Critical aspects of scanning probe microscopy mapping when ... · the direct force modulation...

Critical aspects of scanning probe microscopymapping when applied to cement pastesXiang GaoPhD candidate, Key Laboratory of Civil Engineering Safety and Durabilityof China Education Ministry, Department of Civil Engineering,Tsinghua University, Beijing, P. R. China

Ya WeiAssociate Professor, Key Laboratory of Civil Engineering Safety andDurability of China Education Ministry, Department of Civil Engineering,Tsinghua University, Beijing, P. R. China (corresponding author:[email protected])

Wei HuangProfessor, Intelligent Transportation System Research Center,Southeast University, Nanjing, P. R. China

The scanning probe microscopy (SPM) mapping technique allows the measurement of materials’ mechanicalproperties without causing plastic deformation and with much higher spatial resolution compared to thenanoindentation technique. In order to better utilise the SPM mapping technique to identify and quantify themicrostructure morphology of individual phases in cementitious materials, this study explores several critical aspectsrelated to the experimental protocol and the data processing during SPM measurement for both ordinary Portlandcement paste and slag-blended cement paste. Two data-processing methods are proposed to extract the line data andthe area data from the mapping images. The effects of the pixel spacing, the surface roughness of the sample andthe magnitude of loads on the measured mechanical properties are discussed. The results of this study will helpwith selection of the proper testing parameters for identifying different phases and quantifying their sizes under anon-destructive testing condition at a much higher resolution.

Notationa contact radiusD damping coefficientDi damping coefficient of sensorDs damping coefficient of contactE modulusE′ storage modulus of contactE″ loss modulus of contactF forceF0 amplitude of applied sinusoidal forcehmax maximum indentation depthK stiffnessKi stiffness of indenterKf stiffness of system frameKs stiffness of contactm mass of transducerR radius of indenter tipRq root-mean-squared roughnesst timez sinusoidal displacement responsez0 amplitude of displacement with respect to F0ϕ phase shiftω angular frequency

IntroductionIdentifying different phases in cement paste and quantifyingthe nano-mechanical properties and microstructure morpho-logy of individual phases can help in the intelligent designof cement concrete with enhanced properties. The mechanicalproperties and the microstructure morphology of individualphases have been characterised by different techniques such as

nanoindentation (Wei et al., 2016), scanning and backscatteredelectron microscope (SEM and BSE) image analysis (Scrivener,2004), and scanning probe microscopy (SPM) mapping (Liet al., 2016; Wei et al., 2017; Xu et al., 2015). Among thesetechniques, SPM mapping is a nano-mechanical probe-basedmethod, but characterised as a non-destructive test withcontact stiffness measurement at small quasi-static loads of2�8 μN and small dynamic loads of 0·5�3·5 μN (Asif et al.,2001; Balooch et al., 2004; Wilkinson et al., 2015). This tech-nique relates each pixel in the image to mechanical propertyvalues from each tip–sample response during sample surfacescanning with an oscillation indenter tip. Therefore, images ofmechanical property distribution can exhibit the spatial vari-ation of different phases. SPM mapping excels in characteris-ing composite materials which have a sharp contrast betweenthe mechanical properties of different components, such ascarbon fibre with polymer matrix (Asif et al., 2001), as well asthe calcified tissues in human teeth (Balooch et al., 2004) andorganic-rich shales (Wilkinson et al., 2015). Recently, SPMmapping has been adopted to characterise cementitiousmaterials (Li et al., 2016; Wei et al., 2017; Xu et al., 2015).Considering that it is conducted at a small contact force, theSPM mapping technique enables the acquisition of modulusimages with two orders of magnitude increase in spatial resol-ution compared to the point-based methods, such as quasi-static nanoindentation (Li et al., 2016; Xu et al., 2015). Thehigh spatial resolution helps to quantify the thickness of innerproduct rims of both cement clinker and slag grain (Wei et al.,2017). Moreover, the phase identification results by SPMmapping provide precise locations of indents when conductingnanoindentation on individual phases, which can avoid the

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Cite this articleGao X, Wei Y and Huang W (2018)Critical aspects of scanning probe microscopy mapping when applied to cement pastes.Advances in Cement Research 30(7): 293–304,https://doi.org/10.1680/jadcr.17.00093

Advances in Cement Research

Research ArticlePaper 1700093Received 21/05/2017; Revised 15/11/2017;Accepted 15/11/2017;Published online 18/01/2018

ICE Publishing: All rights reserved

Keywords: modulus of elasticity/non-destructive testing/paste

Downloaded by [ Tsinghua University] on [20/06/18]. Copyright © ICE Publishing, all rights reserved.

mailto:yawei@�tsinghua.edu.cn

blind indentation by discrete nanoindentation alone, as well asthe debated deconvolution of the data from the grid indenta-tion (Wei et al., 2017).

Despite the benefits of SPM mapping, the experimental proto-col and data processing have not been fully explored for charac-terising cementitious materials with multi-scale and multi-phasefeatures. In the nanoindentation test, the indentation spacing(Constantinides and Ulm, 2007), the surface roughness (Milleret al., 2008) and the magnitude of load (Davydov et al., 2011)have been proved as key factors to obtaining accurate mechan-ical properties of individual phases. However, investigationregarding the effects of these parameters on the variation of themeasured results in SPM mapping for cementitious materials israrely found (Wei et al., 2017).

In this study, SPM mapping is adopted to identify differentphases and to measure the nano-mechanical properties andsizes of the individual phases in both ordinary Portlandcement (OPC) paste and slag-blended cement paste. Theeffects of the pixel spacing, the surface roughness of thesample and the magnitude of the applied quasi-static anddynamic loads on the variation of the measured results ofSPM mapping are examined to identify the critical aspects.

Methodology and samples

SPM mapping techniqueScanning probe microscopy mapping is acquired usingthe direct force modulation (nanoDMA) operating mode of aHysitron TriboScope nanoindenter. As illustrated in Figure 1(a),the in situ topography image of the sample surface is created inSPM mode. The mapping mode is accomplished by super-imposing a small sinusoidal force on a quasi-static force duringan indentation test. The testing system of SPM can be modelledas a physical system with force applied to a mass that is attachedto the two fixed Voigt elements, as shown in Figure 1(b). Themodel yields a differential equation describing the relationshipbetween the applied force and the motion

1: F tð Þ ¼ F0 sin ωtð Þ ¼ md2zdt2

!þD

dzdt

� �þ Kz

where F0 is the amplitude of the applied sinusoidal force, m isthe mass of the transducer, ω is the angular frequency, z is thesinusoidal displacement response, D=Di +Ds is the combineddamping coefficient of system and the contact, K=Ki +Ks isthe combined stiffness of spring and the contact, Kf is the stiff-ness of the system frame, which is much greater than the stiff-ness of the contact and can be ignored. The solution toEquation 1 is

2: z ¼ z0 sin ωtþ ϕð Þ

3: z0 ¼ F0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK �mω2ð Þ2 þ Dωð Þ2

q

where ϕ is the phase of the displacement,tan ϕð Þ ¼ � Dω=ðK �mω2Þ� �

.

The storage modulus (E′) and the loss modulus (E″) of contactcan be calculated as

4: E0 ¼ Ks

2a

5: E0 0 ¼ ωDs

2a

6: a ¼ffiffiffiffiffiffiffiffiffi3FR2Ks

s

where F is the contact force and R is the indenter tip radius.Based on the modulus of 69·6 GPa for the fused quartz, theradius of the indenter tip used in this paper was found to be400 nm.

SamplesOrdinary Portland cement and slag were used as cementitiousmaterials in this study. In the slag-blended paste, the OPCwas replaced by the slag at the levels of 50% by mass of thetotal cementitious materials. The water/cementitious ratioof the pastes was 0·3. The pastes were cast into cylindricalplastic tubes with 10 mm dia. They were sealed and placed ina curing room with temperature controlled at 20°C. The curingage was 180 d. The grinding and polishing process (Milleret al., 2008) was conducted using different grits of carbidepapers and different particle sizes of polishing pastes.

Data interpretation from SPM mapping

Output of SPM mappingIn SPM mapping, the direct output parameters are the contactforce on the sample surface, the displacement amplitude of theindenter tip at every pixel, the phase shift between the contactforce and the displacement. The storage modulus and the lossmodulus could be calculated based on these three parametersby Equations 2–6.

Figure 2(a) shows the contact force image of a target areaincluding a tricalcium silicate (C3S) clinker and the hydrationproducts in OPC paste. It is found that the contact forceremains constant around 4 μN as the preset value for the

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Advances in Cement ResearchVolume 30 Issue 7

Critical aspects of scanning probemicroscopy mapping when applied tocement pastesGao, Wei and Huang


quasi-static force, although a small variation can be seen as aresult of feedback error, which is illustrated as the slight colourcontrast in Figure 2(a). Figure 2(b) shows the displacementamplitude of the indenter tip corresponding to the contactforce image. The measured displacement amplitude is primar-ily due to the variation of the mechanical response of thesample to the applied load. It is found that the displacementamplitude on the C3S clinker is remarkably smaller thanthat on the hydration products, and the boundary betweenthe clinker and the hydration products is clearly displayed.Figure 2(c) reveals the phase shift between the load and thedisplacement during scanning. The displacement amplitudesand the phase shifts occur as a consequence of the changes inthe local damping coefficient and the contact stiffness. Thecontrast of colour in the images reflects the variation of thecombined tip–sample elastic and damping response acrossthe sample surface.

The modulus can be calculated from the displacement am-plitude and the phase shift. Figures 2(d) and 2(e) show thestorage and the loss components of the complex modulus.Storage modulus represents the material capacity to storeenergy; loss modulus represents the material capacity to dissi-pate energy. It can be manifested that both the storage and theloss moduli of the clinker are much higher than that of thehydration product. The loss moduli are roughly 1/10�1/8of the storage moduli of both the clinker and the hydrationproduct.

Methods of data extraction from mapping

Line data extractionIn the literature (Li et al., 2016; Wei et al., 2017; Xu et al.,2015), the line data at desired positions were usually extractedfrom the mapping images to reflect the variation of the

Scanning probe microscopy mode In situ topography image

Slag

Quasi-static and dynamic force

Slag20 μm

C2S

C2S

DisplacementTop

plate

Centreplate

Bottomplate Indenter

columnSupportspring

Specimen

Amplitude andphase shift

Storagemodulus

Modulusmapping

Lossmodulus

Kf

KiKs Ds

Di

mz(t) = z0sin (ωt + φ)

F (t) = F0sinωt

Figure 1. (a) Illustration of SPM mapping and (b) physical model of measuring system

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mechanical properties. According to the variation, differentphases in heterogeneous materials can be distinguished, as thedistinct differences of the mechanical properties of differentphases are reflected in the line data. In cement paste, theinner hydration product (IP) forms within the boundary of theoriginal particles and the outer hydration product (OP) formsin the initially water-filled space (Richardson and Groves,1993). The difference between the storage moduli of IP andOP is an efficient indicator to distinguish these two types ofhydration products. Figure 3 shows the modulus images of thetarget areas in OPC and slag-blended pastes. Four verticaldata lines are extracted from the modulus images and the linedata are plotted. The obvious changes of storage modulican be found at the boundary between the C3S clinker or theslag grain and their IP, as well as at the boundary betweenIP and OP. The thickness of IP rims can be evaluated inthis way as 3·7�6·0 μm for the C3S clinker and 0·6�1·3 μm

for the slag grain, respectively. From the BSE images analysis(Gruskovnjak et al., 2006), the IP rims of the slag grainwere also found to be narrower than that of the C3S clinker.However, precise measurements of the thickness of IPrims were not performed in the work of Gruskovnjak et al.(2006), as the colour contrast between the IP and OP in BSEimages is not as clear as the modulus contrast in modulusimages.

Area data extractionThe area data of individual phases are also extracted frommapping images by a newly proposed method. The amount ofdata in the area of individual phases is at least an orderof magnitude larger than that in single lines. Therefore, thestorage modulus can be calculated by one set of data, which isextracted from the area of individual phases, rather than byseveral sets of data, which are extracted from different lines.

2 3 4 5 6

Contact force: μN

0 1 2 3 4

Displacement amplitude: nm

–12 –6 0 6 12

Phase shift: degrees(a) (b)

0 5 10 15 20

Loss modulus: GPa

0 20 40 60 80

Storage modulus: GPa(d) (e)

(c)

OP

IP

C3S

OP

IP

C3S

OP

IP

C3S

OP

IP

C3S

OP

IP

C3S5 μm 5 μm

5 μm 5 μm

5 μm

Figure 2. Mapping images covering an area around a C3S clinker in OPC paste represented by: (a) contact force; (b) displacementamplitude of indenter tip; (c) phase shift between the oscillating force and the displacement; (d) loss modulus; and (e) storage modulus(IP, inner hydration product; OP, outer hydration product). A full-colour version of this figure can be found on the ICE Virtual Library(www.icevirtuallibrary.com)

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1 2 3 4

x di

rect

ion

80 C3SITZIPOP60

40

20

00 5 10

Distance: μm

15 20

Stor

age

mod

ulus

: GPa

IP ≈ 4·6 μm

80 C3SITZIPOP

60

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00 5 10

Distance: μm

15 20

Stor

age

mod

ulus

: GPa

IP ≈ 3·7 μm

C3SITZIPOP

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IP ≈ 4·1 μm

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Distance: μm

15 20St

orag

e m

odul

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PaIP ≈ 6·0 μm

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Stor

age

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IP ≈ 0·8 μm

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Stor

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IP ≈ 1·3 μm

SlagIPOP

SlagIPOP

SlagIPOP

SlagIPOP

80

60

40

20

0

Distance: μm

0 2 3 4 5 61 7 0 2 3 4 5 61 7

0 2 3 4 5 61 7 0 2 3 4 5 61 7

Stor

age

mod

ulus

: GPa

IP ≈ 0·6 μm

80

60

40

20

0

Distance: μm

(b) (c)

(d) (e)

(b’) (c’)

(d’) (e’)

Stor

age

mod

ulus

: GPa

IP ≈ 1·0 μm

OP

IP

C3S 2 μm

1 2 3 4

x di

rect

ion

OP

IP

Slag

1 μm

(a)

(a’)

Figure 3. Line data extracted from the modulus images of OPC and slag-blended paste: (a) and (a′) the modulus image and the locationsof the selected lines; (b), (c), (d), (e) and (b′), (c′), (d′), (e′) phase identification by the variation of storage moduli along the four verticallines in (a) and (a′) and the measured thickness of IP (inner hydration product) rims (ITZ, interfacial transition zone). A full-colour version ofthis figure can be found on the ICE Virtual Library (www.icevirtuallibrary.com)

297





The method for acquiring the area data is accomplished by thefollowing steps, as shown in Figure 4(a).

& Step 1: the mapping images are meshed into 256� 256elements because 256 is the amount of pixels in mappingimages along one dimension.

& Step 2: the boundaries are drawn between different phasesby the contrast of colour and then translated intocoordinates. The properties of individual phases areextracted from the properties matrix by using thecoordinates of the boundaries.

& Step 3: the average values and the standard variation of thedesired properties such as storage moduli of individualphases are calculated based on the extracted area data.

Following these steps, the storage moduli of OP and IP are cal-culated as 24± 7 GPa and 35± 6 GPa in OPC paste and25± 6 GPa and 39± 9 GPa in slag-blended paste, respectively;the storage moduli of the C3S clinker and the slag grain are62± 13 GPa and 69± 16 GPa, respectively. The ranges of thestorage moduli extracted from the area data are consistent withthat extracted from the line data for different phases, as shown

Step 1Meshing

Step 2Boundary drawnig

Step 3Modulus calculation

20 μm

20 μ

m7

μm

7 μm 7 μm

20 μm

256 rows

256 rows

256 columns

256 columns

OP

IP

OP

IP

Slag

C3S

OP IP OP

(b)

(a)

IP SlagC3S

Ave = 24 GPaStd = 7 GPa






OPC Slag-blended100

80

60

40

20

0

Stor

age

mod

ulus

: GPa

Area dataLine data

Figure 4. (a) Steps for extracting the area data from modulus images; (b) storage moduli of individual phases calculated based on thefour sets of line data in Figure 3 and one set of area data of (a). A full-colour version of this figure can be found on the ICE Virtual Library(www.icevirtuallibrary.com)

298





in Figure 4(b). Therefore, the difference of storage moduli ofdifferent phases reflected by the colour contrast in modulusimages can be used to identify the individual phases.

Critical aspects in SPM mapping

Pixel spacingIt has been reported that close indentation distance can leadto interaction between the indentation stress fields during nano-indentation tests (Constantinides and Ulm, 2007). Similarly,

the close pixel spacing in SPM mapping may have an impacton the deformation of adjacent pixels. The effect of the pixelspacing is discussed in this section.

In Figure 5, SPM mapping is conducted on a target area includ-ing a slag grain, a dicalcium silicate (C2S) clinker and thehydration products. Two small areas at the edges of the slaggrain and the C2S clinker are selected to evaluate the effect ofpixel spacing. The pixel spacing can be calculated throughdividing the image size by 256, which is the amount of pixels in

35 μm

7 μm

7 μm

Scan

ning

line

7 μm

7 μm

Scan

ning

line

35 μ

m

Area I

Area I

Area II

Area II

C2S

80

100

60

40

20

0

Stor

age

mod

ulus

: GPa

80

100

60

40

20

0

Stor

age

mod

ulus

: GPa

Distance: μm

0 2 3 4 5 61 7

Distance: μm(d) (e)

0 2 4 6 8 10

(a)

(b)

(c)

Data obtained in (a)with pixel spacing of35 μm/256 = 137 nm

Data obtained in (b)with pixel spacing of7 μm/256 = 27 nm

Data obtained in (a)with pixel spacing of35 μm/256 = 137 nm

Data obtained in (c)with pixel spacing of7 μm/256 = 27 nm

Figure 5. Effect of the pixel spacing on the variability of storage modulus: (a) modulus image of target area with pixel spacing of35 μm/256=137 nm; (b) and (c) modulus images of area I and area II in (a) with pixel spacing of 7 μm/256=27 nm; (d) and (e) storagemoduli along the same selected lines for large and small pixel spacing. A full-colour version of this figure can be found on the ICE VirtualLibrary (www.icevirtuallibrary.com)

299





one dimension. The pixel spacing is 35 μm/256=137 nm inFigure 5(a) and it is 7 μm/256=27 nm in Figures 5(b) and 5(c).Figures 5(d) and 5(e) show the storage moduli along the sameselected lines, but with different pixel spacing. It can be seenthat similar storage moduli are obtained for the pixel spacing of137 nm and 27 nm. The effect of the pixel spacing on storagemodulus is not significant.

The theoretical influencing radius of the indenter tip can becalculated by the Hertzian contact theory using Equation 6.According to the storage moduli of pastes in the range15�90 GPa, as illustrated in Figures 3–5, the influencingradius of the indenter tip is calculated as 24�43 nm whenthe contact force is 4 μN. The pixel spacing in Figures 5(b)and 5(c) is smaller than the influencing radius; nevertheless, themeasured storage modulus is not influence by the close pixelspacing, for that the storage moduli obtained in Figures 5(b)and 5(c) are almost the same as that obtained in Figure 5(a).This implies that the deformation of material under the inden-ter tip is in the elastic region. Once the tip force is removed, thematerial may return to its original shape with no local stress orpermanent deformation. Therefore, the measure storagemodulus would not be influenced by the adjacent pixels.

Surface roughnessIn the application of nanoindentation, Miller et al. (2008) pro-posed a surface roughness criterion for quantifying the micro-mechanical properties of cementitious materials. The root-mean-squared roughness, Rq, is defined as

7: Rq ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N2

XNi¼1

XNj¼1

z2ij

vuut

where N is the number of pixels in one dimension and zij is theheight at position (i, j). Miller et al. (2008) recommended thatRq should be less than 0·2hmax in an area with the size of200hmax, where hmax is the maximum indentation depth.Therefore, 50 nm of Rq in a randomly selected area with sizeof 50 μm� 50 μm is viewed as the threshold for providingvalid data in nanoindentation. However, the roughness atvarious locations on the same sample exhibits significant varia-bility due to the inherently heterogeneous features of cementi-tious materials. The in situ measurements of the surfaceroughness are more reliable to quantify the effect of roughnessthan that measured in a randomly area, as selected in the workof Miller et al. (2008). The SPM technique can measure thesurface elevation of the target area of the modulus images, andthe effect of roughness on storage modulus in exactly the samepositions can be quantified.

When investigating the impact of surface roughness on thestability of the measured storage modulus, the modulus imageand the topography of an area including C3S clinkers and

hydration products, as shown in Figures 6(a) and 6(b), aremeshed into 16� 16 elements. The size of every element isabout 2·2 μm� 2·2 μm. The meshing process refers to thework of Trtik et al. (2012) to provide the data matrix requiredin the calculation of Rq (Miller et al., 2008). The storagemoduli and the surface roughness of the meshed elements areplotted in Figure 6(c). It is found that the variation of surfaceroughness of OP is the most significant, which ranges from10 nm to 200 nm. This is because that OP is formed in theposition occupied by the water initially, and the space cannotbe fully occupied by hydration products during the hydrationprocess, which remains as pores and voids. Therefore, theroughness within the area of OP mixed with pores and voids islarge. Nevertheless, the variation of storage moduli of OP withvaried surface roughness is not significant. The range ofstorage moduli are 17�31 GPa for OP and 31�37 GPa for IP,which are in good agreement with the area data extracted forindividual phases in Figure 4(b). This indicates that less than200 nm Rq within the 2·2 μm� 2·2 μm element is sufficientlylow for the SPM mapping test. As for the entire image inFigure 6(b), the average values of Rq of the different phasesare in the range of 30�50 nm as shown in Figure 6(d). It isfound that the standard variation of the storage moduli ofthe clinker is remarkably large. Considering that the surfaceroughness of the clinker is smaller than that of the hydrationproducts, the large variation of storage moduli cannot be pri-marily attributed to the surface roughness.

Figure 7 provides an explanation of the effect of roughness onthe stability of storage modulus. From Figure 7(b), it is foundthat the surface elevation varies in the range −300�100 nmalong the scanning line, and the variation is mainly induced bythe pores and the interfaces between the C3S clinker and thehydration products; whereas the displacement amplitude ofthe indenter tip is only at the scale of nanometres. This impliesthat the displacement amplitude is two orders of magnitudesmaller than the differences of elevation of the sample surface.Figures 7(c) and 7(d) are schematic representations of thesmall displacement amplitude of the indenter tip on a roughsurface. The description of the rough surface is based on theassumption that the variation of surface elevation follows anormal distribution (Kim et al., 2006). As illustrated inFigures 7(c) and 7(d), the effect of the surface elevation on theindentation displacement is the same, no matter whether thevariation of surface elevation is dozens or hundreds of nano-metres. Therefore, the surface roughness of 10�200 nm has aminor effect on the stability of the storage modulus.

Magnitude of applied load: quasi-static anddynamic loadsIn SPM mapping, the modulus is calculated from the appliedload of both the quasi-static and the dynamic component.Four sets of loads including 2± 1·5 μN, 4± 1·5 μN, 4± 3·5 μNand 8± 3·5 μN (quasi-static±dynamic) are compared in termsof their effects on the displacement amplitudes of the indenter

300




tip and the storage modulus of the measured materials toselect a proper load to quantify the heterogeneous mechanicalproperties. A target area covering a slag grain and thehydration products in the slag-blended paste is used to discussthe effect of different loads on the output parameters. A verti-cal line in Figure 8(a) is selected to extract line data. The slaggrain and the hydration products are identified by the sharpcontrast of both the displacement amplitude and the storagemodulus between these two phases.

Effect on displacement amplitudesAs mentioned above, the displacement amplitude of the inden-ter tip is primarily due to the mechanical response variation ofthe sample to the applied load. The values of displacementamplitudes are small in the stiff phases. When a 4± 3·5 μNload is applied, as shown in Figure 8(a), the displacementamplitude is about 1 nm for the slag grain as compared to2�3 nm for the hydration products. The displacement ampli-tude is smaller in the slag grain, showing that the slag grain isstiffer than the hydration products.

SPM mapping was conducted in the same position as shownin Figure 8(a) for different loads of 2± 1·5 μN, 4±1·5 μN,

4±3·5 μN and 8±3·5 μN (quasi-static±dynamic) to comparethe displacement amplitudes obtained under different loads. Asillustrated in Figure 8(b), it is found that the dynamic force hasa more significant influence on the displacement amplitude thanthe quasi-static force, which can be explained by the motionEquation 1. When the quasi-static force is fixed as 4 μN, theaverage displacement amplitude is about 1·1 nm for the slaggrain and 2·3 nm for the hydration product under the dynamicload of 3·5 μN, whereas it is only 0·4 nm for the slag grain and0·9 nm for the hydration product under the dynamic loadof 1·5 μN. From Figure 8(b), it is also found that when thedynamic load is fixed, smaller quasi-static load induces largerdisplacement amplitude. This phenomenon may be explainedby less resistance provided by the materials under the range ofshallower indentation depth when smaller quasi-static load isapplied. A large dynamic load of 3·5 μN and a small quasi-static load of 4 μN achieve a sharp contrast of displacementamplitudes in different phases, which can be used to distinguishdifferent phases. Moreover, small values of displacement am-plitude may not be sufficient to avoid the influences from thenoise produced by the machine itself (Wilkinson et al., 2015).As a result, the load of 4±3·5 μN is selected for identifyingdifferent phases.

75

65

55

45

35

25

15

Stor

age

mod

ulus

: GPa

75

65

55

45

35

25

15

Stor

age

mod

ulus

: GPa

Surf

ace

roug

hnes

s: n

m

100

150

100

50

0

–50

–100

–150

75

50

25

00 50 100Surface roughness: nm

150 200 250OP

OP

OP

IP

IP

5 μm 5 μm

IP

C3S

C3S

C3S

ModulusRoughness

OP: 17–31 GPa

IP: 31–37 GPa

C3S: 41–77 GPa

nm

(a) (b)

(c) (d)

Figure 6. Effect of the surface roughness on the variability of storage modulus of individual phases in OPC paste: (a) and (b) meshing themodulus image and topography into 16�16 elements; (c) relationship between the surface roughness and the storage modulus ofindividual phases quantified in every element; (d) mean value and standard variation of storage modulus and surface roughness ofindividual phases. A full-colour version of this figure can be found on the ICE Virtual Library (www.icevirtuallibrary.com)

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Effect on storage modulusStorage modulus is the key parameter in SPM mapping toidentify different phases in cement pastes. From Figure 8(c), itis found that, although the average moduli of both the slaggrain and the hydration products increase with the quasi-staticload, the differences between the moduli of the slag grain andthe hydration products are large enough to identify each otherunder all four sets of loads. The small variation of modulus ofindividual phases also helps to identify different phases effi-ciently. From Figure 8(c), it is found that the dynamic loadinfluences the standard variation of the storage moduli of indi-vidual phases significantly. When the dynamic load increasesfrom 1·5 μN to 3·5 μN with fixed quasi-static load of 4 μN,the standard variation of the storage moduli decreases from27 GPa to 16 GPa for the slag grain, and from 9 GPa to5 GPa for the hydration products. Large quasi-static load alsoinduces large variation, but the effect of quasi-static load onthe variation of the storage modulus is smaller when comparedto that of dynamic load.

Figure 8(d) compares the standard variation of storagemodulus of different phases. It is found that the variability ofstorage modulus of the slag grain is significantly large. Atthe same time, there exists a trend whereby the influence ofdifferent applied loads on the standard variation of storagemoduli of individual phases is opposite to that on the dis-placement amplitudes. This implies that large displacementamplitudes help to diminish the variability of storage moduli.Consequently, the load of 4± 3·5 μN is recommended toobtain the large displacement amplitudes for both the slaggrain and the hydration products, such that the variation ofstorage moduli of individual phases can be diminished.

ConclusionsThe technique of SPM mapping was adopted to characterisecementitious materials non-destructively at the nanoscale. Theeffects of the pixel spacing, the surface roughness of thesamples and the magnitude of the applied quasi-static anddynamic loads on the measured storage moduli of individual

Surf

ace

elev

atio

n: n

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–200

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0 7 14 21 28 35

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de: n

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Amplitude

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C3S C3S

C3SC3S

HP

HP HP

Pore

Pore

HP

Scanning line

Indenter tipdisplacement = 2 nm

Indenter tip

Indenter tipIndenter tipdisplacement= 2 nm

Surfaceelevation= 200 nmSurface

elevation= 10 nm

Distance: μm

(b)(a)

(d)(c)

Figure 7. (a) A topography of target area in OPC paste; (b) surface elevation and displacement amplitude of the indenter tip along theselected line in (a); and schematic representations of the small displacement amplitude of the indenter tip on the rough surface with(c) small and (d) large elevations

302




5 μm

Slag

Slag

HP

HP

HP

0 1 2Displacement amplitude: nm

3 0 20 40Storage modulus: GPa

60 80 100

(a)

20

15

10

Dis

tanc

e: μ

m

5

0

3·0

Dis

plac

emen

t am

plitu

de: n

m

2·5

2·0

1·5

1·0

0·5

0

30

Stan

dard

var

iatio

n of

sto

rage

mod

ulus

: GPa

25

20

15

10

00 1 2

Mean value of displacement amplitude: nm

(d)

3

5

Slag

HP

1·5 ±0·4 nm

0·6 ±0·3 nm

0·9 ±0·2 nm

0·4 ±0·1 nm

1·1 ±0·3 nm

2·3 ±0·3 nm

1·5 ±0·2 nm

0·7 ±0·1 nm 25 ±

8 GPa

63 ±23 GPa

72 ±27 GPa

28 ±9 GPa

27 ±5 GPa

70 ±16 GPa

85 ±22 GPa

33 ±6 GPa

Desired load of 4 ± 3·5 μNwhich achieves the largestdisplacement amplitude

Desired load of 4 ± 3·5 μNwhich achieves the smallestmodulus variation120

100

Stor

age

mod

ulus

: GPa 80

60

40

20

0

2 ± 1·5 4 ± 1·5 4 ± 3·5 8 ± 3·52 ± 1·5

2 ± 1·5 μN

4 ± 1·5 μN

4 ± 3·5 μN

8 ± 3·5 μN

4 ± 1·5 4 ± 3·5 8 ± 3·5Magnitude of applied load: quasi-static ± dynamic μNMagnitude of applied load: quasi-static ± dynamic μN

(b) (c)

HP

Desired load

Slag

Figure 8. (a) The variation of the displacement amplitudes and the storage moduli along the selected line under the load of 4±3·5 μN;effect of magnitudes of loads on (b) the displacement amplitude and (c) the storage moduli of slag grain and hydration product(denoted HP); (d) decease of the standard variations of storage moduli with the mean value of displacement amplitude of slag grain and HP

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phases in pastes were examined to identify the critical aspectswhen measuring cementitious materials and for better utilis-ation of this technique in the future. The major findings aresummarized below.

Storage modulus is suitable for phase identification comparedto other measured parameters. The cement clinker, slag grain,inner hydration product (IP) and outer hydration product (OP)can be clearly distinguished and separated from their differentstorage moduli.

Two methods are proposed to extract line data and area datafrom the mapping images for identifying individual phases.The thickness of IP rims can be estimated based on the abruptchanges of the continuously measured storage moduli of theline data. The typical storage moduli of individual phases canbe obtained based on the large amount of extracted area data.

The stability of the measured storage moduli of individualphases is not sensitive to the pixel spacing. Although the smal-lest pixel spacing selected is 27 nm, which is less than the influ-encing radius of the indenter tip with the range of 24�43 nm,the measured storage moduli are almost the same as the resultsunder the pixel spacing of 137 nm, which is much greater thanthe influencing radius of the indenter tip. Therefore, a validresult can be obtained within a mapping size ranging fromseveral micrometres to dozens of micrometres, and the mech-anical properties of individual phases in pastes with differentsizes from the nano to the micro scale can be quantified.

The effect of surface roughness on the variability of themeasured storage modulus is not significant. The roughnesswithin the area of OP is the largest. Nevertheless, the similarmeasured storage moduli of OP are obtained under the root-mean-squared roughness of the sample surface changing from10 nm to 200 nm.

An applied load of 4± 3·5 μN (quasi-static±dynamic) is rec-ommended for characterising pastes. Different phases can beclearly distinguished under this load by SPM mapping. This isbecause the load of 4± 3·5 μN induces a relatively large displa-cement amplitude, which diminishes the variation of storagemodulus within the single phase and facilitates the phaseidentification.

AcknowledgementThe authors would like to acknowledge the National NaturalScience Foundation of China under grant no. 51578316 andno. 51778331.

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http://dx.doi.org/10.1680/adcr.2006.18.3.119






https://doi.org/10.1016/j.matchar.2017.02.029

https://doi.org/10.1016/j.matchar.2017.02.029

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