studies it has longbeen known that friction is greater between surfaces of identicalcrystallographic orientation than between surfaces of differingorientation, because, says Salmeron, "commensurability leads tointimate interlocking and high friction."

However, some recentstudies have reported higher frictional differences, or anisotropy, forincommensurate crystal surfaces when there were periodicity differences.

Tomeasure the frictional effects due to periodicity alone, and not toother factors such as chemical differences, Salmeron, Park, andOgletree worked with decagonal quasicrystals of analuminum-nickel-cobalt alloy (Al-Ni-Co) prepared by their collaboratorsat Ames Laboratory, renowned experts on the surfaces ofquasicrystalline materials.

Stacked planes of Al-Ni-Co crystalsexhibit both ten-fold and two-fold rotational symmetry. By cutting asingle Al‑Ni-Co quasicrystal parallel to its ten-fold axis, theresearchers were able to produce a two-dimensional surface with oneperiodic axis and one aperiodic axis, separated by 90 degrees.

"Strongfriction anisotropy was observed when the AFM tip slid along the twodirections: high friction along the periodic direction, and lowfriction along the aperiodic direction," says Park. "We believe thesource of this friction has both an electronic and a phononiccontribution." Phonons are vibrations in a crystal lattice, like atomicsound waves.

The authors of the Science paper said that newtheoretical models are needed to determine whether electrons or phononsare the dominant contributors to the frictional anisotropy they report.

"Our results finally give theorists a chance to be proactive in their modeling of friction," Salmeron says.

"HighFrictional Anisotropy of Periodic and Aperiodic Directions on aQuasicrystal Surface," by Jeong Young Park, D. F. Ogletree, M.Salmeron, R. A. Ribeiro, P. C. Canfield, C. J. Jenks, and P. A. Thielappears in the August 26, 2005 issue of Science magazine . For moreinformation visit the Salmeron Group website,, andJeong Park's webpage,

BerkeleyLab is a U.S. Department of Energy national laboratory located inBerkeley, California. It conducts unclassified scientific research andis managed by the University of California. Visit our Website at

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