0
Research Papers

Nanoscale Deformation Analysis With High-Resolution Transmission Electron Microscopy and Digital Image Correlation

[+] Author and Article Information
Xueju Wang, Zhipeng Pan, Feifei Fan, Ting Zhu

Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Jiangwei Wang, Scott X. Mao

Department of Mechanical Engineering and Materials Science,
University of Pittsburgh,
Pittsburgh, PA 15261

Yang Liu

Center for Integrated Nanotechnologies,
Sandia National Laboratories,
Albuquerque, NM 87185

Shuman Xia

Woodruff School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: shuman.xia@me.gatech.edu

1Present address: Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27606.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 20, 2015; final manuscript received August 15, 2015; published online September 10, 2015. Editor: Yonggang Huang.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Appl. Mech 82(12), 121001 (Sep 10, 2015) (9 pages) Paper No: JAM-15-1325; doi: 10.1115/1.4031332 History: Received June 20, 2015; Revised August 15, 2015

We present an application of the digital image correlation (DIC) method to high-resolution transmission electron microscopy (HRTEM) images for nanoscale deformation analysis. The combination of DIC and HRTEM offers both the ultrahigh spatial resolution and high displacement detection sensitivity that are not possible with other microscope-based DIC techniques. We demonstrate the accuracy and utility of the HRTEM-DIC technique through displacement and strain analysis on amorphous silicon. Two types of error sources resulting from the transmission electron microscopy (TEM) image noise and electromagnetic-lens distortions are quantitatively investigated via rigid-body translation experiments. The local and global DIC approaches are applied for the analysis of diffusion- and reaction-induced deformation fields in electrochemically lithiated amorphous silicon. The DIC technique coupled with HRTEM provides a new avenue for the deformation analysis of materials at the nanometer length scales.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Johnson, C. , Ruud, J. , Bruce, R. , and Wortman, D. , 1998, “ Relationships Between Residual Stress, Microstructure and Mechanical Properties of Electron Beam–Physical Vapor Deposition Thermal Barrier Coatings,” Surf. Coat. Technol., 108–109, pp. 80–85. [CrossRef]
Nave, M. D. , and Barnett, M. R. , 2004, “ Microstructures and Textures of Pure Magnesium Deformed in Plane-Strain Compression,” Scr. Mater., 51(9), pp. 881–885. [CrossRef]
Rastogi, P. , 2000, Photomechanics, Springer, Berlin.
Grediac, M. , 2004, “ The Use of Full-Field Measurement Methods in Composite Material Characterization: Interest and Limitations,” Composites, Part A, 35(7), pp. 751–761. [CrossRef]
Hung, Y. , and Ho, H. , 2005, “ Shearography: An Optical Measurement Technique and Applications,” Mater. Sci. Eng.: R, 49(3), pp. 61–87. [CrossRef]
Avril, S. , Bonnet, M. , Bretelle, A.-S. , Grediac, M. , Hild, F. , Ienny, P. , Latourte, F. , Lemosse, D. , Pagano, S. , and Pagnacco, E. , 2008, “ Overview of Identification Methods of Mechanical Parameters Based on Full-Field Measurements,” Exp. Mech., 48(4), pp. 381–402. [CrossRef]
McClung, A. J. , Tandon, G. , Goecke, K. , and Baur, J. , 2011, “ Non-Contact Technique for Characterizing Full-Field Surface Deformation of Shape Memory Polymers at Elevated and Room Temperatures,” Polym. Test., 30(1), pp. 140–149. [CrossRef]
Chu, T. , Ranson, W. , and Sutton, M. , 1985, “ Applications of Digital-Image-Correlation Techniques to Experimental Mechanics,” Exp. Mech., 25(3), pp. 232–244. [CrossRef]
Pan, B. , Qian, K. , Xie, H. , and Asundi, A. , 2009, “ Two-Dimensional Digital Image Correlation for In-Plane Displacement and Strain Measurement: A Review,” Meas. Sci. Technol., 20(6), p. 062001. [CrossRef]
Peters, W. H. , and Ranson, W. F. , 1982, “ Digital Imaging Techniques in Experimental Stress-Analysis,” Opt. Eng., 21(3), pp. 427–431. [CrossRef]
Sutton, M. A. , Cheng, M. Q. , Peters, W. H. , Chao, Y. J. , and Mcneill, S. R. , 1986, “ Application of an Optimized Digital Correlation Method to Planar Deformation Analysis,” Image Vision Comput., 4(3), pp. 143–150. [CrossRef]
Delacourt, C. , Allemand, P. , Casson, B. , and Vadon, H. , 2004, “ Velocity Field of the ‘La Clapière’ Landslide Measured by the Correlation of Aerial and QuickBird Satellite Images,” Geophys. Res. Lett., 31(15), p. L15619. [CrossRef]
Krehbiel, J. D. , Lambros, J. , Viator, J. , and Sottos, N. , 2010, “ Digital Image Correlation for Improved Detection of Basal Cell Carcinoma,” Exp. Mech., 50(6), pp. 813–824. [CrossRef]
Chasiotis, I. , and Knauss, W. G. , 2002, “ A New Microtensile Tester for the Study of MEMS Materials With the Aid of Atomic Force Microscopy,” Exp. Mech., 42(1), pp. 51–57. [CrossRef]
Knauss, W. G. , Chasiotis, I. , and Huang, Y. , 2003, “ Mechanical Measurements at the Micron and Nanometer Scales,” Mech. Mater., 35(3–6), pp. 217–231. [CrossRef]
Chasiotis, I. , 2004, “ Mechanics of Thin Films and Microdevices,” IEEE Trans. Device Mater. Reliab., 4(2), pp. 176–188. [CrossRef]
Cho, S. , Chasiotis, I. , Friedmann, T. A. , and Sullivan, J. P. , 2005, “ Young's Modulus, Poisson's Ratio and Failure Properties of Tetrahedral Amorphous Diamond-Like Carbon for MEMS Devices,” J. Micromech. Microeng., 15(4), pp. 728–735. [CrossRef]
Cho, S. , Cárdenas-García, J. F. , and Chasiotis, I. , 2005, “ Measurement of Nanodisplacements and Elastic Properties of MEMS Via the Microscopic Hole Method,” Sens. Actuators, A, 120(1), pp. 163–171. [CrossRef]
Chang, S. , Wang, C. S. , Xiong, C. Y. , and Fang, J. , 2005, “ Nanoscale In-Plane Displacement Evaluation by AFM Scanning and Digital Image Correlation Processing,” Nanotechnology, 16(4), pp. 344–349. [CrossRef]
Sun, Y. , and Pang, J. H. , 2006, “ AFM Image Reconstruction for Deformation Measurements by Digital Image Correlation,” Nanotechnology, 17(4), pp. 933–939. [CrossRef] [PubMed]
Cho, S. W. , and Chasiotis, I. , 2007, “ Elastic Properties and Representative Volume Element of Polycrystalline Silicon for MEMS,” Exp. Mech., 47(1), pp. 37–49. [CrossRef]
Li, X. D. , Xu, W. J. , Sutton, M. A. , and Mello, M. , 2007, “ In Situ Nanoscale In-Plane Deformation Studies of Ultrathin Polymeric Films During Tensile Deformation Using Atomic Force Microscopy and Digital Image Correlation Techniques,” IEEE Trans. Nanotechnol., 6(1), pp. 4–12. [CrossRef]
Sun, Y. , Pang, J. H. , and Fan, W. , 2007, “ Nanoscale Deformation Measurement of Microscale Interconnection Assemblies by a Digital Image Correlation Technique,” Nanotechnology, 18(39), p. 395504. [CrossRef] [PubMed]
Vendroux, G. , and Knauss, W. , 1998, “ Submicron Deformation Field Measurements: Part 1. Developing a Digital Scanning Tunneling Microscope,” Exp. Mech., 38(1), pp. 18–23. [CrossRef]
Vendroux, G. , and Knauss, W. , 1998, “ Submicron Deformation Field Measurements: Part 2. Improved Digital Image Correlation,” Exp. Mech., 38(2), pp. 86–92. [CrossRef]
Vendnroux, G. , Schmidt, N. , and Knauss, W. , 1998, “ Submicron Deformation Field Measurements: Part 3. Demonstration of Deformation Determinations,” Exp. Mech., 38(3), pp. 154–160. [CrossRef]
Kang, J. , Jain, M. , Wilkinson, D. S. , and Embury, J. D. , 2005, “ Microscopic Strain Mapping Using Scanning Electron Microscopy Topography Image Correlation at Large Strain,” J. Strain Anal. Eng. Des., 40(6), pp. 559–570. [CrossRef]
Sabate, N. , Vogel, D. , Gollhardt, A. , Keller, J. , Michel, B. , Cane, C. , Gracia, I. , and Morante, J. R. , 2006, “ Measurement of Residual Stresses in Micromachined Structures in a Microregion,” Appl. Phys. Lett., 88(7), p. 071910. [CrossRef]
Lagattu, F. , Bridier, F. , Villechaise, P. , and Brillaud, J. , 2006, “ In-Plane Strain Measurements on a Microscopic Scale by Coupling Digital Image Correlation and an In Situ SEM Technique,” Mater. Charact., 56(1), pp. 10–18. [CrossRef]
Sutton, M. A. , Li, N. , Garcia, D. , Cornille, N. , Orteu, J. J. , McNeill, S. R. , Schreier, H. W. , and Li, X. , 2006, “ Metrology in a Scanning Electron Microscope: Theoretical Developments and Experimental Validation,” Meas. Sci. Technol., 17(10), pp. 2613–2622. [CrossRef]
Sutton, M. , Li, N. , Joy, D. , Reynolds, A. , and Li, X. , 2007, “ Scanning Electron Microscopy for Quantitative Small and Large Deformation Measurements Part I: SEM Imaging at Magnifications From 200 to 10,000,” Exp. Mech., 47(6), pp. 775–787. [CrossRef]
Sutton, M. A. , Li, N. , Garcia, D. , Cornille, N. , Orteu, J. , McNeill, S. , Schreier, H. , Li, X. , and Reynolds, A. P. , 2007, “ Scanning Electron Microscopy for Quantitative Small and Large Deformation Measurements Part II: Experimental Validation for Magnifications From 200 to 10,000,” Exp. Mech., 47(6), pp. 789–804. [CrossRef]
Kammers, A. D. , and Daly, S. , 2013, “ Digital Image Correlation Under Scanning Electron Microscopy: Methodology and Validation,” Exp. Mech., 53(9), pp. 1743–1761. [CrossRef]
Kammers, A. D. , and Daly, S. , 2013, “ Self-Assembled Nanoparticle Surface Patterning for Improved Digital Image Correlation in a Scanning Electron Microscope,” Exp. Mech., 53(8), pp. 1333–1341. [CrossRef]
Guo, S. , Sutton, M. , Li, X. , Li, N. , and Wang, L. , 2014, “ SEM-DIC Based Nanoscale Thermal Deformation Studies of Heterogeneous Material,” Advancement of Optical Methods in Experimental Mechanics, Vol. 3, Springer, New York, pp. 145–150.
Jin, H. , Lu, W. , and Korellis, J. , 2008, “ Micro-Scale Deformation Measurement Using the Digital Image Correlation Technique and Scanning Electron Microscope Imaging,” J. Strain Anal. Eng. Des., 43(8), pp. 719–728. [CrossRef]
Tschopp, M. , Bartha, B. , Porter, W. , Murray, P. , and Fairchild, S. , 2009, “ Microstructure-Dependent Local Strain Behavior in Polycrystals Through In-Situ Scanning Electron Microscope Tensile Experiments,” Metall. Mater. Trans. A, 40(10), pp. 2363–2368. [CrossRef]
Sabate, N. , Vogel, D. , Gollhardt, A. , Keller, J. , Cane, C. , Gracia, I. , Morante, J. R. , and Michel, B. , 2007, “ Residual Stress Measurement on a MEMS Structure With High-Spatial Resolution,” J. Microelectromech. Syst., 16(2), pp. 365–372. [CrossRef]
Wang, Z. , 2000, “ Transmission Electron Microscopy of Shape-Controlled Nanocrystals and Their Assemblies,” J. Phys. Chem. B, 104(6), pp. 1153–1175. [CrossRef]
Williams, D. B. , and Carter, C. B. , 2009, Transmission Electron Microscopy, Springer, New York.
Hÿtch, M. , Snoeck, E. , and Kilaas, R. , 1998, “ Quantitative Measurement of Displacement and Strain Fields From HREM Micrographs,” Ultramicroscopy, 74(3), pp. 131–146. [CrossRef]
Snoeck, E. , Warot, B. , Ardhuin, H. , Rocher, A. , Casanove, M. , Kilaas, R. , and Hÿtch, M. , 1998, “ Quantitative Analysis of Strain Field in Thin Films From HRTEM Micrographs,” Thin Solid Films, 319(1), pp. 157–162. [CrossRef]
Hÿtch, M. , Houdellier, F. , Hüe, F. , and Snoeck, E. , 2008, “ Nanoscale Holographic Interferometry for Strain Measurements in Electronic Devices,” Nature, 453(7198), pp. 1086–1089. [CrossRef] [PubMed]
Zhang, P. , Istratov, A. A. , Weber, E. R. , Kisielowski, C. , He, H. , Nelson, C. , and Spence, J. C. , 2006, “ Direct Strain Measurement in a 65 nm Node Strained Silicon Transistor by Convergent-Beam Electron Diffraction,” Appl. Phys. Lett., 89(16), p. 161907. [CrossRef]
Jones, P. , Rackham, G. , and Steeds, J. , 1977, “ Higher Order Laue Zone Effects in Electron Diffraction and Their Use in Lattice Parameter Determination,” Proc. R. Soc. London, Ser. A, 354(1677), pp. 197–222. [CrossRef]
Armigliato, A. , Balboni, R. , Carnevale, G. , Pavia, G. , Piccolo, D. , Frabboni, S. , Benedetti, A. , and Cullis, A. , 2003, “ Application of Convergent Beam Electron Diffraction to Two-Dimensional Strain Mapping in Silicon Devices,” Appl. Phys. Lett., 82(13), pp. 2172–2174. [CrossRef]
Usuda, K. , Numata, T. , Irisawa, T. , Hirashita, N. , and Takagi, S. , 2005, “ Strain Characterization in SOI and Strained-Si on SGOI MOSFET Channel Using Nano-Beam Electron Diffraction (NBD),” Mater. Sci. Eng.: B, 124–125, pp. 143–147. [CrossRef]
Uesugi, F. , Hokazono, A. , and Takeno, S. , 2011, “ Evaluation of Two-Dimensional Strain Distribution by STEM/NBD,” Ultramicroscopy, 111(8), pp. 995–998. [CrossRef] [PubMed]
Orlov, A. , Granovsky, A. , Balagurov, L. , Kulemanov, I. , Parkhomenko, Y. N. , Perov, N. , Gan'shina, E. , Bublik, V. , Shcherbachev, K. , and Kartavykh, A. , 2009, “ Structure, Electrical and Magnetic Properties, and the Origin of the Room Temperature Ferromagnetism in Mn-Implanted Si,” J. Exp. Theor. Phys., 109(4), pp. 602–608. [CrossRef]
Wang, J. W. , He, Y. , Fan, F. , Liu, X. H. , Xia, S. , Liu, Y. , Harris, C. T. , Li, H. , Huang, J. Y. , Mao, S. X. , and Zhu, T. , 2013, “ Two-Phase Electrochemical Lithiation in Amorphous Silicon,” Nano Lett., 13(2), pp. 709–715. [CrossRef] [PubMed]
Peters, W. , and Ranson, W. , 1982, “ Digital Imaging Techniques in Experimental Stress Analysis,” Opt. Eng., 21(3), pp. 427–431. [CrossRef]
Sutton, M. , Wolters, W. , Peters, W. , Ranson, W. , and McNeill, S. , 1983, “ Determination of Displacements Using an Improved Digital Correlation Method,” Image Vision Comput., 1(3), pp. 133–139. [CrossRef]
Lu, H. , and Cary, P. , 2000, “ Deformation Measurements by Digital Image Correlation: Implementation of a Second-Order Displacement Gradient,” Exp. Mech., 40(4), pp. 393–400. [CrossRef]
Bornert, M. , Brémand, F. , Doumalin, P. , Dupré, J.-C. , Fazzini, M. , Grédiac, M. , Hild, F. , Mistou, S. , Molimard, J. , and Orteu, J.-J. , 2009, “ Assessment of Digital Image Correlation Measurement Errors: Methodology and Results,” Exp. Mech., 49(3), pp. 353–370. [CrossRef]
Bruck, H. , McNeill, S. , Sutton, M. A. , and Peters Iii, W. , 1989, “ Digital Image Correlation Using Newton–Raphson Method of Partial Differential Correction,” Exp. Mech., 29(3), pp. 261–267. [CrossRef]
Sun, Y. , Pang, J. H. , Wong, C. K. , and Su, F. , 2005, “ Finite Element Formulation for a Digital Image Correlation Method,” Appl. Opt., 44(34), pp. 7357–7363. [CrossRef] [PubMed]
Besnard, G. , Hild, F. , and Roux, S. , 2006, “ ‘Finite-Element’ Displacement Fields Analysis From Digital Images: Application to Portevin–Le Châtelier Bands,” Exp. Mech., 46(6), pp. 789–803. [CrossRef]
Réthoré, J. , Roux, S. , and Hild, F. , 2010, “ Hybrid Analytical and Extended Finite Element Method (HAX-FEM): A New Enrichment Procedure for Cracked Solids,” Int. J. Numer. Methods Eng., 81(3), pp. 269–285. [CrossRef]
Réthoré, J. , Roux, S. , and Hild, F. , 2010, “ Mixed-Mode Crack Propagation Using a Hybrid Analytical and Extended Finite Element Method,” C. R. Méc., 338(3), pp. 121–126. [CrossRef]
Williams, M. L. , 1957, “ On the Stress Distribution at the Base of a Stationary Crack,” ASME J. Appl. Mech., 24(1), pp. 109–114.
Hild, F. , and Roux, S. , 2012, “ Comparison of Local and Global Approaches to Digital Image Correlation,” Exp. Mech., 52(9), pp. 1503–1519. [CrossRef]
Pan, B. , Wang, B. , Lubineau, G. , and Moussawi, A. , 2015, “ Comparison of Subset-Based Local and Finite Element-Based Global Digital Image Correlation,” Exp. Mech., 55(5), pp. 887–901. [CrossRef]
Reimer, L. , 2013, Transmission Electron Microscopy: Physics of Image Formation and Microanalysis, Springer, New York.
Muller, D. A. , Kirkland, E. J. , Thomas, M. G. , Grazul, J. L. , Fitting, L. , and Weyland, M. , 2006, “ Room Design for High-Performance Electron Microscopy,” Ultramicroscopy, 106(11), pp. 1033–1040. [CrossRef] [PubMed]
Lagarias, J. C. , Reeds, J. A. , Wright, M. H. , and Wright, P. E. , 1998, “ Convergence Properties of the Nelder–Mead Simplex Method in Low Dimensions,” SIAM J. Optim., 9(1), pp. 112–147. [CrossRef]
Beaulieu, L. , Hatchard, T. , Bonakdarpour, A. , Fleischauer, M. , and Dahn, J. , 2003, “ Reaction of Li With Alloy Thin Films Studied by In Situ AFM,” J. Electrochem. Soc., 150(11), pp. A1457–A1464. [CrossRef]
He, Y. , Yu, X. , Li, G. , Wang, R. , Li, H. , Wang, Y. , Gao, H. , and Huang, X. , 2012, “ Shape Evolution of Patterned Amorphous and Polycrystalline Silicon Microarray Thin Film Electrodes Caused by Lithium Insertion and Extraction,” J. Power Sources, 216, pp. 131–138. [CrossRef]
Becker, C. R. , Strawhecker, K. E. , McAllister, Q. P. , and Lundgren, C. A. , 2013, “ In Situ Atomic Force Microscopy of Lithiation and Delithiation of Silicon Nanostructures for Lithium Ion Batteries,” ACS Nano, 7(10), pp. 9173–9182. [CrossRef] [PubMed]
Laaziri, K. , Kycia, S. , Roorda, S. , Chicoine, M. , Robertson, J. , Wang, J. , and Moss, S. , 1999, “ High-Energy X-Ray Diffraction Study of Pure Amorphous Silicon,” Phys. Rev. B, 60(19), pp. 13520–13533. [CrossRef]
Wakagi, M. , Ogata, K. , and Nakano, A. , 1994, “ Structural Study of a-Si and a-Si: H Films by EXAFS and Raman-Scattering Spectroscopy,” Phys. Rev. B, 50(15), pp. 10666–10671. [CrossRef]
Kugler, S. , Pusztai, L. , Rosta, L. , Chieux, P. , and Bellissent, R. , 1993, “ Structure of Evaporated Pure Amorphous Silicon: Neutron-Diffraction and Reverse Monte Carlo Investigations,” Phys. Rev. B, 48(10), pp. 7685–7688. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) A TEM image showing the random atomic structure in amorphous silicon (a-Si), which serves as a high-quality speckle pattern for DIC analysis. (b) Schematic illustration of an in situ electrochemical lithiation experiment inside a TEM. (c) Schematic ray diagram of a TEM.

Grahic Jump Location
Fig. 2

Assessment of the DIC errors due to the TEM image noise. Maps of ((a) and (b)) displacements and ((c) and (d)) DIC strain errors resulting from the TEM image noise.

Grahic Jump Location
Fig. 3

Assessment of the DIC errors due to the electromagnetic-lens distortion. Maps of ((a) and (b)) displacements and ((c) and (d)) DIC strain errors resulting from a rigid-body translation of the a-Si sample.

Grahic Jump Location
Fig. 4

Assessment of the DIC errors due to the image shift operation. Maps of ((a) and (b)) displacements and ((c) and (d)) DIC strain errors resulting from a rigid-body shift of the imaging window.

Grahic Jump Location
Fig. 5

Local DIC analysis of the lithium-diffusion-induced strain in a lithiated Si region. ((a) and (b)) Reference and deformed TEM images used for the DIC analysis. ((c) and (d)) Obtained εxx and εyy strain contour plots superimposed on the reference TEM image as shown in (a).

Grahic Jump Location
Fig. 6

Plots of the trial (a) displacement and (b) strain functions used for the global DIC analysis of the reaction-induced strain at an a-Si/a-LixSi phase boundary

Grahic Jump Location
Fig. 7

Global DIC analysis of the reaction-induced strain at an a-Si/a-LixSi phase boundary. (a) The first image in a sequence of TEM images serving as the reference image for the global DIC analysis. ((b)–(d)) Obtained εyy strain contour plots superimposed on the subsequent TEM images at various stages of lithiation. (e) Obtained strain profiles across the a-Si/a-LixSi phase boundary. Note that the strain analysis is made with respect to the reference image in (a). The width of the reaction zone with large strain increases as the lithiation proceeds.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In