Residual Stress Measurements in Polycrystalline Graphite with Micro-Raman Spectroscopy

Radiation Physics and Chemistry 111 (2015) 14–23

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Radiation Physics and Chemistry

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Residual stress measurements in polycrystalline graphite with micro-Raman spectroscopy

Ram Krishna a,n, Abbie N. Jones b, Ruth Edge a, Barry J. Marsden b

a Dalton Nuclear Institute, Dalton Cumbrian Facility, University of Manchester, Westlakes Science & Technology Park, Moor Row, Whitehaven, Cumbria CA243HA, UKb Nuclear Graphite Research Group, School of Mechanical, Aerospace & Civil Engineering, University of Manchester, Manchester M13 9PL, UK

H I G H L I G H T S

� Micro-Raman spectroscopy can measure significantly small residual stresses.

a r t i c l e i n f o

Article history:Received 5 December 2014Received in revised form2 February 2015Accepted 10 February 2015Available online 11 February 2015

Keywords:Residual stressPolycrystalline graphitePGAGilsocarbonNBG-18Raman micro-spectroscopyBinderFillerCracksPores

x.doi.org/10.1016/j.radphyschem.2015.02.0076X/& 2015 Elsevier Ltd. All rights reserved.

esponding author.ail address: [email protected]

a b s t r a c t

Micro-Raman microscopy technique is applied to evaluate unevenly distributed residual stresses in thevarious constituents of polygranular reactor grades graphite. The wavenumber based Raman shift (cm�1)corresponds to the local residual stress and measurements of stress dependent first order Raman spectrain graphite have enabled localized residual stress values to be determined. The bulk polygranular gra-phite of reactor grades – Gilsocarbon, NBG-18 and PGA – are examined to illustrate the residual stressvariations in their constituents. Binder phase and filler particles have shown to be under compressiveand tensile stresses, respectively. Among the studied graphite grades, the binder phase in Gilsocarbonhas the highest residual stress and NBG-18 has the lowest value. Filler particles in Gilsocarbon have thehighest residual stress and PGA showed the lowest, this is most likely due to the morphology of the cokeparticles used in the manufacturing and applied processing techniques for fabrications. Stresses have alsobeen evaluated along the peripheral of pores and at the tips of the cracks. Cracks in filler and binderphases have shown mixed behaviour, compressive as well as tensile, whereas pores in binder and fillerparticles have shown compressive behaviour. The stresses in these graphitic constituents are of the orderof MPa. Non-destructive analyses presented in this study make the current state-of-the-art technique apowerful method for the study of stress variations near the graphite surface and are expected to increaseits use further in property determination analysis of low to highly fluence irradiated graphite samplesfrom the material test reactors.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Graphite has a long and rich tradition of research and haswidespread application as a neutron moderator and is used as astructural component in nuclear reactors (Fermi, 1952; Night-ingale, 1962). In recent years, with interest in Gen-IV reactor de-sign, graphite has attracted considerable attention as a potential

(R. Krishna).

material, since it can be employed as a fast neutron moderator/reflector structural component in Very High Temperature and Gas-cooled reactors (Bonal et al., 2009; Marsden and Hall, 2012).

There are a variety of artificially produced polycrystalline gra-phite grades commercially available as reactor graphite and theyare characterised by their: forming processes (extrusion, pressing,vibration and isostatic moulding, etc.), utilized source coke formanufacturing, their grain size, type of binder and filler particles,their randomly distributed multi-scaled porosities and nano-scale‘Mrozowski’ cracks. Nuclear graphite grades are specifically man-ufactured for use within the nuclear reactors core to a specification

Fig. 1. (a) Raman spectrum from HOPG taken with 532 nm laser excitation wave-length. The spectrum shows the presence of G-peak at 1580 cm�1 (E2g symmetry)and absence of D-peak. (b) A bright field TEM micrograph of HOPG shows layeredstructures of 20–200 nm thickness and a strong orientation [0002] along thestacking direction.

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23 15

that is aimed at retaining its moderating, physical, and mechanicalproperties under nuclear radiation environment even at hightemperatures (Simmons, 1965). However, reactor core graphite issubject to a hostile environment of fast neutrons and hot coolantgas in which it experiences irradiation-induced hardening and insome cases radiolytic oxidation during the exposure life. Theseirradiation-induced effects lead to progressive changes in thephysical, mechanical properties and in particular, build-up of sig-nificant stresses and deformation in the graphite components(Marsden and Hall, 2012; Tsang and Marsden, 2006, 2007). Duringgraphite manufacture, which involves several high temperatureheating cycles (Marsden and Hall, 2012), internal stresses (Kurodaet al., 2005; Rand, 2012) are generated at the micro-scale in theconstituent phases of graphite grades. The manufacturing stressesretained in bulk graphite billets as internal (residual) stresses andmay cause cracking (Hodgkins et al., 2006; Kelly, 2000; Kurodaet al., 2005). In addition, such unintended residual stresses in ar-tificially manufactured graphite grades may limit their service lifedepending up on the neutron irradiation temperature and doses.Therefore, it is important to characterise all grades of graphite toevaluate the irradiation material properties to understand theevolution of these properties and, hence predict component be-haviour under the intended irradiation environment. Importantreactor graphite grades are Gilsocarbon, Nuclear Block Graphite-18(NBG-18) and Pile Grade-A (PGA) considered in the present study.These graphite grades are polycrystalline and heterogeneous;comprised of various carbonaceous phases such as coke fillerparticles, pitch binder phase, quinoline insoluble particles andgraphitic and turbostratic graphite phases. The issues related withthe build-up stresses in the constituent phases are significant.Internal stresses may possibly actuate the initiation and propa-gation of dislocations and nucleation of new cracks and voids.Stresses may also trigger swelling behaviour and dimensionalchange in graphite at low temperature under irradiation conditionas observed in NBG-10 graphite (Burchell and Snead, 2007) andgrade TSX graphite (Kennedy and Woodruff, 1989). Therefore, in-ternal/residual stresses may play a significant role in explainingthe failure of components. There are techniques available formeasuring the distribution of internal strains/stresses in materials;however they are invasive, semi-invasive, require complex com-puter simulated modelling or may be applied to only a restrictedclass of materials. A few techniques such as X-ray diffraction,deep-hole-drilling (DHD), finite element simulations, micro-in-dentation and ultrasonic wave methods have been investigated forapplication in graphite (Nakhodchi et al., 2011; Shibata et al.,2008). In this paper, the internal (lock-in) stresses in variousconstituents of polycrystalline reactor grades graphite such as fil-ler, binder, and along the peripheral of pores and at the tips of thecracks, have been evaluated using micro-Raman spectroscopy, anon-invasive analytic method for stress evaluation in near-surfacesubmicrometer regions of reactor graphite. The applicability of thismethod to both non-irradiated and irradiated graphite is a pro-mising method to access information on residual stresses effec-tively and non-invasively.

Micro-Raman spectroscopy is a non-destructive technique andprovides information on the microscopic state of stresses in theconstituents of materials with up to a micrometre of lateral anddepth spatial resolutions (Anastassakis et al., 1970; Wolf and Maes,1998). The lateral and depth spatial resolution is along the XY andZ directions, respectively and the Z spatial resolution depends onthe confocality of the spectroscope used. In particular, a spatialresolution in the order of 1 μm is effective for the local stressmeasurement and a better spatial resolution can be achieved with‘polished’ samples (Wolf, 1996). An inelastic interaction of lasersource with crystal lattice vibrations is employed for stress mea-surements with high lateral resolution and thus, the crystalline

material can be probed non-destructively without the need forcomplex and time-consuming sample preparations (Wolf, 1996).

The first-order stokes-Raman spectrum of Highly OrderedPyrolytic Graphite (HOPG), with relatively near perfect graphitecrystallographic geometry, exhibits a single G-peak, whichcorresponds to the kE0 vibrations of the doubly degenerate op-tical phonons (E2g symmetry) and the Raman G line representsalmost negligible residual stresses (Ferrari, 2007). The Ramanspectrum and bright field transmission electron (TEM) micrographof HOPG are shown in Fig. 1. However, in artificially manufacturedgraphite, the constituent phases remain under residual stressesdeveloped during fabrication process, which causes polarizationdependent shifts which are observed to be dependent on the in-ternal stress values (Mohr et al., 2010; Sakata et al., 1988). Thus,the Raman G line (optical phonons) in artificially manufacturedgraphite shifts due to the presence of internal stresses and themagnitude of this stress is directly proportional to the Raman lineshift. A candid way to relate measured Raman shift to stressmagnitude is the use of a stress model illustrating the stress statein the constituents or in the bulk sample within crystallites ofarbitrary orientation. A linear relationship between Raman line-shift and stress has been previously applied to estimate the stressvalues in graphite fibre (Sakata et al., 1988), graphene based me-chanical systems (Mohiuddin et al., 2009), quartz (Harker et al.,1970), polycrystalline Mn–Zn ferrite (Yamashita and Ikeda, 2004),polycrystalline silicon (Becker et al., 2007; Wolf and Maes, 1998)etc.

It is well-known that compressive stress shifts the Raman lineto a higher frequency, while tensile stress shifts it to a lower fre-quency, as shown in Fig. 2 (Wolf, 1996). The splitting of doublydegenerated E2g optical mode (G-band) into two components Gþ

and G� is due to the effect of anisotropic (deviatoric) stress thatpossibly changes the crystallographic symmetry and lifts the two-fold degeneracy completely or partially (Mohiuddin et al., 2009;Sakata et al., 1988). However, hydrostatic stress within the con-stituents of graphite only produces a shift and the original sym-metry remains intact (Frank et al., 2011; Ganesan et al., 1970;Tuinstra and Koenig, 1970). Therefore, in the present example, thegraphene hexagonal symmetry – 2D building block of the graphitestructure – remains preserved.

The Raman line-shift is conditional on the material's property –

phonon deformation potential – and corresponds to a change in

Fig. 2. Dispersive Raman spectra of filler–binder region in Gilsocarbon. The shiftingof G peak towards left and right directions implies tensile and compressive residualstresses in the structure. The spectra show first order fundamental bands (D, G andD′) and their overtones (2D(G′), DþD′, 2D′(G′′)).

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–2316

vibrational frequencies (Thomsen et al., 2002). In general, a stressof 1 GPa introduces a Raman line shift of about 2 cm�1 in poly-crystalline silicon wafers, which appears large enough to causecracking in the film (Sarau et al., 2012). Thus, the possibility ofmeasuring residual stresses in the constituent phases of reactorgrade graphite with a spatial resolution of less than 1 μm can beachieved using a Raman microscope.

Few authors have also discussed the effects of external stresseson the Raman spectra (Anastassakis et al., 1993; Frank et al., 2011;Sakata et al., 1988). These studies demonstrate that stress affectsthe stacking order of pristine graphite and induces stress-inducedsymmetry breaking as splitting of G band into two distinct sub-bands (Gþ , G�) is observed. The experimental values for thephenomenological coefficients, which describe the changes inphonon deformation potentials under strains are specific to thematerials properties, and can be obtained from the observedsplitting of the G band (Huang et al., 2009). Taylor et al. (2003)presented a non-intrusive method for measuring residual surfacestress in thin carbon films using Raman spectroscopy and nano-indentation.

Therefore, in the present study the stress evaluation will lead toa better understanding of reactor grade graphite microstructureand its behaviour under the reactor operating conditions (i.e. in-terpresence of fast neutron irradiation and radiolytic oxidation).

2. Materials and experimental procedure

The characteristics of graphite grades used in the present studyare presented in Table 1 (Krishna et al., 2015). All graphite gradesare polycrystalline and diverse in nature. Various carbonaceousphases such as filler particles, binder phase, quinolone insoluble(QI) particles, and turbostratic graphite make these grades com-plex and heterogeneous.

Table 1Characteristics of reactor grades graphite used in the present study.

Graphite grade Manufacturer Forming/mouldingprocess

Bulk density (g/cm3) Particrange

Gilsocarbon AGL, BAEL, UCAR Vibration 1.92 1–300NBG-18 SGL, Germany Vibration 1.85 1–300PGA BAEL and AGL Extrusion 1.74 1–800

NBG-18 is polycrystalline and isotropic grade nuclear graphitemanufactured by SGL Carbon Gmbh. The fabrication process uti-lizes vibration moulding (VM) based on isotropic pitch coke andcoal-tar pitch. The spherical coke filler and isotropic structure iscomparable with the near-to-isotropic Gilsocarbon graphite.

Gilsocarbon is complex, heterogeneous and near-to-isotropicgraphite with an anisotropy factor of 1.1. It is manufactured in theUK by AGL (now SGL) and BAEL (later UCAR now GrafTech) uti-lizing a coke manufactured from Gilsonite – a naturally occurringhydrocarbon. The Gilsocarbon billets were moulded in a press.

Pile Grade-A (PGA) is a heterogeneous high purity graphitegrade, employed in the early Magnox reactor design for neutronmoderation, and is formed by extrusion. It was manufactured byBAEL and AGL and has needle-shaped petroleum coke particles.The extrusion process tends to align coke particles in the directionof extrusion and results in a highly anisotropic microstructure.Thus, the basal layers in extruded PGA tend to lie parallel to theextrusion axis and this is accompanied by a large difference in bulkproperties parallel (With Grains – WG) and perpendicular (AgainstGrains – AG) to the extrusion direction. In this study, samples forcharacterization are taken Against Grain, AG direction, from a PGAgraphite billet.

Filler particles are mainly calcined pitch/Gilsonite coke, whichhas been calcined around 1200 °C. The binder is a thermoplasticmaterial, with a high carbon content usually derived from thedistillation of coal-tar pitch. Porosities and cracks are of differentmorphologies and observed randomly in the microstructure. Theseare one of the salient characteristics of microstructure dependingupon graphitization/gas-evolution processes and exhibit a vitalrole in irradiation induced dimensional change, as this porositytype can accommodate crystallite expansion during irradiation(Hall et al., 2006; Jones et al., 2008).

Micro-Raman Spectroscopy was conducted using a SENTERRARaman microscope (Bruker Optics, Inc.). The Raman vibrationalspectra were measured using a 532 nm wavelength excitation la-ser with a 10 s integration in the confocal mode of operation at aresolution of 3 cm�1. The spectrometer is equipped with OlympusBX51 reflected light and transmission light (R200-L) optical mi-croscope with bright field (BF) illuminator consisting of universalcondenser and illumination source for reflection and transmission(20� bright field, Olympus MPLN 20; NA¼0.40; WD¼1.30 mmand 50� bright field, Olympus MPLN 50; NA¼0.75;WD¼0.38 mm) objective lenses focus the 20 mW laser beam ontoa 1 μm diameter spot on the graphite surface. Sample heating,heat transfer and dissipation to the graphite surface are negligible(Tsang et al., 2005). Spectra obtained from the Ramanscope areaccurate to 71 cm�1. This equipment utilizes SENTERRA's pa-tented Sure_Cals automatic laser and Raman frequency calibrationmethod to produce reliable and reproducible measurements withexcellent frequency accuracy and precision of about 0.1 cm�1. Bymeasuring simultaneously each Raman spectrum from the ex-citation line of the laser and the emission lines from the laser/neonspectrum of a neon emission lamp and employing afterwards anintegral transformation process on these spectra to correct auto-matically and continuously the Raman data for instrument in-stabilities. Due to this Sure_Cals method, the spectrometer is

le grain size(μm)

Source coke Porosity (%) Microstructure Crystallite size (La)(nm)

Gilsonite 16.2 Near-to-isotropic 62.5Pitch 17.8 Isotropic 35.4Petroleum 18.3 Anisotropic 87.3

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23 17

continuously calibrated and therefore, no routine calibration byexternal standard is required. The spectrometer is coupled with acomputer controlled grating turrent monochromator with a grat-ing of 1200 grooves/mm for high resolution and wide range and aCCD thermo-electrically cooled to �65 °C, 1024�256 pixels, filterchanger consisting of Raleigh filter and ND filter wheel for chan-ging the laser power, with a motorized aperture of slit type(25�1000 and 50�1000 μm2) and confocal pinhole type (25 and50 μm) combination.

A computer controlled motorized sampling stage connected tothe device, to move the sample along X, Y and Z coordinates tocontrol the measurement position in a region of the sample sur-face, with an accuracy of 0.1 μm and in this case, the repeatabilitywas observed to be better than 1 μm. The dispersive Ramanspectral information data acquisition, processing and evaluationwere measured using 10 s measurement time with three accu-mulations using intuitive spectroscopic software – OPUS Version7.5. Raman 2D chemical mapping is generated with the live OPUSvideo package. Spectral information computation was achievedusing multivariate analysis tools available in the OPUS softwarenavigation menu. All the measurements were conducted at thesame sample height, z¼0 position. The Raman image/map pro-duced was composed of 20�20 Raman spectra selected from thegraphite surface region of range Y as �230 and X as �320 μmwith an approximately 16 μm step size The maps illustrate thespectral information comprised of Raman data from the selectedsurface region.

Raman imaging of graphite grades reveals the heterogeneity ofthe graphite structure and the spectral information, which is usedto evaluate the magnitude of local stresses near to the surfaceregions. The Raman image is not self-interpreting. Rather, it re-quires a careful attention to the mathematical operations on thedata and the interpretation of the results.

Further, it must be noted here that the pristine HOPG is freefrom the defect D peak, at around 1350 cm�1. The obvious pre-sence of G-peak, the E2g symmetry and absence of D-peak, A1g

symmetry in Raman spectrum can be seen in Fig. 1. Fig. 1 alsoillustrates the bright field TEM micrograph of HOPG. The authorsnote the absence of defects in HOPG resulted in total dis-appearance of D-peak in the Raman spectrum. Therefore, in thisresearch, the authors investigated the G-peak only. In a recentstudy, Peña-Álvarez et al. (2014) reported dispersive behaviour ofstrained HOPG as a result of compression characteristic to theresonant Raman features. The energy dispersion of first and sec-ond order Raman features at ambient conditions with a range ofexcitation energies (measured from 488.0 to 632.8 nm excitationwavelengths) under the strain conditions are evaluated and cor-roborated associated dispersion change to the electronic proper-ties. Raman defect activated bands in nuclear graphite grades areobserved and for a comparison, Raman shifts of various dispersivefeatures are shown in Table 2. These Raman dispersive featuresbehaviour changes with stress attributed to phonon dispersionevolution. In pristine graphite these dispersive features aremediated by the residual stress developed and retained during and

Table 2Raman features shifts for nuclear graphite grades measured with 532 nm excitationwavelength.

Raman features Gilsocarbon NBG18 PGA

D 1350.93 1350.71 1352.34D′ 1620.85 1620.88 1622.02DþD′′ 2456.94 2454.61 2452.852D(G′) 2699.87 2700.67 2704.77DþD′ 2945.00 2945.11 2946.282D′(G′′) 3246.96 3246.42 3248.49

after the manufacturing related processes.

3. Theoretical consideration

Using the generalized Hooke's law which relates an arbitrarystress, sij, to an arbitrary strain, εij, via the compliance, Sij, in acoordinate system (x, y, and z) with x and y in the plane and zperpendicular to the graphite plane, as follows:

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥⎥

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

S S S

S S S

S S S

S

S

S S

0 0 00 0 00 0 0

0 0 00 0 00 0 0

0 0

0 0

0 0 2( )

xx

yy

zz

yz

zx

xy

xx

yy

zz

yz

zx

xy

11 12 13

12 11 13

13 13 33

44

44

11 12

εεεεεε

σσσσσσ

=

−

×

The stress distribution in anisotropic grade graphite is de-scribed as xxσ and yyσ in the x y– plane and for isotropic gradegraphite xx yyσ σ= stress distribution in the sample. In the presentstudy, von Misses/average stresses are used for illustration andevaluation of the residual stresses in the sample, as follows:

xx yy xx yy2 2σ σ σ σ σ= + −

On considering the stress sensitivity under the stress/strainsystem, the resulting strain tensors are given by Sxx 11ε ε σ= = and

v Syy 12ε ε σ= − = (v¼0.16 has been assumed for Poisson ratio) orequivalently with all shears equal to zero:

S (1)xx 11ε ε σ= =

v S (2)yy 12ε ε σ= − =

A phenomenological approach is used to analyse the Ramanoptical phonon mode in the presence of strain (Ganesan et al.,1970). The temporal equation for the E2g mode of graphite (underinternal stresses) following the standard procedure is given as:

A B i

B i A

( ) ( 2 )

( 2 ) ( )0

(3)

xx yy xx yy xy

xx yy xy xx yy

ε ε λ ε ε ε

ε ε ε ε ε λ

+ − − +

− − + −=

where 202λ ω ω= − is the difference between the squared strain-

dependent Raman line frequency ω, and the squared Raman linefrequency in the absence of strain 0ω . ‘A’ and ‘B’ are the constantsfor phonon deformation potential coefficients, and ijε is the straintensor.

The relationship can be approximated as

2 (4)0

0ω ω λ

ω= +

The phenomenological coefficients A and B describe the chan-ges in the elastic constants of kE0 optical phonons (vibrations)with stresses/strains and their experimental values can be de-termined using the measured shifts in Raman line.

Assuming shear component is absent, the temporal equationreduces to

A B

B A

( ) ( )

( ) ( )0

(5)

xx yy xx yy

xx yy xx yy

ε ε λ ε ε

ε ε ε ε λ

+ − −

− + −=

Solving Eq. (3) analytically, two solutions are obtained as fol-lows:

A B A B( ) ( ) (6)xx yy1λ ε ε= + + −

Table 3Elastic compliances (�10�6 MPa�1) of reactor grades graphite (Kelly, 1981).

Elastic compliances Anisotropic IsotropicPGA Gilsocarbon and NBG-18

S11 2150 1370S12 �140 �148S13 �162 –

S33 1087 –

S44 3230 3030

Table 4Correlation between the Raman shift and residualstresses in polycrystalline graphite structure.

Isotropic (MPa) 0.3597 (cm )xx 1σ ω= Δ −

(MPa) 0.1198 (cm )yy 1σ ω= Δ −

Anisotropic (MPa) 0.2019 (cm )xx 1σ ω= Δ −

(MPa) 0.0749 (cm )yy 1σ ω= Δ −

Table 5Raman shifts in binder and filler phases of three different grades of reactorgraphite.

Graphite grades Binder phase Filler phaseRaman shift (cm�1) Raman shift (cm�1)

Gilsocarbon �1.90470.227 1.3070.758NBG-18 �0.90570.264 0.57070.269PGA �1.84270.175 1.01970.876

Table 6Compressive and tensile stresses in binder and filler phases of three differentgrades of reactor graphite.

Graphite grades Binder phase Filler phaseCompressive stresses (MPa) Tensile stresses (MPa)

Gilsocarbon 0.52670.072 0.25870.103NBG-18 0.28770.084 0.13970.035PGA 0.32670.031 0.12470.075

Table 7An averaged residual (compressive) stress distribution at different locations in crack tips and pore peripheries of the reactor graphite grades.

Graphite grades Residual (compressive stresses (MPa)

Crack Pore

Edge (crack tip) 1 Centre Edge (crack tip) 2 End 1 Centre Edge 2

Gilsocarbon 0.81570.113 0.20870.010 0.83970.178 0.70670.151 0.49370.174 0.63370.029NBG-18 0.08170.017 0.02870.025 0.28470.114 0.13970.103 0.04570.051 0.36770.163PGA 0.11270.067 0.05970.064 0.29070.084 0.25470.104 0.11470.138 0.35870.154

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–2318

A B A B( ) ( ) (7)xx yy2λ ε ε= − + +

where S11 and S12 are the elastic compliances. For each of the re-actor graphite grades elastic compliances for isotropic and aniso-tropic structures are tabulated in Table 3.

Substituting the stress–strain relations in (3) into the two so-lutions given by Eqs. (6) and (7) and using the Eq. (4), the stressdependent Raman frequencies now can be represented as

A B S A B S( ) ( ) (8)1 11 12λ σ σ= + + −

A B S A B S( ) ( ) (9)2 11 12λ σ σ= − + +

A B S A B S( ) ( )2 (10)

1 011 12

0ω ω

σ σω

= ++ + −

A B S A B S( ) ( )2 (11)

2 011 12

0ω ω

σ σω

= +− + +

The Raman shifts in frequencies due to strains/stresses, 1ωΔ and2ωΔ , are

A B S A B S

A B S A B S

( ) ( )2

2[( ) ( ) ]

(12)

1 0 1

11 12

0

011 12

ω ω ωσ σ

ωσω

Δ = −

= −+ + −

= − + + −

A B S A B S

A B S A B S

( ) ( )2

2[( ) ( ) ]

(13)

2 0 2

11 12

0

011 12

ω ω ωσ σ

ωσω

Δ = −

= −− + +

= − − + +

The experimental data for the phenomenological coefficients Aand B were taken from Sakata et al. (1988), which are consistentwith values reported in Frank et al. (2011) and Mohiuddin et al.(2009). For the backscattering from the (0001) surface, a doublygenerated Raman phonon mode is observed. Using the values gi-ven in Table 3 and the experimental values for A and B, Table 4outlines the relation between wavenumber based Raman shift,

(cm )1ωΔ − and the residual stress in graphite samples.The correlation in Table 4 illustrates that a negative Raman shift

indicates compressive residual stress, and a positive Raman shiftindicates a tensile residual stress. The doubly degenerate Ramanphonon mode at 1581.118 cm�1 corresponds to Raman allowed E2gmode in HOPG, which having no stress/strain in the structure, wasused to characterise the Raman line shift associated with residualstress/strain in the reactor grade graphite.

4. Experimental results and discussion

Microscopic graphite surface characteristics of assorted reactor

grades graphite are investigated by Raman spectroscope. The re-sidual stress distribution in the region of binder phase, filler par-ticles and multi-scaled cracks and pores of sizes up to 300 μm isevaluated using Raman spectra. A total of 400 spectra are used toillustrate the Raman image(s) from the different region of thegraphite structure. The averaged Raman shifts in binder and fillerphases for all three grades graphite are illustrated in Table 5. Here,the binder and filler particles are representing negative and po-sitive Raman shifts for compressive and tensile residual stresses,respectively.

Table 6 demonstrates the averaged values of compressivestresses (MPa) in binder phase and tensile stresses in filler

Fig. 3. The average residual stress (MPa) values of binder (compressive) phase and filler (tensile) particle region in reactor grades graphite evaluated from Raman spectra.The average residual values are from the 20 different locations in binder and filler particle regions.

Fig. 4. The averaged residual stress at the measured points (tips and the centre for cracks and diametrically end points and the centre for pores) in the cracks and pores ofreactor graphite grades.

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23 19

particles extracted from the Raman spectra of reactor grades gra-phite. It is noted that there are very limited published studiesavailable on stress evaluation in graphite under strained condi-tions, and it is difficult to compare the present results as it isevaluating the stress already present under the pristine conditionand no external stress has been applied to the graphite samples.Tsang and Marsden (2006) studied the stress analysis in nucleargraphite bricks subjected to both fast neutron irradiation andradiolytic oxidation, using material model subroutine called MANUMAT (Tsang and Marsden, 2006).

The stress values reported in Tsang and Marsden (2006) nu-clear graphite bricks under irradiation condition are typicallyseveral orders of magnitude higher than the stress evaluated inthe present study, which is expected as the samples were radiationdamaged. Complex stress fields within the nuclear graphite bricksare expected to develop under radiation environment. Table 7

shows the averaged values of compressive stresses in crack andpore periphery of reactor grades graphite.

The averaged values of the stresses are true representation ofRaman spectral information and the averaged data of stresses arefrom both the tips of crack, diametrically opposite ends of the poreand centre periphery of the pore and the crack. Multi-scaled poresand cracks are characteristics to graphite structures and attributedto the manufacturing and forming operations.

It is interesting to compare the residual stress values obtainedhere with that expected for isotropic (Gilsocarbon and NBG-18)and anisotropic (PGA) graphite grades. The shift in phonon fre-quencies is due to changes in the phonon deformation potentialinduced by the residual strain.

The sign of compressive stresses and tensile stresses are ne-gative and positive, respectively and now onwards tensile andcompressive stresses will be referred without their respective

Fig. 5. Optical micrographs and Raman mappings (230 μm�320 μm) which were created across the regions on polycrystalline Gilsocarbon graphite (a) filler region,(b) binder region, and (c) cracks in the binder phase.

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–2320

signs. Typical Raman spectra from the region of filler particle andbinder phase in Gilsocarbon are shown in Fig. 2. Fig. 2 also illus-trates residual stress nature in the structure; such as compressivestress exists if G peak shifts towards right or tensile stress exists ifG peak shifts towards left.

Fig. 3 illustrates the average residual stress (MPa) values ofbinder and filler particle regions in reactor grades graphite – Gil-socarbon, NBG-18 and PGA. The results showed that compressiveresidual stress in binder phase is the highest for Gilsocarbon and

lowest for NBG-18, although, in filler particles stress is highest forGilsocarbon, but lowest for PGA among the reactor gradesgraphite.

The reason for this is probably due to morphology of the cokeparticles used in the manufacturing and applied techniques forfabrication. The dimensions of filler particles in all reactor gradesgraphite (PGA, Gilsocarbon and NBG-18) are typically in the range0.10–1 mm (Hodgkins et al., 2010). However, Gilsocarbon andNBG-18 graphite filler particles are spherical in shape, particularly

Fig. 6. Optical micrographs and Raman mappings (230 μm�320 μm) which were created across the regions on polycrystalline NBG-18 graphite (a) filler region, (b) binderregion, and (c) cracks in the binder phase.

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23 21

in the case of Gilsocarbon, whereas the PGA graphite contains fillerparticles in the form of laths/needles. The filler particles in PGAgraphite are aligned in the extrusion direction, so properties andmicrostructure are different from the isotropic graphite grades(Mostafavi et al., 2012).

HOPG (SPI-1 grade) sample was employed as a model materialin the present study to evaluate the residual stress values in theartificial reactor graphite grades, as it has no residual stresses dueto the absence of defect volume and constituents phases.

Fig. 4 details the residual stress values of cracks tips and at pore

peripheries in reactor grades graphite. The residual stresses aremeasured at the tips and centres in cracks and in micro-pores atthe diametrically end points and their centres. The nature of re-sidual stresses at the tips of the cracks is mixed – tensile andcompressive. Pores in binder and filler particles have compressivestresses, both at the ends and the centre of the pores. However,centres of cracks and pores have lower stress values than theirends. Gilsocarbon has higher compressive stresses in pores andcracks than the other graphite grades. These stress values are inthe range of several MPa.

Fig. 7. Optical micrographs and Raman mappings (230 μm�320 μm) which were created across the regions on polycrystalline PGA graphite (a) filler region, (b) binderregion, and (c) cracks in the binder phase.

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–2322

The stress values observed in different constituents of thegraphite are small, but these values are critical in graphite bricksfor applications in nuclear reactor. During reactor operation gra-phite brick structures are exposed to gradients of temperature andneutron radiation, which results in significant changes in graphitebrick properties, and develop a complex stress fields within thebrick (Tsang and Marsden, 2006).

Figs. 5–7 present 2D contour plots and optical micrographs ofthe analysed area where these results are spectroscopically ana-lysed the local information along x–y coordinates of the

measurement points. The trace values representing the spectraldata in x- and y-coordinates system from the sample surface re-gion of interest. The z-dimension (trace values) is visualized bymeans of colour-coded contour levels. For this purpose, the rangeof the z-values – trace values – is subdivided into several contourlevels and each contour level is assigned to a certain colour code.This colour-coded contour plot is projected on the two-dimen-sional area of the xy-coordinate system.

The map contours show the Raman spectra featuring the localregions characteristics in the Raman maps. These spectra provide

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23 23

information on Raman shift, which are used to measure the cor-responding residual stresses. The maps show the blue colour hasthe lowest value of stress and the white has the highest value ofstress. Also, the compressive stress would lead to a shift towardshigher wavenumber, which is in contrast to the findings observedfor polycrystalline silicon (Kang et al., 2005).

Stress measurement in polycrystalline graphite is an importantaspect in understanding fracture mechanism under graphite technol-ogy (Hodgkins et al., 2010). Measurement of stress dependence ofRaman active vibrations is notable for both applied and fundamentalstudies and can be used to verify the theoretical models (Tsang andMarsden, 2006). Thus, the Raman microscopy has been evolved as afast, relatively easy to use and non-destructive examination techniquefor potentially useful information source concerning the structure ofgraphite such as the residual stresses developed before and after ir-radiation and can be applied to examine the induced internal stressesin low to high dose radioactive graphite samples.

5. Conclusions

Micro-Raman spectroscopy is an analytical method that can berapidly applied to evaluate internal stresses distribution in theconstituents of polycrystalline graphite. It is sensitive enough tomeasure low stress concentration in constituent phases of gra-phite grades. Three different grades of reactor graphite are con-sidered namely Gilsocarbon, NBG-18, and PGA for the analysis andevaluation. Graphite structural constituents such as filler particles,binder phase, cracks and pores are the salient consideration forresidual stress estimation study and the results revealed thatstresses in filler particles are tensile in nature, and stresses in thebinder phases are compressive in nature. It was found that thebinder phase in Gilsocarbon has the highest residual stress andNBG-18 has the lowest value. Filler particles in Gilsocarbon havethe highest residual stress and PGA has the lowest. Stresses at poreperipheries and cracks tips in the binder and filler particles arealso evaluated and these stresses were found to lie in the range ofseveral orders of MPa. Compressive stresses in binder were in therange of 0.29–0.53 MPa and tensile stresses in filler were in therange of 0.12–0.26 MPa. Stresses in cracks present in binder andfiller particles were of mixed nature, compressive and tensile andtheir values were in the range of 0.11–0.84 MPa. Stresses in poreswere in the range of 0.14–0.71 MPa.

Acknowledgement

The authors would like to thank Prof. Simon M. Pimblott, Di-rector, Dalton Cumbrian Facility (DCF), Dalton Nuclear Institute foraccess to the-state-of-art facilities at Cumbrian site.

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