Fundamentals of Deformation

METALS

This project provides new measurement methods, property data and simulations 

for areas critical to US manufacturing, describing the mechanisms responsible 

for mechanical behavior. The mechanical behavior of virtually all materials (from 

nanostructures to bulk structural steels) depends upon processes active at the 

nanoscale; we provide critical evaluations of the sensitivity of nanomechanics test 

methods to uncontrolled experimental conditions and develop new measurement 

methods for probing elastic strains, defect structures and crystallographic 

orientations at the nanoscale within nanostructured materials and devices.

Objective

Impact and Customers

• We have provided users from industry, academia and national 

laboratories a completely new class of X-ray imaging techniques 

for materials studies (ultra-small-angle X-ray scattering imaging, or 

“USAXS imaging”), which we developed from basic concept to DOEsupported operations at the Advanced Photon Source (APS).

• A new, robust measurement capability has been developed for 

measuring elastic strains, defects and crystallographic orientations 

from buried nanoscale sample volumes within nanostructured materials 

and devices, and is now installed at the APS.

• NIST is working to provide researchers and engineers with a nanoNewton (nN)-level force standard. Quantum level simulations of gold 

nanowire deformation have confirmed that this system is suitable for an 

intrinsic force standard. 

• We are providing the nanoindentation community with critical, 

quantitative evaluations of the indentation’s sensitivity to unavoidable 

variations in indenter tip shapes and sample roughness.

Approach

Materials Science and Engineering Laboratory

The mechanical behavior of materials during device processing, assembly, and lifetime is a critical factor for 

nearly all industrial products. This behavior is generally determined by complex nanoscale processes such as the 

evolution of local stress concentrations, defect propagation, local slip, and 

delamination. Targeted quantitative measurement and modeling techniques 

are critical for making new products affordable and reliable. Topic areas 

include: 1) quantitative, experimentally validated computer simulations to 

evaluate nanoindentation and nanowire failure, and 2) new spatially resolved 

synchrotron X-ray diffraction and small-angle scattering measurement 

techniques for probing elastic strains, defect structures, crystallographic 

orientations and densities at the nanoscale, within nanostructured materials 

and devices.

For example, USAXS imaging is now being used at the APS for research 

as diverse as the self-assembly of conductive nanowire networks and the 

distribution of second phase particles in artificial rubber materials.

855-12-25b
Materials Science and Engineering Laboratory

High impact and effective dissemination 

of NIST measurement capabilities can be 

achieved by directly incorporating these 

experimental techniques into national 

user facilities such as the DOE-operated 

APS. One such measurement method is 

USAXS imaging, which was conceived by 

NIST scientists in 2000. Since that time, 

the required instrumentation, experimental 

techniques and underlying theory have 

been developed and implemented. USAXS 

imaging is extremely sensitive to density 

changes in materials, and provides 

quantitative measurement of the sizes, 

shapes and spatial arrangements of their 

underlying microstructural features. In 2005, 

DOE added USAXS imaging to the APS ten 

year tactical plan, with the highest possible 

priority. It has now been incorporated into 

a new imaging beamline and the first 

DOE-supported user experiments (with 

no NIST involvement) were conducted in 

November 2007. Continued development 

of USAXS imaging is supported through a 

Partner User Agreement between NIST and 

DOE.

In a similar vein, NIST staff are collaborating 

with researchers from Oak Ridge and 

Argonne National Laboratories to develop 

a robust measurement capability for 

measuring elastic strains, defect densities 

and crystallographic orientations from 

buried sample volumes smaller than 0.004 

μm3. This technique was first utilized in 2006 

to measure elastic strains within individual 

dislocation cell interiors in plastically 

deformed Cu, with a 3D spatial resolution 

of 0.5 μm. Full diffraction line profiles 

can now be obtained from contiguous 

buried sample volumes. For example, in 

a recent experiment, diffracted intensity 

from a 0.07 μm3 sample volume, buried 

11 μm deep in a deformed Cu sample, 

was isolated and analyzed. This sample 

volume contained a single dislocation 

wall, separating two low dislocation 

density regions. Independent line profiles 

were extracted from all three sub-volumes, 

allowing quantitative determination of 

local elastic strain, dislocation density and 

angular misorientation. The figure below 

shows the diffraction line profile from the 

dislocation wall. The location of the peak 

gives the average elastic strain, while the 

width of the peak is determined by the 

dislocation density.

On another topic, current methods for 

measuring local mechanical properties at 

the nanoscale are sensitive to nanoscale 

variations in the probe geometry, but the 

magnitude of this sensitivity is largely 

unknown. NIST researchers used atomic 

force microscopy to characterize the 3D 

shape of a new nanoindenter tip which 

was subsequently used to indent single 

crystal tungsten. Stress estimates obtained 

from the resulting experimental data, 

using conventional approaches (Hertizian 

approximation for a spherical tip), were 

over 30 % larger than those determined 

from a detailed finite element model of this 

experiment. 

Finally, plastic deformation of gold 

nanowires has received considerable 

attention recently, due to their ability to 

form single atom chains which result 

in quantized conductance. NIST has 

identified the breaking of such nanowires 

as a likely candidate for a much needed 

intrinsic force standard for very small 

loads, and accurate quantum mechanics 

simulations have been used to explore the 

deformation behavior over a wide range 

of deformation conditions. It was found 

that single atom chains are easily formed, 

and that the breaking force of these chains 

is extremely consistent, (1.53 ± 0.02) nN, 

confirming that this system is suitable for 

an intrinsic force standard.

Accomplishments

Li Ma

Francesca Tavazza

Dylan Morris

Doug Smith

Rick Wagner

John Pratt (MEL)

Anne Chaka (PL)

Lyle E. Levine

(Metallurgy Division)

(301) 975-6032

lyle.levine@nist.gov

www.nist.gov/metallurgy

Learn More Publications

Ma L, Morris D, Jennerjohn S, Bahr DF and Levine LE Finite-element Analysis and Experimental 

Investigation of the Hertzian Assumption on the Characterization of Initial Plastic Yield Journal of 

Materials Research, 24: 1059 (2009)

Zhang F, Long GG, Levine LE, Ilavsky J and Jemian PR Quantitative Characterization of the Contrast 

Mechanisms of Ultra-Small-Angle X-ray Scattering Imaging Journal of Applied Crystallography, 41: 

416 (2008)

Levine LE, Long GG, Gerhardt RA, Ou R, Ilavsky J and Parker CA Self-assembly of a Nanoscale 

Three Dimensional Conductive Network Within a Polymer Matrix Applied Physics Letters, 90: 

014101 (2007)

Levine LE, Larson BC, Yang W, Kassner ME, Tischler JZ, Delos-Reyes MA, Fields RJ and Liu W X-ray 

Microbeam Measurements of Individual Dislocation Cell Elastic Strains in Deformed Single Crystal 

Copper Nature Materials, 5: 619 (2006)

Line profile from individual dislocation wall

Deformed gold nanowire