STRUCTURAL VARIATIONS IN CHRYSOTILE ASBESTOS FIBERS REVEALED BY SYNCHROTRON X.RAY DIFFRACTION AND HIGH.RESOLUTION TRANSMISSION ELECTRON MICROSCOPY


 Raymond Terry
 2 years ago
 Views:
Transcription
1 257 The Cndin Minerlogist Vol. 32, pp (1994) STRUCTURAL VARIATIONS IN CHRYSOTILE ASBESTOS FIBERS REVEALED BY SYNCHROTRON X.RAY DIFFRACTION AND HIGH.RESOLUTION TRANSMISSION ELECTRON MICROSCOPY BARBARAA. CRESSEY Deprtment of Geology, {Jniversity of Southmpton, Southmpton, SO9 snh, U.K: GORDONCRESSEY Deprtment of Minerlogy, Nnrl History Museum, Inndon, SW7 5BD, U.K ROBERTJ. CERNIK SERC Dresbury lbortory, Wrrington, WA4 4AD, U.K. ABSTRACT Four smples of chrysotile sbestos hve been studied by synchrotron Xry diffrction. One of these smples exhibits symmetricl 00/ diffrction profiles, nd lso shows chrcteristics of "Povlentype" chrysotile in Xry fber photogrphs. The 001 pek symmetry is interpreted s indicting the presence of two lyerspcings, one bout 7.3 A, in common with the other chrysotile smples, nd one bout 7.2 A. TEM imges of the chrysotile with two ppxent lyerspcing show the presence of fibers with both curved nd flt lyers in vriety of disordered tubulr structffes hving only pproximte cylindricl symmetry. The flt lyers in these fibers my hve smller interlyerspcin S Q.2 A) reltive to the curved lyerspcing (7.3 A; becuse of the possibility of incresed hydrogen bonding between flt lyers tht re stcked in register with one nother. In this smple, fibers with flt lyers prllel to one direction only, joined t ech end by curved lyers re observed to occur commonly. Also present re fibers with polygonltube cores mde up from flt lyers, with outer lyers tht re curved in more norml wy. This type of structure ppers to be the closest tht hs been observed to the lterntive structurl model proposed by Middleton & Whittker (1976) for'?ovlentype" chrysotile. ln the sme specimen, cylindricl chrysotile fibers tht possess 5fold symmetry hve been imged, in which the lyer stcking is pprently in register rdilly t 15 points round the circumference, rising from the &/3 repet of the hydroxyl lyer. Keywords: chrysotile, "Povlentype" chrysotile, trnsmission electron microscopy, hydrogen bonds, symmetricl diffrctionpek. Sonnerc Qutre dchntillons de chrysotile ont fit l'objet d'une 6tude pr diffrction X vec un synchrotron comme source du ryonnement. Dns un de ces 6chntillons, qui possdde les trits de chrysotile de type '?ovlen" dns des clich6s de fibres, les profils de diffrction 001 sont sym6triques. L'sym6trie serit due I l pr6sence de deux espcements_ distincts entre les feuillets, un d'environ 7.3 A, en commun vec les utres 6chntillons de chrysotile, et l'utre d'environ7.2 A.I*s imges prises pr microscopie 6lectronique pr trnsmission montrent l pr6sence de fibres ynt d l fois des feuillets courbes et plts dns une vri6t6 de structures tubulires d6sordonn6es qui n'ont qu'pproximtivement l symdtrie cylindrique. Nous pensons que les feuillets plts dns ces fibres pounient voir un espcement interfeuillet plus petit (7.2 A) que les feuillets courbes (7.3 A) d cuse de l possibilit6 ccrue de liisons hydrogdne entre les feuillets plts, empil6s en registre les uns sur les utres. Dns cet 6chntillon, les fibres ynt les feuillets plts prllbles b une seule direction etjoints ux deux bouts pr des couches courbes sont trbs r6pndus. Sont ussi pr6sents des fibres ynt un centre tubulirc polygonl A feuillets plts, vec des couches extemes courbes de l fgon plus cournte. Ce type de structure semble se rpprocher le plus du moddle structurl lterntif propos6 pr Middleton et Whittker en 1976 pour expliquer le chrysotile de type "Povlen". Dns le mome 6chntillon, des fibres cylindriques de chrysotile poss6dnt un xe de sym6trie 5 ont 6t6 photogrphi6s dns lesquels I'empilement des couches serit en registre de fgon rdiire i 15 points repbres utour de l circonf6rence, cons6quence de l pdriode b/3 de l couche des groupes hydroxyles. (Trduit pr l R6dction) Motscl6s: chrysotile, chrysotile de type '?ovlen", microscopie 6lectronique pr trnsmission, liison hydrogdne, pic de diffrction sym6trique.
2 258 TIIE CANADIAN MINERALOGIST lntroducrron methods. More exmples of similr polygonl fibers, nd more complex structures with flt lyers stcked The cylindricl structure of chrysotile ws first in sectors, hve been observed in subsequent TEM estblished by Xry diffrction (Whitlker 1951, studies (Cressey 1979, Wei & Shoying 1984, Mellini 1952,1953,1.954,1955, b, c, d, 1956,b, c,1957). 1986, Yd & Wei 1987, Mitchell & Putnis 1988). The tubulr morphology of chrysotile ws imged by Other, irregulr structures involving curled lyers trnsmission electron microscopy (TEM) by vrious pssing lterlly into flt lyers hve been recorded, workers in the 1940s nd 1950s, but cler confirmtion tht the tubulr morphology is formed by cylin Hutchison (1984). e.8., by Veblen & Buseck (1979) nd Cressey & dricl lttice ws provided by highresolution TEM In this study, we show how modem highresolution (Yd L967,1971). In his microgrphs, the 7.3 A diffrction nd imging techniques (synchrotron Xry (002) lttice fringes show tht the sheets re curved s diffrction nd trnsmission electron microscopy) single or multiple spirls or s concentric cylinders. hve provided new evidence on the nture of curvedlyer nd fltlyer structures in fibrous serpentines. [The fringes corresponding to individul lyers index s (002) becuse twolyer cell (c = 14.6 A) is usully used for clinochrysotilel. Rdil 4.5 A (020) fringes E)cERMEl.rrAL lso were resolved; they re generlly not stright but zigzg in direction, s dditionl unit cells re incorported round the circumference with incresing sbestos from the collection of the Nturl History We hve investigted four smples of chrysotile rdius of the curved lyers. Some of the microgrphs Museum (Tble 1) by Xry diffrction using the lso show some unusul growthhbits, with irregulrly shped fibers tht seem to hve grown in stges. Dresbury Lbortory, Wrrington, U.K. These Synchrotron Rdition Source (SRS) t the SERC Xry nd electron diffrction ptterns produced by smples ll consist of bundles of fibers up to 4 cm splintery or lthlike vrieties of chrysotile, commonly long which, in hnd specimen, pper similr to mny known s "Povlentype" chrysotile, exhibit dffierences other (silky) chrysotile fibers, except tht specimen from the ptterns produced by fibers of "norml" 8M1929,t974 is more splintery thn most. (silky) chrysotile (Eckhrdt 1956, Zussmn et l. Synchrotron Xrdition is tuneble to chosen 1957, Krstnovic & Pvlovic 1964,1967). These wvelength nd is delivered s monochromtic, pt0ernshow series of shrp i&/ reflections on i odd highintensity, wellcollimted, nerprllel bem, lyer lines insted of, or superimposed on, the hk} nd thus instrumentl pek brodening is minimized. reflections with diffrrse tils chrcteristic of the cylindricl wrpping of the structurl lyers in chrysotile. peks tht re brodened becuse of the fine size of Consequently, lthough chrysotile specimens produce Middleton & Whittker (1976) studied diffrction the fibrils (generlly bout 150 A in dimeter;, resolution of the diffrction pttern is suffrciently good to ptterns produced by "Povlentype" chrysotile in detil nd concluded tht the extr reflections resulted enble observtion of subtle structurl vritions in the from polygonl tubulr structure, possibly with diffrction profiles. core of norml, cylindricl chrysotile. An lterntive Bundles of sbestiform chrysotile fibers 2G30 mm rrngement of polygonl core surrounded by cylindricl mteril lso ws proposed, but considered less horizontlly on the xis of the goniometer of Sttion long nd bout 0.5 mm in dimeter were mounted likely to occur. 9.1 of the SRS (Cernik& BushnellWye 1991). With By using trnsmission electron microscopy, count time of I second per step nd step size of Cressey & Zussmn (1976) observed fibers ofpolygonl se4rentine of the kind postulted by Middleton & DebyeSclerrer geometry from the sttionry bundles 0.01' 20, diffrction dt were recorded in Whittker. These polygonl fibers re composed of of fibers. In this orienttion of the cylindricl lttice, sectors of flt lyers rrnged to form polygonl only 001 nd 0ft0 reflections re observed. Thus prisms, either with or without core of cylindricl recorded, the Xry diffrction pttern of one of the chrysotile. All the polygonl fibers observed in crosssection using TEM hve unusully lrge fiber di chrysotile specimens (8M1929,1974) shows mrked meters (up to 2000 A) compred with norml chrysotile (generlly A in dimeter). "Povlentype" diffrction effects lso hve been observed in single chrysotile fibers of "norml dimeter" (up to 200 A) seen longitudinlly in the TEM TABTJ 1. SAMPLESOFCHRYSOULESTT]DIED (Middleton 1974),bt until now crosssections of normldimeter'?ov1entype" fibers hve never been EMLn9Jn4 Nil D spesdun ine, Zvishvne, Znbbrye 8M1924,429 Duros' mino, Zvishpsle, Zimbbwe observed. This my be becuse of the difficulties E,!},[7r29,2fi Sherbc&, Western Austrlis involved in obtining thin, electrontrnsprent crosssections of fibers by ionbem thinning or BMl974,l18 Cesit, Briti$ Cohmbi other
3 STRUCTURAL VARIATIONS IN CHRYSOTILE ASBESTOS FIBERS 259 symmetry of 00/ peks. To investigte further the cylindricl cmer using CuK rdition) of the significnce of this unusul symmetry in the pek, we chrysotile smple with two pprent lyerspcings hve exmined this specimen by highresolution TEM. shows chrcteristics of oopovlentype" chrysotile, l. e., Smples were vcuumimpregnted with epoxy resin, dditionl shrp reflections pper superimposed on nd then crosssections of these fiber bundles were cut the diffuse til of the 130 reflection. The other smples nd prepred for TEM by ionbem thinning. Thinned with single 00/ peks in their synchrotron Xry diffrction ptterns (corresponding to lyerspcing of smples were exmined in JEOL JEM 2000FX TEM, operting t n ccelerting voltge of 200 kv. pproximtely 7.3 A) hve fiber photogphs typicl of norml chrysotile. XN,qy frffrqrpn Figure 2 shows the symmetricl diffrction profiles, pek profile fits nd their residuls for the 004, The 004 diffrction profiles from the four smples 0012 nd 0016 reflections, recorded from chrysotile of chrysotile recorded using synchrotron rdition re 8M1929,1974 us,ing synchrotron rdition. A pseudoshown in Figure 1. Clerly, one of these smples Voigt function ws used to model the peks. Clerly, (8M1929,1974) shows distinct symmetry of the two peks re required to fit the min pek nd the 004 pek. Anlysis of this profile, using pek deconvolution procedure, suggests tht two lyerspcings centered bout vlues tht yield 7.3 I A nd 7.21 A for shoulderegion on the highngle side, nd these re (7.31 A nd7.2l A) my be present. Subsequently, the lyerspcing dom nd 0016 profiles lso were recorded; these show The profile fitting in Figure 2 ws constrined by t}le sme slmmetry with befter resolution. This symmetry of 001 peks ws not observed in ptterns from provides simple interprettion in terms of two llowing only two peks to contibute to the fit; this ny ofthe other chrysotile smples. In ddition, conventionl Xry photogrph (recorded on film in my be more complex, s vritions in distinct lyerspcings. However, the rel sitution lyerspcings 73L A hyer spcing 7.21, A lyer spcing 16.5 L7.A e(l:1.1019A) Frc. 1. Profiles of the 0M Xry diffrction pek recorded from sttionry smples of chrysotile fibers using synchrotron rdition. (A) 8M1929,1974:. (B) 8M1929,429; (C) BM1974,118; (D) BM1929,250.
4 260 THE CANADIAN MINERALOGIST etI= A) zo()=1.1019a) 2o 1) = l.m3 A) Ftc. 2. Synchrotron Xry diffrction profiles recorded from chrysotile 8M1929,1974, together with profile fits (solid lines) nd their residuls. In ech cse, two peks hve been used to fit the min pek nd the shoulder. Note the reltive decrese in the pekheight intensity of the shoulder with the incresing order of reflection. lntensities reltive to the 0M pek re indicted on the verticl scle. could occur, depending on the exct structure of the serpentine. Therefore, we lso hve performed fits with up to twelve peks with unconstrined widths. By fitting with multiple peks, it is pprentht the fine structure of the profiles cn be modeled in more detil, suggesting tht it my be pproprite to model these profiles with peks tht extend over rnge of dvlues corresponding to lyerspcings between 7.2 A nd 7.4 A. lt. is lso pprent tht greter spred of dvlues conributes to the shoulder region thn to the min pek. Modelling with multiple peks still wits quntittive nlysis of pek positions nd their widths, nd further work on this is in progress. However, qulittive ssessment of reltive pekwidths cn be mde. It is evident tht the reltive pekheight of the shoulder component (representing the 7.21 A lyerspcing) decreses lmost linerly with 1./d, nd this reduction in pek height is likely to integrl bredtl, nd 7 denotes the microstrin. We therefore drw the conclusion tht the serpeltine structure with the smller lyerspcing (7.21 A) is significntly more sffined. As this chrysotile specimen is known to possess "Povlentype" chrcteristics, it is likely tht curved nd flt lyer structures re present (Middleton & Whittker 1976, Cressey & Zussmn 1976). The observed strinbrodening is consistent with the hypothesis tht the structure of fltlyer serpentine is more strined thn tht of curvedlyer structure. In chrysotile, structurl curvture enbles prtil compenstion for the misfit between the sheets of octhedr nd tetrhedr. Presumbly, no such compenstion occurs in fltlyer serpentine, unless substntil Al3+ nd Fe3+ substitutions re present in the octhedrlly nd tetrhedrlly coordinted sites. Energydispersion Xry nlysis of chrysotile be due to pek brodening. Both pek components 8M1929,1974 in the SEM indictes the presence of (7.31 A nd 7.21 A; in the profile re brod, owing to only 1.5 tntclo Fe nd negligible Al. Structure refinements by Mellini (1982) nd by Mellini & Znzzi the smll size of the crystllites, but sizebrodening is independent of the order of reflection. However, (1987) show tht in lizrdite (flt lyers) the lyer of pek brodening tht rises from microstrin does tetrhedr is distor0ed to ditrigonl symmetry by rottion of tetrhedr to fcilitte incresed interlyer depend on the order of reflection, with pek bredth incresing s l/d increses. This hs been expressed hydrogen bonding, even though n undistorted hexgonl rrngement of the lyer of tetrhedr would by Lngford et l. (1988) s p = 4V124, where B is the be
5 STRUCTURAL VARIATIONS IN CHRYSOTILE ASBESTOS FIBERS 261 more likely to reduce the intrlyer misfit strin with nd the unexpected 7.2I A lyerspcings in the synchrotron XRD pttems, we hve sought explntions the lyer ofocthedr. Chisholrn (1992)hs discussed the effects of intrlyer nd interlyer strin on the for tfiese fetures by highresolution TEM. Our TEM totl strin ssocited with curved nd flt lyers in observtions of crosssections of these fibers revel serpentine; from this ssessment of strin, it cn be tubes mde up of curved nd flt lyers in disordered pprecited tht unless the fiber rdius of chrysotile is cylindricl structures, with only pproximte rottionl symmetry. We hve not, however, found ny lrge, either very smll or very lrge, curved structure is likely 10 possess less totl strin thn fltlyer polygonl fibers with clerly defined boundries structure. There is, however, no cler indiction in between sectors of flt pltes, such s those seen published cell prmeters tht smples of lizrdite previously in specimens of "Povlentype" chrysotile. generlly hve smller interlyer spcings thn Fibers tht most closely resemble the'?ovlentype" smples of cbrysotile. chrysotile imges previously published hve cores of flt or gently curving lyers. Curved sheets lck Elrc"rnox MrcRoscopy smooth, continuous cylindricl curvture but re Hving seen fetures of '?ovlentype" nnged with discontinuously curved sections which, chrysotile in like the flt sheets, form pproximtely polygonl singlecrystltype diffrction ptterns from specimen tubulr cores. Exmples re shown in Figure 3. The number 8M1929,1974, nd evidence of both 7.31 A lttice fringes re, unfortuntely, little fint becuse Frc. 3. TEM imge of chrysotile 8M1,929,1,97 4 with the bem prllel to the fiber xes, showing (002) lttice fringes. Note tht severl fibers hve polygonl cores mde up of flt lyers, with outer lyers tht re more smoothly curved,
6 262 TIIE CANADIAN MINERALOGIST Ftc. 4. Fiber sections recorded with the bem nerly prllel to the fiber xes. (A). These fibers hve elongte crosssections with stright (002) lttice fringes prllel to the elongtion. (020) fringes re visible in curved sections of some fibers. (B). A fiber from (A) showing (002) nd (020) fringes in opposite qudrnts, both prllel to the plne contining the {iber xis nd the bem. (C). A fiber from (A) showing (002) nd (020) fringes tht re not in exctly opposite qudrnts, nd the two fringe sets re not prllel to one nother.
7 STRUCTTIRAL VARTATIONS IN CHRYSOTILE ASBESTOS FIBERS 263 these fibers re in very thin re of the specimen. the ppernce of n ovl running trck. A typicl re Ionbem thinning lwys produces dmged, morphous surfcelyer. Adjcent to the edges of the holes shown in Figure 4. It is not possible to ccount for contining such elongte crosssections of fibers is produced by ionbem thinning, the very thin prts of such elongtion by ssuming tht the fiber xis is the specimen will therefore consist lmost entirely inclined to the electron bem; tilt of 60' would be of morphous mteril. The outer lyers of the fibers necessry to produce rtio of minor to mjor xis of in Figure 3 re prticulrly indistinct becuse they l:2, s is observed here. In ny cse, such tilt would hve lrgely become morphous, either during ionbem thinning or during exposure to the electron leve them on t}re curved ends, which is the opposite extinguish the (002) fringes on the long sides nd bem. Howevero the outer lyers, where visible, of wht we observe. pper to be curved in more norml wy. These In the re shown in Figure 4, (002) fringes (concentric or spirl) re generlly less cler round the structures seem to be the closest tht hve been observed to the lterntive model of tle structure proposed by Middleton & Whittker (1976) for "Povlen suffer dmge under the electron bem less quickly curved prts of fiber sections. The flt lyers seem to type" chrysotile. We hve found them occurring only thn the curved prts. Commonly, (020) fringes (from very infrequently in the electrontrnsprent prts of center to circumference) re visible in the curved this specimen. sections insted. If there is slight mislignment of We hve, however, observed nother structure the fiber xis with respect to the electron bemn then involving flt nd curved sheets in fibrous hbit in the (020) nd (002) fringes would tend to persist in this specimen. In the thinned res exmined, it occurs lternte qudrnts, nd both sets of fringes would with firly high frequency. Fibers of this type consist be prllel to the plne contining the fiber xis nd of flt lyers prllel to one direction only, joined the bem. Generlly, this ppers to be the cse in coherently t ech end by curved lyers, resembling Figure 4 (e.9., Fig. 4B), where the xes of elongtion o02 F==r t >eerc  >+Jr< t  ' l '  t t .t I t t ' t t FIc. 5. A cylindricl rry of ltrice points (fter Whittker 1955b) joined in such wy s to representhe lnice fringes shown in Figure 48. Note, however, tht in Figure 4 the (002) fringes re mostly stright, not curved s here, becuse the fiber is ovl in crosssection. not circulr.
8 264 TIIE CANADIAN MINERALOGIST hppen to be roughly prllel to the plne contining the fiber xes nd the bem. It should be noted tht (020) fringes re not truly rdil, or they would diverge from the center with dditionl unit cells dded round the circumference s the rdius of the curved lyer increses, givitrg the zigzg ppernce shown by Yd (1971). In Figure 4, the (020) fringes re generlly stright nd eqully spced over considerble res, to fir degree of pproximtion, though there re some deprtures. Whittker (1955b) used msk for opticl diffrction in which the dots lined up over considerble res. In Figure 5, section of Whittker's cylindricl msk is reproduced, with lttice points joined up in such wy s to resemble the distribution of (020) nd (002) fringes tht we observe. In Figure 4, some sections (e.g., Fig.4C) show cler (020) nd (002) fringes tht re not strictly in lternte qudrnts, nd (020) fringes re not prllel to (002) fringes. This suggests tht the position nd orienttion ofthe plnes where the points of the circulr (or distorted circulr) lttice line up with ech otler need not be in lternte qudrnts. It seems resonble tht they could esily be offset by up to 36o from the obvious positions, i.e.n the ngle between the cler (002) nd (020) fringes could be nything up to this ngle, nd not constnt from center to circumference, s ppers to be the cse in some of the fiber sectionshown here. Not ll fibers re elongte in crosssection with flt lyen. Some re elongte but consist of curved sheets with vrible rdii of curvture, prticulrly in the core regions, nd others re more nerly circulr in section. Multilyer spirls lso re found firly commonly. A few exmples re shown in Figure 6. Boundries between fibers commonly re indistinct, with spces between fibers filled by morphous or Ftc. 6. Fiber sections exhibiting vrious growth irregulrities, including vrible rdii of curvture nd multilyer spirls. 2[H
9 STRUCTI]RAL VARIATIONS IN CHRYSOTILE ASBESTOS FIBERS 265 poorly crystlline mteril, or curved sheets. Centrl hs implictions concerning the nture of the interlyer bonding in this specimen, it is lso described voids in fibers re commonly filled with similr mteril, nd some fibers hve very irregulrly shped here. but continuous sheets in the core regions, which my Where fibers re exctly prllel to the bem, diffrction contrst mkes them pper completely drk. bridge the centrl holes. Whittker (1957) suggested tht such infilling would be likely, nd would explin With incresed exposure to the electron bem, the the observed mesurements of density. It is not drk contrst breks into rdil bnds, with the diffrction contrst being lost from the outside edge fust nd possible to know how much of the mteril with no pprent structure ws originlly morphous nd how extending towrd the center with time. Figure 7 shows much hs become so becuse of dmge in the electron bem or during specimen preprtion. culr in section. Drk diffrctioncontrst remins exmples of this behvior. In this req fibers re cir In prts of the specimen tht re thicker, combintion of strong diffrctioncontrst nd degree of the fringes dispper s these res become mor where (002) fringes re clerly visible nd fdes where dmge under the electron bem shows pttern tht phous under the bem. There re lmost lwys indictes the existence of fivefold symmetry. This 15 rdil bnds; the number 15 is significnt. As frst demonstrtion of fivefold symmetry in nfurl pointed out by Whittker (1954),2n d*, is pproximtely equl to 5b, so tht ifnvo successive lyers re crystlline mteril hs been reported elsewhere (Cressey& Whittker 1993). Becuse this observtion in step with one nother somewhere, then they will be ftc. 7. Sections of fiben with their xes exctly prllel to the bem. Strong diffrctioncontrst. which initilly mde the fiber sections pper completely drk, hs broken into 15 rdil bnds fter period of exposure to tle electron bem hs cused some of the structure to become momhous.
10 266 TT{E CANADIAN MINERALOGIST..\... r i"'..f. ;.'\'...ot.. Ol r I O,.A.r oo l 7'o. to. ^v 'l6or oo^ t^. "oo "or in step five times round the circumference of the fiber. If ll the lyers re in step on rdil plne, then they re ll in step five times. In Figure 8, we reproduce Whittker's msk, mrking with open circles those lttice points tht line up rdilly. On the msk, the liningup occurs ten times round the circumference becuse the lttice points re seputedby blt to llow for the effect of projection of the centered unitcell down. [This is, of course, why we lwys observe (020) fringesl. If the structure were more susceptible to decomposition under the electron bem where the lyers re out of step, then one could produce n effect similr to tht in Figure 7, but with only five spokes. However, the hydroxyl side of the serpen llto looo ollro lo! oo l lf tt I.t' j O+O+ o.o.o ' FIo. 8. A cylindricl rry of lnice points (fter Whitrker 1955b), representing projection of ttre chrysotile lttice in crosssection. The points re sepxted cicumferentilly by b/2 to llow for the effect in projection of the centered unitcell down, nd those mrked with open circles re rows of points tht exctly line up rdilly, ien tirnes in projection. Note tht lternte rows of open circles represent lnice points t height zero nd /2, so the overll symmetry is fivefold. Ticks with circumferentil spcing of l/3, to representhe repet of the hydroxyl side of the serpentine lyer, re shown for successive serpentine lyers in one of the five sectors. Solid lines represent the 15 rdil positions (rising from the bl3 repet of the hydroxyl groups) where locl sirnilrity of structure between the hydroxyl groups of one lyer nd the bsl oxygen toms of the next lyer outwrd could llow hydrogen bonding to occur between successive lyers, tine lyer hs repet of only bl3, so there is locl similrity of the rrngement of the bsl toms of oxygen of one lyer with respect to hydroxyl groups of the next inwrd 15 times per circumference. These 15 positions re mrked on the digrm in Figure 8. The res between these 15 spokes, where lyers re out of step nd so hydrogen bonding between lyers is not possible, could well produce 15 rdil bnds where decomposition under electron bombrdment tkes plce more redily, s seen in Figure 7. Chisholm (1.992) hs pointed out tlt polygonl serpentine lmost lwys hs 15 sectors (or, less commonly, 30), becuse miniml misfit occurs only for polygonl microstructures with 15 or 30 sectors,
11 STRUCTURAL VARTATIONS IN CHRYSOTILE ASBESTOS FIBERS 267 depending on the exct cell dimensions of the flt comes from serpentinite tht hs undergone progrde lyers. A close inspection of Figure 7 suggests tht metmorphism fter the initil serpentiniztion. The possibly, in some fiber crosssections, the (002) lyers polygonl fiber shown in Cressey & Zussmn re not smooth, continuous curves. In the bnds where (1976,Fig.4) ppers to hve overgrown erlierformed cylindricl fibers of chrysotile. A high less decomposition hs occurred (i.e., those regions where successive lyers re probbly more nerly in resolution microgrph of nother polygonl fiber from step with one nother), the lyers my seem to be the sme specimen, shown in Figure 9, shows tht fltter. (Cre must be tken not to mistke confist lyers re mostly coherent cross sector boundries. reversls long lyer for discontinuities of curvture). Possibly, under the right geologicl conditions, core. the sheets seem to be somewht disordered in This microgrph lso shows tht in the cylindricl fibers such s these could recrystllize to form lrge, comprison with the outer, flt lyers. These observtions re in ccord with our proposed mechnism for welldeveloped polygonl fibers similr to ttrose seen in previous TEM studies, with 15 sectors, s discussed the formtion of polygonl fibers by recrystlliztion, by Chisholm. Such recrystlliztion would increse involving n djustment of the interlyer stcking the extent to which sheets could be stcked in register from disordered to more ordered rrngement. The with one nother. For lrgerdius fibers, this would fiber section is not complete polygon, nd in the be much more stble mngement, s pointed out by missing prts where the sheets re not constrined, Chisholm (1992). they tend to curl. These curved sections hve smll The specimen in which Cressey & Zussmn (1976) rdii of curvture, similr to the norml, cylindricl originlly found high proportion of polygonl fibers fibers. 200 &: rs* Figure 94
12 268 THE CANADIAN MINERALOGIST Fto. 9. Highresolution TEM imge of polygonl serpentine fibeg specimen (see Cressey & Zussmn 1976). (A) The whole fiber section nd (B) enlrged deil from prt of (A), showing flt lyers pssing coherently cross sector boundries nd continuirg llerlly into curved sheets. Note lso the degree of disorder between lyers in curved sheets ner the fiber center. Where fiben re slightly tilted with respect to the electon bem, then the (020) nd (002) fringes tend to persist in lternte qudrnts, s described bove. Such degree of mislignment gives rise to four rdil drk bnds of diffrction contrsto replcing the complete drkness or mny (generlly 15) bnds seen where lignment of the fiber xis with the bem is more perfect. With slightly more mislignment, or greter dmge under the electron bem, or both, the (020) fringes tend to dispper, leving only the (002) fringes nd one pir of drk diffrctioncontrst bnds t 180o. This pttern of diffrctioncontrst behvior with tilt ws noted by Cressey & Zussmn (1976), though t tle time there ws no evidence to explin why it hppens. DIscussIoN From the split (00/) reflections observed in the synchrotron diffrction profile of specimen 8ML929,L974, two lyerspcings pper to be present. One is 7.31 A, bout the vlue normlly found for chrysotile, nd the other is bout 7.21 A. Electron microscopy suggests tht the most obvious difference between this nd other chrysotile specimens is the presence of substntil numbers of fibers with flt lyers in this specimen. It ppers tht the flt lyen in mny of the fibers hve smller interlyerspcing becuse of the hydrogen bonding developed between flt lyers tht re stcked in register with one nother. In cylindricl lyers of chrysotile, microgrphs such s
13 tht shown by Yd (l97l,fig. 14) illustrte fiben in which lyers re stcked completely rndomly, out of register with one nother. In the cylindricl fibers shown in this pper, the lyer stcking is pprently in register t fifteen points round the circumference, but t ll other positions the lyers must be stcked out of register with one nother. In cylindricl fibers, therefore, hydrogen bonding between lyers is not generlly possible. Published vlues for the lyerspcings of chrysotile nd lizrdite, the fltlyer vriety of serpentine, suggest tht there is rnge of vlues from little bove 7.2 A le.s., A for " lizrdite reported by Mellini (1982)l to over 7.3 A. However, there is no cler pttern of lizrdite tending towrd the lower vlue nd chrysotile the higher. Lizrdite commonly hs significnt degree of disorder in its structure, nd commonly contins more AI nd Fe thn chrysotile. When we study ionthinned specimens by TEM, it is inevitble tht we cn only imge tiny proportion of the mteril in ny specimen. This is especilly true for sections of sbestos fibers embedded in resin; the vst mjority of the res thinned to electron trnsprency consist of the resin. Therefore, we cn never STRUCTT.JRAL VARTATIONS IN CHRYSOTILE ASBESTOS FIBERS 269 be sure of the extent to which our TEM observtions re representtive of the whole specimen. Xry diffrction, however, gives us informtion verged over much lrger volume. We cnnot sy with confidence tht in specimen 8M1929,1974, the proportion of flt lyers reltive to curved lyers seen in the TEM corresponds with the rtio of 7.21 A to 7.31 A lyerspcing detected by Xry diffrction, but the com serpentine. Cn. Minerl. 30, CrilsHou\4, l.e. (1992): The number of sectors in polygonl prison seems resonble, s fr s we cn judge. It would be interesting to crry out synchrotron Xry Cnssssv, B.A. (1979): Electron microscopy of serpentinite diffrction experiments on fiber bundles consisting textures. Cn. Minerl. 17, 74l756. entirely of wellformed polygonl serpentine if sufficiently lrge bundles of long, prllel fibers could be & HrncilsoN, J.L. (1984): Microstructure of ntigorite reveled by high resolution electron microscopy. found. Inst. Pltys. Conf., Ser. 68, In specimen 8M1929,1974, the elongtesectioned fibers tend to be ligned with the xes of elongtion ll & Wnrrrrsn, E.J.W. (1993): Fivefold symmetry in roughly the sme direction. Possibly these fibers in chrysotile sbestos reveled by unsmission electron suffered directionl pressure during growth, or lter microscopy. Minerl. Mg. 57, deformtion while still in the host rock. The possibility of deformtion during specimen preprtion & ZussrrN, J. (1976): Electron microscopic studies must be considered, but it seems more likely tht such of serpentinites. Cn. Minerl. 14,307'3I3. processes would cuse brittle frcture rther thn plstic deformtion. We hve seen no evidence of ECKHARDT, F.J. (1956): Rd,ntgenogrphische Untersuchungen m Schweizerit. Neues Jhrb. Minerl' broken fibers. Moruttsh,3243. Our findings show, yet gin, tht the serpentine group of minerls cn form in numerous complex structurl rrngements tht my seem difficult to clssify. Imging by highresolution TEM shows tht, on fine scle, the structtues commonly consist of mixtures or intermedite forms. Lyers commonly pss coherently from one structure type to nother over few unit cells. Nevertheless, ll the observed vritions cn be described s consisting of components of the three known structure types: cylindricl chrysotile, fltlyer lizrdite or lterntingwve ntigorite. A single fiber my therefore consist of both chrysotile nd lizrdite. Trnsitions from one structure type to nother occur s the best solution to the prblems cused by interlyer nd intrlyer sgin.t ihe time of crystlliztion (or recrystlliztion) in response to the locl physicochemicl conditions ffecting ech group of toms. Most serpentinites hve been formed under disequilibrium conditions, so perhps it should not seem surprising to find tht io ny composite or intermedite structures exist. ACIC.IOWI.EDGEIVIEI.ITS We thnk Dr. Eric Whittker nd Prof. Jck Zussmn for helpful comments on our observtions, kindly shring with us their considerble wisdom nd experience of the serpentine minerls. The referees re lso thnked for their comments nd suggestions. Mr. Tony Wighton, Nturl History Museum, is thnked for producing excellentqulify demountble polished thin sections of chrysotile. We cknowledge funding by SERC glnt to crry out the synchrotron Xry diffrction experiments. REFERENCES CERNIK, R.J. & BusuNrLLWYE, G. (1991): The use of DebyeScherrer geometry for high resolution powder diffrctton. Mter. Sci. ForurnT9'\z' KnsreNovtd, I. & PAvLovlC, S. (1964): Xry study of chrysotile. Ant Minerl. 49, &  (1967): Xry study of sixjyer orthoserpentine. Am. Minerl 52, LeNcrono, J.I., Dnlusz, R., pr KstrsnR' T.H. & MttrnvrEunn, E.J. (1988): Profile nlysis for microcrystlline properties by the Fourier nd other methods. Azst J. Phys.4l,
14 270 THE CANADIAN MINERAIOGIST MELLINTT, M. (1982): The crystl structure of lizrdite lt: hydrogen bonds nd polytypism. Am. Minerl. 67, (1986): Chrysotile nd polygonl serpenrine from the Blngero serpentinite. M inerl. Mg. 50, & Zyezzt, P.F. (1987): Crystl structures of lizrditelt ndlizrdite2hi from Coli. Itlv. An. Minerl. 72, MIDDLEToN, A.P. (1974): Crystllogrphic nd Minerlogicl Aspects of Serpentine. D.Phil. thesis, Oxford Univ., Oxford, U.K. & Wurrrerrn, E.J.W. (1976): The structure of Povlentype chrysotite. Cn. Minerl. 14, Mncurl4 R.H. & Punrs, A. (1988): Polygonl serpentine in segregtiontextured kimberlite. Cn. Minerl. 26, VEBLEN, D.R. & Busncr<, P.R. (1979): Serpentine rninerls: intergtowths nd new combintion stmctures. Science Wst, L. & SueovrNc, J. (1984): The discovery of Povlentype hydroxylchrysotile nd its minerlogy. Act Minerl. Sinic2. I lll16. WHrrrrcn, E.J.W. (1951): An orthorhombic vriety of chrysotile. Acl Crystllogr. 4, (1952): The unir cell of chrysotile. Acr C rystllogr. 5, , (1953): The structure of chrysotile. Acr Crystllogr. 6, i 48. (1955b): The diffrction ofxrys by cylindricl l^ttice. m. Act Crystllogr. 8, (1955c): The diffrction of Xrys by cylindricl l^ttice. IV. Act Crystllogr. 8, (1955d): The clssifiction of cylindricl lttices. Act C ry stllogr. 8, _ (1956): The structure of chrysotile. II. Clinochry sotile. Act C rystllo gr. 9, (1956b): The structure of chrysotile. III. Orthochry sotile. Act Crystllogr. 9, , (1956c): The structure of chrysotile. IV. Prchrysotile. Acr Crystllogr. 9, (1957): The structure of chrysotile. V. Diffuse reflections nd fibre textlure. Act Crystllogr. 10, Yoe, K. (1967): Study of chrysotile sbestos by high resolution electron microscope. Act Crystllogr. 23, (1971): Study of microstructure of chrysotile sbestos by high resolution electron microscopy. Acr C ry sr I I ogr. M & Wr, L. (1987): Polygonl microstructures of Povlen chrysotile observed by high resolution electron microscopy. Eurocly 87 (Sevill, Spin), Abst. ZussMAN, J., BnrNnrsv, G.W. & Cousn, J.J. (1957): Electron diffrction studies of serpentine minerls. Am. Minerl. 42, (1954): The diffrction of Xrys by cylindricl Ittice.I. Act Crystllogr. 7, (1955): The diffrction ofxrys by cylindricl ltt\ce. II. Act C rystllo g r. 8, Received Apil 7, 1993, revised mnuscript ccepted Augu.st
Graphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationPlotting and Graphing
Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured
More informationThe Velocity Factor of an Insulated TwoWire Transmission Line
The Velocity Fctor of n Insulted TwoWire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationHCP crystal planes are described using the MillerBravais indices, (hkil) Draw the hexagonal crystal planes whose MillerBravais indices are:
.6 How re crystllogrphic plnes indicted in HCP unit cells? In HCP unit cells, crystllogrphic plnes re indicted using four indices which correspond to four xes: three bsl xes of the unit cell,,, nd, which
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationDiffraction and Interference of Light
rev 12/2016 Diffrction nd Interference of Light Equipment Qty Items Prt Number 1 Light Sensor CI6504 1 Rotry Motion Sensor CI6538 1 Single Slit Set OS8523 1 Multiple Slit Set OS8523 1 Liner Trnsltor
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationaddition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.
APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The
More informationSection 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables
The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine soclled volumes of
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationOBJECTIVES PRELECTURE
69 L5 DIFFRACTION Aims OBJECTIVES From this chpter you should gin n understnding of the process of diffrction nd its role in producing distinctive interference ptterns. You should lso im to understnd how
More informationAAPT UNITED STATES PHYSICS TEAM AIP 2010
2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS  75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD
More informationNet Change and Displacement
mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the
More informationAn OffCenter Coaxial Cable
1 Problem An OffCenter Coxil Cble Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Nov. 21, 1999 A coxil trnsmission line hs inner conductor of rdius nd outer conductor
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments  they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in pointdirection nd twopoint
More information14.2. The Mean Value and the RootMeanSquare Value. Introduction. Prerequisites. Learning Outcomes
he Men Vlue nd the RootMenSqure Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationN Mean SD Mean SD Shelf # Shelf # Shelf #
NOV xercises smple of 0 different types of cerels ws tken from ech of three grocery store shelves (1,, nd, counting from the floor). summry of the sugr content (grms per serving) nd dietry fiber (grms
More information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is soclled becuse when the sclr product of two vectors
More informationSymmetry in crystals National Workshop on Crystal Structure Determination Using Powder XRD
Symmetry in crystls Ntionl Workshop on Crystl Structure Determintion Using Powder XRD Muhmmd Sbieh Anwr School of Science nd Engineering Lhore University of Mngement & Sciences (LUMS) Pkistn. (Dted: August
More informationElectric Circuits. Simple Electric Cell. Electric Current
Electric Circuits Count Alessndro olt (74587) Georg Simon Ohm (787854) Chrles Augustin de Coulomb (736 806) André Mrie AMPÈRE (775836) Crbon Electrode () Simple Electric Cell wire Zn Zn Zn Zn Sulfuric
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationLet us recall some facts you have learnt in previous grades under the topic Area.
6 Are By studying this lesson you will be ble to find the res of sectors of circles, solve problems relted to the res of compound plne figures contining sectors of circles. Ares of plne figures Let us
More informationWhy is the NSW prison population falling?
NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationUnit 29: Inference for TwoWay Tables
Unit 29: Inference for TwoWy Tbles Prerequisites Unit 13, TwoWy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
More informationWeek 11  Inductance
Week  Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 12015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
More informationTheories of light and Interference S BALASUBRAMANYA SGL IN PHYSICS SARVODAYA PU COLLEGE, TUMKUR Important paints
Theories of light nd nterference S BALASUBRAMANYA SGL N PHYSCS SARVODAYA PU COLLEGE, TUMKUR mportnt pints Theories of Light Newton s Corpusculr theory (1675) Christin Huygen s Wve theory (1678) Mxwell
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationPHY 140A: Solid State Physics. Solution to Homework #2
PHY 140A: Solid Stte Physics Solution to Homework # TA: Xun Ji 1 October 14, 006 1 Emil: jixun@physics.ucl.edu Problem #1 Prove tht the reciprocl lttice for the reciprocl lttice is the originl lttice.
More informationChapter G  Problems
Chpter G  Problems Blinn College  Physics 2426  Terry Honn Problem G.1 A plne flies horizonlly t speed of 280 mês in position where the erth's mgnetic field hs mgnitude 6.0µ105 T nd is directed t n
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationTheory of Forces. Forces and Motion
his eek extbook  Red Chpter 4, 5 Competent roblem Solver  Chpter 4 relb Computer Quiz ht s on the next Quiz? Check out smple quiz on web by hurs. ht you missed on first quiz Kinemtics  Everything
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, crossclssified
More informationOn the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding
Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl
More informationSquare Roots Teacher Notes
Henri Picciotto Squre Roots Techer Notes This unit is intended to help students develop n understnding of squre roots from visul / geometric point of view, nd lso to develop their numer sense round this
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationIntroduction to Mathematical Reasoning, Saylor 111
Frction versus rtionl number. Wht s the difference? It s not n esy question. In fct, the difference is somewht like the difference between set of words on one hnd nd sentence on the other. A symbol is
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationImpact Testing. Ductile to Brittle Transition in Steel. Charpy Test. Outline. Impact Testing
Impct Testing Outline Impct Testing Chrpy Test Ductile to Brittle Trnsition Temperture Metllurgicl Fctors Affecting T T Ftigue Ftigue Testing Types of Ftigue Chrpy nd Izod tests mesure impct energy or
More informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More informationAnswer, Key Homework 8 David McIntyre 1
Answer, Key Homework 8 Dvid McIntyre 1 This printout should hve 17 questions, check tht it is complete. Multiplechoice questions my continue on the net column or pge: find ll choices before mking your
More informationLecture 3 Basic Probability and Statistics
Lecture 3 Bsic Probbility nd Sttistics The im of this lecture is to provide n extremely speedy introduction to the probbility nd sttistics which will be needed for the rest of this lecture course. The
More informationHow the relationship between wood density and shrinkage depends on the microstructure of the cell wall
How the reltionship between wood density nd shrinkge depends on the microstructure of the cell wll Klmn Schulgsser* nd Alln Witztum Deprtment of Mechnicl Engineering Deprtment of Life Sciences BenGurion
More informationt 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam
Cndin Assocition of Physicists 1999 Prize Exm This is three hour exm. Ntionl rnking nd prizes will be bsed on student s performnce on both sections A nd B of the exm. However, performnce on the multiple
More informationPROBLEMS 13  APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS  APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
More informationChapter Outline How do atoms arrange themselves to form solids? Types of Solids
Chpter Outline How do toms rrnge themselves to form solids? Fundmentl concepts nd lnguge Unit cells Crystl structures Fcecentered cubic Bodycentered cubic Hexgonl closepcked Close pcked crystl structures
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More informationDouble Integrals over General Regions
Double Integrls over Generl egions. Let be the region in the plne bounded b the lines, x, nd x. Evlute the double integrl x dx d. Solution. We cn either slice the region verticll or horizontll. ( x x Slicing
More informationTITLE THE PRINCIPLES OF COINTAP METHOD OF NONDESTRUCTIVE TESTING
TITLE THE PRINCIPLES OF COINTAP METHOD OF NONDESTRUCTIVE TESTING Sung Joon Kim*, DongChul Che Kore Aerospce Reserch Institute, 45 EoeunDong, YouseongGu, Dejeon, 35333, Kore Phone : 824286231 FAX
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nmwide region t x
More informationClassification of Solid Structures
Clssifiction of Solid Structures Represents n tom or molecule Amorphous: Atoms (molecules) bond to form very shortrnge (few toms) periodic structure. Crystls: Atoms (molecules) bond to form longrnge
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More information4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A
Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter
More informationChapter 1 : Genetics 101
Chpter 1 : Genetics 101 Understnding the underlying concepts of humn genetics nd the role of genes, behvior, nd the environment will be importnt to ppropritely collecting nd pplying genetic informtion
More informationReview Problems for the Final of Math 121, Fall 2014
Review Problems for the Finl of Mth, Fll The following is collection of vrious types of smple problems covering sections.,.5, nd.7 6.6 of the text which constitute only prt of the common Mth Finl. Since
More informationSo there are two points of intersection, one being x = 0, y = 0 2 = 0 and the other being x = 2, y = 2 2 = 4. y = x 2 (2,4)
Ares The motivtion for our definition of integrl ws the problem of finding the re between some curve nd the is for running between two specified vlues. We pproimted the region b union of thin rectngles
More informationTHERMAL EXPANSION OF TUNGSTEN
. THERMAL EXPANSION OF TUNGSTEN S515 By Peter Hidnert nd W. T. Sweeney ABSTRACT This pper gives the results of n investigtion on the therml expnsion of tungsten (99.98 per cent) over vrious temperture
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationTests for One Poisson Mean
Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution
More informationMATLAB: Mfiles; Numerical Integration Last revised : March, 2003
MATLAB: Mfiles; Numericl Integrtion Lst revised : Mrch, 00 Introduction to Mfiles In this tutoril we lern the bsics of working with Mfiles in MATLAB, so clled becuse they must use.m for their filenme
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More informationSection 74 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 74 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationANALYSIS OF THERMAL STRATIFICATION IN THE PRIMARY CIRCUIT WITH THE CFX CODE
ANALYSIS OF THERMAL STRATIFICATION IN THE PRIMARY CIRCUIT WITH THE CFX CODE Ildikó Boros, Dr. Attil Aszódi Budpest University of Technology nd Economics, Institute of Nucler Techniques Abstrct The therml
More informationData replication in mobile computing
Technicl Report, My 2010 Dt repliction in mobile computing Bchelor s Thesis in Electricl Engineering Rodrigo Christovm Pmplon HALMSTAD UNIVERSITY, IDE SCHOOL OF INFORMATION SCIENCE, COMPUTER AND ELECTRICAL
More informationChapter 6 Solving equations
Chpter 6 Solving equtions Defining n eqution 6.1 Up to now we hve looked minly t epressions. An epression is n incomplete sttement nd hs no equl sign. Now we wnt to look t equtions. An eqution hs n = sign
More informationr 2 F ds W = r 1 qe ds = q
Chpter 4 The Electric Potentil 4.1 The Importnt Stuff 4.1.1 Electricl Potentil Energy A chrge q moving in constnt electric field E experiences force F = qe from tht field. Also, s we know from our study
More informationDispersion in Coaxial Cables
Dispersion in Coxil Cbles Steve Ellingson June 1, 2008 Contents 1 Summry 2 2 Theory 2 3 Comprison to Welch s Result 4 4 Findings for RG58 t LWA Frequencies 5 Brdley Dept. of Electricl & Computer Engineering,
More informationWarmup for Differential Calculus
Summer Assignment Wrmup for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:
More informationApplications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
More informationPolygons, Pingos, and Thermokarst! Oh my!
Polygons, Pingos, nd Thermokrst! Oh my! Overview: Ares underlin with permfrost exhibit common fetures due to freezing nd thwing in such res. Ice wedge polygons, pingos, nd thermokrst re some of the most
More informationVolumes of solids of revolution
Volumes of solids of revolution We sometimes need to clculte the volume of solid which cn be obtined by rotting curve bout the xxis. There is strightforwrd technique which enbles this to be done, using
More informationIncreasing Q of Waveguide PulseCompression Cavities
Circuit nd Electromgnetic System Design Notes Note 61 3 July 009 Incresing Q of Wveguide PulseCompression Cvities Crl E. Bum University of New Mexico Deprtment of Electricl nd Computer Engineering Albuquerque
More informationRational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and
Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions
More informationHomework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.
Text questions, Chpter 5, problems 15: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed
More informationBiostatistics 103: Qualitative Data Tests of Independence
Singpore Med J 2003 Vol 44(10) : 498503 B s i c S t t i s t i c s F o r D o c t o r s Biosttistics 103: Qulittive Dt Tests of Independence Y H Chn Prmetric & nonprmetric tests (1) re used when the outcome
More informationCurve Sketching. 96 Chapter 5 Curve Sketching
96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationConic Sections. The coefficient of x 2 is positive, so the parabola opens. y up. The vertex is the lowest point on the parabola, or
SECTION. Conic Sections SECTION. Conic Sections OBJECTIVE A To grph prol The conic sections re curves tht cn e constructed from the intersection of plne nd right circulr cone. The prol, which ws introduced
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More information