Ic" ,I.."..."...,...,.."., " ,I..,..,"."., \',..,..,...:~..~..I.\,.., tl.i., "...1""".";1"\.,..1.,,,,,,'1',,-1 """"""""".1

J..'I"'\I,"."."I.I"'II'.\~I'I~"'.:II..\'..:I'('I.;:I;.'.:24.I;CIIIIIII!lIii,

The Zero Point of Charge of Calcite

I". RO~[.\'~UXJ).\I{"\X A~D (; I~. A(:,\lt

lnl,-rllal;"nal Mirll"rfll... .t- Chclnil"al Corporation. Grolcth Scicncc.~ Cc:nlcT, Libcr/!Inlle, lliinoiJi 6001,8

I1f'('('ivcd ~ovf'ml)Cr 28, ]!)(ill; revi.'!Ctl Jullu:1ry 16, 1967; revised March 3, 1967

TI,t~ zcrt. ",.illt tlf loharl:c (ZPC) tlf cILlcile \\°1&8 illvcsligatcd by mea.~uring theI'trc:lmill~ 1)Cllclllial, !ltIIUlioll equilitlrillm, ILnd fu)t:\tion ~ponse as a function or"nllltiUII plio Th~ ZPC "":\1\ ~h(\\\"11 to lie ~'itllin thc range of pil 8 to 9.5.

Th..rmlKIYllanlic CILlcm:lLioll of lhc SOlllliulI equilibrium suggests that tile poten-ti:,I-Jclcrmillilllt, i"11S ure Cu1-+. IICO,-. CO;-. H+. and 011-.

Mechalli.~nlS uf clI:Lrge dcveloplllcnt. ilL Iohe calcite-water interfacc are discu.qsed."'h,' "rcf~rellli:11 hydruly...is of sIIrfacc iollS or tbc adsorpti()n. at thc intcrfnce. of tilet~ompl~xcs foMlled ill ROlllti()n aplJC:lrs tn pIlL}" an import:llit part in cst:lblishing thesllrfure chlLrge. s.,llllinns \\ilh all initial pH near thc isoclectric point. showed acllunge in zcl:l polellti:tl :Uld pH initia.lly in one direction and laler in the oppositcdircclion. !illggc.o;ting lbala combination of fast and slow reactions is responsible forthc charge dcvclopmcnt at the interface.

.>

INTROl>UCTION

KIIII\Ol'<lgC of the pl"flpcrtics uC the 5(lliu-li<luid illtl'rC:lcc is IICCl'f's"'\ry tQ ullderst:uldillll'rC:lci:11 phCIIOmt'II:L ~tI<:h liS flocculati<m,nds~fJll ifIll, :LIIU (JUl.ltiun. Thc intcrfuci:1lPl'lllll'rtil'~ Ilf ~implc Ilxiue:'i and silic~Lt~ illSOlllt illil II:IV(~ IX'CII stuuil'<1 in detail, but!ittlc \vork h:l.,; lx-en d(IIIC ,\-ith salt.-tYIJCJI1inc~r:ll." !'I:('II :I~ (~:llcitc to tllldel'J;t:lJld thc'm<:t:b:lllixill Ilf cll:trgc dcvcllllJfilCllt .It. thcilltl~rf:I(~C. :\llllllu~h thc 5()!llbilily Qf c:LI(~itch:L." I){~'II :o;lllui~ ,viue!y (1-5), fc\v clcc.-trtlkillet.i(~ ~luuil's h:LVl~ 1)(,'(.'11 m:lde to de.tenllill(' jllc zcta IIIIU'llti:LI (G, 7), alld olleC:lllllllt Ilut:lill thc ZCI"<I 1)(lillt uf churKefl'fll\l t.Jlt':o;l~ ctt'("trt Ikill('tic xuluil'S, since thesiKII Ilf tll(~ ~llrf:lc'(~ 1)('t(~llti:ll l'f'lll:lin~ llll-

('halll-!;('(1 :,t :(11 pI! v:LII\(~ t.JI:(t. \v('re ~"tlllit.u.

It i~ tilt, 1"lrl"l~ of thi~ ~t.I\(!Y w dct.('r-IIliliC j 11(' ZCI'II 1)(lillt. (If CII:LI~l~ (ZP(~), to

it!('lltif.,. j ht, J",t.elll ial-d('I.('m1illill~ i(III...,

alld II' prl'IIf':O;l' :l1l1('('h:LlliRIII fIll" tlll~ rrc:Lt.illll

Ilf j 11(' f'lIrf:I("(' (:h:LrK<' I'll t~Llcit.l~.

It is \\ctl :lc:(~('pt(~1 tll:Lt. W!II"I :, ~,Iicl

dis"'I,I\"c'~, hflt II IICK:Lt.ivc :laid I)(,~it.vl: slj(~i('~.In' Ilrc~'1I1 ill RAlhltinrl :'l'IU tll:\t tl,('r(' (!::ixts

a particulur cundition callcd the L';{}electricpoillt (JEP) (8) at \Vllich the t\VO ch:lrgesare C<luivalcllt <,'Icctricully. ,,\ simil:lr situ-ation prev:Lils :~t the ~lid-Sl>ltllifltl intt-r-f:lcc, p:~rticulnrly for oxides :Uld silicates,for \vhich H+ and OH- llave l)eell ShO\\'lt.o be potenti:LI dctcnnining (9). At romep:\rticular solution pH the surf:1CC ,viii beclect11cally neutral, ftlld tlli8 pH \vill idelltifythe zero [I(}int uf ch:1rgc. "llcn thc solutionpH is more u.'\Sic than the ZPC, IIt'gnti,-ei(ItIS :Lncl complt'xes \vill Ilrcdomill:1tc :~t tIleilltcrf:~ce alld tIle -"urf:~cc \\ill bc Ilt'gativclych:u"gcd. Simil:trly, ,vhell thc rolutioll pH ismore acidic Lh:Ul the ZPC, I>ositivc species,\ill p~omill:ltc and tht' slIrf:lce ,viii be1)(1Sitivcly ch:LI'g('(I. Th(! clf"sc cor~llolldl'nccb<.-t'V(!C11 tIle isocl(~tric I)()illt of thc sc>lutillll:\lId tile Z<"f{1 I)()illt (,f clu\fgc of tllC solidlcnd tll I.IIC 1}ClSt UI:Ltc (10) th:lL tht~y arcgtlvcmro by t,h~ R:Lm~ Nillilibrilim \rltichC:Ln IK~ C;Ut~UI:Ltt'(l "..'m thcrlllfI(IYII:\micf4tllllllilily tl:LI.:L.

(::u(~iCt., \\'h('11 cli:-"""llvt~1 ill \\':LC,C!r, \vill

p"'I(IIIC(~ tll(~ rc,llc,\\'iil~ c!lc'lllic::11 !(p('(~i(~,

II:!<.'f}", IICO,,-, ('0;--, C:\++, C:LII(~O,,+.~:t:1

o"It)~I.\"':IIXI).\I:.\X ;\NIJ ,\C;;\I:I:~

:111.1 (':~('(I"(d'" II," "ill. ..UIC'Zl.(~.

/l1,'cll' 041" f,.r cl.~u~rmilli/l~ the(';I()III. (';I«)II)::I",,"tflt, r(llIcl\vill~ fI':Lt:licIIIS:

'-'

Re(erenceIII ('1\('0",\ ::; C:\~'()118ql K. = 10-$.. .1"1( ' ( '0 - (' ++ + ( '0 - - L- 10-.2' .- :l. "84' -.:1 . I A2 = .131 CO;- + 11:0 ::; IICO.-+ 011- KI - 10-1." (I, II)1.IIIIC()I- + II:') ::; II.COI + 011- K. - 10-'." (1,12)15111:COI ::; CO2(c1 + 1120 K, = 101.4' (I, 13)161 Ca+" + IICO.- ::; CaliCO." K, - 10..'~ (14)(71 CaHCOI+ ::; H+ + CaCOl18Ql K, - 10-'-'0 (14)(81 C:1- + 011- ::; CaOH+ K. = 10l.4. (15)(91 C:LOII+ + OH- ::; Ca(011)218QI K. = 10'.1' .

(101 C:l(OII)21841 ::; Ca(OIl)2w Kio = 102.4' .. KI calculated from the eq\lilibrium con.~tant Cur the reactions (31. (61.171 alld III1 CaCOJ(81 ~ C~-+

CO;- Kit = 10-'.14 (rcCerence 16).. K2 cnlc\uated from thc cq\lilibrium constants for the re:l.ctions [1) and (11].. K. And K.. cll.lc\uated using the calcium b.'llancc. ionic balance, K. And the following dnt:1: pH of

sal\\ralcd lime - 12.4 (reference 17), total solllbility of lime in wAter - 2 X 10-2 mole/litA!r (reference 18),

~

All cxnminatiun of thc prccroing cqu.\ticmssho,"s th.lt, ",hen calcite :1pproachcs cqui-Jibrium ,,'itll ,vater I\.t hi~h pH values, :l!\cxccss of the ncg:uive HCO3- ~uld CO;--t'pccics '\Oill exist, ,\"hCrc:ls ilt Jo,v pll valucs~\fi excess of thc positive C:1++-, C:lHCO3+,!lnd CIlOH+ spccics ,viiI OCCllr. Thcsc ionic~pecies mllY be prtaduccd nt thc solid-solution illtcrfllcc or may foran in solutiunnnd sub5cclucntly adsorb on the n1incrnl innmounts proportionnl to their CC)llCcntrn-tions in Mllrticm. Thc net reiiult ,,'illl.>c thcS3.mc in eithcr case: ~l I)()sitivc ch:lr~c onthe ..,urf~lce :It lo,v pII Clr I\. neg:ltivc chart,;-cat higll 1)11. It is inlpclrtant to rccu~nizcthl\l th~e t,,"O methods of surf1u;c Ch:ll"gCgcllcr:1tilm arc indi:o;tillgni!;hablc t.hcrn\o-dymLmic:uly.

When tIlc II-:}) :md t lie ZPC :lrc iclC:lltic:ll,thc ndditi(m of !;IJlid to :L sclluliOll at thc pHcorresponding to thc IJ~P "oil I causc nochnngc in the solution pH, sincc <.'qualnmounts of H+ and OH- ,vill I>c cc)nsumedto produce thc spccics mcntion<.-d.

Bcsides the usual clcctrokinctic mcthods,the ZPC c:m 1>c dc~rn\ined from the flotl\.-tim\ rc5lxmsc of thc I)(llid when trc:\tccl ,vithphysic.'\lly ndsorbcd :\nionic and cntioniccoll<.octol"S" Thc physically adsorbed sur-factants ,,'ill adsorb stroll~ly only ,vhcn tIlesurface is charged uppositcly to the col-Jcctor. This tcchniquc has been uscd before(19) flnd has bccn sho,vn to corr('l:\tc ,veil

In this study, th(!Sc thrt'C mcthods, elec-trokinetics, solution cquilibrium, :'lld flota-tion, h:l.ve becn used to dctcrmine the zcropoillt. of ch:lrgc of c.~lcitc.

EXPEmME~TAL MATEllI.o\LSIceland Spar c:l.lcitc \vas crushcd in a

mort.~r and pestlc and sized. The 35/65mcsh size fraction uscd for thc ~1Jerimcnts\\-as stored in conductivity \V:l.ter. All solu-tions \vere madc \\ith conductivity \vaterthat \vas prepared by passing distillcd \vaterthrou~h a deminernlizillg column :l.ndthrough a two-st:\ge Hert\Cus quartz still.The \v:\ter \vas uscd for cxpcriments onlyif the condltcti\rity \V:\S les.~ than 7 X 10-7ohm-I cm.-I. It. 'V:\5 st£lrcd in :\ stoPIK'rOOPyrcx but.t.lc. Siu(:c thc \vat.('r \\':L'I uscd l:Ltcrf(Ir Nlllilibr:,t.i('I\ (If t.hc ~y~l.I~m iu t.I\C Pl"t'S-cucc (If :Lir, no :Lt.t.t'mpt. \\":~ n\:Ldt~ lo kL'Cp:Lir (mt. of the t)lltt.lC. nc:l.~cnt gr:\dc nitricIlcid :Lud s()()ium hydrl,xidc \vcrc 'lsed forpH ooj\lstmcllts.

EXPERIMENTAL pnOCEDUREThe rroctions at the e.~lcitc-\\1\tcr iuter-

facc \\"crc studicd by mcnsuring the r po-tentit\l, the pH of the systcm, and thcealciulU mid e.'\rbonate conccntr:\t.ion~ asfunctions of the equilibration timc. The- rpotenti:l.l 'V:\8 dctcrmincd by thc streamingpotcntial tcchniquc.

TIlt, apparatus used for stre.~lUing po-

,

,.TIll-: 1;..:1:.. I".I~T c ('11.\1:';": ('..' ':"I-(~rrl': I:~.-J

1"llli;II ,.lllIli,~ i~ II:I~'(I \,illa ~III'" 1I1,..lili.(':llil'll" "11 IIII~ ~:LIII(' Iwilll'illll'!C :111(1 :I~~'IIIIIJydl~'ril"'(" ('Ilrli~r (,-I() :!".!.). l\JIII."xilll:llclyI(x) ~" Ilr (':ll('ill' :llld ."iOO 1111. (I( ~llul ilill \\"(ore

lI~..J rllr ('11('11 ~tn':llllil.g ('XJ)('rillll'llt. 'fllcl'lll il'C' IMI"III~ plll~ \\":l:i 1II:ldc Ilf :J.i:'Ii.:;111(':11. (':II('itc p:lrti('ll~. .\11 :.;0 1II(~ll pl:ltilllim\\"in' ~lIIZC \\"cld('(1 11111(1 th(' ell~I.,lt!c pre.\O('IIINlllll' l~lJ)(.' Ilf :llIY J):lrticlc.-; f.,lm tll(~plll~" .\Il illllK'd;.lII('C bridgc (,(1\l1,lro to ndt.'C:ldc (":III:I(~itnr \\11" \...~ f(Jr ~i:;l:mcc11\(':I:;III'('III('llt~. 'fill' ~ttt':ll"ill~ IM'l('llli:ti E:lllU 111(' «riving: p~...ure P \\"cre ~iluul-tall(,(lu!'I~' m(':&S\lrro hy thc f(Jli()\\-ing metl)t)(j,J\s tilt' :'(lillti(1Il flll\\OO th.,I\lgh tllc lli\Igl\ndcr pn."'Sllrc, :l ~tl"("..minJt l)()tellti:Li \\":lSdcvellllK'(1 :lIId \\":lS flod Cfllltilltlflll$ly illt(J :~vihr:~tin~ n'Ct1 Nl'Ct"lml'lcr :lIld tll(! (J"tlnal\\":t~ f('('(lnJcd. TIIl~ flc)\\" \\":I!' ~llddclll."sloPIK't1 h~' t"nlillJt :l ~tollC()Ck \\"ith ()flChmld \\"hill' nt the s:~mc inst:lllt thc 1'~'Ureill 1 he m:lIllmlct~r \\":15 lockcd by t\ln)illJ;by .Jc;; df'J:n't'S wit II t tIc (Jt her II:lDU n 3-\\-:l.\"st(JflCU('k IK'l \\"cell tile m:\lInmetcr :\nd tllOstr~:mlinJt IM)tCllti;ll fl:l!;k. Thc !'trC1\millg1M It ('III i:II :11. t tIc in!St:lllt ftn\\' sl()I>I)C(; \\":'5I'C:l« ("'1111 tlac rt'CtlrdillK by n(,tillg: thc dirrer-CII(:(' 1"'1\\1'('11 I.he rc:ldill~ jllst hef(lre and:~fl(~r !'1('I'Jlillg tllc nO\\", The Pf('$SUI'C nt thcin!'t:lnt ,,"lacn lhc ftU\\" stnpllCd \\":15 read Ullthc 1II:lIIomctcr. 1'hc ('I)Cration \\":1.'; I'C-Pl-ntl-d :'Cvcr:\i tinlcs in both dirccti()115 offtcl\' , unci UII I~VCr:I~l' E,' P "-:IS obt:\illl..J.Thi~ nlctll/lt! \\"US mllch ftilllplcr tllnll t1\O~ust'd JIl'CVi"UMiy, sillcc it \\"nR not IIl'C('~O;:lr.\'tl) IIl:Iilltuill t hc driving p""~~ur(' C<'IL~tnnttll.,llIjtllllllt Ihe cxlK'rimCllt, AIS<I thc ('rrl~t.(If IJlliuriz:II ion 011 t Ilc M1 n':Lmill~ I)()tcnti:«vnlllc nbt:~illcd wus elimillulcd.

Tllc z~t:ll)()tenti:tl III c.1.Jcitc ,,-n.~ c:\lclImtcdll!iillg tllc fllrm\tla (::!O, 21)

1I1:.clc', ZC'L:L 1",I,~.li:tl~ :u.cl'lll L'..'n! 1II(:%tSlan.'(1:ulcr !'In::lllli'l~ ill (':1(:1. dirl'rlillll, Th('III~L"iUr\:hIC'lIt~ "'Cr\: Clint ilttll-<1 ,"alii lhcre\v:\s IIC, :tpp:tn'IIL ,-IUUIgl' IJCt"'N'll suC'c-essivcrc:\dill~'8. IL \\11~ "bo'It!rvoo lh:,I., ulllikc thcC:lSC "f insfllublc uxidl.'S "lId 8ilic:Llcs, thissyslcm did lICIt re:tch l'CJtlilillrilam by strc:\111.illg thc ~IhltifHl thrcl'a~h lhc plu~, Hcllce,thc ~luti'HI c()nt:,inillg tllc mi IIca-:, 1 \\":'str:\nsfcrrt-<1 II) :\ )<xx> C.c. Ra.'Ik :lald mixedon :1 tllruhlcr for ~v('r.LI \vreks, Thc zcto"()()tcllli:tI "f thc c:1lcitc,~ pH, ""d c:,lciumaatd c:\rbon:ltc l"mccnlmtiol~ of thc systen1"'('I'C mefLSltrlod pcriodically, Mi.'\:ing \,,asCfilltilluc<l ulltil V:,l.l('1) of r and pH hadremuilll-<1 CI)n:it.:ult f"r :L IJCrind of nt le:1Stt,,'o \vCC!ks. Tn ubt:,in .Ci\lclt :111 apparentCfJ'lilihriullI, it w:tS nflClt l\l'C~lry to mixf.,r 1It.':lrly t.wn mfHltlts. C()lIlinUflllS mixingfnr matgcr times C:"L~ rol~dcr:tble Conna.-tiolt ()f filtcs.

Cnlcilm\ ill soluti'Ht "':18 mcnsurcd byntnlllic nbsc)rpti()n, Tot31 mrholl3tc insolution was :\nnl-,"%~ by mixing thc solu-tion with acid diluent nnd absorbing therelcnS(!c} c:&rt)()11 di()xidc ill nn nlknline Mlu-tioll conbillin~ phcnolphth:tlcill, Thc chnngcin color of tho solut iota \,.n.~ dctcm1inedusing an autoau:1lyzcr :1t 5;-,0 mp.

E.~pcrimCilts "'ere dolle ill this manner,,'ith \,'nter ndjusted to difTcrclit initi:tl pHvnlucs, as C()llo\\-s:E.'\:pcl'iment 1: 110 :lcid or :1tk:ui addcd-

illiti:~1 pII ;j,G;Expcrimcllt 2: :11kali addt'd to give nn

illiti:,l pH "f 8,2;E.'\:pcrinlCnt 3: ruk:ui :Iddl.-d tlJ gi\'c :1lt

iJlili:~I'III of 9,«;);Exl»crimcltL 4: :l.lk:Lli :\dd.~ to givc ai'

illili:1.l pl( nC 11.5;Expcrilll(~IIL 5: :~cid :lddro to givc nn initial

pH of 3.0;Exl>crimcuL G: acid oodl.od to givc Bli illitinl

pII of 1,9.Flol:lolioll e.'\:p<'I;mcnts \'-ere nl.'\de ill a

HnJlimolid cell (23, 24) with dodccyL'\.m-m()llillm ncct.'\tc (DD.\) :is tlw mtioniccollector nlld d.Jd<.'Cyl sulr:~tc (ODSO,) :IStoo nl1iOllic l'OU~t~r, A 2-g. I:LInple of tile35/6.'; l'lCSll Iccl:uld 81).'\.r \"1lS conditioncdfor 10 min. \vilh the rcquircd an10ullt oracid .ir IJnsc; th('ll the collt'Ctor W:1S added

\UI(:I'C I is tll(: lcmpcr:,tuI'C nr thc solution ii,°C, /~ is t hc stn~'llIill~ IMltClltial ill volts,/' i~ tilt, driving prc.'I.'iure in Ct'ntilllctcrs ofllIl'rCtlf)', :uld 'Y is tlac stK'Cific conductivityur tlal~ :;4)llltif)/1 ill Uhlll-1 cm.-I.

Tllc roJJI)\\'illg pn~.cJ"I'C \\':\5 uscd ill thcstud,\' flf tllc rate or CCluilihrntion lit thc~llrr:lrc. :\rtcr a plug of tlac lIiineral \\-:lS

.1:\1; ..,;oMAXUNI),\I:,\N ,\NI) ,\GAlt

:llltl (,mtli,i.llll'(l f..r ~ Illill- ~ilnlgl.:l1 "":IS1111b111L'l1 tllf,,"~11 tllc ('<'il :11. lilt! 1":11(' (If :to1II1_/lIIill. fllr I Illill., :(11(1 111(' 1I.1:ll :\11(1IIUllfl(I:It IMI11i"II~ \\"('r(' lillt-f('(I, tlri("(I, :111.1

,,"('i~IIt.'(I.

.l1E.'-ilj:rs :\XI} I)ISCU~I.():\"

Zrla J't,[l'IIliul. Yi~urc ] ~ives lhc zct;~pUtl'lIli;~lllf (':ucitc ;15 :~ flinctiull of Jill forvnriuus illlcrvais of mixin~ the )\1illcr:tl\,"ith t hc ~)I\1t i(1I1. Tilc clo!!ro ('ir(~ll'5 ill ]:ig, 1give tIle v:uucs obtained f'lr zct:\ potCllti;\1:Ifter the SOllltioll Il;id lX'Cn strc:tn\ootllro\lg11 t 11C plllg :\ li\lnlbcr of tim~, but11Ot, mixc<1 nil the tumbler, On mixillg t11Cmi\1cr:~1 \,"itli thc wlution OIl :\ tumhlcr,fllrt her ch:1nges in r :Illd pI [ ,,"cre (tbscn'ro:and :Irc ~11(l""ll hy ot hlor (:\II"\'CS in ]:i~. 1.It (":Ul }t(~ -"l'CJ1 tll:\t. ~lrc:~mill~ J)(lt('llti~\1J11(':ISUI,'m('llls ~:~vc ~Ill illiti:11 v:llllC (If 10.8for tIle ~1'('. l':(tuilibr:ltillli (111 tile tumblert;hift<.'(1 tIle ~PC to 1(1,\"cr v:uu<"5. J\ fin:\lvm\lc of 9.5 '\":\s ()Itt~lill('(l for c(tJ1dit iOI1Sunder wlli<:h t Ilcre "11~ WI :lpp:lrcnt (~h:lllgcin ItII of I h(~ Sftlutiltll llll l\1ixillg for :\t Ic:L"tt\\"O ,'cck~, T1lc Ch:llIgC o£ '( is "lao,,"n ill Vi~.2. Z(~t.:\ JKllcllti:u illcr(':\soo ill m:lhrnil;!dcbotll (111 tllC :~lk:uillc (cxpcrimcnt, 4) mIdun t}IC :i('iJ t'idc (cxpcril\1CnlS 5, (j) (1£ tilezrc. III tllc intcrmroi:llc pII r:11\gC, ini-tially tile Ilcll;~vior ''.is ~inlil;lr to t 1t:ll (1£ t h(~ulk:tlillc I':UI~C. :\11 rcplic.'\t iulI~ ill tll(,~~ r:UI~('~Shll\\"OO t lie ~:Imc ('h:ul~('~. TII(~ ~})C ub-

"-"

,. I I I ."'". I

. .. .",., ,." s"".",

. ,., wilt .",.,6 ,., .'.'.1."'.'

(..,. "

"t...00

l~tillC'(l (1'(1111 I.IIC' r 1IIC':t~llr('mcllt:; 1":1)"

(lifTI'r fl'1ll" 01(' 11,:1) if ~IH'('ilil~ :t<.1:';'lrptiOlI'If :IIIY illil t 11'1'1 Ir..;. II t':tll :11:';'1 IH' IliIT('rMlt.if ('(lllililwilllll II:I~ 11111. .\.(1 IM'('II :IU.:tilll~l"If, :I~ IMI:.;1111:tll'(l ~1111~'(IIII'IIt.ly, (':L't. :tll(1ll('();, :trl' 1111' Jlnllrill:11 1"11.t'lIli:LI.«(:t('r-millill~ illll~, 01('11 :, Zl)(~ Ili~hcr 111:tll t.hcIf:I' (:IIUI<.1IH' ('XIII:liIIL.<J, Ix.'(;;tu:o;c thc c.'\lciumiOll, 1H.'illg «iv:tlcllt, \,.ould IJC ~I)CCifi~nll:,.a<.1s()rl)(..<J.

.5,llltliolL J:."fjllilibriuIIL I EP and ,,\1 i"i11lumS,dulJih"ly. Fi~l1rc :3 ~hll'\.R the cll:tllgcs inpII 11£ the ~llutiulI~, ~tll« l"i~8. .. :l1ld ;j ~ho\vthe c:,lcium :'lId c~'rlloll:,tc SI,ll1bility :tS nfllllCtioll of mixin~ il,tcrv:IIs, 1Iost nf thcch:'llgcs in pH n£ the I'Illutill1lR tlCcun-cdimmcdit,tely ~,ftcr c:,lcite \,-:tS oodL-d tcl therolutioll. Evcn the ~olution \,.ith :," illitialpH v:,lue a:; lo,y tl5 1.9 g".lve a pH n£ 7.0soon ~,ftcr coming in eont:l.ct \yith thenlincn,l. Addition tIC n1ore acid to obt:\indnt:.l. nt still lo,,'cr pH vnlucs \yas not done,since it \yould result ill Ctlllsidl'r:lblc dissolu-titlll (1£ the c:.\lcil(~.

Th(~ pH uf t tIC su111t ilills :,1)t)vC S.'.? isfoulI<.1 to dccrel:O;C, \yhcrc:,.-; 1;I11'ltillll.c: IlClo\vS.2 illcrC:Lo;c \\'ith mixin~ lilll(!. ~\ ~llutiont,t Jill S.2 \y(lu1(1 Ulldcl"gO llCl lIet CII:lllgC inpH 011 cquilibl":ltill~ \\'ith Illc mincml. Inuther \,.ords, nt this pH, cquiv:tlcllt :111111untsof hydl'1lgcll :,n<.1 hydroxyl :'fc consumed byrc:U'.tiulIs such :\5 hy«rclly:;i~ 11£ cal(:illlll al,dc:,ru. 11I:,tc ions t\l1<.1 ad~wllt il)l) :\t thel1Iill~l":ll-sCllllliun illt,I'rf:,(~(:. AI'cul"(lill~ tcltllc «t'lillitiOlI ~iVMI I':lrli('r, I,IT s.~ i,-, thl~r('-fl)I"(', tile ('XI)('rilllC~lll:ll i:itI('\I'(o.!,ril' I"Iillt. ofc:,lt,ile. At. 1111 v:lllI(':; \lI\,'('r 111:111 Illc 11':11,th(~ Hlllllt.iOlI \,.ill 11('(~IIII1(, llltlr(~ :\lk:lliIIC 011ooditillll uf c:u(,it(:, bL'C:'II8e uf IT':lctillllS[3) alld [4] prc)Cccdillg in th(~ ftlr\vard directionalld rcnCtillllS [8] :'lId [9] ill th(: fC\"Crscdil'<.'CliOll. At hi~h pH v:,lues, the rcvcrsc istrue, nud t,hc pH of the ~Iutioll \vill dc-creIL'!C.

G1~rrels :,"d Christ (1) h:,vc calculatrotIle pH of \ynt('r ii, L'(lllilibrillm \vith calcitennd nir, :1.nd Iu,vc :1.rrivro :,t, pH 8.4, \vhicht~rl'C:i cll~ly \yith I hc CXI)('rilllent:~1 v:\lueobt.:,inl'(l here. ;\t. thi~ pII they :1.1811 ct\lcu-1:,t('(1 I.he tl)t:~l 1':lrIMln:LtC' :\11« c:,lcilllli I'IIlu-hilil.\." t.ll t~ I(} -J 1111(1 1() -:14 II1III(,~/II., n~-

RIH'(~I iVI,Iy, \,.11il,JI l'II1IIII:lrl'~ f:~vlwl~IIly \,.il-h

~...-+.

.18' I I I I t t. r 4 . . II It '4

"

Flo. J. '/.ct:, potential (){ c:,lcit~ in cqllilihriulIlwith ftCjIICOIlf; ~.tUlinM nll.1 air UK " {lIlIrli(J1I ufJIll ami mixillg.

,.,

,-1:~7""11': 1;I':I:CI I'CII~I (II" (;111\11(;1-: cII,' (:1\1.(;111':...

-20

-H . NO ADOITIOH - EXPT. 1.0 ,..OH AOOED TO PH' 2- EX9T. 2

0 H.OH ADDED TO pH ..9 EXPT.3

. N. DH ADO£D TO pH 115' EXPT. 4

. HNO, ADDEO TO pH30-EXPT.5Y HNO, ADDED TO pH t.e - EXPT. 6

.

/ ;--0-. . .-1O

~.my 0 ~

~ .+10

/ 0""'" ""+20 T

+3011 I I I30 100 300 1000 3000

HOURS OF MIXINGFIG. 2. Variation of zeta potentiw of calcite with mixing ill 1U111CO1L'I solutiflllS at different pH values

~

-.

8'

pH 6 . NO AOOITION - EXPT. 1

0 N.OH TO pH 8.2 . EXPT. 2

a N.oH TO pH 99 EXPT.3. NaOti TO pHI1'S-EXPT..

.. HNO. TO pH3-o, EXPT. S

. HNO. TO pHI.9. EXPT. .

4

2 . pH OF SOLUTION 8EFORE CONTACTING

O' I I I ,. ~O 100 ~OO 1000 ~OO

HOURS OF MIXINGFIG. 3. Change ill pll or the aqlleollS solutions with mixillg inpre.'lCncc or ca.lcitc and air

""",,-~.. .. '. -"

r#~

I:~' ~1.\1A...tINII,\I':\N .\NII .\li.\11

--..' ~~9"""'-- . I_. :~;(' 1'~"!~'!',!1

£ .. £,Pf. ~1O' .6..-

C..

Mil

-.10 ,

.., .. "',. . -EUT.4

...- I I 1 , I18 ~ - 280 -~-

HOUftS OF MIXING

FIG. 4. ('tll1C'Clltratit)n of lolal calcium in thenqllcolL" ~n1l1tio)1S in Cilililibrilim with culcitc antIair, at diffCrt'nt pH values.

-,.

'-"

co.Mi'

10

Ii 30 100 HO 1000 ~ooo

HOURS Of MIXING

)0'111. 5. ('AJII('ClIl.rati(11I of totul c:,rh(III:,tc ii,II..! :1(ltlf'illl!' ~nllltiorlS ill eqtlilillrillrn willi 1':\lcilc"lid :Iir, ~t dilTrront pI I v3111CS.

cltlr t'XIlC'rimcllt:11 v:llul'S or IO-~ :llld 10-3.4

"\lIII~il.WI; C::111 l'v:llu:Llc thl' 11-:1' rrom :LV:1il:1Ulc

t 'ICrIIll J(IYII:mlic d:LI:l tlY ('.:llcul:ll.ill~ thcC:IIJICI'llln1lillJl"; fir varill\I"; ~IK'(:il:S ill Ntui-lihrillill ,,'itll c:LII:itc llt diITc:I"ClIl II}( v:11I1c~,I1Sill~ t hc C'Cluilihrium C~IIII!\t:Ult H ~iVl~11 ,,'itllJ-:Cts. {I] to [10], Illld :l cILrllllJl cli(lxidc1lllrti:ll Ilr~..,urc of 10-35 Iltm. This ml:th(>c!

Ilf :\II:l.lysis, ,vhich h:l." })CCn '1!c1Cd ill similarSYHtCIl\S (10, :!5, ,->ti), is ilIll~tr:l.tcd in Fig. 6\\11<1 J(iv~ t.llc 1)-;1) :1." pH X.4. Tllc figurenlRlI tihll\\.~ th:l.t. JI(;():a- :tlld (~:I.++ :1fC themnjor tiUrf:ICC 1){,tl~llti:tl-dM('rmining ions.Abclvc pH IJ tll 10, h.l\v(~\'cr, tltc CO;-iollH :tl~1 \vill h:tvc :1. m:\jllr rIlle ill dctcr-minillg tllc 1)(llclltinl"f c:tlcilc. H+ :uld OH-illns nrc, uf cnll~, Imtcllti:1.1 dctcrminillgsince tll(~y a\re ill t,<)uilibrilm\ ,\;th HCO3-,C:I.++, etc.

neck (27) 11as 8hll\Vll t 11:\t. \vhcn :1. sulutionis in equilibrium ,vitb :1. ~llid phnse, t.hc IEP\\;11 cnrre-,p.lI1d to thc pH I>f minimum solu-bility. RillCC the isoclcctric POillt is the condi-tion :I.t ,vhicll thc ch:lrg(~ jn thc solutionnrc eqllivl\lcllt elcctriC:l.lIy, it C:Ul bc cv:\l-u:l.u..-l if thc m:l.jllr sp(.'Ci~ Jlr~nl. ill ~)Illtiollarc kllll\\'ll :1.11<1 if th(~ Clmct,.,tl":\tillll~ of tot:lldi~-;()I\'c<l SI)CCil'S :I.rc mC:L--Ur(-<1. l.'jgurc 7gi\'t,~ till' mt~L--ur('(l V:l.lIl<:1' fill" tflu\1 COllccn-tr:ttillil of c:l.lcium auld c:trb.lll:\tl'; ~IK'Cie:;ill ~lltllillll. lTnd('r L'f)ttilibritlm CI)llditillnstlll~ rc~illll Ilf millillllUIl t.111:1\ di~o;<)lvooSJl(,<~i(~R i~ ~'Il tn I>c :I.t Jill X tn 10; t}lisCllllfjrlll~ t.llc v:llu(~ 111'(~lict(,<1 ill J'i~. 7 :\Ildis c(lnlJ1:I.r:I.I)I(~ tl. Illc ~ulll' (IIJI.:lill(.(}fl'lll1\ 1))1 nll~tl'tlrl'lll('IIII'.

Fic'/fuj."t. 'fll(' fl.II':l.lillll rI~IIII~ \villl ('111-IL'Ctllr (~III(~~IIII-:l.li.lIl~ Ilf 1.li :,1111 ;,.:, X 1()-~mlll(osil. :~ ~11I1\Vn ill J.'i~. X. ""illl~l~ I.III~ 1») )1\flO:l.t~ lIte (~:I.I(~ill' 1I111y :1.1)1)\"(' 1III 9, thc Kur-fatcc must IJC llCJ!;:tt i\'(~ly c}I:I.I~(,<l t\}){)V(~ t hiM

'""",

,-; Z\-;I((t I'(t\:-,. CIV (:1\.\1((:1-; C.I,' <:,\1,(;111': 4:~!).'.,

-

.0 ..0Q...

..0...... ..

\:

~

.*~~

_. - .ci

. ..pH

FIG. ~. 1)('I"rmi'I:~li.", nf lCro I)(Iillt. uf ch:1rgcfrom n"taliull ..f ~:,I~iIC "ith d<ldecyl:,mm<.lIillm:'ccl:~I" (1)1).\) :"'0 sodilllli d.Jdccylslllf:ltc(Ol)~),) lSulllliulIR.

1111. f'illlil:lrly, tIlt, J)1)~O4 ful:\t~ tlac c.'\Jcilc""ell cIIII~" IK'ICI"" pH :-\, ,,"IIt'rc the fiurf:Lcemtlslll:tvc :L 11I1.-;it ivc (')1:Lr~c. Tlll~(~ mC:LStlrC-mclIl~ pJ:I(:C lla(: ZPC J)(~l"-(~'11 IIII 8 nnd 9.

Jfcchallib"11t cif Cllargc Gcllcralio't. Tlacsurr~LCC -C~L+ tLnd -CO3- j(IIIS C:LIl undcrguhydl"!,IY8j~ :LCC()rdillg to £(IS. [:1), [4), [8),alld [9). As mcnt jcHlro ClLrlicr, at Ifl"" pIIvnJucs, rc:LctiOlIS [~] :Llld [-t) ,,"ill pr(lCccUin th(~ ror"":Lrd direclil'll :Llld rc:Lc:tiolls [R)ulld [9) ill tlac rc,'c~ din-ct.icHL, "-JICrc:l.,, :Lthi~11 1111 v:tlll(~ tlac rcvc'~ i~ tl'\IC. Tlai~

IlilTl'rl'IICi:,1 1',Vllrtll,VNis \\'ill Kivl' ri~I' III ;~III'C, I'II:~I~I' fIll IIII~ sllrf:II'I'.

'1'111' f.I",lil'IIIIII~ coJI:I'I~I' ill j(f'I:1 1",II'lIli:~1111111 I,ll \\illt IIIixil'~ 1'11'1 1M' ,.x:I"Ii'Il't1 filltill' II:I~is "f C III' IIIM'\'I~ II"'I'h:~Ili"," f'lr thecoJl:II~I' 111.v('I.'IIIIII'III. I I lOll" IMO SI~II fnlmJ"i~.;~ 11I:lt 111(' ~llllliflll.-; ill ~'lIcr:II ~1\(1\"cd an~pid ill(Orl~:lm' ill 1111 iml'l\(~i:llcl,V fill con-t.:~1 illg tllc c:~lcilC, fllllfl\\'OO hy:\ slf"\' change11,,('r ~<.'\'rr:tI \",~k.';. 'I'llis i'l<.li(~:~tM that amCt:h:~lIi.-;m iIlVIII,'ill~ ;~ C(}mhim~tiflll offll~f, :IIIU ~Iu\" gt('II~ i~ rI.'SIJ()lIsible fur theIII).~(~oo Ch:lll~l'S ill 1 IIc ~y~t('m. Such II.Ilfl..;...illlc m(.'Ch:~IIiNm is thc hydn,lysis I)fsllrf:~ce c:lrhclll:~t~ ()r (~:Ilcium i()ns :lccom-p:~lIil-d hy the difTlI..-illll (If hy<.lrogell orhydnlxyl i('I1~ thrc"I~h the double layerintI) (Ir :1\\'ay fr(Im t hc intcrf:lcCo Thus inthe expcrimcllts dm\c ,,'ith nn ncidic solu-tion (cxpcrimcnts'!) and G) the hydrolysis ofsurface carbonate ions

-co.- + H2O ~ -HCO. + OH-

continues tu tukc pl:lcc m:lking the milleralmore Ix.siti"e :lnd the SfHutiun more alka-linc. Similarly, ill thc case of cxperimcntsdullc in the ulk;tlinc r:\n~e (experiment 4),culltinucd h)'drolysis or C:llciUl\1 ions

-Ca+ + 1120 ;::: -CaOH + H+

is re<;})(lnsible fur the IIhscrvoo change in rnnd pH of thc !;cHlltiflll ",ith time, Here thesurf:lce bcc()m~ le~s I)(,~itivc t\nd the pHof the ~)llItifll\ dl'CI,(,:1."i'S ,,'ith timc. Th:\t adilTu.-;illn-c(lI\tnllll'tl I)rf~~.. is ill\I)f)rt:~l\t inthc :;(Hul)ilizatillll .If (~:~Icitc is ~upportcd bysucl. "'llrk~ :L-; th:lt. I,f T:~lc (28) in hisrecCllt ch(~mic:tI ki'lctic study Ilf c:tlcite-,vater H\.strm I\lId that of O'IlI(I:~ :md de-BrlI)'ll (2(;) in ,vllich they pt'tlpo.'Icd ditTu-sima of pro!tlns th")II~h :~ hy<.lr:\too gel-likeinterph:l~ :18 th~ r:\t~-culltrc)lIill~ .<;tep intl\c cquilibn~ti(HI (IC ferric ()xid(~ \\'ith :L(}IINIUSSOI\lt.illl\s.

An allcnl:rtc mechallism for calcite in-volvCR t.1\c diR.'illlutiIHl ()C c:t.1Cill\\1 and c..'tr-bunat~ jon~. follu\\"cd by tbcir hydn}lysisinto compl('xcs in thc solutim\. the com-plcxcs in him ;w~lruin~ at tIle interf:lcc.Tllc difTusi(Hl of t I\c C(lI\lIHCXCS to thc inter-face mi~llt. IIC tll(' ~Ifl\\' ~tcp ill thi~ c:\se.re.'ltrlf,i,,~ ill t hI" (11~rv('t1 chl\n~<.'S ill r:~lId III1 ,,'ill. limc, .\ ~III\\' prcfcrcllf,inl dig-

-I It' t«':\I\~'I~tIAt:.\~ :\:\:11 At:.\I:

I48lltllillll,.r.o:.lrjlllll'lrr:.rl"'II:II.oj"II",.I.oI"olillill~ IIII 1111' 1111, :I~ jlllljr:~I.'C1 II," fi~~o

,I :11111 ."'1 rllilitl :II~I "","11 ill 1111' 1111.~'rvI'C1

C'h:III~.~.

i. I:t;t;", I. "'. :\1 II t;"'.t;". \\'. II.. A"'" 1."tK".II"'~""~. I:. I':.. ":H!/ .Ui,.'H!I J. 167, K7( I!N~il.

~. (;,.A",,"""Nt:. ,..;.. "IIII"'HIIII.,i..., I" 1':lretr".,'I"'lIli"lry." \'n" ~""tr:tl"I. ~ew York,1!II1.

9. PAliK". (i. ,\., ("', In. 1:"1'.65, l;i (1!)G.~,.1(1. I'AIIKM, (;. :\.. ANI' "E"KUYN, I'. L., J. Php.

(~~:"'. 66, !Nii (1!162).11. 11.'Kxt:t,. II. R.. A~lt !o:._",.",~, S. I:", J. AWl.

CII..",. ,"'Ir. 63, 1;~ (1911).12. 11.\lt~t:lt. II. ~.. AND "ftXNER, F. T., J. Alii.

Client. ,~VC. 61, 1026 (1915).13. M.\ltKltA:\t. .\. A., AND KURt:, K. II., J. AWl.

Chclfl. .Wc. 63, 4~9 (1911).14. GItt:£:If".ALD, I., J. Iliol. CM"'. ~1. i89 (19-11).15. Bt:LL. n. P., AND GEOltGK, J. H. n., Tram.

Faraday SiN;. ~6, 619 (1'JS3).10. LAR.,\()N, T. E., AND nUK".i:LL, A. M., J. AR.

"'al8r "'ork- Auor-. M, 1r~; (1942).17. "II:\lIdllf'.lk or Chemml ry Itn" Ph)osics.."

44th ed., p. 1727. Tht' Chemicltl RubberI'ublishiltg Cumpltny, ClcvclAlld, Ohio, 1002.

18. IJA~KTr, J., J. cUm. Snc. 19M. 12iO (193'().19. 1\\"A8A~I, I.. el al.. U. S. nure3u or ~Iilles,

nl 55!}3, l~i MOl», H. J., AND l':UER.~TE.NAC, D. \V.. TrAU. AI."l': 211, 381 (I~);CltOl, H. S.. AND WIIANG, K. U., J. Korea.Chem. ScIC.1, 91 (1«:M"h1).

20. &tMAHUNUARAN, It.. Ph.l). TI1e5is, Universityor Culirnmia, nt'rkrlf'Y. IIJ(H.

21. s.,\1ASUNUARAN, P., IlEAL\", T. W., ANPFu Ell"Tt:N AU, I). W., J. 1"'9-'. CACIr&. 68,3.~.! (196-t).

22. K,,'RI'I, G. K.. M.:;:. Th,'"i.~, ~t:L~:LchlltietlsIILSlit.IlLe or 'rcchll"ltlV-}", C:1R\briJgc, J!}I"~.

23. 1;'\IKI~"K~Au. U. W., M..-rZG&K. I'. n., A~DSEt:LE, G. 0., E~g. Minillg J .158,93 (1957).

2.(. FUt:IISTKNAU, O. W., IIXALY, T. W., A~DSn\1ASUNDAIt.\.'f, P., TrtllI~. Al.1/E 229,321 (I~H).

25. S~IT1I, G. W., A:lfD SALII.,"', T., CUll. .'/~lnl-lurgi("tJl Q'ttJrt. 6, 03 (I!kWi) ,

26. FUER.~TE~AU, M. c., ANP MILLEI&, J. D.,"TIlt: 11.Jlc or tIlt: Hy,I"M"lI.rfM>t1 Ch.'\in iDAlliumc Flnl.'1Lioll nf Cnl..ile." Pnoscntcdlit tIle Allllu:1l AIM!:: Mcctillg iI& New\i'rk, New \'ork, Fchm:lry 1!)(j(j.

77. nt:CK. M. T., .4cla Chim. .I d. Sci. Hung.~, 2'.!7 (1~I).

~. T.,,',:, J. V., "Thc Kill~tit~ :LIIIl M~"f"h:LIli.'im ortho ~1..llili~I,1 Hili .tf (:l\ll'illlli f'.:,rl,n"'Ltc by<~:LrIH'" l)i..xi.I" ill 11M' ~Yltll'"' CILlt,illlI\(:"rllfllt:Ltr'(~:LrIH"1 Ilio,xi,lr,Wl\lrr." .'"'-"""lt~1 I\L llM' Ir':!I,,1 .\('", M,~,I illlt in NewV'"rk, Nr,,' ","rk. !o:.'I'I"IIIIM'r 1!It~i.

29. ():'I"I'A, (i. V., J'I., ANI' ".;I'"UYN, P. I..,"".rJ"..c ,.;ci. t, 1M (1!It~i,

'-'

HII;\I:\I,\I:\'

I. 1114' XI"'O 1)I,illl ,or ("h:I~I~ IJ ~:tlc~ill', :I~Illt':I!'III'C'O II,\' lilt, ,,In':~llIill~ 1)lllt~llti:u 1('(,1,-lIitt\I(', tlhirlt'(l ~r:tclll:III.\' (I'CIIII :tll illili:"pll v:,ltlC' tOr 10..'\ tll\\1,nJ:i 9... :L,; Nluilihri"m\\':15 :11111"'1:I~h(.~. '1'114' i""lC.'ll'Ct ric IMlillt. fJ thc8(IlllI,illll, Ilbt:~ill~1 rl"llm mf~'!\UreIIlC'lIfli fH8(llutioll "II c.h:ul~c~ Ctlu:;(.~ II) thc :tdditilOIlcor c~lcil(', i.'l ",.2, ill tlJ!;rf'{'mM,t \\.ith thcv:,luc flhl :tillc.~ ~r:ttlhic:tlly tLosing thcn"cl-dyrnullic Otlt:~. "I1c cc'n"(O:;llclndin~ CXPCI;-m<"Ilttlll.\' mc:a..;'lrcd minim'lm of lot:,1 s"ccicsill SC,lhlt iflll lics IJCl\\.C<:1I pH .'\ auld 10. }o1ota-tiflll cxl)('rilllc.'llts "ltlct-'d t hc ZI)C het\\.ccnpH 8 tlliO 9.

s. Till' rrillci,,:,( prltcllti:\l-dctcrllullillg8pcci~ I\re icit.'lltilic.~ :L" C:\++, HCO3-, H+,and on-. CO;- illll!; :\I!!fl I\:,vc a m:\jorrfllc :\bcl\.C' 1111 9.

S. Thc rrincij}:11 mcch:\lIism or ch:\r',!.Cdc\"clopmCl'l :tt. thc !\"rfacc is pmh:\hly thatof pn'fcn'llt i:,1 h.'.dnll)"I'i~ IH ~urftlcc c;,lciumulld c:'rIMIII:\IC ilIIIS, fIr thc h."cil'llysis I'Ir thcb\llk 1'(11111 illll il'lns, rCIIIII\\'NI h.\' thc tldSllrl)-tiflll (J tl\(' ~\lltiIlK c(lmpl('xc~ at thc sur-f:lcc. (:r:,ci":11 ch:~"~~ ill zet:\ IMllcnti:"and pH 'If tllc Hy~tcm \\"crc flli!'crvccl forscv(',~~l d:IY~, indicatill~ !'III\\' ~tc~I)." invtllvwin thc rn,...imlS dcvcltlpillg thc cha\~c :t.tt hc intcrr:tcc.

, ACI(NOWr,EIJGMI:;~TS

TIlt: :tlllh'l'" .-i.'!h ltl th:1l1k JMC {'Ir (Ienni.'I.~iOlIto p"I,li"h ItM' re2'lIllII nr tlli.'! fttlldy AIIII 'It.hcrnM'IIII",~ fIr '"Ir SllLlT, p:trtirm:trly Mr. J. A,Hcrlml, ~-h" ".I,",IIClcli I hc ft"I:Ltirnl cx(lCrinlClll!i.

Il";F)':nEN(~I';")I. (:"Rltt:'~'" It. M., "NU CnIIIMT. C. I.., "0011.1-

tiOIUO, ;\till~mls, and 1':clllilil,ri:1." Uur(1Crullcl I:(J\\", New York, t!Ki5.

2. .;LLI~, A. J., AM. J. Sci. ~, ~ (~I:1rch,I!V',J).

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