Microstructure of carbon blacks determined by X-ray diffraction profile analysis

Transcription

1 Crbon 40 (00) Microstructure of crbon blcks determined by X-ry diffrction profile nlysis * U T. Wldek Zerd, b Tms Ungr, Jeno Gubicz, Gbor Ribrik, Cristin Pnte, b Eotvos University, Deprtment of Generl Physics, P.O. Box 3, Budpest, H-1518 Hungry b TCU, Deprtment of Physics, Fort Worth, TX 7619, USA Received 18 April 001; ccepted 1 August 001 Abstrct The microstructure of crbon blcks is investigted by X-ry diffrction pek profile nlysis. Strin nisotropy is ccounted for by the disloction model of the men squre strin in terms of verge disloction contrst fctors. Crystllite shpe nisotropy is modeled by ellipsoids incorported into the size profile function. Different grdes of crbon blcks, N990, N774 nd N134, untreted, het-treted nd compressed t.5 GP hve been investigted. The microstructure is chrcterized in terms of crystllite size-distribution, disloction density nd crystllite shpe nisotropy. Het tretment results in incresed verticl nd lterl sizes of grphitic crystllites. Postproduction pressure tretment hs little effect on the verge sizes of the crystllites, however, it ffects the crystllite size distribution function. The verge sizes of the crystllites obtined by X-ry diffrction gree with those estimted from Rmn spectr. Applied pressure ffects the mgnitude of strin within the crystllites. 00 Elsevier Science Ltd. All rights reserved. Keywords: A. Crbon blck; B. High pressure; C. X-ry diffrction; D. Crystllite size 1. Introduction [1 5. The lyer stcking disorder cn be observed in principle by nlysing HK bnds in the diffrctogrms. Crbon blck is generlly used s filler in rubber Rocking curves of the HK.0 type reflections would show production to modify the mechnicl properties of the tire. extr brodening due to rottions round the hexgonl c Although the smllest indivisible unit of crbon blck is xis wheres the 00.L type reflections would be broder in the ggregte, in the TEM imges ggregtes pper to be the u u rdil direction. This kind of lyer stcking formed by sphericl prticles, which re fused together. disorder cn be hndled s effective boundries of coher- Aggregtes connect through Vn der Wls forces into ently scttering domins where diffrction pek brodening networks clled gglomertes [1. The internl structure of is mesure of the size of these objects. ggregtes is not well understood. Grphite-like, The structure of crbon blck prticles nd their surfce qusicrystlline domins, in which bsl plnes re prllel properties re importnt for mny resons. Different sites but ngulrly distorted nd the spcing between the lyers present on the surfce determine reinforcing properties of is different from tht of pure grphite, hve been detected crbon blck in rubber [6. Energy of interction between in crbon blck prticles [1. Biscoe nd Wrren identified the polymer nd crbon blck depends on nture nd those structures s intermedite between crystlline nd popultion of different sites. The most energetic sites, morphous mterils [. Herefter, the turbostrtic qusi- which very effectively dsorb polymers, re usully idencrystlline domins re referred to s grphitic crystllites tified s crystllite edges. Crystllite flt surfces nd or nnocrystllites. Due to the lck of three-dimensionl morphous crbon present on the surfce re considered ordering, this nomenclture is not rigorously correct, but less energetic sites. Thus to chrcterize reinforcing propppers to be generlly ccepted in the scientific literture erties of crbon blck it is necessry to determine the frction of the surfce occupied by morphous crbon nd *Corresponding uthor. Fx: estimte the size of the crystllites nd their surfce E-mil ddress: ungr@ludens.elte.hu (T. Ungr). density. Reltive concentrtion of morphous crbon cn / 0/ $ see front mtter 00 Elsevier Science Ltd. All rights reserved. PII: S (01)004-X

2 930 T. Ungr et l. / Crbon 40 (00) be evluted from Rmn mesurements [3. Energies of microstructure: (i) m nd (ii) s, the medin nd the dsorption of different dsorption sites nd their reltive vrince of the log-norml crystllite size distribution popultions hve recently been evluted by gs dsorption function, (iii) the ellipticity of crystllite shpe, (iv) r nd technique [7. The sizes of grphitic crystllites hve been (v) M, the density nd the rrngement prmeter of estimted from X-ry diffrction [5,8, neutron scttering disloctions nd (vi) q or A nd B, the relevnt prmeters [9, tomic force microscopy [10, nd Rmn spectros- describing the verge disloction contrst fctors in cubic copy mesurements [3 5. Those studies showed tht the or hexgonl crystls, respectively. verge size of crystllites, L, is similr for ll commer- In this pper the effect of nneling nd pressure on () cil crbon blck grdes produced in furnce rectors nd the size distribution nd (b) the shpe of crystllites s well roughly equl.3 nm. This ws surprising result becuse s (c) the strin (disloction density) in the crystllites of different grdes hve completely different rubber reinforc- different grdes of crbon blck smples is studied by ing properties. X-ry diffrction profile nlysis. The vlues of the Smll crystllites re not energeticlly fvorble struc- verge crystllite sizes determined by X-rys were comtures. One possible explntion for their presence in crbon pred with those obtined from Rmn mesurements. blcks is tht lrge strins re developed in production, i.e. during ggregte growth t high tempertures nd lso during wter quenching, when the temperture of crbon. Evlution of X-ry diffrction profiles blck is rpidly reduced from bout 16008C to bout 8008C. Strin is relieved when lrger structures brek to.1. The method of whole profile fitting by Fourier form smller crystllites. Chrcteriztion of strin remin- coefficients ( WPFC) ing in the crystllites is n importnt problem, which so fr hs not been ddressed. Strin cn chnge bond lengths Within the kinemticl theory of X-ry diffrction the nd ngles, nd thus ffect surfce potentil nd in turn physicl profile of Brgg reflection is given by the reinforcing properties of crbon blcks. Reinforcing prop- convolution of the size nd the distortion profiles [17: erties of crbon blck re lso expected to be function of P S D crystllite size distribution. Crbon blck with uniform I 5 I 3 I, (1) crystllites tht ll hve similr sizes is expected to hve where the superscripts S nd D stnd for size nd more homogenous surfce potentil thn crbon blck distortion, respectively. It follows from Eq. (1) tht the exhibiting wide distribution of sizes. Fourier coefficients of the physicl profile re the pro- X-ry diffrction pek profile nlysis is widely used duction of the Fourier coefficients of the size nd strin method for the determintion of crystllite size nd lttice profiles: defect structure in crystlline mterils. The evlution procedures re bsed on the different diffrction order S D A(L) 5 A (L) A (L), () dependence of size nd strin brodening. In the simplest cse the size brodening is independent while the strin where A(L) re the bsolute vlues of the Fourier co- S D brodening is dependent on the diffrction order. Both efficients of the physicl profiles, A nd A re the size dependencies become, however, complicted if shpe or nd the distortion Fourier coefficients nd L is the Fourier strin re nisotropic. Shpe nisotropy hs been modeled vrible. by cylindricl [11 bodies nd strin nisotropy hs been In the cse of sphericl crystllites, size brodening is ccounted for either by phenomenologicl model of diffrction order independent [18. Rmn spectroscopy nisotropic elstic constnts [1 or by the nisotropic hs shown tht the crbon blck crystllites re non- strin fields of disloctions [13,14. The size-distribution of sphericl flt discs [3 5. Since the size brodening cused sphericl crystllites hs been recently suggested to be by non-sphericl crystllites is diffrction order dependent, determined by whole profile fitting in the bsence of strin the size profiles of ellipsoids of revolution hve been by using theoreticlly clculted size profiles [15. elborted. A brief description of this derivtion is given In the present work it is shown tht theoreticl diffrcdimeters Dc nd D, prllel nd perpendiculr to the xis below. It is ssumed tht ellipticity,, the rtio of the tion profiles cn be constructed in the presence of lttice distortions using the strin profile derived by Wilkens for of revolution, is the sme for ll crystllites, nd tht the dislocted crystls [16. A procedure is described in which crystllite size distribution density function, f(x), is log- the Fourier coefficients of the experimentlly determined norml: physicl pek profiles re fitted by the Fourier trnsforms 1 1 [ln (x/m) of b initio size nd strin profiles. In this method the f(x) 5 exph J, (3) Œps x s strin is ssumed to be cused by disloctions nd the crystllites re modeled by ellipsoids with log-norml size where s is the vrince nd m is the medin of the size distribution. The only fitting prmeters re well estb- distribution density function f(x). According to Bertut lished physicl prmeters being chrcteristic of the [19 nd Guinier [0 the size prt of the Fourier trnsform

3 T. Ungr et l. / Crbon 40 (00) of the () diffrction pek t given vlue of the Fourier where m is the medin of the size distribution of vrible L cn be clculted s the common volume to the dimeters of ellipsoids perpendiculr to the xis of revolucrystl nd its ghost obtined by trnsltion by L in the tion. If the reltive orienttions of the crystllogrphic direction norml to the reflecting plnes. To clculte directions to the xis of revolution re known, cos cn the Fourier trnsform corresponding to crystllite, divide be expressed by the indices of reflection. The xis of the crystl into cylindricl columns norml to the revolution is tken to be perpendiculr to the bsl plne of lttice plnes nd set dsm for the cross section of the hexgonl crbon blck crystls, therefore cos cn be column with the height m [0. The volume common to given s: this column nd its ghost is: l ulu cos 5, (10) S A sld5s1 Dm ds m. (4) 4 c m sh 1 k 1 hkd 1 l œ3 The common volume to the irrdited crystllites nd to their ghosts shifted by L cn be obtined by summing for where c/ is the rtio of the lttice constnts of the ll columns existing in the crystllites. Let us set s the hexgonl crystl. ngle between the xis of revolution nd the diffrction The diffrction profiles cn be brodened due to the vector with the indices. Summing up the common strin field of the lttice defects in the crystl. The point volumes of the columns prllel to the diffrction vector defects hve diffrction effects fr from the fundmentl for one crystllite the following formul is obtined for the Brgg reflections, often clled Hung scttering, becuse normlized size Fourier trnsform: of their short-rnge strin field [1. The strin fields of disloctions re of long-rnge chrcter, therefore their 3 3uLu ulu diffrction effects cluster round the fundmentl Brgg S if ul u# D A sld5 D D (5) reflections. This diffrction effect is clled the diffrction 50 if ul u$ D pek brodening. The strin fields of plnr defects re spce independent thus, in the first pproximtion, they where D is the dimeter of the ellipsoid in the cuse lttice prmeter chnges nd shift Brgg reflections. direction which cn be given in terms of : In relity lttice defects re more complex nd their effects on pek shpe cn be mixture of three well-seprted D D 5 (6) cses: (i) Hung scttering, (ii) pek brodening nd (iii) cos pek shifts. Stcking fults, for exmple, cn cuse pek sin 1 œ shifts nd pek brodening simultneously since they re usully bounded by prtil disloctions. Despite this where D is the dimeter of the ellipsoid perpendiculr to complex behviour, disloctions ply specil nd unique the xis of revolution. Mking the summtion for ll the role: they re lwys present (1) either s the mjor crystllites hving the log-norml size distribution the component in complex lttice defects or () s the only following formul is obtined for the normlised size lttice defects which distort the crystl lttice to such n Fourier trnsform: extent tht it becomes visible s profile (or line) brodening in diffrction experiment. For this reson, in the 1 ln sul u/m d S A (L) 5 erfcf 1.5Œs Œ G present ccount we consider the effect of disloctions on s strin brodening. 3 ln sul u/md Œ uluerfcf sg Assuming tht in the crystl the lttice distortions re 4m exps8.15s d Œ s cused by disloctions, the Fourier coefficients of the 3 ln sul u/m d strin profile cn be given s [16, 3 1 L erfc 3 u u F G (7) 4m exps10.15s d Œ s D A (L) 5 exp[rbl f(h) gc, g (11) where erfc is the complementry error function defined s: where g is the length of the diffrction vector, B 5 pb /, ` where b is the length of the Burgers vector, h L/R e, erfc(x) 5 E exps t d Œ dt, (8) p where Re is the outer cut off rdius of disloctions, r nd x C re the density nd the contrst fctors of disloctions nd m is the medin of the distribution of dimeters in nd f(h) is the L dependence prt of the men squre strin the direction given s: in dislocted crystl. In the following f(h) will be clled the Wilkens function. This function strts with logrithm m 5 (9) mic term nd continues s hyperbol for lrge L vlues: 1 1 1S 1Dcos 7 œ f(h) ln h 1S ln D 1???for h # 1 (1) 4

4 93 T. Ungr et l. / Crbon 40 (00) the diffrction profiles hs been observed. The overlpping f(h) 1???for h $ 1. (13) peks hve to be seprted since the present evlution 90p h method is worked out for individul profiles. Bckground The detiled expressions for f(h) re given in Eqs. A.6 subtrction nd the seprtion of overlpping peks re to A.8 in Ref. [16 nd hve been cited in Eqs. () nd crried out in one step. Two or more nlyticl functions, (3) in Ref. [18. In the procedure developed here the full usully of PersonVII or Pseudo-Voigt type plus liner or expressions in A.6 to A.8 in Ref. [16 were used. It is second order polynomil bckground re fitted to the physiclly more pproprite to use the dimensionless overlpping peks. Bckground correction ws crried out prmeter M 5 R eœr defined by Wilkens s the disloc- fter the diffrctogrms hve been rescled to sin u/l tion rrngement prmeter [3. The vlue of M gives the insted of u. This procedure enbles the correct bckstrength of the dipole chrcter of disloctions: the higher ground subtrction even in the presence of non-negligible the vlue of M, the weker the dipole chrcter nd the smll ngle scttering contributions. In the next step the screening of the displcement field of disloctions. unwnted fitted peks together with the liner bckground The verge disloction contrst fctors re the weighted re subtrcted leving the trgeted pek free of overlp nd verge of the individul C fctors either over the disloc- bckground. The procedure is then repeted for other tion popultion or over the permuttions of the indices trgeted peks. The seprted profiles re tken s in- [ 4. Bsed on the theory of line brodening cused by dividul diffrction profiles in the evlution procedures. disloctions it cn be shown tht in n untextured hexgon- Due to very lrge strins nd nnometer size crystllites, l polycrystlline specimen the vlues of C re simple pek brodening of the crbon blck specimens is bout functions of the invrints of the fourth order polynomils two orders of mgnitude lrger thn the instrumentl of [5: effects. For this reson no instrumentl corrections were [A(h 1 k 1sh 1 k d ) 1 Bl l crried out. C 5Chk Fh 1 k 1sh 1 kd 1 SD l G 4 c 3. Experimentl (14) where Chk0 is the verge disloction contrst fctor for the 3.1. Smple preprtion hk0 reflections, A nd B re prmeters depending on the elstic constnts nd on the chrcter of disloctions (e.g. Three different grdes of crbon blcks were selected edge or screw type) in the crystl nd c/ is the rtio of the for this study, N990, N774 nd N134. They differ in two lttice constnts of the hexgonl crystl. verge ggregte dimeters rnging from 85 nm (N990) A numericl procedure hs been worked out for fitting to 18 nm (N134), surfce re rnging from 8.5 m / g the Fourier trnsform of the experimentl profiles by the (N990) to 145 m /g (N134), nd their reinforcing prop- product of the theoreticl functions of size nd strin erties (N134 is minly used in tred pplictions while Fourier trnsforms given in Eqs. (7) (10) nd (11) (14), N774 is used in tire crcsses, for exmple). N134 nd respectively [6,7. The method hs the following steps: N774 re obtined in furnce rectors using similr (i) the Fourier coefficients of the mesured physicl processes. N990 is therml blck nd is produced by profiles hve been clculted by non-equidistnt sm- therml decomposition of hydrocrbon gses in the bpling Fourier trnsformtion, (ii) the Fourier coefficients of sence of flme. the size nd strin profiles were clculted using Eqs. Crbon blcks were het-treted for 0 min t 7008C (7) (10) nd (11) (14), respectively, (iii) the experimen- nd those smples re lbeled s G (grphitized). To void tl nd the clculted Fourier coefficients were compred oxidtion the chmber of the induction furnce ws purged by the lest squres method. The procedure hs seven nd filled with gseous nitrogen. After the het-tretment fitting prmeters for the hexgonl crbon blck mteri- the smples were llowed to cool down slowly to room ls: (i) the medin, m, nd (ii) the vrince, s, of the temperture. High pressure experiments were conducted t log-norml crystllite size distribution function, (iii) the room temperture inside piston cylinder cell t the ellipticity of the crystllite shpe,, (iv) the density, r, nd pressure of.5 GP (5,000 br). The smples were (v) the rrngement prmeter, M, of disloctions nd llowed to remin compressed for bout 0 min. The rw (vi vii) the prmeters A nd B for the verge disloction crbon blcks exposed to high pressure re denoted s P, contrst fctors. Further detils of the fitting procedure re those which first underwent het tretment re clled PG. given elsewhere [6,7. The specimen N134 ws not subjected to high pressure experiments therefore P134 is bsent from the series... Corrections for instrumentl effects, bckground nd overlpping peks 3.. X-ry diffrction technique For the crbon blck powder smples strong overlp of Two different X-ry diffrctometers were used for the

5 T. Ungr et l. / Crbon 40 (00) nlysis of pek profiles. (i) A conventionl u u diffrc- 4. Results nd discussion tometer ws used to obtin n overview of the diffrctogrms, (ii) the individul pek profiles were mesured in 4.1. Averge size, size distribution nd shpe of specil double crystl high resolution diffrctometer with crystllites negligible instrumentl brodening. The first (i) diffrctometer ws Philips X pert diffrctometer using Cu The typicl powder ptterns for the initil N774 nd the node nd pyrolitic grphite secondry monochromtor. grphitized G774 smples re shown in Fig. 1 nd b, The second (ii) diffrctometer (Nonius FR 591) enbles respectively. It cn be seen tht fter het tretment t better seprtion of the overlpping peks due to the 7008C the pek profiles become rther nrrow. Note tht bsence of the K lph doublet. In this diffrctometer in Fig. 1b the intensity is scled logrithmiclly in order to fine focus rotting coblt node ws operted s line show the detils of the peks t lower intensities. The focus t 36 kv nd 50 ma (l nm). The symmetri- diffrctogrms show strong overlp of the peks for both cl 0 reflection of Ge monochromtor ws used in smples. The overlpping peks were mesured by the order to hve wvelength compenstion t the position of double crystl diffrctometer nd were seprted by the the detector. The K component of the Co rdition ws method described in Section.. The Fourier coefficients eliminted by 0.16 mm slit between the source nd the of the mesured profiles for N774 smple nd the fitted b Ge crystl. The profiles were registered by liner position initio functions normlized to unity re shown in Fig.. sensitive gs flow detector, OED 50 Brun, Munich. In There is good greement between the two sets of dt. order to void ir scttering nd bsorption the distnce The mesured nd seprted profiles nd the inverse between the specimen nd the detector ws overbridged by Fourier trnsform of the fitted Fourier coefficients norml- n evcuted tube closed by mylr windows. Seven ized to unity for N774 re shown in Fig. 3. Agin good diffrction peks indexed s 000, 1010, 1011, 0004, 110, 11 nd 0006 were recorded nd 1011 s well s 110, 11 nd 0006 overlp nd were seprted by fitting procedures. The most intense five profiles 000, 1010, 1011, 0004 nd 110 were used in the evlution method Rmn spectroscopy Complementry dt on verge sizes of grphitic crystllites were obtined from Rmn scttering mesurements. In ddition, Rmn studies llowed us to estimte the reltive concentrtion of morphous crbon on the surfce of crbon blck ggregtes. Rmn spectr were obtined using home-mde spectrometer equipped with confocl microscope. To void lser heting crbon blcks were plced inside groove in steel disk spinning t speed of 3000 rev./min. The verge size of nnocrystllites cn be determined in terms of chnges in position, width nd intensity rtio of two Rmn peks observed t cm (the disordered, or d pek) nd 1575 cm (the grphite, or g pek). The shpe of those peks depends on the crystllite sizes. When the crystllites become lrger, the peks become nrrower, their mxim move to higher frequencies nd the intensity of the g pek systemticlly increses in comprison with the d pek. Using the empiricl formul found by Tuinstr nd Koenig [8 L I /I (nm) (16) g d it is possible to evlute L, the lterl size of the crystllites. Amorphous crbon is observed s brod pek 1 centered t bout 1530 cm. Its intensity reltive to tht Fig. 1. The powder diffrctogrms for the N774 crbon blck of the d nd g peks is n estimte of the reltive specimen in the initil stte () nd for the specimen G774 fter concentrtion of morphous crbon on the surfce of nneling t 7008C (b). The intensity in logrithmic scle in (b) crbon blck ggregtes [3. shows detils of low intensity peks.

6 934 T. Ungr et l. / Crbon 40 (00) N134, N774, nd N990. The greement between the dt from X-ry diffrction nd Rmn mesurements is usully better thn 5%. The discrepncies for the smples N990 cn be explined s follows. X-rys esily penetrte through crbon blcks nd the line profiles re determined by scttering on grphitic lyers present throughout the mteril. On the other hnd, Rmn intensity is strongly ttenuted by crboneous mterils nd 30% of the Rmn intensity origintes from lyers lying less thn 10 nm below the surfce, nd 90% from the outer lyer of thickness less thn 40 nm [9. It is possible tht for the smples N990 with verge ggregte dimeter of bout 85 nm, lrge crystllites re present under the skin lyer nd thus re not detected by Rmn. For other grdes of Fig.. The Fourier coefficients of the mesured (open circles) nd smll ggregte dimeters it is sfe to ssume tht the the fitted theoreticl functions (solid lines), normlized to unity for Rmn signl origintes from groups distributed through- the specimen N774. The differences between fitted nd mesured out the smple. dt nd the indices of reflections re indicted. Crystllites were pproximted by ellipsoids nd mc is the medin of the dimeters of the crystllites perpendiculr to the hexgonl bsl plne, i.e. it mesures the correltion between the mesured nd the fitted dt cn be observed. The medin, m, nd the vrince, s, of the size stcking heights of grphitic nnocrystllites. In good distribution of the crystllite dimeter prllel to the greement with previous studies the vlue of 5 m c/m is hexgonl bsl plne, the ellipticity of the crystllite between 0.5 nd 1.0, i.e. the heights of the crystllites vry shpe,, nd the density, r, of disloctions re determined between 50 nd 100% of their corresponding lterl sizes. from the fitting procedure nd listed in Tble 1. The shpe nd the size of crystllites vry significntly Rmn spectr of crbon blcks were resolved into two in different grdes of crbon blck s well within the sme components by fitting procedure s shown in Fig. 4 for specimen due to pressure nd het-tretment. The clcu- the smple N134. The rtio of these two components gives lted size distributions for different grdes re compred in the verge lterl sizes of the crystllites prllel to the Fig. 5. For N990 the verge size of the crystllites is only hexgonl bsl plne. The precision of the fitting routine 5.6 nm, but Fig. 5 indictes tht for this crbon it is ws better thn 10% nd reproducibility ws better thn possible to find crystllites s lrge s 16 nm cross. 5%. The clculted L vlues re listed in Tble 1. Compring these vlues to the medin dimeter dt, m, obtined from X-ry nlysis it is seen tht both techniques give similr results. As expected, m vlues increse with incresing dimeters of the ggregtes in the order grphitic crystllites (both in the initil nd the grphitized sttes), with the exception of the P990 where the crys- tllites becme significntly smller. The crystllite size Fig. 3. The mesured intensity profiles (open circles) nd the inverse Fourier trnsforms of the fitted Fourier coefficients (solid lines), normlized to unity. The differences between fitted nd mesured dt nd the indices of reflections re indicted. Different shpes for the size distribution function obtined for different grdes re probbly ssocited with different production conditions, such s temperture, speed of the rection, composition of the feedstock, the residence time in the flme zone, nd the position of quenching zone. Het tretment increses the verge sizes of grphitic crystllites. This effect hs been observed before by Rmn, TEM, AFM, nd lso by X-ry diffrction using the Scherrer method. These techniques proved tht t elevted tempertures crystllites grow both in the lterl nd verticl directions. This study confirmed this result. In the untreted smples the lterl sizes of crystllites (L or m ) re usully twice the size of the stcking height of the lyers, m c. But fter het tretment the lterl nd verticl dimensions become similr, compre Tble 1. These effects re ccompnied by modifictions of the shpes of the distribution functions, which for grphitized crbons become more symmetric. Concentrtion of morphous crbon is reduced fter het tretment. Prcticlly no significnt contribution cn be detected in smples heted to 7008C. Hydrosttic pressure did not chnge the verge sizes of

7 T. Ungr et l. / Crbon 40 (00) Tble 1 Lterl crystllite size, L, nd reltive content of morphous crbon, I /I totl, obtined from Rmn spectroscopy; the medin, m, nd the vrince, s, of the distribution of the crystllite-dimeters prllel to the hexgonl bsl plne, the ellipticity of the crystllite shpe nd the disloction density, r, (strin) determined by X-ry diffrction for crbon blcks of different grdes nd vrious histories of temperture nd pressure tretments Smple 5 D /D L (nm) m (nm) s r I /I c totl 15 Rmn (10 m ) Rmn N G PG N P G PG N P G PG previous neutron scttering nd Rmn in situ high-pres- sure studies on crbon blcks indicted tht under pressure the turbostrtic structures become orgnized nd crbon crbon bonds pproch vlues typicl for grphite crystl [4. The current study ws conducted fter the pressure tretment nd since we did not observe ny significnt chnges in the crystllite sizes we concluded tht the system returned to its originl configurtion. Pressure ws lso pplied to previously grphitized crbon blcks. No significnt chnges in the sizes hve been observed. However, the distribution functions ll distributions for the specimen N990 in the initil stte s well fter het-tretment nd pressure-tretment re shown in Fig. 6. In the cse of this prticulr crbon blck, before het-tretment the lrgest crystllites pproch 16 nm. Externl pressure might brek those lrge crystllites into smller units nd s result the distribution function becomes less symmetric nd its mximum is shifted towrd lower L vlues. This effect is lso clerly seen for other crbon blcks. The distribution functions become nrrower nd more symmetric indicting tht in those smples lrger crystllites re reduced to smller ones. Our Fig. 4. Rmn spectrum of the specimen N134. Solid line, the best fit to sum of three components. Disordered, d, morphous,, nd grphitic, g, components re shown s broken lines.

8 936 T. Ungr et l. / Crbon 40 (00) used in this study did not brek crystllites into smller units but ws sufficient to induce strin. Pressure tretment of previously grphitized smples lso resulted in incresed vlues of r. 5. Conclusions A procedure hs been developed to evlute X-ry diffrction pek profiles using the Fourier coefficients of b initio theoreticl size nd strin profiles. The crystllites re modeled by ellipsoids with log-norml size distribution nd the strin is ssumed to be cused by disloctions. The procedure enbles the determintion of the medin nd the Fig. 5. Crystllite size distribution for N134; N774 nd N990. vrince of the crystllite size distribution, the ellipticity of the crystllite shpe nd the disloction density. This method ws pplied to different grdes of crbon blck powders before nd fter het- nd pressure-tretments. becme very nrrow. It indictes tht lrger crystllites re The verge crystllite size is found to be in the reduced to smller units but in wy tht leves the nnometer scle for ll crbon blck powders. Different verge vlue unchnged. After pressure tretment con- verge sizes nd size distributions of crystllites hve centrtion of morphous crbon either slightly decresed or been identified in different grdes of furnce crbon remined unchnged. blcks, which is explined by the difference in the production conditions. It ws found tht for crbon blcks 4.. Disloction density (strin) of lrge ggregtes, the chnce of finding lrge crystllites is incresed. The verge crystllite sizes determined by The mgnitude of strin is chrcterized by the disloc- X-rys gree well with Rmn results except for the tion density, r. In the untreted smples its vlues re very smples N990. For these specimens Rmn mesurements 16 lrge, of the order of 10 m (see Tble 1). Popultion indicte smller crystllites thn those mesured by X-rys of disloctions or the mgnitude of strin drmticlly becuse the Rmn spectr re minly due to the outer skin decreses with grphitiztion but increses fter pressure of the ggregtes while X-ry diffrction detects crystretment. This is n expected result. High temperture tllites throughout the volume. In the untreted smples the tretment followed by slow cooling nnels the smples lterl sizes of crystllites re usully twice the size of the nd decreses the mgnitude of strin. Hydrosttic pressure stcking height of the lyers. Het-tretment increses the verge sizes of grphitic crystllites nd the lterl nd verticl dimensions of the crystllites become similr. The disloction density is incresed during nneling. Concentrtion of morphous crbon is decresed upon het tretment. We interpret this observtion s result of morphous crbon being grdully incorported into grphitic lyers. The pressure-tretment hs no significnt effect on the size nd the shpe of the crystllites nd the popultion of morphous crbon while the disloction density (or strin) in the crystllites hs been incresed. Acknowledgements The uthors re grteful for the finncil support of the Hungrin Scientific Reserch Fund, OTKA, grnt nos. Fig. 6. Crystllite size distribution for the s-received specimen T031786, T nd D-9339 nd Texs Advnced N990, fter het tretment t 7008C, fter pressure tretment t Technology Progrm. We thnk Dr. M. Gerspcher, Sid.5 GP, nd grphitized blck fter pressure tretment. Richrdson Crbon Co., for numerous discussions.

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