Name: quantitative hardness measurement by instrumented afm-indentation
Uploaded: 2016-11-22T14:00:00
Description: Watch this Scientific Journal Video about Quantitative Hardness Measurement by Instrumented AFM-indentation at JoVE.com

A.C. is grateful to KoreaTech for financial support.

1. Instrumental Set-up and Calibration

<ol>
	<li>Instrumental set-up
	<ol>
		<li>Use a stiff diamond-coated cantilever of the type DT-NCLR or CDT-NCLR with a first free resonance frequency f0,1 &#8805; 180 kHz, a quality factor Q &#8805; 300, and a bending stiffness k &#8805; 40 N/m.</li>
		<li>Mount the selected cantilever onto a clamping holder provided by the AFM manufacturer. Take special care to place the cantilever such that its long axis is p...

<ol>
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E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nanomechanical+Properties+of+Au(111)+(001),+and+(110)+Surfaces.">Nanomechanical Properties of Au(111) (001), and (110) Surfaces.</a> Phys. Rev. B. 57 (19), 12588 (1998).</li><li>Kiely, J. D., Jarausch, K. F., Houston, J. E., Russell, P. E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Initial+Stages+of+Yield+in+Nanoindentation.">Initial Stages of Yield in Nanoindentation.</a> J. Mater. Res. 14 (19), 2219-2227 (1999).</li><li>Egberts, P., Bennewitz, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Atomic+Scale+Nanoindentation:+Detection+and+Indentification+of+Single+Glide+Events+in+Three+Dimensions+by+Force+Microscopy.">Atomic Scale Nanoindentation: Detection and Indentification of Single Glide Events in Three Dimensions by Force Microscopy.</a> Nanotechnology. 22 (42), 425703-1-425703-9 (2011).</li><li>Filleter, T., Bennewitz, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nanometer+Scale+Plasticity+of+Cu(100).">Nanometer Scale Plasticity of Cu(100).</a> Nanotechnology. 18 (4), 044004-1-044004-4 (2007).</li><li>Asenjo, A., Jaafar, M., Carrasco, E., Rojo, J. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Dislocation+mechanisms+in+the+first+stage+of+plasticity+of+nanoindented+Au(111)+surfaces.">Dislocation mechanisms in the first stage of plasticity of nanoindented Au(111) surfaces.</a> Phys. Rev. B. 73 (7), 075431 (2006).</li><li>Paul, W., Oliver, D., Miyahara, Y., Gruetter, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Minimum+threshold+for+incipient+plasticity+in+the+atomic-scale+nanoindentation+of+Au(111).">Minimum threshold for incipient plasticity in the atomic-scale nanoindentation of Au(111).</a> Phys. Rev. Lett. 110 (13), 135506 (2013).</li><li>Kracke, B., Damaschke, B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Measurement+of+nanohardness+and+nanoelasticity+of+thin+gold+films+with+scanning+force+microscope.">Measurement of nanohardness and nanoelasticity of thin gold films with scanning force microscope.</a> Appl. Phys. Lett. 77 (3), 361-363 (2000).</li><li>Sansoz, F., Gang, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+force-mapping+method+for+quantitative+hardness+measurements+by+atomic+force+microscopy+with+diamond-tipped+sapphire+cantilevers.">A force-mapping method for quantitative hardness measurements by atomic force microscopy with diamond-tipped sapphire cantilevers.</a> Ultramicroscopy. 111, 11-19 (2010).</li><li>Silva, E. C. C. M., Van Vliet, K. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Robust+approach+to+maximize+the+range+and+accuracy+of+force+application+in+atomic+force+microscopes+with+non-linear+position-sensitive+detectors.">Robust approach to maximize the range and accuracy of force application in atomic force microscopes with non-linear position-sensitive detectors.</a> Nanotechnolgy. 17 (21), 5525-5529 (2006).</li><li>Caron, A., Bennewitz, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Lower+Nanometer-Scale+Size+Limit+for+the+Deformation+of+a+Metallic+Glass+by+Shear+Transformations+Revealed+by+Quantitative+AFM+Indentation.">Lower Nanometer-Scale Size Limit for the Deformation of a Metallic Glass by Shear Transformations Revealed by Quantitative AFM Indentation.</a> Beilstein J. Nanotechnol. 6, 1721-1732 (2015).</li><li>Andriotis, O. G., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nanomechanical+assesment+of+human+and+murine+collagen+fibrils+via+atomic+force+microscopy+cantilever-based+nanoindentation.">Nanomechanical assesment of human and murine collagen fibrils via atomic force microscopy cantilever-based nanoindentation.</a> J. Mech. Behavior Biomed. Mater. 39, 9-26 (2014).</li><li>Bischel, M. S., Vanlandingham, M. R., Eduljee, R. F., Gillespie, J. W., Schultz, J. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=On+the+use+of+nanoscale+indentation+with+the+AFM+in+the+identification+of+phases+in+blends+of+linear+low+density+polyethylene+and+high+density+polyethylene.">On the use of nanoscale indentation with the AFM in the identification of phases in blends of linear low density polyethylene and high density polyethylene.</a> J. Mater. Sci. 35 (1), 221-228 (2000).</li><li>Zhang, L., Wang, W., Zheng, L., Wang, X., Yan, Q. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Quantitative+characterization+of+mechanical+property+of+annealed+monolayer+colloidal+crystal.">Quantitative characterization of mechanical property of annealed monolayer colloidal crystal.</a> Langmuir. 32 (2), 451-459 (2016).</li><li>Ne&#269;as, D., Klapetek, P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Gwyddion:+An+open-source+software+for+SPM+data+analysis.">Gwyddion: An open-source software for SPM data analysis.</a> Cent. Eur. J. Phys. 10 (1), 181-188 (2012).</li><li>Hahn, B. H., Valentine, D. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Essential Matlab for Engineers and Scientists. , (2013).</li><li>Nonnenmacher, M., Greschner, J., Wolter, O., Kassing, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Scanning+Force+Microscopy+with+Micromachined+Silicon+Sensors.">Scanning Force Microscopy with Micromachined Silicon Sensors.</a> J. Vac. Sci. Technol. B. 9 (2), 1358-1362 (1991).</li><li>Cannara, R. J., Brukman, M. J., Carpick, R. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Cantilever+tilt+compensation+for+variable-load+atomic+force+microscopy.">Cantilever tilt compensation for variable-load atomic force microscopy.</a> Rev. Sci. Instrum. 76 (5), 053706 (2005).</li><li>Johnson, K. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Contact Mechanics. , (1985).</li><li>Mohr, M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Young's+Modulus,+Fracture+Strength,+and+Poisson's+Ratio+of+Nanocrystalline+Diamond+Films.">Young's Modulus, Fracture Strength, and Poisson's Ratio of Nanocrystalline Diamond Films.</a> J. Appl. Phys. 116 (12), 124308-1-124308-10 (2014).</li><li>Arnault, J. C., Mosser, A., Zamfirescu, M., Pelletier, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Elastic+recovery+measurements+performed+by+atomic+force+microscopy+and+standard+nanoindentation+on+a+Co(10.1)+monocrystal.">Elastic recovery measurements performed by atomic force microscopy and standard nanoindentation on a Co(10.1) monocrystal.</a> J. Mater. Res. 17 (6), 1258-1265 (2002).</li><li>Cao, Y., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nanoindentation+measurements+of+the+mechanical+properties+of+polycrystalline+Au+and+Ag+thin+films+on+silicon+substrates:+Effect+of+grain+size+and+film+thickness.">Nanoindentation measurements of the mechanical properties of polycrystalline Au and Ag thin films on silicon substrates: Effect of grain size and film thickness.</a> Mater. Sci. Eng. 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A method has been presented for performing a series of indentations on an Au(111) thin-film surface with a diamond-coated AFM tip. Non-contact AFM imaging and AFM indentation were performed with the same force sensor. The requirements for non-contact imaging are a high first free resonance frequency f0,1 &#8805; 180 kHz and a high quality factor Q &#8805; 300. In AFM indentation, the vertical force to be applied is in the range of several micro-newtons, and a cantilever with a high bending st...

For the last 150 years, hardness values have been used to characterize the mechanical behavior of materials and to predict their performance under various loading conditions. The hardness of a material describes the resistance of its surface to the penetration of a harder indenter. For metallic materials, the hardness relates to resistance to plastic flow.
Although the implementation of hardness testing has proven to be relatively easy, the yielded results have long been rather empirical, making them unable to describe the intrinsic properties of the investigated material. The empirical nature of hardness testing results has been a consequence of the use of various indenter geometries, each of which has a different established hardness scale. However, all empirical hardness scales, such as the Brinell hardness (HB) test for spherical indenters and the Vickers (HV) and Knoop (HK) hardness tests for different types of four-sided pyramids, have one thing in common: the hardness number is determined from the ratio of the applied load to the developed area of the remaining indent. In an attempt to relate the hardness of metals to their fundamental mechanical properties, the hardness measured with a spherical indenter has been defined as the ratio of the applied load to the projected area of the remaining indent. This hardness value, also known as the Meyer's hardness (H), is equal to the mean contact pressure and directly relates to the yield strength of non-work-hardening metals1. 
Hardness testing has long been limited to the macro-scale, in which case the sizes of indents have been measured by optical means. The development of instrumented indentation, where force-displacement curves are recorded, has been recognized as a valuable alternative for determining the hardness of a material, although the size of the remaining indent may be too small to be accurately imaged. In this case, the projected area of the indent is calculated from the tip displacement according to a so-called indenter-area function2. Due to this development, the analysis of the curvature of force-displacement curves and of the occurrence of distinct plasticity events in the shape of pop-ins is now widely used to study the mechanisms of plastic deformation at the micrometer scale, such as by means of nanoindentation3.
It is well accepted that the carriers of plastic deformation in metals, i.e., dislocations, operate at the nanometer scale. To understand their modes of operation at the atomic level, new experimental techniques with atomic resolution are needed. Initial investigations of atomistic plasticity events at the interfaces between nanometer-sized single asperities and single crystalline Au surfaces of different orientations have been carried out by interfacial force microscopy (IFM)4, 5. Atomic force microscopy (AFM) indentation has been applied to observe the nucleation and gliding of single dislocations in KBr(100) single crystals6, Cu(100)7, and Au(111)8, 9. There, atomistic plasticity events were observed in the shape of pop-ins, with lengths in the range of 1 &#197;. AFM indentation has also been used to measure the nano-hardness and -elasticity of gold nano-island grown on mica10. In this work, the nano-hardness was found to be smaller than the bulk value and was observed to depend linearly on the indentation area. Also, a detailed measurement protocol has been proposed to determine the hardness of hard surfaces, such as fused quartz and silicon, by AFM indentation with a diamond-tipped sapphire cantilever11. In particular, this method takes into account the non-linearity of the photo-sensitive deflection detectors for large cantilever deflection12. More recently, AFM indentation and non-contact AFM imaging have been combined to quantitatively determine the hardness and the fundamental mechanisms of plastic deformation of a Pt(111) single crystalline surface and Pt-based metallic glass13. For Pt(111), plastic deformation mechanisms at the nanometer scale were found to be consistent with the discrete mechanisms established for larger scales. Further, the nanometer-scale plastic deformation of the metallic glass was found to be not discrete, but rather continuous and highly localized around the indenting tip. These results revealed a lower size limit for metallic glasses, below which shear transformation mechanisms are not activated by indentation. AFM indentation has also been used to determine the hardness values of biological samples (such as collagen fibrils)14, polymers15, and colloidal crystals16.
In the present work, a careful experimental procedure is described that includes the force sensor selection, its calibration, the calibration of the cantilever deflection detection system, and the minimization of instrumental drift for accurate and reproducible force-distance measurements. Also, a method for the data analysis is presented that allows the extraction of force-penetration curves from recorded force-distance curves. Further representative results are shown and discussed in the light of recent findings in the field of plastic deformation of small volumes.
For this experiment, an atomic force microscope (AFM) was used. The cornerstone of an AFM is its micro-fabricated force sensor (usually a cantilever beam), with a sharp tip at the end whose radius is in the range of several nanometers. In the particular configuration of the instrument used for this experiment, the cantilever is mounted onto a piezo-electric z-scanner, while the sample to be investigated is mounted onto a piezo-electric x/y-scanner. During AFM imaging, the force sensor tip is scanned over a sample to register interaction forces with the sample surface that result in a deflection of the cantilever according to Hooke's law. The static or dynamic deflection of the cantilever can be measured with an optical beam deflection detector, consisting of a laser diode, a set of mirrors, and a photodiode that converts the cantilever deflection into a voltage. During imaging, the signal at the photodiode is controlled by a feedback loop so as to keep the interaction forces at the sample surface; this results in adjustments of the z-scanner position, which are recorded and displayed as a topography image.
Prerequisites for the experiment described below are that the piezo-electric scanners of the atomic force microscope are well-calibrated and that the instrument stays in the laboratory at a constant temperature and humidity level. The reader should be aware that, depending on the atomic force microscope model, some of the experimental procedure steps may have to be modified. In particular, all measurements are performed after setting the scanners' ranges to "small"; this function allows for the reduction of the x/y-scanner range to 5 x 5 &#181;m&#178; and the z-scanner range to 4 &#181;m, which ensures a resolution at small scales. This function is not available on all commercial AFM and is not mentioned in the remainder of the text.
For data analysis, the use of the free SPM data analysis software Gwyddion17 and the Matlab software package18 are recommended.
This protocol gives a description of the experimental procedure to be followed in order to perform instrumented hardness measurements by AFM. Since the handling of different commercial AFMs may differ from one model to the other, the reader should refer to the manual provided by the AFM manufacturer for detailed setting procedures and software information. In the following text, in order to reproduce the described experiment, it is assumed that the reader is familiar with the handling of the particular AFM used here.

<table border="0" cellpadding="0" cellspacing="0" width="573">
	<tbody>
		<tr height="63">
			<td height="63" style="height:63px;width:216px;">AFM XE-100</td>
			<td style="width:71px;">Park Instruments</td>
			<td style="width:119px;">discontinued</td>
			<td style="width:167px;">Atomic force microscope</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:216px;">CDT-NCLR</td>
			<td style="width:71px;">NanoSensors</td>
			<td style="width:119px;">CDT-NCLR</td>
			<td>Conductive diamond coated non-contact lever</td>
		</tr>
		<tr height="42">
			<td height="42" style="height:42px;width:216px;">100 nm thick Au(111) thin film on Mica</td>
			<td style="width:71px;">Phasis</td>
			<td align="right">20020011</td>
			<td>atomically smooth gold thin film</td>
		</tr>
	</tbody>
</table>

quantitative hardness measurement by instrumented afm-indentation

In this work, a combination of amplitude-modulated non-contact atomic force microscopy and atomic force spectroscopy is applied for instrumented hardness measurements on an Au(111) surface with atomistic resolution of single plasticity events. A careful experimental procedure is described that includes the force sensor selection, its calibration, the calibration of the cantilever deflection detection system, and the minimization of instrumental drift for accurate and reproducible force-distance measurements. Also, a method for the data analysis is presented that allows the extraction of force-penetration curves from recorded force-distance curves. A typical curve displays a clear elastic deformation regime up to the first plasticity event, or pop-in, with a length in the range of one to two Burger's vectors. Later plasticity events exhibit the same magnitude. The work of plasticity is further extracted from the measurements. Finally, the hardness is determined in combination with the indentation curve using non-contact atomic force microscopy images of the remaining indents.

In this work, the bending stiffness of the cantilever k was calculated according to the geometrical beam theory19. For the particular diamond-coated cantilever used in this work, we found k = 55.69 N/m. Note that we neglected the diamond coating; the thickness of the diamond coating is one to two orders of magnitude smaller than the cantilever thickness and thus does not significantly increase its bending stiffness (although its Young&#39;s modulus is signific...

Watch this Scientific Journal Video about Quantitative Hardness Measurement by Instrumented AFM-indentation at JoVE.com

Quantitative Hardness Measurement by Instrumented AFM-indentation

This experimental protocol describes how atomic force microscopy can be used to measure hardness at the true nanometer scale and to detect single atomistic plasticity events.

In this work, a combination of amplitude-modulated non-contact atomic force microscopy and atomic force spectroscopy is applied for instrumented hardness ...

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