Journal of Crystal Growth Volume 20 Issue 3 1973 [Doi 10.1016_0022-0248(73)90002-x] Maurice a. Larson; John W. Mullin -- Crystallization Kinetics of Ammonium Sulphate

7/24/2019 Journal of Crystal Growth Volume 20 Issue 3 1973 [Doi 10.1016_0022-0248(73)90002-x] Maurice a. Larson; John W

1/9

Journalof Crystal Growth 20 (1973) 183 191 North-HollandPublishing Co.

CRYSTALLIZATION KINETICS OF AMMONIUM SULPHATE

MAURICEA. LARSON* andJOHN W. MULLIN

DepartmentofChemical Engineering, University College London, TorringtonPlace, London WCI, England

Received 2 8 February 1973; revisedmanuscript received 10 May 1973

Nucleation and growth rates ofammonium sulphate in aqueous solution are measured by several differentechniques and comparisons are made. TracesofCr

3 + suppress both nucleationand growth and modifythcrystal habit.

1. Introduction the maximum allowable supersaturation, b the batch

cooling rate, anddc*/dO the slope of the saturationThe crystallization ofammonium sulphate has re- curve (cf. section 6, Notation). Recognizing tha

ceived considerable attention in recent work andsomeACmax =(d c*/d O ) AOmax,

progress has been made in determining the applicable

kinetic relationships for nucleation and growth. The substitution intoeqs. (1) and (2 ) gives

purpose of this paper is tocompare some ofthe data k(dc*/dO)b =k~[(dc*/dO)A O ~m (3maxi ,previously availablein the literature, which havebeen

obtainedin various ways, and to presentnew data on or

nucleationandgrowth measured in pure aqueous solu-log b =K+ m logA O m a x . (4

tion. Inaddition, preliminaryresults are given showing

the effect ofCr 3 + (added as CrCl3) on the nucleation The slope ofa plot oflog b versus log AOmax is the

and growth processes. order ofnucleation, m, in eq. (1). They found tha

seeded systems, containing one or two individual cry

2. Crystallization from pure solution tals, exhibited ordersof2.620.92, i.e., in terms o

In a recent paper, Mullin et al.1) presented data on eq. (1),

2.620.92the nucleation of ammonium sulphate obtained by a B= k1 1 ACmax . (la

batch cooling technique previously described by

N~vlt2).This technique was developed froman anal- Mullin et al.1) also presented data for the growth rate

ysis of the nucleation process using the assumption of various faces of the ammonium sulphate crystal

that the nucleation rate is proportional to: (a) the They found that the (100) faces grew at a first orde

maximum allowablesupersaturationtomth power, rate withrespect toAc overan undercoolingrange o

2.1 C,whereasthe (001) face growth rate was shownB=k Ac~~z (1)n max, to be approximately second order. These results sug

and (b) the cooling rate gest that the habit (and thus the crystal shape factor) iB=k (dc*/dO) b, (2) very dependent on the level ofsupersaturation in the

liquorin which thecrystali s growing.

whereBis the birthrate ofzero-sized crystals, Acmax Because of the very low levels of supersaturation

supported by ammonium sulphate, stirredtank growth*Present address: Department of Chemical Engineering and ratemeasurements have generally proved unsuccessfulEngineering Research Institute, Iowa State University, Ames,

Iowa, U.S.A. Growth is extremelyslow in the supersaturation range

183


2/9

18 4 MAURICE A. LARSON AND JOHN W. MULLIN

where nucleation does not occur. N~vlt3),however, TABLE I

has suggested that growth under these conditions ap- Experimental operating conditions and results for ammonium

pearsto be first order. - ~~lPh~t~

In a more direct approach toward measuringnude- M G nt L0

ation kinetics, Chambliss4) measured the relativeorder (g/lOOml)(pm/min) (No/pm) (pm)

ofnucleation and growth.His approach used the data M 3analysis method proposed by Timm and Larson5) for 2.55 7.01 2.42x l0~ 3(6

3.16 3.89 1.53 x l0~ 350a mixed suspensionmixed product removal (MSMPR) 3.36 2.63 1.52x iO~ 355

crystallizer. For such a crystallizer,a population bal- M= 4

ance shows that the size distribution, in terms of the 3.92 6.97 3.32x l0~ 3144.01 3.86 2.20x l0~ 348

crystalnumber density a, is given by 4.33 2.68 l.89x l0~ 362

M 75n = n 0 exp(L/Gi), (5) 5.78 7.34 5.05 ~ l0~ 330

6.58 6.93 6.38 t< l0~ 312ifgrowth i s nota function ofsize. G is thegrowth rate 7.40 3.94 3.86 ~ lO~ 354

(dL/dt) of a characteristic crystal dimension, i is the 7.46 2.61 3.92x i0~ 352

crystal mean retentiontime, L is the crystal size, and 7.42 2.56 4.25x l0~ 346

n0 is the number density ofzero-size crystals (nuclei). f n correctedto thevalueofthe suspension density M(g/l00 ml

The nuclei population density, n0, is related to the shown above each set ofruns and based on total crystallizevolume.

nucleation rate, B,by

B=Gn. (6) vary from0.3 to 0.7 giving a relative order of nucleation and growth, rn/g, equal to 1. 50.2. Theseexper

Ifa power law secondary nucleation kinetic model, ments were carried outat 22 Cin a highly agitated 1

B= k~M~(Ac)6, (7) litredraft tube type crystallizer.The suspension densitywas varied by changing the concentration of the feed

anda power lawgrowth model, stream.

Assuming an order of growth g = I, the order oG =kg(Ac)~ (8)nucleation, rn, becomes 1 .50.2, which is on the low

are assumed, eqs. (6) to (8) may be combined torelate side compared with that obtained by Mullin et al.)

the nuclei population density with the kinetics. Thus However, if a more realistic order ofgrowth is used

a0 = kNMjG(m/9)~, (9) say 1. 5 (estimated from Mullins data forfacial growth)then the nucleation order obtained i s 2.30.3, which

where Mi s the suspension density and M~empirically ____________________________106

represents the nucleation rate dependenceon the quan-

tity ofcrystals in suspension.

Experimental size distributions obtained from con-

tinuous MSMPR experiments yield, through eq. (5),

E

0values ofnand corresponding values of G. Thesevalues are usually obtainedby plotting the size distri- z

bution on semi-log paper. The intercept is nand the ~V = I I

slope ( 1 /Gr) contains the crystalgrowth rate. l0~- e - 22CPlots oflognversus G give lines ofslope (ni/g) 1 , o M - 7-5g/IOOmI

fromwhich the order ofnucleation, rn, can be obtained A M 4Og/IOOm~U M- 3Og/IOOn~I

if the order ofgrowth, g, is known.

In experiments at various suspension densities and 2 4 6 8 10 20

residencetimes, Chambliss4)obtained the results shown G, ~m/min

in table I. In fig. I, logn 0 is plotted versus logG for Fig. I. Nucleation and growth kinetics of ammonium suvarious suspension densities. The slopes of these plots phate4).


3/9

CRYSTALLIZATION KINETICS OF AMMONIUM SULPHATE 185

__ VA~OTTLE

,,,,,,.4// SAT URAT OR

L ~jWTER0 G 2 6~im/min

l0~I 2468 10 20 CRYSTALLIZER

M, g/IOOml ROT AM ET ER

Fig. 2. Nucleation rate ofammonium sulphate as a functionof Fig. 3. Experimental MSMPR crystallizer.suspension density

4).

isin close agreement with Mullinsvalue of 2.620.92. order,j, with respect to suspension density of 0.98

To determinethe order ofnucleation,], relatedto the These results are inquite closeagreementwiththe above

suspension density, Chambliss plotted the nucleation

rate versus suspension density at constant growth rate 3. Experimental

(fig. 2). Clearly the nucleationis secondary and is ap- The data of Chambliss4) were extended using a

proximately first order in relation to suspensionden- litre beaker(working volume 800 ml) as a crystallize

sity. and a stainless steel cooling coil as a draft tube. A

Youngquist and Randolph6) studied the secondary marine propeller was used as an agitator withstirringnucleation rateofammonium sulphate bydetermining sufficient only toensure a well-mixedsuspension. Th

the size analysis ofcrystals generated in a continuous apparatus is shown in fig. 3. Thevessel was fed con

crystallizer using in :situ measurements witha Coulter tinuouslyby gravity from a heated reservoir through

counter. Theiranalysis gave a relativenucleation order Rotameter. Feedsolution was saturatedat 40 C.Heat

with respect togrowth, m/g, of 1 .22 and a nucleation ing was providedb y circulatingwaterfrom atempera

TABLE 2

Nucleation and growth data for ammonium sulphate: 800 ml MSMPR crystallizer operated

at 1 8 C;feed saturated at 40C

Run No. Cr3~ M M(calc.) B G(ppm) (mm) (g/l00 ml) (g/l00 ml) [No./(100 ml) (min)l (j.tm/min) (pm)

8 0 8.5 3.8 3.9 2.7 x l0~ 13.5 3454 0 11.1 3.8 3.9 2.1 > < i0~ 10.5 350

9 0 19.6 3.8 3.9 1 .8>< i0~ 9.1 34510 5 8.5 3.8 3.9 1. 1 x i0~ 18.3 467

II 5 8.5 3.8 3.9 1. 1 x10~ 18.3 46712 10 8.5 3.4 3.9 8.7 x l0~ 19.2 490

2 10 11.4 4.1 3.9 7 .3>< l0~ 14.6 5003j~ 20 10.9 2.5 3.9

1 The crystals from run 3 wereimpossible to size.


4/9

18 6 MAURICE A. LARSON AND JOHN W. MULLIN

ture-controlled water bath, through a coil in the reser- The intended suspension densitywas4 g/I00 ml and the

voir. Product slurrywas removed intermittentlywith temperature of crystallization was maintained a

avacuum bottle. 18 0.5 C.

To makea run the crystallizer was operatedfor 6 8 The results ofseveral runs, along withresults when

retention times. At the end ofa run the entire contents Cr3 + waspresent, are shown in table 2. The nucleation

of the crystallizer were filtered, the crystals washed and growth ratesfor pure solution were obtained fromwith methyl alcohol and dried. The size distribution plots of these data as illustrated in fig. 4 for run 8.

was determined with 2 in. diameter standard sieves. Fig. 5 shows the results ofChambliss4) together with

I0~_________________________________ those ofthe present experiments. Here Bis plottedrather thann.The data have been puton the common

basisofnumber per 10 0 ml permm. The agreement i

tO 3 - 8-5rmo quite good consideringthe different apparatus geome : 376g/lOOml tries used, the different temperature of crystallization

B=2-7IO4No/000mI)lmIn) the different raw material,and above all, the probabl

I0~ difference in stirring intensity.The agitator speed in the

o\ present work was approximately 500 rpm compared

with 1700 rpm used by Chambliss4). This, along with

0 the lower temperature level in the present experimentsexplains the lower nucleation ratesobserved.

Itshould be noted that, within the accuracyofmeas

urement, the crystal yield was the expected yield caculated assumingthe mother liquorwas at saturation

concentration, confirming the existenceofan extremely

low supersaturationwithin the crystallizationvessel.0 400 800 1200

L, ~um 4. Crystallization i n the presence of impurities

Fig. 4. Crystal size distribution ofammonium sulphatecrystal-lized from pure solution. 4.1. MSMPR EXPERIMENTS

40 ______________________________ Theone litre MSMPR crystallizer discussed abovewas used to determine the effect ofCr3~(added a30 / /$ CrC!

3) on the nucleationrateof ammonium sulphate

20 7 at the same conditions used forthe pure solutionexI / periments (feedsolution saturated at 40 Cand a crysa. JO l0~E RUNI20 8Q ~ =6-5r,in

6 0 V litre ~ 102 ~)~ :0 M 4g/lOOmI ... 5=87~lO~No./tIOOrnll(rnin)

Z ~ 5=22C ~. lOppm Cr

3~

T15to45r,,in ~ 0

il55C

-* V = 800nIM = 38g/lOOrnl018C Z

T 8-5 to 12-6m ixC

2 4 6 8 0 20 0 400 800 200 1600

G, ~Jryt/min L.,pm

Fig. 5. Nucleation and growth kinetics ofammonium sulphate Fig. 6. Crystal size distribution of ammonium sulphate crys(dashed curve taken from ref. 4). tallized in thepresence ofCrCI

3.


5/9

CRYSTALLIZATION KINETICS OF AMMONIUM SULPHATE 187

tallization temperature of 1 8 C).Againthe supersat- known if the normal equilibrium solubility, c~,applie

uration was not measured becauseit was too low. In under these conditions.

anycase the term supersaturationloses a measure of A typical size distribution is shown in fig. 6 and th

its meaning when impurities are present, since it is not results ofall runs are given in table2 . Photographs o

I, the crystalline product obtained from pure solutionand

- ~ in the presenceof 10 and 20 ppmCr3~(parts ofCr3

permillionparts by weight of solution) are shown i

figs. 7a, 7b and 7c. Fig. 7a is the crystalline produc

~ from pure solutionand exhibits the characteristic habi

of ammonium sulphate. Fig. 7b shows the produc

from solution containing1 0 ppmCr3~added as CrCl3

and fig. 7c shows the crystals produced when 2 0 ppm

Cr3 +are present. Fromfig. 7b it appears thatthe initia

effect is the development of(110) or (111)faces resul

ing in a more pyramidal habit. This, along withthe

evidence infig. 7c, showsthat the presence ofCr3 + ob

viously changes the relativeface growth rates and en

(7a) couragesthe appearanceofhigherindex faces, butu________ timately there is a breakdown ofregular growth leadin

______ tothe formation ofcrystalsofgrotesqueshape.Another pronounced effect ofCr3~is the suppre

~ sion ofnucleation. In an MSMPR crystallizer this re

__________ sults in an increase in mean crystal size as shown i_____ table 2 andfig. 6 . Thesedata were obtained from th

size distributions obtained from sieve analyses. In ca

culating the number distribution a volume shapefac

tor* ofunity was used. Clearly, the shape factors ofthcrystalsin fig. 7 have a variety ofvalues, so the result

can only beinterpreted in aqualitative way. It is clear

~ however, that the general trend is for nucleation ratet

(7b) decrease as Cr3~ concentration increases. This ishown in fig. 8 for three runs at a residence time o

8.5 m m and two runs at 1 1 mm.

Theresults also show that growth rate increasesa$ Cr3~concentrationincreases, butthis is in directcon

~ . tradiction to the single crystal growth resultsto be di

. cussed below.As aconsequence,these MSMPRresult

. . ~ canonlybe explained by recognizing, under the con4 straintsof equal production rate, that if the nucleation

rate decreases, the resulting decrease in crystal surfac

area canonlyresult in a higher supersaturation. Thimeans that a much higher effective supersaturation

- existed athigh Cr3~concentrations resulting in highe

growth rates.(7c)

Fig. 7. Aiiimonium sulphate crystallized (a) from pure solution, *IfL is the characteristic screen size ofa crystal, its volume i

(b) in the presence of10 ppmCr31 (as CrCI

3 iii solution), and k5L

3,wherek, is the volume shape factor. Forcubes k = I,foIc) in thepresence of20 ppm Cr3~(as CrCI

3 in solution), other shapes k. ~ 1.


6/9

188 MAURICE A. LARSON AND JOHN W. MULLIN

slopes of these lines as a measure of the order o

26 r=n m m nucleation1 2) then the order in the presence o

I -\ 0 t-~5m,n Cr3~would appearto be virtuallyinfinite suggesting22 - \ the occurrenceofmassive nucleation at the boundary

I \ ofthe metastablelimit.This is clearly inconsistent with0 \

Q 18 the observations in the MSMPR experiments wherno massive nucleationoccurred.

~ 4 4.2. SINGLE CRYSTAL EXPERIMENTS

x 0 In order to characterize more fully the phenomenadescribedabove, experimentson growth ofsinglecrys

6 I tals ofammonium sulphate in the presence ofCr3 +0 5 0 were made. In one set ofexperiments the facial growth

Cr3~,ppm rate wasmeasuredand in the other the growingsurface

(a) was observed usingreflection microscopy.

20 4.3. GROWTH BEHAVIOUR OF SINGLE CRYSTALS

16 It is clear from the above work that the presenceo

T=llmin12 0 85 n E A 4lg/IOOrnl

- 15 8 3-4g/IOOmIa. B B or , A bas,s

8 1 /0 5 10 0 B/

0

Cr~pp m ~

Fig. 8. Effect ofCr3~on the crystallization kinetics of am- ,.~ .monium sulphate; (a) nucleation rate. (b) growth rate. /A

C 6- /

The results ofruns2 and 12are plotted in fig. 9 in an 10 I~ 2b 30

attempt to determine the order ofnucleation inthe pres- G, ,um/min

ence ofimpurities. The data are limited andthe result Fig. 9. Nucleation and growth kinetics ofammonium sulphate

is notconclusive, butthereis no indication of any pro- in the presence ofCr3 ~

nounced change in order. Whenboth data points are 100

puton the same suspension density basis, the order is 80

within the rangeofthat for the puresystem. It is inter- 60

esting tonote that ShorandLarson8) found that while 4 0 y b c dseveral additives changed the nucleation rateofK NO

3,

they had only minoreffect on the order. 20

When Cr

3 + was used in nucleation experiments simi=

lar to those described by Mullin et al.2), the results .~

shownin fig. 10 were obtained. Line a is fora seeded 3 10Pure 35ppm 21 p pm 36ppm

pure system. Theother lines are the results for various

levels ofimpurity. The main point to note i s that the 8 10 20 30

metastableregionis considerably widenedinthepres- undcrcooIIn4, ~eC

ence of CrTt This finding is consistent with the Fig. 10 . Maximum allowable undercooling as a function o

MSMPR experiments. However, if one regards the cooling rate in the presence ofCr3t


7/9

CRYSTALLIZATION KINETICS OF AMMONIUM SULPHATE 18 9

certain impurities, such as Cr3~,exert aprofound effect _______

on the crystal growth process. Some growth rate meas- - -

urements of the (00 1 1 ) faces ofsingle ammonium sul- -.,~

phatecrystals were madeby a technique describedby

Mullin et al.7). The runs were carried outat 25 C

with a fixed crystal, 2 - 4 mm in size, located in a solu- ~ -

tion flowing at 3 cm/s. -~

In pure solution the growth rate in the (001) direc-

tion was found tobe similarto that determined previ-

ously), ranging from about 2 x 10-8 rn/s at Ac =

3 x l0~kg per kg ofwater to about lxl0~rn/s at ______ -

Ac = 5 x l0~kg per kg of water. Thesecond order ~-~

dependence of growth rate on supersaturation was

confirmed. (a)

The presence of I ppm Cr3 + (introduced asCrCI3) in

the solution had no noticeable effect on the (001) ______

growth rate. The presenceof 2 ppm appeared tohaveno effect in the early stages ofgrowth, butafter about

an hour irregularities were noted on several of the

crystal faces and the (001) growth rate slowed down ________ _______

slightly. At 3 ppm therewas definite evidenceofgrowth _____ _____

irregularities on the faces almost as soon as the im-

purity was introduced. At 5 ppm Cr3~there was a

virtual stoppage ofnormal growth on all faces. In all _______

the runsmade in the presence ofimpurity, the supersat- -,

uration, Ac, was maintained at 5x l0~kg perkg of

water.

(b)

4.4. LAYER GROWTHS ON CRYSTALFACES

Fig. 11. Growth layers on the faces of ammonium sulphatSome observations of surface growth features on crystals growing in (a) pure solution, and (b) a solution contain

ammoniumsulphate crystals growing in aqueoussolu- ing 5 ppm Cr3t

tion at25 C,usingreflectionmicroscopy, indicate thationic impurities influence the growth mechanism. The growth layers became slow-moving and polygonized

crystalswere nucleated andgrownin a small observa- as shown in fig. 1 lb.

tion cell, and were approximately 0.5mmin sizeat the These observationsare compatible withthe kinema

timeofobservation. Thecrystals were stationary and ic theories ofcrystal growth9 10)in which visiblelayer

the solution flowed past them at a slow but unmeasured result fromstep bunching due toperturbations within

rate, elementary step trains. The initiations of such ste

Growthin puresolution was generallycharacterized bunches have beenobserved atwell-defined points o

by layers originatingat random points on the crystal the faces of sucrose11) and ammonium dihydrogen

surfaceand apparently moving inwards on themselves, phosphate2), corresponding presumably topoints ofinally to disappear at somew ell-defined point near the emergence of groups of screw dislocations or othe

centre of the crystal face. Fig. I Ia shows a typical ex- defects.

ample withthe layersmoving inwards, away fromthe Thepresent observations with ammonium sulphat

edges of the crystal. Thelayerpatterns were generally suggest that the step bunches are notformedatgrowth

elliptical. When the solution was contaminated with centres but at random points along the step trains

5 ppm of Cr3 (introduced as CrCI3) the surface giving rise tovisible layers. For growth in pure solu


8/9

190 MAURICE A. LARSON AND JOHN W. MULLIN

tion,the elliptical nature ofthe layersreflects theaniso- nucleation kinetics ofthe puresystem near some poin

tropy ofthe surface structure, which consists ofalter- a a on the upper line. Consequently substantially th

nate regions ofpositive and negative ions, and suggests same result would be expected and this, in fact, ha

that surfacediffusion is importantin the growth mech- been found. In the presence of Cr3 + the metastabl

anism. region i s widened(see fig. 10), as indicated by lines b

The polygonizationof the growthlayers in thepres- c and d in fig. 12 , but in a back-mixed system undeence of Cr3 + is consistent withadsorption of these doing secondary nucleation some nucleationundoub

foreign ionsat kink sites along the elementary steps, edly takes place in the metastableregion, as indicate

effectively reducing the number ofkinksites, imposing by the lines oflow slope.

a crystallographic dependence on the step velocity and The method of Timm and Larson would very likel

reducing the overall face growth rate, measure nucleation rateswithin the metastabie zonea

pointsnear b b or d d , giving a verylow order nuclea

5. Discussion ion. This is entirelyconsistent withthe MSMPRex

Thetwo different methodsofdetermining nucleation perimental results reported above. On the other han

rate described in this paper appear to give similarre- the method of N)2vlt, carried out under conditions o

suits for the pure system, but partially contradictory mild agitation and in the presence ofonlyone or two

results in the cases where impuritiesare present. crystal seeds, would not show nucleation until th

It is clear, however, that the two analyses are to limit of the metastable zonewas reached. Hence thsome degree different in concept.The method ofN~vlt near-vertical lines in fig. 10 , which correspond to th

essentially determines the slope of the nucleationcurve lines of high slope in fig. 12, indicating a very high or

[the order ofnucleation,m, in eq. (1)] forthe point der nucleation, in an MSMPR crystallizer operating

at which massive nucleation occurs, that is, at the with a reasonable suspension density, it is extremely

boundary of the metastable zone. On the other hand, unlikely that the region ofmassive nucleation is eve

the method ofTimmand Larsondetermines the slope reached,

ofthe nucleationcurve in systems where onlymoderate The single crystal studies confirm a pronounced

nucleation is occurring, effect on thegrowth ofammonium sulphate crystalsb y

A loglogplot of the nucleationkinetics ofthe pure traces of the ionic impurity Cr3t The relative growth

ammonium sulphate system may diagrammaticallybe ratesofthe variousfaces aredrastically altered and the

represented by line a infig. 12 . The system has a nar- character itself is changed,as seen in fig. 11 . It appearrow metastable regionand relatively low order kinetics that thesechanges in growth mechanism insome way

when substantial nucleationoccurs, It is reasonableto affect the secondary nucleation kinetics, although i

assume,therefore,that both methodswould determine would seem that the nature of this growth would b

____________________ favourableto higher nucleation rates.

b-d increasing Cr3 6. Notation

~ b Cooling rate (C/min)

B Nucleationrate (numberper m m per 10 0 ml)c Solution concentration (g/lOO ml)

a b C d c* Equilibrium solubility (g/lOO ml)

Ac Supersaturation, c_c* (g/l00 ml)

~ Maximum allowable supersaturation (g/l00ml

a g Order of crystal growth [eq. (8)]

:::: i--- G Crystal growth rate, dL/dt(j.tm/min)] Order ofnucleation withrespectto suspension

Log Ac density, M [eq. (9)]-. k Constant in eq. (2)

Fig. 12 . Nucleation kinetics of ammonium sulphate shossing

effect ofCr3 ~. kg Growth rate constant [eq. (8)]


9/9

CRYSTALLIZATION KINETICS OF AMMONIUM SULPHATE 1 91

k,, Nucleation rate constant [eq. (1)] the manuscript. The authors are also indebted tothe

k0 Nucleation rate constant [eq. (7)] Iowa State University Faculty Leave Program fo

kN Nucleation rateconstant [eq. (9)] making this collaborationpossible.

K Constant in eq. (4)

L Crystal size (j.tm ) ReferencesLD Dominant crystal size (i.tm )

I) J. W. Mullin,M. Chakraborty and K.Mehta, J. AppI. Chem

rn Order ofnucleation 20 (1970) 367.

M Suspension density (g/lOO ml) 2) J. N~vlt,J. Crystal Growth 3/4 (1968) 377.

n Crystal numberdensity (number per m m per Rm) 3 ) J. N~vIt,private communication,4) C. W. Chambliss, Nucleation and Growth Kinetics in

n Number density of nuclei (number per m m per Cooling Crystallizer, UnpublishedPh. D.Thesis,Iowa Stat

lim) University, 1966.

I Time (mm) 5) D. C. Timm and M. A. Larson, AIChEJ. 14 (1968) 452.6) G. R. Youngquist and A. D. Randolph, AIChE J. 18(1972

- r Crystal mean retention time (m m ) 421.O Temperature (C) 7)J. W. Mullin et al., J. AppI. Chem, 17 (1967) 151; Trans

Inst. Chem. Engrs. London 45 (1967) 285; Can. J. Chem0* Equilibrium saturation temperature (C) Engng. 47 (1969) 483.

A0 Supercooling, O~O(C) 8) S. M. Shor and M. A. Larson, Chem. Eng. Progr. Sympo

AOi,,ax Maximum allowablesupercooling (C) SeriesNo. 11067(1971) 32.

9) F. C. Frank, in: Growth and Perfection ofCrystals, EdsAcknowledgement R. H. Doremus et al. (Wiley, New York, 1958) p. 411.

10) N. CabreraandD.A. Vermilya, in: Growth andPerfection o

The authorsare indebted to RogerJ. Davey of Uni- Crystals, Eds. R. H. Doremus et al. (Wiley, New York

versity College Londcn for the photographs in fig. II 1958) r i. 393.II) N. Albon and W. J. Dunning, ActaCryst. 12(1959) 219.

and for useful discussions during the preparation of 12 ) R . J. Davey, Ph. D.Thesis, University ofLondon, 1973.

Documents

Journal of Crystal Growth Volume 20 Issue 3 1973 [Doi 10.1016_0022-0248(73)90002-x] Maurice a. Larson; John W. Mullin -- Crystallization Kinetics of Ammonium Sulphate