Statistical analysis of backscattered electron image of hydrated cement paste

Transcription

1 Advances in Cement Research, 2016, 28(7), Paper Received 02/01/2016; revised 04/03/2016; accepted 21/03/2016 Published online ahead of print 25/04/2016 Keywords: concrete components/electron microscopy/ microstructure ICE Publishing: All rights reserved Statistical analysis of backscattered electron image of hydrated cement paste Chuanlin Hu Post-Doctoral Research Fellow, Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada Hongyan Ma Assistant Professor, Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO, USA (corresponding author: Backscattered electron (BSE) imaging has been widely used to investigate the microstructure of cement-based materials, and it has shown specific advantages in determining the fractions and distribution of individual phases. The lower and upper grey level thresholds for the investigated phases need to be determined as the key references for BSE image analysis. However, the traditional determination of the grey level thresholds for phases is quite arbitrary. A novel method is proposed to analyse BSE images of cement-based materials using statistical analysis, avoiding the subjective choice of grey level thresholds. Notation C i weight fraction of element i f surface fraction m number of elements N total number of pixels N x number of pixels at grey level x n number of phases P experimental probability density function (PDF) p j theoretical PDF of the grey level of phase j s j standard deviation of normal distribution of phase j UH 0 initial volume fraction of cement in paste UH α volume fraction of unhydrated cement x grey level Z atomic number α degree of hydration of cement η backscattering coefficient average value of normal distribution of phase j μ j Introduction Backscattered electron (BSE) imaging is a widely used technique for material characterisation. The grey level on a BSE image is a function of the local average atomic number and local density, which allows phases of different composition and density to be distinguished by image analysis. Since the pioneering work of Scrivener and Pratt (1984), this technique has been employed to quantify the distribution of phases in cement-based materials (e.g. unhydrated cement clinker, portlandite, pores, unreacted fly ash and slag) (Ben Haha et al., 2010; Bentz and Stutzman, 1994; Igarashi et al., 2004; Kocaba et al., 2012; Ma and Li, 2013; Wong et al., 2006) through phase segmentation. The key issue for phase segmentation is the choice of grey level thresholds for each phase. However, to the authors knowledge, there is still no standard and reliable method that can be employed for the determination of such thresholds. To avoid artificial choice of grey level thresholds, a novel method to analyse BSE images is proposed in this paper. The method is applied to quantify the fractions of unhydrated and hydrate phases present in a hydrated cement paste, and is verified using other techniques. Experiments ASTM type I Portland cement was used to prepare cement paste with a water/cement ratio of 0 4. The chemical composition of the cement is listed in Table 1. The fresh paste was mixed and cast into steel moulds. After 24 h, the specimens were demoulded and cured in moist conditions at 23 ± 1 C and 95% relative humidity to an age of 90 d. For BSE image acquisition, a sample was cut from the middle portion of a specimen, vacuum dried and then impregnated with low-viscosity epoxy. Before placement in the microscope, the sample was carefully polished with abrasive papers (180, 240, 400, 600, 800 and 1200 grit in order) to achieve a smooth surface, following a procedure used in previous work (Hu and Li, 2014, 2015; Hu et al., 2014). BSE imaging was performed using a JSM-6390 scanning electron microscope; the images were acquired at an acceleration voltage of 20 kv and a magnification of 500. Note that the higher the acceleration voltage, the larger the interaction volume and the higher the intensity of electrons (Scrivener et al., 2016). BSE imaging requires a sufficiently low acceleration voltage to mitigate the composition complexity of the interaction volume and a high enough acceleration voltage to ensure sufficient electron intensity. The acceleration voltage of 20 kv used in this work was selected as a good compromise between these two considerations. Each BSE image consists of pixels with 256 integral grey levels ranging from 0 (black) to 255 (white). 469

2 Proportion: % Calcium oxide (CaO) 62 6 Silicon dioxide (SiO 2 ) Aluminium oxide (Al 2 O 3 ) 4 67 Iron oxide (Fe 2 O 3 ) 3 31 Sulfur trioxide (SO 3 ) 2 25 Magnesium oxide (MgO) 3 08 Sodium oxide (Na 2 O) 0 21 Potassium oxide (K 2 O) 0 54 Loss on ignition 0 78 Table 1. Chemical composition of the cement used in this study image, can be written as 5: PðxÞ ¼ N x N where N x is the number of pixels at the grey level x and N is the total number of pixels. The unknowns (μ j, s j and f j ) can be determined by minimising the difference between the experimental PDF and the theoretical PDF weighted by the surface fractions 6: min X255 x¼0 X n j¼1 f j p j ðx; μ j ; s j Þ PðxÞ! 2 Methods and results Theoretical basis In BSE imaging, the brightness on an image is proportional to a backscattering coefficient defined as number of backscattered electrons 1: η ¼ number of incident electrons However, it is difficult to calculate the accurate value of η due to the complexity of the scattering process. For a pure element i, an empirical relation between η and the atomic number Z has been given as (Reuter, 1972) 2: η i ¼ þ 0016Z i Z 2 i þ Z 3 i Furthermore, Castaing (1960) proposed the following simple rule to predict η for a homogenous mixture of m elements 3: η ¼ Xm i¼1 C i η i where C i denotes the weight fraction of element i. It is assumed that a BSE image is composed of n phases with sufficient contrast in grey level, and each phase occupies a surface fraction of f j,wherej is an integer from 1 to n. Thegrey level distribution of each phase can be approximated by a normal distribution, characterised by an average value μ j and a standard deviation s j. The theoretical probability density function (PDF) of the grey level of phase j can thus be formulated as 4: p j ðx; μ j ; s j Þ¼ p 1 ffiffiffiffiffi exp ðx μ! jþ 2 2π 2ðs j Þ 2 s j where x denotes the grey level. The experimental PDF, obtained by counting pixels of different grey levels on a BSE and the surface fractions are constrained by 7: X n j¼1 f j ¼ 1 Image analysis Based on Equation 3, the backscattering coefficients of the main species present in a hydrated cement paste were calculated and are listed in Table 2. According to Table 2, the descending brightness order on a BSE image should be C 4 AF, C 3 S, C 2 S, C 3 A, CH (portlandite), C-S-H (calcium silicate hydrate), Mono (mono-sulfate calcium sulfoaluminate), Ett (ettringite) and epoxy-filled pores. In these phases, C 3 S, C 2 S, C 3 A and C 4 AF are unhydrated minerals, while C-S-H, CH, Ett and Mono are hydration products. In the unhydrated cement minerals, the brightness contrast between C 3 S, C 2 S and C 3 A is too small to be distinguished. The unhydrated phases are thus classified into two groups the brightest (C 4 AF) and the second brightest (C 3 S, C 2 S and C 3 A). This hypothesis was verified by energy dispersive x-ray spectroscopy (EDX) performed at the two brightest phases on a BSE image, as marked in Figure 1. The results show that the brightest phase, located at positions 1 and 2, is an iron-rich and silicon-poor phase, while the second brightest phase (positions 3 and 4) is silicon-rich and iron-free. Based on Monte Carlo simulations performed according to Drouin et al. (2007) and Wong and Buenfeld, (2006), the sampling depth of BSE trajectories into C-S-H, CH, Ett and Mono, under the operation conditions adopted in this study, is 1 2 μm. At such a scale, there are three distinct agglomerations of C-S-H-containing hydration products present in hydrated cement paste (i.e. a very porous product, outer product and inner product) and each is a composite of C-S-H, nano-sized pores and nano-sized crystalline hydration products (CH, Ett and Mono) (Hu and Li, 2014; Ma et al., 2014). Except for the distinguishable or micro-sized CH on a BSE 470

3 Phase Formula Average atomic number Density: g/cm 3 η C 4 AF 4CaO.Al 2 O 3.Fe 2 O C 3 S 3CaO.SiO C 2 S 2CaO.SiO C 3 A 3CaO.Al 2 O CH Ca(OH) C-S-H 1 7CaO.SiO 2.1 8H 2 O Mono 3CaO.Al 2 O 3.CaSO 4.12H 2 O Ett 3CaO.Al 2 O 3.3CaSO 4.32H 2 O Epoxy C 10 H 18 O Table 2. Physical properties and backscattering coefficient of the main species present in cement-based materials kv µm HKUST Figure 1. BSE image showing unhydrated cement clinkers image, non-distinguishable CH, Mono and Ett should exist in different types of C-S-H-containing products, and this is responsible for the higher overall calcium/silicon ratio of the C-S-H phases compared with the classical value (1 7) (Chen et al., 2010). A more realistic calcium/silicon ratio of the C-S-H phase in these agglomerations can only be determined by identifying the data cluster edge on an aluminium/calcium versus silicon/calcium plot based on EDX (Whittaker et al., 2014). Different C-S-H-containing products are composed of the elementary C-S-H particles and nano-sized crystal phases with different packing densities, and the local brightness on a BSE image is influenced by the local density. Therefore, the brightness order of distinguishable hydrate phases is very porous product, outer product, inner product and CH, in ascending order. According to the above analysis, the descending brightness order of the distinguishable phases with sufficient contrast on a BSE image is C 4 AF (denoted here as CM1), C 3 S/C 2 S/C 3 A 4 (denoted CM2), CH, inner product (IP), outer product (OP), very porous product (VP) and epoxy-filled pores (P). A BSE image of the tested paste is shown in Figure 2(a) and the corresponding experimental PDFs and cumulative distribution function (CDF) are plotted in Figures 2(b) and 2(c), respectively. In light of the proposed analysis method, the theoretical PDF was calculated and plotted in Figure 2(b), and the values of μ j, s j and f j of the distinguishable phases are summarised in Table 3. On a CDF plot, the grey level thresholds of distinguishable phases can be determined by points at which the CDF values equal the cumulative surface fractions, as marked by the vertical lines in Figure 2(c). Based on the determined thresholds, the image shown in Figure 2(a) was segmented and the distribution of phases in the hydrated cement paste shown with specified colours, as presented in Figure S1 (see Figure S1, which won t reproduce in grayscale so is online only). Statistical results and validation After analyses of 20 randomly chosen BSE images, the average surface fractions were estimated as follows: CM1, 2 4% ± 1 6%; CM2, 6 6% ± 1 5%; CH, 3 6% ± 2 6%; IP, 27 2% ± 3 3%; OP, 27 0% ± 3 3%; VP, 22 2% ± 2 9%; P, 11 1% ± 3 4%. Noting that the surface fractions of phases obtained from a large number of BSE images are equal to their volume fractions (Igarashi et al., 2004), the degree of hydration of cement can be calculated as 8: α ¼ 1 UH α UH 0 where UH α is the volume fraction of unhydrated cement and UH 0 is the initial volume fraction of cement in the paste. UH α is equal to the summation of the volume fractions of CM1 and CM2, and UH 0 = 44 2% in the tested case. Substituting these values into Equation 8, the degree of hydration is determined as For validation, the degree of hydration of cement in the paste was also determined by the classical 471

4 thermogravimetric analysis (TGA) method (Wong and Buenfeld, 2009) the result was 0 803, which agrees well with the result from the proposed method. Another quantity that can be determined from TGA is the mass fraction of CH according to a well-documented method (Schöler et al., 2015; Whittaker et al., 2014). After being transformed into a volume fraction, this percentage appears to be higher than the value of 3 6% determined by the proposed method. This inconsistency is, however, easy to understand: only a part of CH can be detected using BSE image analysis, while CH particles of small sizes that form intermixtures with C-S-H gel cannot be distinguished. PDF (a) Grey level (b) kv µm HKUST P VP OP IP CH Experimental Theoretical 200 CM2 CM1 250 Discussion A prerequisite for application of the proposed method is that the BSE image is composed of n phases with sufficient contrast in grey level. For any cementitious composite that fulfils this prerequisite, the proposed method can be used effectively to quantify the distinct phases. However, the number of distinguishable phases (n) has to be determined carefully before performing the statistical analysis, as shown in Table 2 and the associated text. The method can even be used for multi-component cementitious composites such as ground granulated blast-furnace slag (GGBS) and cement pastes incorporating fly ash. Unreacted GGBS particles are relatively easy to distinguish on a BSE image due to their unique grey level (Kocaba et al., 2012). Therefore, in statistical image analysis, unreacted GGBS particles can be considered as one of the distinguishable phases. A fly ash blended cement paste is more complex because the grey level of unreacted fly ash may overlap with those of C-S-H and CH, which means that the prerequisite of the analysis method is not fulfilled. Fortunately, a method for the segmentation of unreacted fly ash has been proposed (Ben Haha et al., 2010; Deschner et al., 2013). After the removal of unreacted fly ash particles from a BSE image, the statistical method proposed here can be used to analyse the remaining material phases, so that the whole image can be segmented into n + 1 phases. CDF P VP OP IP CH CM 2 CM 1 Conclusions A novel method for the analysis of BSE images of hydrated cement paste has been presented. According to this method, after the number of distinguishable phases has been determined through analysis of average atomic number, a BSE image can be segmented into corresponding phases in three steps Grey level Figure 2. Illustration of the BSE image analysis method: (a) BSE image; (b) corresponding experimental and theoretical PDF plots; (c) estimation of thresholds from CDF plot (c) & & & fitting the experimental PDF of grey values using the number of phases as an input parameter determining volume fractions of the phases according to the fitting results determining the threshold grey values of distinguishable phases on a CDF plot and segmenting the image based on the thresholds. Using this method, seven phases in a hydrated cement paste C 4 AF, C 3 S/C 2 S/C 3 A, CH, inner product, outer product, very 472

5 Phase P VP OP IP CH CM2 CM1 μ S f: % Table 3. Statistically estimated parameters of individual phases porous product and epoxy-filled pores were distinguished and quantitatively characterised. The method was partly somewhat by means of EDX and TGA. Acknowledgements Technical support from the Materials Characterization and Preparation Facility at the Hong Kong University of Science and Technology and financial support from Missouri University of Science and Technology (new faculty start-up funds RDW14 R ) are gratefully acknowledged. REFERENCES Ben Haha M, De Weerdt K and Lothenbach B (2010) Quantification of the degree of reaction of fly ash. Cement and Concrete Research 40(11): Bentz DP and Stutzman PE (1994) Evolution of porosity and calcium hydroxide in laboratory concretes containing silica fume. Cement and Concrete Research 24(6): Castaing R (1960) Electron probe microanalysis. In Advances in Electronics and Electron Physics (Marton L (ed.)). Academic Press, New York, NY, USA, pp Chen JJ, Sorelli L, Vandamme M, Ulm FJ and Chanvillard G (2010) A coupled nanoindentation/sem-eds study on low water/cement ratio Portland cement paste: evidence for C-S-H/Ca(OH)(2) nanocomposites. Journal of the American Ceramic Society 93(5): Deschner F, Münch B, Winnefeld F and Lothenbach B (2013) Quantification of fly ash in hydrated, blended Portland cement pastes by backscattered electron imaging. Journal of Microscopy 251(2): Drouin D, Couture AR, Joly D et al. (2007) Casino V2.42 a fast and easy-to-use modeling tool for scanning electron microscopy and microanalysis users. Scanning 29(3): Hu C and Li Z (2014) Micromechanical investigation of Portland cement paste. Construction and Building Materials 71(November): Hu C and Li Z (2015) Property investigation of individual phases in cementitious composites containing silica fume and fly ash. Cement and Concrete Composites 57(March): Hu C, Li Z, Gao Y, Han Y and Zhang Y (2014) Investigation on microstructures of cementitious composites incorporating slag. Advances in Cement Research 26(4): Igarashi S, Kawamura M and Watanabe A (2004) Analysis of cement pastes and mortars by a combination of backscatter-based SEM image analysis and calculations based on the Powers model. Cement and Concrete Composites 26(8): Kocaba V, Gallucci E and Scrivener KL (2012) Methods for determination of degree of reaction of slag in blended cement pastes. Cement and Concrete Research 42(3): Ma H and Li Z (2013) Realistic pore structure of Portland cement paste: experimental study and numerical simulation. Computers and Concrete 11(4): Ma H, Hou D, Lu Y and Li Z (2014) Two-scale modeling of the capillary network in hydrated cement paste. Construction and Building Materials 64(August): Reuter W (1972) The ionization function and its application to the electron probe analysis of thin films. In Proceedings of 6th International Conference on X-ray Optics and Microanalysis (Shinoda G, Kohra K and Ichinokawa T (eds)). University of Tokyo Press, Tokyo, Japan, pp Schöler A, Lothenbach B, Winnefeld F and Zajac M (2015) Hydration of quaternary Portland cement blends containing blast-furnace slag, siliceous fly ash and limestone powder. Cement & Concrete Composites 55(January): Scrivener K and Pratt P (1984) Back-scattered electron images of polished cement sections in scanning electron microscope. Proceedings of the 6th International Conference on Cement Microscopy, Albuquerque, NM, USA, pp Scrivener K, Snellings R and Lothenbach B (2016) A Practical Guide to Microstructural Analysis of Cementitious Materials. CRC Press, Boca Raton, FL, USA. Whittaker M, Zajac M, Ben Haha M, Bullerjahn F and Black L (2014) The role of the alumina content of slag, plus the presence of additional sulfate on the hydration and 473

6 microstructure of Portland cement slag blends. Cement and Concrete Research 66(December): Wong HS and Buenfeld NR (2006) Monte Carlo simulation of electron-solid interactions in cement-based materials. Cement and Concrete Research 36(6): Wong HS and Buenfeld NR (2009) Determining the water-cement ratio, cement content, water content and degree of hydration of hardened cement paste: method development and validation on paste samples. Cement and Concrete Research 39(10): Wong HS, Head MK and Buenfeld NR (2006) Pore segmentation of cement-based materials from backscattered electron images. Cement and Concrete Research 36(6): WHAT DO YOU THINK? To discuss this paper, please submit up to 500 words to the editor at Your contribution will be forwarded to the author(s) for a reply and, if considered appropriate by the editorial panel, will be published as a discussion in a future issue of the journal. 474

7 Fig. S1 Phase distribution corresponding to Fig. 2(a) (Black: P; Red: VP; Green: OP; Blue: IP; Yellow: CH; Magenta: CM2; White: CM1)