Jaroslav Nfvlt , Joachim Ulrich

Admixtures in Crystallization

Weinheim - New York Base1 Cambridge - Tokyo

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J. Njrvlt, J. Ulrich

Admixtures in Crystallization

0 VCH Verlagsgesellschaft mbH. D-69451 Weinheim (Federal Republic of Germany), 1995

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ISBN 3-527-28739-6

Jaroslav Nfvlt , Joachim Ulrich

Admixtures in Crystallization

Weinheim - New York Base1 Cambridge - Tokyo

Dr. Sc. Ing. Jaroslav Syvlt Institute o f Inorganic Chemistry of thc Academy of Scicnces of the Czech Republic I’ellCova 24 16000 Prague 6 Czech Kcpublic

Priv.-Doz. Dr.-Ing. Joachim Ulrich Universitat I3remen Vcrfahrenstechnik/I;B 4 Postfach 330440 D-28334 Bremen Germany

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Die Deutsehe Bibliothek - CIP-Einheitsaufnahmc N+vlt, Jaroslav: Admixtures in crystallization I Jaroslav NCvlt ; Joachim Ulrich. - Weinhcim : New York : Basel ; Cambridgk : Tokyo : VCH, 1995 ISBN 3-527-28739-6 KE: Ulrich. Joachim:

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Industrial crystallization has been considered for many years to be

more a magic than a science. One of the reasons has certainly been the fact

that additives or impurities even in the smallest amounts have tremendous

effect on nucleation. crystal growth, crystal forms and dissolution rates.

In recent years, not only has the level at which impurities are detec-

table decreased dramatically, but also the understanding of the interaction

of substances has increased by the same extent. Although there is still not a

complete understanding of the functioning of additives and impurities in

crystallization, there are many interesting new approaches in this field

which should lead to helpful models soon.

The authors want to contribute by gathering every piece of informa-

tion together in this book to help to contribute for a better understanding of

the whole matter. Data of crystallizing substances are presented here

together with the examined admixtures and the found effects, extracted

from the literature databases of both of the authors.

The authors hope that the use of the tables presented wffl lead to a

better design and understanding of crystallization processes, especially of

the functioning of additives. and thus facilitate a proper choice of additives

in order to obtain the required product properties.

The authors would acknowledge the support of the Czech Grant

Agency (Grant No. 203/93/0814) and of the Volkswagen Stiftung.

J. Njrvlt. J. Ulrich December 1994

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2. Classification of Admixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3. Influence of Admixtures on Nucleation . . . . . . . . . . . . . . . . . . . 9

3.1. Homogeneous Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2. Heterogeneous Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3. Secondary Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4. Influence of Admixtures on Crystal Growth . . . . . . . . . . . . . . . 16

4.1. The Role of the Solid Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2. 22 The Role of the Interphase Solid - Liquid . . . . . . . . . . . . . . . . . . . .

5. Influence of Admixtures on Crystal Shape . . . . . . . . . . . . . . . . 24

6. Influence of Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

7. Distribution of Admixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7.1. Solid Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

7.2. Isomorphous Inclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7.3. Anomalous Mixed Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7.4. Adsorption Inclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7.5. Mechanism of Internal Adsorption . . . . . . . . . . . . . . . . . . . . . . . . 43

7.6. Mechanical Inclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.7. Materials Balance for Crystallization in Presence of Impurities . . . 45

7.8. Cascade Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1

Contents 3

8 . Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

9 . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

10 . Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Formula Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

11 . References to Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

12 . SubjectIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389

1. Introduction

Crystallization is one of the oldest separation operations in chemical

industries. I t serves not only to separate and purify substances, but also to

produce crystals with a required shape. Both of these aspects are closely

connected with the presence of admixtures in the solution. Among the

many factors affecting the process of crystallization I1 72,2261, [e.g.,

temperature, supersaturation, agitation). admixtures often exhibit the most

pronounced effect. Even traces of admixtures can influence the nucleation.

crystal growth, shape and size of product crystals, and also other properties

(caking. hygroscopicity. etc.). On the other hand, they may be entrained into

crystals and lower their purity.

A few years ago, a largely empirical approach was used to quantify

the effect of admixtures and solvents. A theoretical description of the effect

of admixtures has been developed only rather recently. Nevertheless, a

consistent theory of the effect of admixtures on individual aspects of the

process of crystallization is sti l l missing. Various admixtures probably

operate with different mechanisms. Some of them are selectively adsorbed

on crystal faces and deactivate individual growth centers, others can

change the structural properties of the solution or of the interface; they may

be incorporated into the crystal lattice or pushed away by the growing

crystal and sometimes there exists a chemical interaction between the

micro- and macrocomponents. I t is obvious that this situation enables u s to

give subsequent explanations of individual effects but the prediction is

1. Introduction 5

still difficult. Computer simulations available in recent years [2.123.124]

facilitate the choice of tailor-made admixture but their use is sti l l limited.

Although the literature on crystallization in the presence of admix-

tures is very extensive, most papers exhibit just an empirical character.

Reasonably complete information on the effect of admixtures can be found

in monographies on crystallization and in surveys. At this point we have to

mention in particular the books by Buckley [32], Khamski [101.102]. Mug

[ 1121. Kuznetsov [120], Matusevich [133j. Matz 11341. Melikhov (1421. Mullin

[152]. Njrvlt [169.171.172] and Ohara and Reid 11791. and papers by Broul

[30]. Cabrera and Vermilyea (411. Chernov [46]. Davey [SO]. Garrett I711 and

Wirges [2421. The purity of crystals and distribution of impurities is dealt

with in many papers, e.g. by Melikhov (1421. Stepin et al. [211] or Slavnova

12061. More detailed information can be found in the literature which

exceeds 2000 papers; the aim of this book is to give a survey of the state of

the art of this subject and of a number of these papers in appended tables.

Before we continue we must mentlon the pioneering work of late Dr. Broul

who started the work on survey of the effects of admixtures 1291.

2. Classification of Admixtures

Crystallization from aqueous solutions can be understood as a

physical process where a pure solid A precipitates from its solution in pure

solvent B. Systems met in practice are usually more complex and in

addition contain several non-crystallizing substances, often in low concen-

trations. Crystallization itself therefore proceeds in a multicomponent

system and the result may be affected by these foreign substances - ad-

mixtures.

An admixture may be defined I301 as a substance present in a crys-

tallizing system that itself doesn’t precipitate as a separated solid under

given conditions. Such a broad definition comprises the solvent as an

admixture as well. This affects the crystallization parameters in many cases

encountered in crystallization from various pure or mixed solvents. Besides

the general term admixture we shall use a more specific term impurity for

substances, unintentionaly present in the solution (e.g.. coming from the

raw materials. from dissociation and other reactions, from corrosion of the

equipment). and addftlue for substances that we add to the solution in order

to modify its crystallization properties. The amount of admixtures is very

different in individual cases. Substances whose concentration is comparable

to that of the crystallizing macrocomponents are called macroadmixtures.

whereas those present in a concentration lower by two orders than that of

the macrocomponent are called microadmixtures or microcomponents [ 10 11 .

2. Classification of Admixtures 7

Additives are put into the solution with the purpose of affecting the

parameters of the process of crystallization and the product quality. Addi-

tives employed for aqueous solutions can be subdivided into several groups:

a) nee acids and/or bases, adjusting the pH value of the solution. The pH

modifies the nature and the concentration of ions in solution. particularly

when the latter contains salts of weak acids or bases 118). This pH value

has a dramatic effect on the shape (40,1291 or size I1681 of product crystals

and affects also the growth rate [148]. Acids or bases most frequently used

usually have a common ion with the crystallizing substance.

b) Inorganic additives can be subdivided into highly and less active ones.

High active additives include polyvalent cations such as Fe3+. Cr3+, A13+,

Cd2+, Pb2+, as well as certain anions like W0,2-. PO,3-. Very low

concentrations of these additives are sufficient to exhibit a dramatic effect

on crystallization (0.001 to 0.1 wt. %). In order to obtain a similar effect

with less active additives we have to use much higher concentrations (1 - 10

wt. 96). Inorganic additives affecting the crystal growth rate often exhibit a

similar influence on crystal dissolution 152.68.76.1991.

c) The most frequently used organfc addftfues exhibiting high effectiveness

are surface active substances and organic dyestuffs. I t has been observed

I461 that 1 molecule of such an additive per lo4 to lo6 molecules of an or-

ganic macrocomponent decreases its growth rate. The effect of big orga-

8 2. Classifiatlon of Admixtures

nic molecules is usually not specific to that molecule: a substance can

modify the growth of several macrocomponents and a similar modification

can be obtained using very different organic additives 1411. This property

may be ascribed to the fact that big organic molecules can be adsorbed at

any site on the crystal surface s o that their size is a deciding feature. Like

in catalysis, the position of substituents in the molecule should also be

very important [32]. The influence of organic substances on the growth rate

of crystals is usually very dramatic but their effect on the dissolution rate

can usually be neglected [41.46.240]. In many cases, where the additive is

very active on crystal growth, even a 1000 fold concentration has no effect

on dissolution 1321.

The effectiveness of an admixture is closely bound to the given sys-

tem and cannot be simply generalized. For the activity of additives on the

crystal shape, Buckley 1321 defined the measure of the effectiveness of the

additive as the number of weight units of the crystallizing substance per one

unit of the additive that causes a certain shape modification. Another way

of measurement and evaluation of the effectiveness of admixtures has also

been described in the literature I2191. The influence of admixtures drops

with increasing temperature and growth rate 1321.

3. Influence of Admixtures on Nucleation

Several mechanisms of nucleation can be distinguished according to

conditions in a supersaturated solution 11781:

nucleation - primary - homogeneous

- heterogeneous

- secondary - originatedfrom solid phase

- originatedfrom the interphase solid-liquid

- collision breeding

A basic criterion for this distinction I1 781 is the presence or absence of a

solid phase. While primary nucleation occurs in the absence of solid particles

of the crystallized substance, secondary nucleation is dependent on the

presence of crystals. For homogeneous nucleation. no solid phase is required,

while heterogeneous nucleation is catalytically initiated by any foreign

surface. Many details on the mechanisms of secondary nucleation can be

found in the literature 1152,177,178,214,215,225j.

Strong effects of the admixtures can be observed with primary

nucleation and with secondary nuclcation due to mechanisms of the

interphase. There are several papers dealing with the theory of the effect of

admixtures on nucleation: in addition to those mentioned below, i.e. papers

(23.78.1571.

10 3. Influence of Admivtures on Nucleation

3.1. Homogeneous Nucleation

According to the theory of homogeneous nucleation. the nucleation

rate increases as the interfacial surface tension, asl decreases. As the sur-

factants dramatically lower the surface tension, their presence in solution

strongly increases the nucleation rate [44.55.83.176]. We may expect,

however, that other admixtures when present in higher concentrations raise

the surface tension and thus decrease the nucleation rate.

Very active inorganic admixtures characterized by a strong tendency

to form coordination complexes decrease the nucleation rate: the stronger

their influence, the higher the complex stability. One of the explanations

tells that heteroclusters are formed in the bulk solution with the centre

formed by the active ion 179.803. The number of these heteroclusters cor-

responds to the number of ions of the admixture, their size being given by

the ratio of the supersaturation and the admixture concentration. The effect

then consists in redistributing of the solute forming supersaturation to

these heteroclusters s o that the supersaturation is effectively decreased.

Clusters can grow only when the supersaturation is increased again. The

effect of admixtures can here be explained by the electric field of the ad-

mixture affecting the behaviour of the macrocomponent [ 1551.

The inhibiting effect of polyphosphates on the nucleation of sparingly

soluble carbonates and sulphates is well known 186,1923. It can be explai-

ned thus: due to the geometric similarity of the active ion and the surface

3.1. Homogeneous Nucleation 1 1

structure of the macrocomponent. polyphosphate ions are adsorbed on the

surface of undercritical embryi of the macrocomponent so that these clus-

ters cannot continue to grow (33.55.1891. The static adsorption model as-

sumes that the embryo surface is covered by a monomolecular layer of

admixture molecules [62,146.147.180]: the dynamic model of adsorption

1144,160.1611 is based on the probability of collisions of the particles of the

macrocomponent with those of the admixture. Calculations of the Me time

of embryi and the time elapsed between two collisions of the embryi with

the admixture show that the collision mechanism prevails in the initial

periods of the nuclei formation, whereas later the adsorption mechanism

with adsorption of the admixture on active centres of the macrocomponent

prevails. The endothermic adsorption of the admixture decreases the

stability of the surface and raises the energetic barrier of critical nucleus

formation. For thts reason, the complex formed by adsorption dissociates

before it could form a critical nucleus. This leads to increased stability of

the system. Incorporation of admixture particles in the first period of

precipitation is not expected by thts model. Nevertheless, experiments have

shown 11801 that the first fractions of precipitated crystals contain much of

the admixture. so that the assumptions of thts model are not completely

realistic.

Admixtures belonging to the group of water-soluble wUoids (dextrin.

gelatlne) raise the solution viscosity: the diffusion and mobility of particles

are then decreased so that their growth to a critical size is more difficult

[ 133,1691.

12 3. Influence of Admixtures on Nucleation

There are also examples described in the literature 1167,1691 where

the admixture accelerates the nucleation. This may be encountered in cases

where the admixture reacts with the macrocomponent to form less soluble

substances. Admixtures that have a common ion with the macrocomponent

can decrease its solubility, this leading to a rise in supersaturation and

thus to a decrease of induction periods of nucleation [ 10 1,102.2441.

Another reason can be given in the case of admixtures with a significant

hydration ability: they remove water from the hydration spheres of the

macrocomponent [82.170,1741 and in this way decrease the solution sta-

bility 11331.

3.2. Heterogeneous Nucleation

Using a droplet technique for investigations of the induction time of

nucleation, Wen (2391 was able to differentiate between homogeneous and

heterogeneous nucleation mechanisms. With pure NaCl solutions he found

both the mechanisms but in the presence of Pb2+ ions the induction time

measurements indicated no effect on the homogeneous nucleation. H e

therefore concluded that impurities affected nucleation by working on the

substrate rather than the nucleating crystal. Nevertheless, measurements

carried out on only one system does not allow such a generalization. The

additive may adsorb onto the heteroparticles making them either more or

less active as catalysts [55]. This would either increase or decrease the

nucleation rate. Alternatively, the additive molecule may itself act

3.2. Heterogeneous Nucleation 13

as a heteroparticle providing a template 11961 for the precipitating sub-

stance. This would lead to an increase in nucleation rate proportional to the

additive concentration.

The heterogeneous nucleation can be treated as secondary nuclea-

tion with the mechanism of interphase layer. At the solid surface there are

more or less oriented clusters that may be removed by fluid shear back into

the bulk of solution 120.43.97.188.2161. These clusters, if they are of the

critical size, can survive and form new nuclei.

S@me mtlve substances deactivate heterogeneous particles and thus

increase the width of the metastable region 1165,1831. The extent of this

action is given by the amount and catalytic activity of foreign particles. An

opposite influence [203.204] can be explained by the fact that surface active

substances decrease the surface energy so that the nucleation rate can

increase. The shape of the curve of nucleation rate vs. the admixture

concentration resembles the adsorption isotherms of surface active

substances on solid surfaces so that there may be expected a direct link of

the nucleation rate rise with the adsorption of the admixture on the surface.

14 3. Infruence of Adrnivtures on Nucleation

3.3. Secondary Nucleation

One of the mechanisms of secondary nucleation is the mechanism of

interphase layer. At the solid surface there are a more or less oriented

clusters that may be removed b y w d shear back into the bulk of solution

143,188,2161. These clusters, if they are of the critical size, can survive and

form new nuclei.

Some admixtures call forth formation of rough surfaces or even

dendrltes [loo]. Due to fluid dynamic forces or due to partial dissolution

these dendrites can be removed back to the bulk of solution, where they

serve as new nuclei [6 1.1401.

Active inorganic admixtures dilate the metastable zone in super-

saturated solutions. In absence of admixtures, the probability of formation

of stable aggregates at the solid surface is higher than that in the bulk of

solution [177]. This is due to the physical adsorption of the particles of the

macrocomponent and thus due to higher local supersaturation. In analogy

with heterogeneous chemical reactions, adsorption occurs preferentially a t

energetically advantageous active sites on the surface. If these advanta-

geous sites are blocked by the admixture, however, then the probability of

formation of a critical cluster diminishes and the nucleation rate decreases

1203,2041. In addition, adsorption of ions of an admixture that possesses

higher charge than those of the macrocomponent damages the balance of

electric charges on the surface [156] and this leads also to a decrease in the

nucleation rate 1203,2041.

3.3. Secondary Nucleation 15

In systems where the admixture can easily be incorporated into the

growing crystals' lattice. the so-called impurity concentration gradient can be

effective I22.611. Nucleation in the bulk of solution is hindered due to

presence of the admixture at high concentration. Incorporation of the ad-

mixture into the crystal lattice leads to a decrease of its concentration close

to the surface so that spontaneous nucleation In the intermediate layer

becomes possible again. Presence of growth-restrainers also exhibits an

effect on nucleation I1261 (they enlarge the metastable zone width [ZlO]).

4. Influence of Admixtures on Crystal Growth

There exist a number of books and papers dealing with the theory of

crystal growth [ 100,112.130.152.178,179,184.185.202.243]. Quantities,

necessary for the application of these theories, are often not known so

several simplifications have to be adopted. Fundamental physical quantities

then lose their physical meaning and become adjustable parameters. I n

addition, experimental methods 172,1781 provide data of limited accuracy so

that the fit of experiments and theory often becomes a matter of statistics.

This must be kept in mind when discussing the effect of admixtures on the

growth rate of crystals.

Due to the different structures and energetical situations growth rate

of individual crystal faces is also different. This also holds for the effect of

admixtures on the growth rate of crystals and this is why individual crystal

faces must be considered separately. The effect of growth rate dispersion

can lead to different values on individual crystals, however, and this may be

one of the reasons why the literature data are scattered and differ from

those obtained by measurements in suspension [ 116. 2261.

4.1. The Role of the Solid Surface

Kossel 1114.1 151 and Stranski 1212.2131 recognized the importance

of atomic inhomogeneities of crystalline surfaces and its relevance to growth

processes. They distinguished three different regions on a crystal

4.1. The Role of Solid Surface 17

surface: a) frcct surfaces. which are atomically smooth: b) steps, which

separate flat terraces: c) kinks. which are formed in incomplete steps. Kinks

present the most probable position for solute integration because the

highest bonding energy associated with integration occurs here. Flat

surfaces are the least energetically probable sites for incorporation. Never-

theless. admixtures. according to their nature, can adsorb on different sites

on the surface: they can affect the relative interfacial energy of individual

faces or block the active growth centres [30,38J. The effect of admixtures is

different if they are adsorbed on different sites 1531.

Fig. 4.1: Surface growth sites

According to growth rate equations and considering that adsorption

lowers the edge or surface energies and the size of the critical two-dimen-

18 4. Infruence of Admixtures on Crystal Growth

sional nucleus, we see I181 that the expected result of adsorption is an in-

crease in the crystal growth rate. Other parameters must then act in the

opposite direction in order to explain the decrease of the growth rates

generally observed in habit change phenomena: the slow down of the flux

towards to the steps 1371, the decrease of the lateral advancement velocity

of growth layers due to step pinning [41.66.186.187.1981. a decrease of

number of kinks available for the growth [48,491.

In general, admixtures can be subdivided into strongly adsorbed and

weekly adsorbed ones. One can suppose that physical adsorption is

characteristic for weekly adsorbed admixtures whereas chemical bonds are

typical for strongly adsorbed substances 1491. Mechanism of strongly

adsorbed admixtures [41.158.179,234] assumes that immobile particles of

the admixture are spread over the crystal surface. When a moving growth

step hits such a particle, its edge becomes deformed. In the case where the

distance of two neighbourlng adsorbed particles is smaller than the size of

two-dimensional critical nucleus, the movement of the step will cease [67],

otherwise the step will be deformed and pushed through the slot between

adsorbed particles and continue in its movement but with a reduced rate l'i

[9.41,186,187].

(4.1)

where l', represents the growth rate in absence of an admixture and n is

4.1. The Role of the Solid Surface 19

assumed to be the average density of admixtures on the ledge ahead of the

step 1411. This equation indicates that the velocity of steps is reduced by an

amount proportional to the concentration of adsorbed admixtures on the

terrace. If such a foreign particle is incorporated into the crystal lattice, it

causes some deformation of the lattice. Joining of another particle of the

macrocomponent to such a deformed lattice may be difficult (1691. The re-

tardation of growth takes place only if the height of the adsorbed particle

can be compared with that of the moving step 1461. Some inorganic admix-

tures can form complex substances (double salts) in combination with the

macrocomponent: such complex nuclei are formed at the sites with strongly

adsorbed admixture. These complex nuclei are not stable, they may

redissolve but the admixture remains adsorbed on the surface [34].

Another mechanism is encountered with weakly adsorbed admixtures.

Here, the retarding action is due to blocking of the active growth centres.

The strength of bonds between the lattice particles and the admixture

determines the mobility of the admixture. Weakly adsorbed admixture can

diffuse two-dimensionally on the surface and can be expelled by the movlng

step, but at the cost of growth rate reduction. If the growth is sufficiently

slow and the amount of admixture is not too high, adsorption equilibrium

can be attained at the surface. The relationshlp between the linear growth

rate of the face r' and the concentration of admixture wi can be described

I12.151 by Wl

1' = 1 6 - ( 1 6 -1'- ) . - B +w,

(4.2)

20 4. Infruence of Admixtures on Crystal Growth

where lv0 and l ' , represent respectively the growth rates in absence of

admixture and in presence of admixture when all of active growth centres

are occupied 12341. The surface fraction covered by the admixture can be

determined using, for example, the Langmuir adsorption isotherm with the

constant B. The linearized form of this equation I531 allows us to obtain the

value of free enthalpy of adsorption [ 13.16.171. The Langmuir isotherm has

been used also by other authors I581 considering surface diffusion to be the

rate-determining step. The equation above holds even here if we take l'=- 0

130.1 121.

Another model is based on a n estimate of the probability of occur-

rence of free growth active sites and uses the Freundlich adsorption iso-

therm to predict the movement rate of a growth step 14,661. All of the

models mentioned above have been experlmentally verified with a satisfac-

tory result [53]. A survey of adsorption models is given in several papers

153.55.58.1 121.

When the growth of a crystal face is governed by the mechanism of

two-dimensional nucleatton, then the effects of admixtures on nucleation that

are mentioned in the preceding chapter may come into consideration. The

size of a two-dimensional nucleus is [10.411

2a Q

kTS 21, =- (4.3)

4.1. The Role of Solid S@me 21

where a is the lattice constant, o the surface energy and S relative super-

saturation. Since the size Zc , which can be compared with the admixture

spacing on the surface, determines whether the step can advance or not,

this equation indicates a critical supersaturation that must be exceeded in

order to allow growth.

According to Glasner I79.801 the crystal growth is executed by

deposltlon of heteronuckl on the crystalline surface. The effective supersatu-

ration is then given by the product of the number of heteronuclei (i.e. of the

amount of molecules of the admixture) and of the average size of a

heteronucleus as expressed by the number of molecules of the macrocom-

ponent forming an average heteronucleus.

Su.@atants and organic dyesbgs usually exhibit a very sensitive effect

on the crystal growth rate; their big molecules are attached to the crystal

surface through their polar I301 or hydrocarbon Ill21 portions and prevent

the access of the macrocomponent molecules to the surface 1361. Complexlng

agents, e.g. EDTA. remove certain ionic admixtures from the solution and

therefore act in an opposite direction I116.2101.

Certain admixtures. when present in low concentrations. can accek-

rate the growth of crystals [121.148]. First, this are admixtures lowering the

surtace energy; one can expect those crystal faces possessing higher specific

surface energy adsorb more admixtures and thus grow faster (141. In some

cases, when the admixture has a similar structure parameters or forms

complexes with a structure close to the lattice of the macrocompo

22 4. Infieme of Admixtures on Crystal Growth

nent. adsorbed admixture molecules can form new active growth sites on

the surface that are energetically more advantageous for further growth

I 12,1691.

Available data thus clearly substantiates the necessity for geometric

simflarlties between the additive and the crystal surface 1551. Whether ad-

sorption occurs due to surface interaction between ionizable groups on the

additive molecule and ions in the crystal surface or due to a surface

replacement mechanism is unresolved 1551 and will probably be different in

different cases. In the case of crystal growth such adsorption mechanisms

are easily visualized to involve the blocking of key sites on the surface and

hence reduction in growth rates.

The effect of admixtures can be combined with other factors, like pH

(acid or base can be considered as a second admixture) or, if a higher

amount of admixture affects the solubility of macrocomponent. we can

speak of the combined effect of admixture and supersaturation I10 1,1341.

4.2. The Role of the Interphase Solid - Liquid

The growth of a crystal can be represented as three successive steps:

a) Transport of the substance from the bulk of solution to the crystal; b)

transport of the substance through the layer close to the crystal surface: c)

incorporation of the substance into the crystal lattice, either by surface

diffusion a t the kink or by formation of a two-dimensional nucleus. The first

step is largely affected by the fluid dynamics of the system

4.2. The Role of the Interphase Solid - Liquid 23

and its role is usually not too important. The last step has been discussed

in detail in the preceding chapter; we shall thus pay attention to the second

step.

The interphase or the "interface phase" 1511 is understood to be the

region between the "perfect" solid phase and the "perfect" liquid phase. It

can be diffuse (1.e. there are layers at the phase interface and it is

impossible to say clearly whether they belong to the solid or to the liquid;

the changes of physical quantities occur within the distance of several

lattice constants) or it can consist of a quasi-liquid layer, which usually has

a higher concentration of the solute in the bulk of solution 128,1751. The

structure of the interphase has been studied using the theory of fractals

[42.127.128.194] with the result that different growth models led to the

formation of clusters in the interphase with different fractal dimensions.

These characterize the shape of clusters or the roughness of the interphase.

Transport of molecules through the layer adsorbed on the crystal

surface is reallzed through diffusion. The admixture can play different roles

in this step. It can affect the viscosity of the solution. in particular at higher

concentrations. It has been shown 11 131 that even small amounts of surface

active substances can dramatically raise I1 13.1181 or decrease I1 191 the

viscosity.