Effects of impurities on crystal growth processes

Pergamon

Prog. Crystal Growth and Charact. Vol. 32, pp. 3-43, 1996 Copyright © 1996 Published by Elsevier Scier~e Ltd Printed in Great Britain. All rights reserved 0960-6974/96 $32.00 PII: S0960-8974(96)00008-.3

EFFECTS OF IMPURITIES ON CRYSTAL GROWTH PROCESSES K. S a n g w a l Department ot Physics, Technical University ot Lublin, ul. Nadbystrzycka 38, 20-614 Lublin, Poland

ABSTRACT The mechanisms of adsorption of impurities during the growth of bulk crystals are surveyed. "The impurities considered are foreign substances deliberately added to or inherently present in a growth medium. After a brief introduction to different growth models, the nature of impurities and types of impurity effects on growth kinetics, adsorption of impurities on F faces at relatively low and high impurity concentrations is first discussed. Here mechanisms of adsorption at kinks in steps and surface terrace in the presence of low concentrations of one impurity and two eompetitive impurities are presented. Then the concepts of adsorption of impurities involving the formation of two-dimensional impurity layer and three-dimensional impurity clusters as growth promotors on a growing face are developed. Thereafter the mechanism of adsorption of impurities on S and K faces and the determination of the adsorption mechanism on a growing face from the kinetic data are discussed. Finally, impurity effects on surface morphology of bulk crystals, and growth morphodroms of alkali halides are briefly reviewed. Copyright © 1996 Published by Elsevier Science Ltd

KEYWORDS Adsorption isotherms, adsorption mechanisins, growth mechanisms, growth models, growth morphodroms, impurities, surface morphology.

1. INTRODUCTION Influence of foreign particles present in growth media has long been recognized in changing growth habits of crystals. The literature existing prior to 1950 on the habit modification of crystals by impurities has been surveyed in the classic monograph by Buckley (1951). After the publication of this monograph, studies on the effects of impurities were diverted to understand the mechanisms involved in changing the growth habit on microscopic level. The first important works in this direction were published during the late fifties and sixties by Frank (1958), Cabrera and Vermilyea (1958), Sears

K. Sangwal

(1958), Dunning and Albon (1958), Dunning et al. (1965), Bliznakov (1954, 1958, 1965), Bliznakov and Kirkova (1957, 1969), Bliznakov et al. (1965), Bienfait et aL (1965) and by Kern (1967). Cabrera and Vermilyea (1958) considered theoretically the adsorption of impurity particles on surface terrace in the motion of ledges across the surface. Sears (1958), and Dunning and Albon (1958) and Dunning et al. (1965) proposed the model of adsorption of impurity molecules at ledges of a face, and tested the validity of their model against the background of the dependence of rates of motion of growth layers on impurity concentration. Bliznakov (1954, 1958, 1965) introduced the model of reduction of growth rates by impurity particles adsorbing on active growth sites on a face, and reported experimental results in support of the model for a number of water-soluble compounds. Chernov (1961, 1984) treated the adsorption of foreign substances in kink positions in a ledge and showed a close relationship between Bliznakov's model and his concept of adsorption at kinks. Apart from the above kinetic models involving adsorption at surface terrace (Cabrera-Vermilyea model), ledges (Sears model) and kinks (Bliznakov model), on the basis of their experimental results on growth forms of alkali halides as a function of supersaturation and impurity concentration, Bienfait et al. (1965) and Kern (1967) advanced structural interpretation of habit modification in terms of the formation of two-dimensional adsorbed-impurity layer structurally similar to the growing crystal face. The second phase of investigations on impurity effects started from the works of Davey (1974) and Davey and Mullin (1974b, c), who studied layer displacement rates as a function of impurity concentration, and confronted the experimental data with different kinetic models of impurity adsorption. The last phase of the studies on impurities beginning from the early eighties deals with the design of structurally specific additives, called tailor-made impurities (Addadi et al., 1985; Berkovitch-Yellin, 198.5; Berkovitch-Yellin et al., 1985; Shimon et al., 1986). Any foreign substance other than the crystallizing compound is considered as an impurity. Thus, a solvent used for growth and any other compound deliberately added to the growth medium or inherently present in it is an impurity. Different terms, such as additive, admixture, inhibitor or poison, are used in the literature for foreign substances other than solvent. Irrespective of its concentration, a deliberately added impurity is called additive, but by the term admixture we mean an impurity added in relatively large amounts (up to several percent). A surfactant may be any chemical compound active on the surface in changing its growth behaviour. An impurity can accelerate or decelerate the growth process. The impurity that decelerates growth is called a poison or an inhibitor, while the one that accelerates growth is said to be a growth promotor. The literature on the effects of impurities on crystal growth is quite voluminous, and has been reviewed several times (Boistelle, 1976; Davey, 1979; Simon and Boistelle, 1981; Chernov, 1984; Van Rosmalen el el., 1989; Van Rosmalen and Bennema, 1990; Sangwal, 1993, 1994) since the publication of Buckley's monograph (Buckley, 1951 ). The experimental data on impurities deal with the following topics: habit modification and morphodroms (Bienfait et al., 1965; Kern, 1967; Mullin et al., 1970; •lulg and Deprick, 1983; Aquilano et al., 1984; Black et al., 1986; Davey, 1986; Davey et al., 1986; Sano et al., 1990; Li et al., 1990; Van der Voort and Hartman, 1990; Sasaki and Yokotani, 1990; Owezarek and Sangwal, 1990a; Levina, 1992; Surender and Kishan Rao, 1993; Ristid et al., 1993, 1994), Rinaudo et al., 1994), kinetic data on face growth rates (Bliznakov, 1965; Bliznakov and Kirkova, 1957. 1969; Bliznakov et al., 1965; Mullin et aI., 1970; Kirkova and Nikolaeva, 1971, 1973; Nikolaeva and Kirkova, 1975/1976; Troost, 1968, 1972; Botsaris et al., 1973; Simon et al., 1974; Davey and Mullin, 1974a; Dugua and Simon, 1978a, b; Belyustin and Kolina, 1978; Punin and Vorob'ev, 1978; Draganova, 1981; Draganova and Koleva, 1980; Kimura, 1985; Beckmann and Boistelle, 1985; (~hernov et al., 1981, 1986, 1987; Bredikhin et al., 1987; Chernov and Malkin, 1988; Chu et al., 1989; Malkin et al., 1989; Sasaki and Yokotani, 1990; Owczarek and Sangwal, 1990a, b; Zipp and Rodriguez-Hor,ledo, 1992; Tai et al., 1992; Davey et al., 1992; Barsukova et al., 1992; Okhrimenko

Effects of Impurities on Crystal Growth Processes

5

et al., 1992; Velikhov et al., 1992; Velikhov and Demirskaya, 1993; Ristid et al., 1993, 1994; Forsythe and Pusey, 1994; De Vreugd et al., 1994) and layer displacement rates (Dunning and Albon, 1958; Dunning et al., 1965; Davey and Mullin, 1974b; Dam and Van Enckevort, 1984; Chernov et al., 1987; Hottenhuis and Oudenampsen, 1988; Onuma et al., 1990; Shekunov et al., 1992; Bikov et al., 1994; (;ratz and Hillner, 1993; Ristid et al., 1994), observation of the presence of dead supersaturation zones at low impurity concentrations (Troost, 1968, 1972; Botsaris et al., 1973; Simon et al., 1974; Dugua and Simon, 1978a, b; Belyustin and Kolina, 1978; Punin and Vorob'ev, 1978; Chernov et al., 1986; Bredikhin et al., 1987; Chu et al., 1989; Malkin et al., 1989; Chernov and Malkin, 1988; Velikhov, 1992; Velikhov et al., 1992; Velikhov and Demirskaya, 1993; Alexandru and Berbecaru, 1995), ex-situ (Dugua and Simon, 19783, b; Hottenhuis and Lueasius, 1986; Yokotani et al., 1987; Hottenhuis and Oudenampsen, 1988; Owczarek and Sangwal, 1990b; Ristid et al., 1993; De Vreugd et al., 1994) and in-situ observation of crystal faces (Dunning and Albon, 1958; Dunning et al., 1965; Davey, 1974; Davey and Mullin, 19743, b, c; Chernov et al., 1981; Dam and Van Enckevort, 1984; Beckmann and Boistelle, 1985; ttottenhuis and Lucasius, 1986; Onuma et al., 1990; Shekunov et al., 1992; Bikov et al., 1994; Gratz and Hillner, 1993), nucleation and precipitation kinetics (Weijnen and Van Rosmalen, 1984; Hamza et aI., 1985; Weijnen et al., 1987; Boistelle and Astier, 1988; Roberts et al., 1990; Kubota et al., 1990; Kern and Dassonville, 1992; Triboulet and Cournil, 1992; Ginde and Myerson, t993; Antinozzi et al., 1992; Monaco and Rosenberger, 1993; Herden et al., 1993; Renaudo ctal., 1994), and chemical constitution of impurity species and chemistry of adsorption in solution growth (Reich and Kahlweit, 1968; Mullin, 1972; Dam and Van Enckevort, 1984; Nielsen, 1984; Kimura, 1985; Veintenlillas-Verdaguer and Rodriguez-Clemente, 1986; Sangwal, 1987; Hottenhuis and Oudenampsen, 1988; Monaco and Rosenherger, 1993; Velikhov and Demirskaya, 1993; Herden ct al., 1993). Recently, it has been found (Gratz and Hillner, 1993) that atomic force microscopy is a very powerful tool to study the nature of adsorption processes on atomic scale.

In recent years, theoretical papers dealing with the elementary processes of adsorption have been published (Voronkov and Rashkovich, 1992, 1994; Potapenko, 19933, b). Moreover, attempts have been made to model the morphology of organic crystals growing in the presence of tailor-made impurities (ClydesdMe et al., 1994a, b). The aim of this review is to survey our present understanding of the mechanisms of adsorption of impurities during growth. Here the impurities considered are foreign substances deliberately added to or inherently present in a growth medium. The role of solvent and the effect of impurities on three-dimensional nucleation are not discussed. These topics are discussed in other contributions of this volume. The review is based on the ideas contained in author's earlier works (Sangwal, 1993, 1994) on the effect of impurities on crystal growth.

2. GROWTH MODELS Impurities contained in a growth medium affect the kinetics of growth of all types of faces present ill tile growth form of a crystal. According to Hartman's concept of periodic bond chains (PBC) (Hartman, 1973, 1987; Sangwal, 1994), F faces are smooth on a molecular level and contain a low density of kinks, while S and K faces are rough and contain a relatively high density of kinks. Therefore, the growth of F faces is possible only when growth layers emitted by dislocations emerging on the surface or two-dimensional nuclei forming on it provide kinks necessary for the attachment of growth entities. Because of their roughness, S and K faces, on the other hand, do not require the presence of dislocations or two-dimensional nucleation for growth.

6

K. Sangwal

2.1. Growth of F face In order to describe the effect of impurities contained in a growth medium on the kinetics of growth of an F face, for the sake of simplicity we consider the following models.

2.1. I. Dislocation growth models (a) Burton, Cabrera and Frank's (BCF) surface diffusion model. According to this model (Ohara and Reid, 1973; Sangwal, 1994), the rate of motion of parallel straight ledges, voo, and the rate of growth of a face, R, are given by v~ = 2~rA~flAhu e x p ( - W / k T ) tanh(yo/2A~),

(1)

and

Yo

~J

where the constants C* and ~r1 are given by C* =/~Af~n~ov exp(-W/kT),

(3)

~r~ = 197fl/2kTA~.

(4)

and

In these equations, the distance Y0 between ueighbouring ledges emitted by a spiral is expressed as Yo = 19r¢ = 192Ft/2kT In,5',

(5)

rc is the radius of critically-sized two-dimensional nucleus on tile face, h is the ledge height, 3' is the interracial tension, k is the Boltzmann constant, T is the temperature in Kelvins, the supersaturation ratio S = (cf/c~fo) = (l+c,) (where a is the supersaturation, and f and fo are the activity coefficients of the solute at the actual c and equilibrium solute concentration co, respectively, at the temperature T), ns0 is the number of growth units per unit area of the surface, W is the activation energy required by growth units to enter into kinks, As is the diffusion distance of the adsorbed molecule on the surface, f~ is the molecular volume, u is the atomic/molecular frequency,/3 is the kink retardation factor, and A is the step retardation factor. If a is the diameter of a molecule/atom, the maximum surface concentration (for example, for a face entirely composed of kinks) of growth units n,0 is 1/a 2.

(b) Chernov's direct integration model. According to this model (Chernov, 1984, 1986; Sangwal, 1994),

tanh(yo/2As),

vcc = ansoflff([c,T/hp) e x p ( - W / k T )

(6)

and R = ( 7 - - tanh O t

,

(7)

Effects of Impurities on Crystal Growth Processes

7

where the constant

C = ~,~o~(kT/hp) e x p ( - W / k T ) ,

(8)

hp is the Planck constant, and all other symbols have been defined above in the BCF model. It should be noted that the form of the rate equations in the BCF and Chernov models is essentially the same.

2.1.2. Birth-and-spread model of two-dimensional nucleation (B+S model) The two-dimensional nucleation rate J, ledge velocity v~o and the face growth rate R are given by the following equations (Ohara and Reid, 1973; Saugwal, 1994): J = (2/rr)n~F(~'t/h)'/2a '/2 exp(-~rh72~/k2T2a),

(9)

v~ = 2D, um~I/3Aa/hA,,

(]0)

and

R = hJ'/'~v~{ a = A(D,nso/3A/)~,O)'2/aa s/s exp(-rrh.72~t/ak2T2a),

(11)

where A is a constant, D, is the surface diffusion coefficient for solute molecules/atoms adsorbed on the surface, nl is the concentration of monomers on the surface, and $ = (8kT/rrm) 1/2 is the average speed of surface adsorbed atoms/molecules (m is their mass). According to eqs. (2) and (11), growth rates of faces having a high density of kinks (i.e. at high supersaturations) may be expressed by R =/~A~Noav e x p ( - W / k T ) ,

(12)

R - - A( D, Nofi A / A,~)2/a os/6.

(13)

and

Thus at high supersaturations, R increases more or less linearly with supersaturation.

2.2. Growth of S and K faces S and K faces are endowed with a high density of kinks on them. Therefore, as in the case of growth of F faces at high supersaturations, their growth rate increases linearly with supersaturation and may be given by

R = (kT/hp)~tNo(aexp(-Wkr),

(14)

where No is the kink density (number of kinks per unit area of the surface), the parameter ( describes the density of kinks in the presence of impurities and is equal to unity for a pure system, and W is the activation energy required to transfer an atom from the medium to the crystal.

8

K. Sangwal

3. IMPURITY EFFECTS ON CRYSTAL GROWTH Adsorption of an impurity on an F face affects three parameters, namely, the thermodynamic and kinetic terms involved in the growth models and the crystal solubility. The thermodynamic parameter in the growth models is the surface energy % It is usually assumed that adsorption of an impurity increases the value of ~ (Ohara and Reid, 1973). The consequence of this increase in 7 is to decrease the nucleation rate J in the two-dimensional nucleation models (the exponential term in eq. (9)) and to increase the radius r~ of critical two-dimensional nucleus and hence the spacing Y0 between the spiral steps in the BCF theory (eq. (5)). The growth rate R based on these theories will thus be decreased (see eqs. (2) and (11)). In contrast to the above assumption that an impurity increases the value of 7, consideration of the adsorption process in terms of adorption isotherms and reversible adsorption equilibrium shows that impurity adsorption decreases the value of 7 (Kern, 1967; Davey, 1979). This decrease in 7 will, consequently, cause an increase in R. The kinetic term in the growth theories is directly related with the velocity voo of movement of steps on the crystal surface. Impurities adsorbed on the surface decrease this velocity by decreasing the values of the kink retardation factor/3 (eqs. (1) and (6)) and the step retardation factor A (eq. (1)). Adsorption of an impurity at kink sites decreases their mean distance xo, which results in a decrease ill t~ and, consequently, in voo (eqs. (1), (6) and (10)). ('hernov (1961, 1984) treated the adsorption of foreign substances in terms of density of kinks in a ledge. According to him, when impurity adsorption at kinks render them ineffective, the average distance x0 between kinks is increased (i.e. their density is decreased), which leads to a decrease in the layer displacement rate v~ and the linear growth rate R with an increase in impurity concentration. It is difficult to predict the effect of impurities oil crystal solubility. A change in the solubility of the crystallizing substance caused by all impurity, associated with the reversible formation of a new chenfical compound, may change the surface concentration ns0 of growth species and the surface energy % An increase ill solubility increases no, which leads to a decrease in 3' (Sangwal, 1989, 1994). ('onsequently, the rates v~ and R of the above models are increased (see eqs. (1), (2), (6), (7), (10) and (11)). In general, an impurity with solubility higher than that of the crystallizing substance will increase the growth rates, and, conversely, an impurity with solubility lower than that of the crystallizing substance will decrease the growth rates. Thus, the effects of changes in solubility due to the addition of an impurity suppliments changes caused by thermodynamic and kinetic paralneters. ttowever, at low concentrations, the effect of impurities on solubility is usually negligible (Kirkova and Nikolaeva, 1971, 1973; Davey et al., 1986; De Vreugd et al., 1994). It follows fronl the above considerations that, at relatively low impurity concentration, the theoretical models of growth predict opposite effects of impurities on growth kinetics. The thermodynamic effect tends to increase the growth rate while the kinetic effect tends to decrease i t . . A t relatively high supersaturations when a high density of kinks is available at the ledges, additive adsorption always decreases the rates v and R for all values of impurity concentrations. However, at low supersaturations which ensure a low density of kinks at the ledges, the rates increase for small additive concentrations and decrease as the additive concentration is increased. This behaviour is illustrated ill Fig. 1 for the linear growth rates of the {100} and { l l l ) faces of Pb(NO3): grown from aqueous solutions in the presence of methyl blue.

Effects of Impurities on Crystal Growth Processes

9

.g" o

)

~

n-

lO

20 c~p

Fig. 1.

'

30

4(J

50

"

( lO-Sg/[l

Dependence of linear growth rates R of (100) and (111) faces of Pb(NOa)2 grown from aqueous supersaturated solutions on concentration ci,,,p of methyl blue. From Bliznakov a]}d Kirkova (1957).

It should be mentioned that tile value of the impurity concentration, at which a peak in the 'O(Cimp) and R(Cimp) curves is observed, depends on the supersaturation used for growth, the temperature of growth, the nature of the adsorbing impu,'ity, and on the nature of the crystal face. For example, in the case of growth of the {100} faces of KDP in the presence of organic impurities (Barsukova et al., 1992), the peaks at ~r = 1.5% appear at 0.27 lnol%, 0.07 tool% and 0.0005 tool% of glycerine, ethyleneglycol and EDTA, respectively. Moreover, the corresponding impurity concentrations are 0.006 tool% and 0.0001 tool% for polyethyleneglycol of molecular weights of 300 and 2000, respectively. The inhibiting effect of the above additives is negligible on the {101} faces of KDP, which grow about 8 times faster than the {100} faces. Barsukova el al. (1992) suggested that the initial increase in R is due to tile ability of formation of inactive complexes by the additives with inorganic impurities present in the solution. In any case, these results reveal that the effect of an additive is related with the size of inhibiting species and with the rate of growth (i.e. with the growing face). Ill the case of inorganic salts growing in the presence of nonselectively adsorbing (i.e. mobile) impurities, the maxima in tile curves of growth rate R against impurity concentration ci,,v are usually observed at relatively low impurity concentrations (Bliznakov and Kirkova, 1957; Kirkova and Nikolaeva, 1973). In the case of immobile impurities, such maxima are ]ant observed in the R(Cimp) curves (Black el al., 1986; l)avey st al., 1986; Clm et al., 1989; Ristid et al., 1994). The above consideration of tile simultaneous effects of tlmrmodynanlic and kinetic parameters is valid for any impurity which is capable of adsorhing at kinks as well as tile surface terrace, in the case of adsorption at surface terrace, some impurities are practically immobile, while others are mobile and may easily deadsorb from the surface. Differences ill the rates of exchange of impurity particles (k~a) and growth species (kg~) between the growth medium and the integration site on the surface deterlnine the nature of adsorption during growth. In the case of immobile impurities, the rate k~d of adsorption of impurity particles is usually small in comparison with the ]'ate kgs of deposition of growth entities (i.e. k~d < ks~), and therefore adsorption mainly affects the thermodynamic parameter. However,

10

K. Sangwal

in the case of mobile impurities, the rate of adsorption of impurity particles is large in comparison with the rate of deposition of growth particles (i.e. k~e > kg,), and then adsorption has a dominating effect on kinetic parameters. Since the rate constant ko = ( k T / h ~ )

exp(-ZXCo/kT),

(15)

where AG~ is the corresponding activation energy and the suffix '%" denotes the processes of capture of impurity and growth species, AG~a > AGs~ and AGed < AGs. for immobile and mobile impurities, respectively. In terms of the adsorption sites, two extreme cases of adsorption of impurity particles may be considered. Mobile impurity particles are able to migrate over the surface, reach the kinks and adsorb at kinks while immobile impurity particles mainly adsorb at the surface terrace. However, in both cases some contribution due to adsorption at ledges is also possible. In contrast to the growth of F faces by the displacement of ledges on the surface terrace, growth of S and K faces takes place by statistical deposition of growth molecules at growth sites (i.e. kinks), resulting in the displacement of a face in a direction normal to it (eq. (14)). Therefore, adsorption of impurities at kinks on S and K faces leads to a decrease in the ~" parameter by blocking the access of solute to them and, consequently, in the growth rate of these faces. Typical plots of the v(c,,~n) and R(ci,,~p) dependences for the {111 } and {1~7-} faces of NaC1Oa crystals are illustrated in Fig. 2. In the case of NaC1Oa crystals, the { 111 } and {1-]-1} faces, respectively, are smooth and rough on molecular level (Ristid et al., 1994).

4. PHYSICAL AND CHEMI(:AL PROPERTIES OF IMPIIR1TIES Foreign substances which influence crystal growth processes can, in general, be divided into tailormade, polyelectrolyte (multifunctional) and electrolyte (single-functional) ilnpurities (Van Rosmalen et al., 1989; Van Rosmalen and Bennema, 1990); also see the chapters by Veintemillas-Verdaguer, and Furedi-Milhofer and Sarig in this volume. Tailor-made impurities are usually composed of giant molecules whose molecular structure is similar to that of the substrata molecules comprising the crystal but this structure is specifically modified with respect to the substrata only at one site of the impurity molecules. The impurity molecules are selectively adsorbed onto only those faces where their modified part emerges from the face. Growth normal to these faces is retarded because through its modified part the adsorbed impurity molecule disturbs the regular deposition of consecutive growth layers. Polyelectrotyte (multifunctional) impurities are phosphonic acids, l)olycarboxylic acids, polysulphonic acids, and different low and high molecular weight copolymers with various acidic groups. The inhibiting action of polyelectrolytes is essentially due to the long-distance electrostatic interaction between the polyelectrolyte groups or negatively charged ligands and cations of the crystal surface, followed by the formation of bonds with possible substitution of surface anions by the ligands (Van Rosmalen et al., 1989; Weijnen and Van Roslnalen, 1989). Simple electrolyte (single-functional) impurities, on the other hand, are composed of various polyvalent cations as well as anions (Mullin, 1972; Kimura, 1985; Hottenhuis and Lucasius, 1986; Sasaki and Yokotani, 1990; Owczarek and Sangwal, 1990a). Their inhibiting behaviour is due to electrostatic interaction between the impurity species [hydrated ions (Reich and Kahlwet, 1968; Mullin, 1972; Chernov et al., 1984; Hottenhuis and

Effects of Impuritieson Crystal Growth Processes

?

11

E

Q

11="

rr 1

>

R 2

4

6

Cimp ( 10= ppm] Fig. 2.

Dependences of step velocity v on { 111 } faces and linear growth rate /g of { 111 } faces of NaCIOa crystals on the concentration ci,,w of dithionate ions at, ~r = 4 × 10-a and cr = 3 × 10-2, respectively. Note that {11l} faces of Na(',lO3 crystals are rough. From Risti+" et al. (1994}.

Lucasius, 1986; Hottenhuis and Oudenampsen, 1988) or metal complexes (Mullin, 1972; Veintemilla.sVerdaguer and Rodriguez-Clemente, 1986; Sangwa[, 1987; Velikhov and Demirskaya, 1993)] and the crystal ions of opposite charge at kinks or surface terrace, followed by chemical reactions on the surface. Tailor-made, polyelectrolyte and simple electrolyte hnpuriti~s usually have molecular weights of about 104, 103 and 102, respectively. The former two types of impurities are composed of long chains, while molecules of impurities of the last type are quite small, usually up to 2 3 atomic dimensions. In growth media (e.g. solutions) their chemicai structure can undergo change, but the above order of the size of the "effective" impurity species is maintained. Therefore, it may be believed that molecules of tailor-made and polyelectrolyte impurities adsorbed on a surface remain practically immobile due to the need of simultaneous rupturing of their bonds with the surface, while those of simple electrolyte impurities may remain mobile or immobile.

K.

12

Sangwal

5. IMPURITY ADSORPTION ON F FACES As pointed out above, the consideration of the simultaneous effects of thermodynamic and kinetic parameters is valid for any impurity which is capable of adsorbing at kinks as well as onto the surface terrace. However, in order to discuss the effect of an impurity on growth kinetics, it is useful to introduce a parameter 0 characterizing the coverage of sites available for adsorption. The number nm~xof sites available for adsorption per unit area of a surface at given growth conditions is constant, but, for a particular concentration of impurity, a fraction 0 of the n,,,,~ sites available for adsorption is occupied by the impurity particles. Corresponding to a given concentration Cimp of the impurity, if the number of adsorption sites occupied per unit area on the surface at a particular temperature is n~a, the coverage of adsorption sites 0 may be expressed by o = ",.<,/" ......

(16)

The parameter 0 is essentially similar to the surface coverage 0 of adsorption isotherms. When all available sites on the surface are occupied by impurity molecules, 0 = 1. Since usually a small amount of the impurity decreases the rate of ledge motion enormously, it can be believed that in the case of adsorption at kinks, ledges or surface terrace, 0 _< 1. With increasing impurity concentration, 0 increases until 0 = 1 when all adsorption sites are occupied. However, with further increase in impurity concentration, 0 can exceed unity and the surplus potent inhibiting species tend to form aggregates around some adsorption sites, thereby initiating the formation of a two-dimensional layer of the adsorbed impurity. Thus, with increasing ilnpurity concentration, one has the following two situations, namely, 0 < 1, and 0 > 1.

5.1. Adsorption at low impurity concentrations In the case of adsorption at low impurity concentration (i.e. 0 < 1), two extreme cases, i.e. adsorption at kinks (mobile impurities) and the sm'face terrace (inunobile impurities), may be distinguished (Fig. 3). The models of impurity adsorption considering kinks and the surface terrace deal with the kinetic aspect of adsorption of impurities on an F face, neglecting the thermodynamic effects•

5. I. 1. Adsorption at kinks Assuming that kinks are the preferred adsorption sites, following Bliznakov (Bliznakov, 1954, 1958, 1965; Bliznakov and Kirkova, 1957), we consider that a part of the adsorption sites is occupied by the impurity particles, while the remaining sites are unoccupied. The movement of a growth ledge is ensured simultaneously by different rates of attachment of growth entities at occupied and unoccupied sites. These different attachment rates result in ledge displacement rates v0 and vi,w, respectively. The effective displacement rate of the ledge is then v = v0(1 - 0) + vi,wO,

(17)

or the coverage of adsorption sites 0 ~--

V0 - - V "UO - - V i m p

The coverage of adsorption sites may be described by the usual adsorption isotherms, i.e.

(18)

Effects of Impurities on Crystal Growth Processes

13

a

o j y

b Fig. 3.

•

~'/3:t/~

o

c Different sites for impurity adsorption on the F face of a crystal: adsorption at (a) kinks, (b) step ledge and (c) surface terrace. After Davey and Mullin 1974a).

0 = l(lCiml,/(l + KlClmp),

Langmmr isotherm,

/

0 = Z log Co + Z log ca,,p,

Telnkin isotherm,

/

0 = K'c~v,

Freundlich isotherm.

(19)

In these relations K, K', Ka, (70 and Z are constants. The constant K1 is given by (Davey and Mullin, 1974b; O~cik, 1982) I¢ 1 = e x p ( - A G a d / ] C W ) ,

(20)

the constant (70 is expressed as (O,4cik, 1982) Co = e x p ( - A G % / k T ) ,

(21)

the constant K is given by (Eggers ctal., 1964) K = k T l ~ ....

(~2)

and K' = K/Chnpl, - K where Cimpl iS the impurity concentration corresponding to 0 ~ 1. In eqs. (20) and (21), the differential heat of adsorption AGed corresponding to 0, and the initial heat of adsorption ._&Godcorresponding to 0 ----* 0, are related by (Eggers ct al., 1964) ,'.X(;~,, = Aa°,~(l - b0),

(23)

where the constant b < I. In eq. (22), em is a constant which is a measure of the distribution of energies of adsorption sites. In the case of growth of F faces by the spiral growth mechanism, the face growth rate R is proportional to voo. Therefore, if the contributions of sites unoccupied and occupied by impurity particles to the

14

K. Sangwal

growth rate a r e / ~ and Rimp, respectively, the resulting growth rate R in the presence of an impurity with coverage 0 of adsorption sites may be written as R = R0(1

-

0) +

Ri~pO,

(24)

where 0 is again given by eq. (19). Unlike in spiral growth mechanism, the face growth rate R ~x v~ a in birth and spread model of two-dimensional nucleation. Therefore, the corresponding equation of the dependence of R on 0 is somewhat complicated. Equations (18) and (24) in combination with equations of adsorption isotherms (eq. (19)) are usually used to test the validity of the model of adsorption at kinks. However, in many cases it is assumed that vi,,p and Ri,,p are zero. For Langmuir and Temkin isotherms, in the case of spiral growth mechanism the relationship between the layer displacement rate v and the face growth rate R, and ci,,~v may then be given by

(llKieimp),

~o1(~o - ~) = l +

Ro/(Ro - R) = 1 + (1/Klqmp); and

I

(25)

I

(Vo -- v)/vo = Zlog C0 + Z log Cimp,

/

( Ro - R) I Ro = ZIogC0 + Z log cimo,

/

(26)

respectively. Thus, rates v and R monotonically decrease with increasing ci,,p. Figure 4 shows the R(qmp) data for the {100} and {111} faces of NaCIO3 crystals growing from aqueous solutions in the presence of Na2SO 4 impurity in the form of plots of (/7o - R) -1 against Cimp -1 (eq. ( 2 5 ) ) and (Ro - R ) against log Cimp (eq. (26)), predicted by Langmuir and Temkin isotherms, respectively. As shown by the example of Fig. 4, the experimental V(Cimp)and •(eimp) data for different faces of tile same crystal may follow different isotherms, and it is impossible to predict the isotherm that would explain the data for different crystals or for different faces of a crystal. 5.1.2. Adsorption on the surface terrace (a) Adsorption of one type of impurity. An entirely different mechanism holds when an impurity strongly adsorbs on the surface rather than at kinks. Cabrera and Vermilyea (1958) considered the adsorbed particles to be immobile in comparison witb the mobility of ledges. According to them, tile velocity v0 of a straight step and the velocity vr of a step of curvature r are related by

v,/~o =

1

-

,.Jr.

(27)

If the nulnber of the possible adsorption sites per unit area on the surface is n~,~, and 0 is the fraction of these sites covered by impurity particles, then the average distance between the adsorbed species may be expressed as d = 2 r = ('i'2maxO)-1/2.

(28)

When the advancing ledge contacts an impurity particle, it tends to curl around this particle. The step will stop when d < 2rc, while it squeezes between a pair of neighbouring impurity particles when

Effects of Impurities o n Crystal G r o w t h Processes

15

b

4

a 4 c

3

~

2t,

.>

K I

IIo

-3

10"=/Cir..

Fig. 4.

(mot/tr'

log [Cim p, [ITIO~/ [}]

Plots of the dependences of (a) (Ro - R) -1 against Ci-m~vand (b) (R0 - R) against logci~,p for the {100} and {111} faces of NaC1Oa crystals grown from aqueous solutions in the presence of Na2SO4 impurity, respectively. In (a) and (b), growth temperature: (1) 10, (2) 17, (3) 22 and (4) 27°C. From Bliznakov and Kirkova (1969).

d > 2re. The configuration of straight ledges is thus modified by tile impurity particles and their average velocity will be smaller than v0. Assuming that the mean velocity of the step v = (VoVr) 1/2, from eqs. (27) and (28) one may write v

=

Vo(1 - 2 r ~ / d ) a/2 = Vo {1

-

(29)

2rc(r~maxO)'/2} 1/2 .

Using eq. (19), eq. (29) may be written in the form v0 v0~ - v ~ /

1 1 = 4r~n,oax + 4re~nmax~"l Clmp • "

(30)

Similarly, the relationship between the rate R of a face growing by spiral growth and the impurity concentration ci,,~v may be given by

R~-

R 2}

4rc27tmax~- 4r~nrnaxA'lCimp

(31)

For Temkin isotherm, the V(Cimp) and •(Cimp) dependences may be given by

{(v02 _ v2)/~o}~ = {(~

4rcnmaxX2(logC0+logqmp), }

- R~)/,~} ~ = 4,'b, .... z (log Co + log q~i,) •

f

(32)

16

K. Sangwal

The supersaturation In S* of the growth medium above which a ledge can overcome the impurity barrier is given by the Gibbs-Thomson relation, i.e.

(33)

7f/

rc = k T l n S*'

Using eqs. (28) and

(33)

and eq. (19) of the Langmuir isotherm, one obtains

1

1

(Kl@,p)

(INS*) 2 - ( l n S ~ ) 2 l +

,

(34)

where the supersaturation barrier given by

1

__ (k2@~):~ 1

(35,

corresponds to 0 --* 1, i.e. when Klcirap >> 1. When Klclmp << 1, eq. (34) may be written as In S* = In S~nax(Klcimp) 1/2.

(36)

Similarly, in the case of Temkin isotherm, one may write (In S*) ~ - Z(ln SL,x) 2 (ln Co + In Cirnp) . 2.3A

(37)

Equations (34), (36) and (37) show that the displacement of a ledge and a face in growth medium containing an impurity can occur only when the supersaturation in S > In S', and that the value of this critical supersaturation increases with increasing impurity concentration. Thus, the validity of the Cabrera-Verrnilyea model of impurity adsorption at surface terrace can be verified by comparing experimental data with eqs. (30), (31), (32), (34), (36) and (37). There are several experimental observations of the existence of critical supersaturation In S* below which no growth takes place i.e. dead zones occur (Troost, 1968, 1972; Simon et al., 1974; Dugua and Simon, 19783, b; Belyustin and Kolina, 1978; Punin and Vorob'ev, 1978; Dam and Van Enckevort, 1984; Beckmann and Boistelle, 1985; Black et al., 1986; Davey et al., 1986; Bredikhin et al., 1987; Chernov et al., 1987; Chernov and Malkin, 1988; Chu ct al., 1989; Sasaki and Yokotani, 1990; Owczarek and Sangwal, 19903; Velikhov, 1992; Velikhov et al., 1992; Velikhov and Demirskaya, 1993; Alexandru and Berbecaru, 1995), and the value of In S* increases with the impurity concentration in the solution (Troost, 1968, 1972; Simon et al., 1974; Dugua and Simon, 199783, b; Belyustin and Kolina, 1978; Punin and Vorob'ev, 1978; Chernov et al., 1981; Bredikhin et al., 1987; Chu et al., 1989; Sasaki and Yokotani, 1990; Owczarek and Sangwal, 19903). Figure 5 shows two typical examples of the Cabrera-Vermilyea mechanism. Figure 53 reveals that, for ~r > Or*, the growth rate curves for different concentrations of an impurity are similar and may be described by the usual growth-rate equations with corrected supersaturation (or - a*) instead of the applied supersaturation a. The R(c~) dependence in Fig. 5b may also be described in terms of corrected supersaturation, but the R(a) dependence becomes increasingly steep with increasing impurity concentration. Curves similar to Fig. 5b have also been obtained for the v(a) dependence of tile {010} faces of ADP grown from aqueous solutions containing different concentrations of Cr a+ impurity (Chernov et al., 1986), and for the R(a) of the {110} faces of C polymorph of stearic acid crystals grown from butanone solution containing emulsifier (span 60) (Beckmann and Boistelle, 1985) and for fructose grown from aqueous solutions containing glucose impurity (Chu et al., 1989).

Effects of Impurities on Crystal Growth Processes

17

D

2'

1G

8

{,

o

ct-

n-

4

2

•

,

•

ff Fig. 5.

0

4

8 0" ( % )

(a) R(cr) curves of (110) face of paraffin C36H74 from petroleum ether solutions containing increasing concentration (from left to right) of dioctadecylamine impurity (Simon and Boistelle, 1981; Simon et al., 1974). (b) R(~) curves {100} faces of KDP crystals grown from solutions of different purity (Belyustin and Kolina, 1978).

However, in the latter two cases, the R(a) dependences become less and less steep with increasing timp. This type of increasing or decreasing steepness of the curves of Fig. 5b is associated with contributions from changed solubility of the substance in the presence of the impurity, changed surface energy of the crystal-medium interface and/or changed activity of sources of steps. The former two factors lead to a change in the thermodynanfic parameter, while the last factor to a change in the kinetic parameter (see Sec. 2.1). As mentioned in Sec. 3, in the case of immobile impurities the rates v and R decrease monotonically with an increase in ci,,~ without exhibiting a maximum. Tailor-made impurities, which disrupt growth by stereoselectively incorporating into the growing surface via host-like parts of their molecule, always follow Cabrera Vermilyea mechanism of adsorption (Black et al., 1986; Davey et al., 1986; Chu el al., 1989). (b) Adsorption of two competitive impurities ~. When a growth medium contains two different types of impurity partMes, say A and B, then both act as obstacles for the motion of growth layers by adsorbing simultaneously on the surface to an extent 0A and 0B, respectively. If the number of the possible adsorption sites per unit area of the surface is r ~ x , then the average distance betw~n the adsorbed species m~v be given by d = 1/(dA 1 + dB1) : (n .... 0A) 1/2 + (n ..... BOB)112.

(38)

In the case of mixed Langmuir adsorption isotherm involving species A and B, the coverages 0A and

18

K. Sangwal

0B are related by (Eggers et al., 1964; O§cik, 1982)

K]ACA ~ Oa =

(39)

1 4- K 1 A C A ] "

(1 -- 0B)

Using the condition d -- 2rc for the blocking of the step ledge by an impurity and using eqs. (38), (39) and (29), one obtains (In S ~ x ) ~ - (In S**) 2 (INS* - In S**) 2

1 - (In S*') 2

-

1 -

1 +

-

-

(40)

K1ACA '

where In S* and In S**, respectively, denote the individual contributions the new supersaturation barrier In S*', and In S~, X is given by eq. (35), the main impurity A, and the constant KLA is given by eq. (20). In eq. supersaturation barrier due to the presence of impuriuty B in impurity ILL,5;],*ax> In 5'* > In S**, and

of impurities A and B to CA is the concentration of (40), In S*' is the resulting A. Eq. (40) is valid when

In S* 1 l n S ~ x - (1 + K, AC4)~/2"

(41)

As in the case of a single type of impurity, when K1AeA << 1 eq. (40) may be written as = (ln S*') 2 = K1ACA.

(In S* - In ,5'**)2

(42)

(in 5',*,~,,)2 - (In 5'**) 2

TILe dependence of (INS") 2 on 1~Kin, according to eq. (40), is illustrated in Fig. 6 for different constant concentrations of impurity B. The concentration of B in the system is defined by the ratio p

KIA CA

< 1.0 .....

o.s , "

o2

o:1 --./I

Q8

b t-

0.6 "

O.4-

,

,

4

In Smax

,

,

8 1/K1ACA

Fig. 6.

,

~

1

IL

,~

Plots of the dependence of (In S*') -2 on (KIACA) -1 for impurity A in the presence of different surface coverages of impurity B (parameter p), according to eq. (40).

19

Effects of Impurities on Crystal Growth Processes

of supersaturation barrier In S** due to impurity B to the maximum supersaturation barrier In , 5 ' ~ , i.e. p = In ~'**/In S ~ x . From Fig. 6, the following points may be noted: (1) The supersaturation ratio term In S** is associated with the presence of the impurity B (fig. 6). In the absence of the impurity B i,e. p = 0, eqs. (40) and (42) reduce to the relations (34) and (37), respectively; i.e. In S*' = In S*. (2) In the presence of impurity B, In S*' > In S* and the supersaturation ratio difference (In S " - l n S') increases with increasing p i.e. with increasing B. (3) For a constant concentration of A, the difference (ln,5'*' - In S*) remains constant for small cB but it increases for large cB. (4) Approximation (42) holds only for small p and small K1A. Using eqs. (29), (38) and (39), one also obtains v~ ,U 2

__

712

-

,~

1/2

(43)

+

~l'c 7Lmax

and a similar equation relating R and CA. Typical examples of the dependence of growth rate of crystals grown from solutions involving two competitive impurities dllring growth on supersaturation are shown in Fig. 7. The R(cQ curves represent solutions containing different concentrations of the added impurities. As seen from the

a

I

E

r~

o

01a

o.1

o~ Fig. 7.

b

/ E

IT

.

0

Ol

Q2 d

Typical R(a) curves for different faces of sodium perborate crystals growing from aqueous solutions containing increasing concentration (from left to right) of surfactant (sodium salt of butyl ester of oleic acid), showing two types of dead zones. The (011) and (100), and (10T) and (001) faces of sodium perborate show dependences of the type of (a) and (b), respectively. After Simon and Boistelle (1981 ).

Q3

20

K. Sangwal

6" I%,)

4

0 !

!

8 t

12 |

1.2

0.4

0 at (°C I Fig. 8.

Growth rate R of the {100} faces of KDP crystals against supersaturation a for various A13+ and Cr 3+ impurity concentration: (a) impurity free, (×) 10 -4 wt% A13+, (D) 10-4 wt% Fe3+, (o) 10-3 wt% Al3+, and ((.~) 10 -3 wt% Fe3+. After Bredikhin et al. (1987).

figure, at a particular impurity concentration, growth is completely stopped below (z0, but beyond this value of supersaturation the growth rate shows the usual supersaturation dependence in the presence of an impurity following Cabrera-Vermilyea mechanism of impurity adsorption. In the presence of an impurity, the growth rate is lower than that in systems without the impurity in the first case (Fig. 7a), while it is nearly equal in the second case (Fig. 7b). Figures 7a and 7b represent situations corresponding to relatively low and high inherent impurity concentrations cA, respectively. Curves similar to Fig. 7b have also been reported for adipic acid (Botsaris et al., 1973). Some other interesting results at very low impurity concentrations deal with fluctuations in face growth rates with time (Chernov ¢t al., 1981: 1986, 1987; Chernov and Malkin, 1988) and supersatuiation (Chernov ¢t al., 1986), and with anomalies in rates of layer displacement with supersaturation ((:hernov et al., 1986, 1987). III the case of growth of KDP, even two values of critical supersaturations have been reported (Chernov ct al., 1986; Bredikhin et al., 1987). Figure 8 shows the dependence of linear growth rate R of the (100) face of KDP on supersaturation expressed as supercooling At for different concentrations of A1:3+and Fe3+ under conditions of natural convection. In the supersaturation range 0 < At < Ata growth does not occur, but in the range Ata < At < At1 the face grows slowly following the dependellce: /~ o( ( / ~ ) 2 . For At > Ata, R o( (At - A t l ) l'2s. According to Bredikhin et al. (1987), for

Effects of Impurities on Crystal Growth Processes

21

At < At1 growth is determined by the kinetic step and the supercooling Ata corresponds to In S* in the Cabrera-Vermilyea model, while that for At > Atl it is diffusion-controlled. Bredikhin et al. (19871 also mentioned that the value of Ate characterizes the growth properties of the solution and is associated with its impurity content. it should be mentioned that for At > At1, a vahle of 1.25 of the exponent does not necessarily mean that growth is controlled by bulk diffusion. Such values are also observed for growth controlled by surface diffusion (Sangwal, 1994). The above data of Ata and At1 as a function of impurity concentration may be better explained in terms of two different impurities competing in adsorption. Then the data of Ata and at1 on concentration Cimp of both AIa+ and Fe3+ impurities should be represented by eq. (40) or (42). Figure 93 shows the log-log plots of the dependence of Ata and At1 on concentration Cimpaccording to eq. (42). The figure reveals that both of them may be represented by eq. (42), although the fit is better for At1 than for Ata. The corresponding values of the exponent are 0.13 and 0.35, respectively, rather than 0.5 predicted by eq. (42). This deviation in the value of the exponent is due to the fact that the assumption KIACA << 1 no longer holds here. Equation (40), however, describes the data satisfactorily as shown by Fig. 9b. Using T = 313 K, 7 = 0.02 J / m -2, ~ = 4.05 x 10-28 nl'~, and assuming 0 ~ 0, the estimated values of different parameters of eqs. (20) and (40) are listed in

Table 1.

Table 1.

Values of different parameters of eqs. (20) and (40)

Supercooling

L/11~.'~"~'~.x

I(1B (tool/tool)-'

AG~a (kJ/mol)

n .... B (sites/m 2)

Ata At1

200

7544

23.2

3.55 X 1014

200

69408

29.0

3.55

X 1014

Table 1 reveals that the adsorption of an impurity involving a lower value of the activation energy A(;~d for impurity adsorption is favoured at low supersaturations. Physically this means that impm'ities involving a low value of activation energy for adsorption participate in adsorption at low inlpurity concentrations.

(c) Adsorption processes and chemical constitution of adsorbing species. Adsorption of impurities nla.y affect growth by physically blocking the entrance of growth entities to kinks. Mullin (t9721 and Mullin et al. (1970) suggested that the influence of trivalent cations in inhibiting the growth of ADP and KDP is to soxne extent associated with the hydration of ions. The hydrated ions are much larger than bare ions and would be less easily adsorbed and accomodated in the kink sites. The positively charged ions would be attracted by phosphate groups in the vicinity of certain ADP and KDP crystal faces but they do not necessarily have to be adsorbed in the surface in order to be effective. According to Mullin (1972) and Mullin et al. (1970), the mechanism of impurity inhibition might be considered as one in which the complex aquo ions attracted into the vicinity of a crystal face exert a dilation effect, retard diffusion, hinder aggregation of growth units and thus retard the ledge displacement rate. In the absence of specific adsorption, the aquo ions would lose some or all of their hydration molecules and the subsequent transport of water molecules away from the interfacial layer

22

K. Sangwal a 0.6

..~

•

e.,.jfle...., ~

x~ ~-

%/"

o o/ /o/

•

a

o

,

O~

o

Q2

/ o

/

/ /

N

o

Z°

o

/ /n

I

5.10-s

J

I

Cimp

b

|

5.'e"

10-4 I wt O/oI

/

o. zx: AI =* o. x: Fes*

G

%

"'

,b

.....

~

. . . . .

I0"**/ Cimp I m o V n l o t ) "1

Fig. 9.

(a) Log-log plots of the dependences of critical supercoolings Atd and A6 for the growth of {100} faces of KDP on impurity concentration ci,,p (wt%) (cf. eq. (42)): (D,e) A13+, (o,x) Fe3+; ([],o) AQ, (~:),×) A t t. After Bredikhin et al. (1987). (b) Data of (a) replotted as 1/o .*2 against 1/Ch,p for tile growth of {100} faces of KDP, according to eq. (40) assuming OA ----+ 0. The values of supersaturation a* were calculated from Ata and Art of (a); curves (1) and (2) correspond to Ata and Art, respectively.

Effects of Impurities on Crystal Growth Processes

I

I

I

I

I

|

f

I

f

I

23

11

-a£ t

f

.

o

/

1 -3.4

I

-6

I

I

-4

tn[cimp Fig. 10.

I

I

-2

I

I

0

t

(wt%)]

Log-log plots of the dependence of dead supersaturation zone a* for the growth of {100} faces of KDP crystals on clmp (wt%) of different impurl'ties (cf. eq. (42)): (1) ascorbic acid, (2) adipic acid, and (3) boric acid; growth temperature 40.75°C. Data from Velikhov et al. (1992).

would further retard the layer displacement rate. It is also possibte that the effects of pH on growth rate are caused by similar effects with hydrated hydroxonium ions. As lnentioned ill Subsec. 5.1.2, the vahle of dead supersaturation zone In ,5'* changes with the impurity concentration in the solution (Troost, 1968, 1972; Simon et el., 1974; Dugua and Simon, 1978a, b; Be|yustin and Kolina, 1978; Punin and Vorob'ev, 1978; Chernov e.t el., 1981; Bredikhin e¢ eL, 1987; (',hu ct el., 1989; Sasaki and Yokotani, 1990; Owczarek and Sangwal, 1990a). The value of the dead zone indeed depends on a number of factors. Its value decreases with an increase in the temperature of heating of supersaturated solution hefore growth (Velikhov, 1992) as well as with an increase in the temperature of growth (Velikhov and Demirskaya, 1993), while increases with decreasing pore size of filters used for filtering the solution (Velikhov, 1992). lts value also depends on the concentration and nature of the added impurity (Velikhov et el., 1992). The effect of temperature is predicted by the Cabrera Vermilyea adsorption mechanism. However, changes in a* with heating treatment and filtration are associated with the presence of heterogeneous particles and associated ions, which are removed by filtration and thermal treatment, respectively. The influence of addition of organic impurities to growth medium of inorganic salts oil the value of dead zone is so complex that no systematic trend regarding tile effect of an impurity on the dead zone can be predicted. An example to illustrate this behaviour is shown in Fig. 10, which presents the dependence of ~* for the growth of the { 100} faces of KDP at 40°C on tile concentration clm~,

24

K. Sangwal a

J pH

b 127

05 6

/ o3

7

,

ol 2

3

4

5

6 ~

pH

Fig. 11.

Effect of solution pH on {a) a* for the growth of {100} faces of KDP, and on (b) the relative concentration a of different ionic species in KDP solution; temperature 40°C. Species: (1) n2PO~, (2) HzPO °, (3) (H2PO4)~-, (4) HPO]-, (5) nz(PO,)~-, and (6) Hs(PO4)~-. After Velikhov and Demirskaya {1993).

(wt%) of adipic, ascorbic and boric acids. The data are shown as plots of In a" against In Clmo, aS predicted by the Cabrera-Vermilyea adsorption mechanism; cf eq. (36). Figure 10 reveals that the (',abrera-Vermilyea mechanism, which predicts a slope of 0.5 for In a*/In cimp, is not applicable for any of the impurities. For boric acid, a* increases with ci,~p but the slope lnlr'] In cimo is very

Effects of Impurities on Crystal Growth Processes

25

low (0.03). In the case of ascorbic acid (and also glycerine and potassium phthalate) a ~ regularly decreases with increasing Cimp, while for adipic acid (and phenol) a* initially decreases and then, after passing through a minimum, increases with increasing Cinw. The results of a decrease in a* with increasing Cimp may be explained in terms of a change in the solubility of the crystal upon the addition of an impurity e.g. glycerine (Velikhov et al., 1992), and the capability of formation of poorly inhibiting complexes by the added impurity with unintentional impurity ions present in the starting solution (ascorbic acid, potassium phthalate and also glycerine) (Barsukova et al., 1992; Velikhov et al., 1992). Changes in a ~ are also possible when the added impurity leads to a change in solution structure by affecting the solvation of ions of the crystallizing COlnpound (Velikhov et al., 1992) and when the concentration of complex ionic species present in the solution, which take part in growth, is altered (e.g. solution pH) (Velikhov and Demirskaya, 1993). Figure l l a shows the relationship between a* and pH of KDP aqueous solutions, while Fig. l l b illustrates the dependence of fraction c~ of species present in solutions of different pH. The figure clearly reveals that the value of or* is directly connected with the existance of (H2PO4)~- dimer, which acts as growth inhibitor. Growth of crystals in the presence of impurities often leads to the incorporation of the latter into the growing faces. However, the chemical nature of the incorporated impurity species during the growth of ADP-type compounds, gypsum and other crystals has drawn considerable attention (Mullin, 1972; Fontcuberta et al., 1978; Veintemillas-Verdaguer and Rodriguez-Clemente, 1986; Chernov et al., 1986; Velikhov and Demirskaya, 1993; Witkamp and Van Rosmalen, 1991; Witkamp et al., 1990; De Vreugd et al.. 1994). In the case of ADP-type crystals, it is believed that the incorporated entities are not solvated species but isolated ions occupying interstitial sites (Fontcuberta et al., 1978; Barret ctal., 1989; Ristid and Sherwood, 1991). According to Ristid and Sherwood (1991) and Ristid et al. (1990), ill the case of the {100} faces of KDP growing in the presence of trivalent cations, the cation has two oxygen nearest neighbours acting as bridges to the phosphorus of the ADP and its incorporation in the interstitial site displaces the proton shared between the two oxygen. This leads to the breaking the strong O---H O bonds along <100} directions, and, consequently, to the reduction ill the attachment energy and hence to the growth rate [cf. Hartman's PBC theory (Hartman, 1973, 1987)]. Moreover, the breaking of the O 4t-O bonds generates lattice strain in the [100] and [010] directions, wbich leads to a reduction in the supersaturation and hence in the growth rate. This mechanisnl is responsible for the growth rate variation and the incorporation of impurity striations (for example, see: Sangwal and Rodriguez-Clemente, 1991; Sangwal and Benz, 1995). 5.2. AdsorptioT~ at high impurity conceutratio,ts 5.2. I. Formation of two-dimensional adsorption layer When tile concentration of an impurity in the growth medium is high (i.e. 0 > 1), the above lnechallistns of adsorption involving kinks and surface terrace cemse to be important. In that case, decrease in the growth rate of a face is possible due to the inaccessibility of growth units to the surface caused by the formation of a uniform two-dimensional layer of the adsorbing impurity. This layer has a crystallographic similarity with the growing face (Bienfait et al., 1965; Kern, 1967; Simon and Boistelle, 1981; Aquilano et al., 1984). Figure 12 illustrates the formation of a two-diinensional adsorption layer of Cd 2+ ion's on the (111) face of NaCI. The alternate layers of this plane of NaC1 are composed of Na + and CI- ions coordinated octahedrally. In the subsequent layer of C1- ions, Cd 2+ ions can occupy the sites normally occupied by Na + ions, which have similar ionic radii. Stacking of the layer of (:1- ions above the Cd 2+ layer leads to the formation of a two-dimensional layer A2 with ('.d(:12 structure. Such a situation takes place also for Mn 2+ and Zn 2+ but with a poorer fit.

26

K. Sangwal

B

1 Fig. 12.

Projection of successive { 111 } planes of an NaC1 lattice on the (1]-0) plane. B represents the NaC1 crystal while A2 the two-dimensional adsorption layer of CdC12. After Bienfait ct al. (1965).

Tile mechanism of formation of uniform two-dimensional layer of the adsorbing impurity is essentially similar to the Vohner-Veber mode of the growth of epitaxial layers (Sangwal and Rodriguez-Clemente, 1991). The formation of adsorption layer is favourable in systems involving inhibiting species of large size because the interaction between a large inhibiting species and an adsorption site is expected to be relatively weak in comparison with the adsorbed species. Consequently, in the case of large impurity particles, tile impurity concentration required for inhibiting the movement of ledges is also hiNh.

5.2.2. Formation of su'rface macroclustcrs In systems where two-dimensional impurity layers are not forlned, localized insoluble thr~-dimensional impurity clusters may be produced on the surface of a crystal. These impurity clusters are the cause of the so-called irregular growth for supersaturations ao exceeding some critical values a. Irregular growth corresponding to irregular growth morphology results when some parts of the face of a crystal grow according to the usual growth mechanisms involving two-dimensional nucleation or dislocations with or without impurity adsorption, while growth of other parts is entirely blocked by the ilnpurity (Simon and Boistelle, 1981; Owczarek and Sangwal, 1990b). Surfaces growing with the participation of three-dimensional impurity clusters may exhibit hillocks on them (Wojciechowski, 1989; Risti~ et al., 1993). Thus, irregular growth is essentially due to nonuniform adsorption of the impurity on the growing surface. Below we consider the general possible situations of growth in the case of formation of localized itlsoluble three-dimensional impurity clusters.

(a) Three:-dimcnsional impurity cluster~ as growth inhibitors. In this case, in addition to the usual reduction in growth rate of a face by impurity particles, the impurity clusters act as additional ~hstacles for the motion of growth layers. Then resulting supersaturation barrier In S " due to the fi~rmation of impurity clusters is given by an equation similar to (40), where now we denote the added impurity and the impurity clusters by A and B, respectively.

Ettects of Impurities on Crystal Growth Processes

Fig. 13.

27

Deposition of impurity clusters in the form of needles on the {100} faces of KDP crystals growing at cy = 6.3% from aqueous solutions at 30°C containing 6.8 x 10 -6 m o l / m o l Fe 3+ impurity (Owczarek and Sangwal, 1990a).

As mentioned in Subsec. 5.1.2, growth can take place only when the supersaturation difference (In 5'*~ - ln,q'* > 0. However, in the supersaturation region of complete stoppage of growth, the condition ln,q*' < In S* is also possible, and is associated with the fact that 0B > 0A above In S *~. This condition may be interpreted to mean that B species do not adsorb preferentially on the surface but. simply precipitate randomly on it, and that the A species have a tendency to join the clusters of B species rather than to adsorb on the surface. When ca > cm growth proceeds following the usual growth mechanisms for supersaturations above in 5'*'.

(b) Three-dimensional impurity clusters as grvwth promotors. In this case too, the A species join the clusters of B species but now ca < cB. Then a situation may arise when the impurity clusters (or precipitates) supply additional sources of steps for growth (Fig. 13). Thus, instead of a decrease, there is an increase in the growth rate of a face with impurity concentration Cimp- Assuming the formation of three-dimensionM impurity nuclei on the surface and the absence of adsorption of A by the Bliznakov or Cabrera-Vermilyea mechanism, the face growth rate may be given by (Owczarek and Sangwal, 1990b) R = ]:lo ÷ K2 exp

~

l(3eimp) ,

(44)

whert' /~,) is the face growth rate in the absence of the impurity, K2, K,~ and ra are constants and A(;~,,,,, is the activation energy for homogeneous nucleation of the impurity on the surface. When l'2:,ciil,pA(;~,m/l,:7'<< 1, eq. (44) may be writ!en as

H = (Ro + ~(~)- ~ ( ~ , ; c i G a G o ~ J k T .

(45)

When the contribution of the three-dimensional impurity nuclei to the growth rate is much greater lhan that of the usual surface kinks, i.e. (fro + K2) << K,~K~c~:,pAG~,~m/kT, then

28

K. Sangwal

I a

0

4.m,,/o

2

4 C imp

-15.5

6

8

( 10-= g" ion/I I

b

t,/)

-16.0

.E -16,5

-i

-6 In [Cimp ( g.ion/tJ]

Fig. 14.

(a) Dependence of R of (10]-1) face of NaNO3 crystals grown from aqueous solutions containing Co 2+ ions at two different ~ (Kirkova and Nikolaeva, 1971). (b) Data of (a) replotted ms In R against In Cimp.

R = lqqT.~,

(46)

where the uew constant l i 4 --= - h 2 h z A G h o , . / k T . Any of tile above equations can be used to verify the validity of the model of three-dimensional surface clusters acting ~s growth promoters. However, the simplest way is to use eq. (46), which predicts a maximunl value of growth rate R .... = K4 for ci,,v --~ ~ -

Effects of Impurities on Crystal Growth Processes

!

29

!

/ -2

0

rr

-3

e,-

-4

I

--15

I

-14

-13

I

-12

[n Cimp

Fig. 15.

Dependence of linear growth rate R along <001> directions of KDP crystals grown from aqueous solutions at o- = 13% on concentration Clmp of (O) Cr a+ and ( x ) Fe a+ ions (Owczarek and Sangwal, 1990b). Note that both i m p u r i t i ~ follow the same dependence.

Figure 14a presents the data of growth rate of the (10]-1) face of NaNO3 crystals grown from aqueous solutions containing Co 2+ ions at supersaturations of 3.81% and 4.76% (Owczarek and Sangwal, 1990b). As may be seen from the figure, tile rate asymptotically attains a constant maximum value. The same data are plotted in Fig. 14b according to the dependence (46). The curves give maximum growth rate R .... = 1.79 x 10 .7 m/s, and exponent m = 0.111 and 0.082 for supersaturations of 3.81% and 4.76%, respectively. Figure 15 illustrates a similar dependence for the linear growth rate along {001) directions of KDP crystals grown at 30°C and supersaturation a = 13% fi'om aqueous solutions containing Cr a+ and Fe a+ ions. As expected from this model of growth promoting effect of an impurity, all data for both Cr a+ and Fe a+ ions follow the same curve with the values of constants R ..... = 2,45 x 10 -6 m m / h = 8.8 x 10 -6 m/s and m = 1.33. However, the growth data on NaNOa from aqueous solutions containing Co 2+ ions, presented in Fig. 14, suggest that the exponent m is a function of supersaturation.

6. I M P U R I T Y A D S O R P T I O N ON S AND K FACES As mentioned in Subsec. 2.2, growth of S and K faces takes place by statistical deposition of growth molecules at growth sites (i.e. kinks), resulting in the displacement of a face in a direction normal to it (eq. (14)). Because of the statistical nature of deposition and the high density of kinks present on tllem, the concentrations of an impurity required to inhibit the growth rates of these faces is much higher than that required for inhibiting the growth rates of F faces. In order to describe the effect of

30

K. Sangwal

l

!

=

,'o Qg

1 lPl Cimp

Fig. 16.

20

30

{ppmq=1

Plot of linear growth rate R of {1-]]-} faces of NaCIO3 crystals against Cimp 1/2 of dithionate ions. The data are from Risti(~ et al. (1994) and are shown in Fig. 2.

impurities oll the growth rate R of S and K faces, we consider the ~ parameter of eq. (14), which may be written as ~" = (1 - 0) = (1 - N~a/No),

(47)

1/2 the dependence of growth rate where N~d is the concentration of inhibited kinks. Since N~d c( cimp, of a rough face on impurity concentation may be given by the relation 2

1/2

R = Ro - (Roa /No)cimp,

(48)

where a is the distance between nearest neighbour atoms. Figure 16 illustrates the dependence of growth rate R of the {l-i]-} faces of NaCIO3 on the S20~concentration added to aqueous solutions. The figure shows that, for this face which is rough, the curve is composed of two parts with the transition occurring at Cimp ~,~ 200 ppm. The estimated kink density No in the low and high impurity range is 1.7 x 1017 and 8.2 × 1018 sites/m s, respectively. As expected, the value of No for a rough face is much higher than the density of adsorption sites on an F face (see Table 1). At high impurity concentrations, S and K faces can also appear in the morphology of a crystal when adsorption takes place by the formation of a two-dimensional impurity adsorption layer on the surface due to a structural similarity between them. The character of an S or K face resembles that of an

Effects of Impurities on Crystal Growth Processes

31

F face, and a face grows by the free development of growth layers (Hartman, 1973, 1987; Li et al., 1990). However, transition of a K face to an F face may also involve the piling up of steps of growth layers on the F faces of the growth morphology. The piling up of the steps results in an S-type face, rather than the original K-type face consisting of only kinks (Li et al., 1990).

7. DETERMINATION OF IMPURITY ADSORPTION MECHANISM From the above discussion, it follows that chemical nature of an impurity and interactions between impurity atoms and atoms of the adsorption site determine the processes of adsorption. In general, in terms, of the concentration of an impurity in the growth medium, the mechanisms of adsorption of impurities on crystal surfaces may be classified as follows.

(a) Low impurity concentrations (low site coverage, i.e. 0 < 1). In this case, adsorption can take place at kink sites (Bliznakov mechanism) or at a surface terrace (Cabrera Vermilyea mechanism). The former medlanism involves mobile impurities while the latter immobile ones. (b) High impurity concentrations (high site covernge, i.e. 0 > 1). In this ease, two situations are possibie: (1) formation of two-dimensional impurity layer having a structural relationship with the underlying face, and (2) formation of three~dimensional impurity clusters randomly distributed on the surface. In the former mechanism, the growing face, irrespective of its type, exhibits regular growth with all features of an F face. The face growth kinetics may be described by two-dimensional or spiral growth mechanisms with or without the impurity. In the latter mechanism on the other hand, some parts of the face grow while others do not, thus exhibiting irregular growth. However, the adsorption effects can be explained by considering two types of immobile impurities participating in the (?ahrera---Vermilyea mechanism. In the extreme case, in addition to growth by layer mechanism, the impurity clusters ,n~, serve as additional sources of growth steps, thus leading to an increase in the face growth rate. It, should be mentioned that the growth of a face, involving two dimensional impurity layer in some range of impurity concentration, can become irregular at relatively high impurity concentrations. The formation of two-dimensional impurity layers and three-dimensional impurity clusters follows the usual concepts involved in the formation of epitaxial layers and thin films (Sangwal and Rodriguez( !lemente, 1991 ). The ledge displacement velocity v on a face and the face growth rate R are related. Therefore, from experimentM data of the dependence of v or R on Cimp, it iS possible to establish the adsorption mechanism. This can be done from the dependences predicted hy eqs. (25), (26), (30), (31), (32) and (43). In terms of adsorption energy, its low value indicates adsorption at kink sites while a high value suggests adsorption at the surface terrace. However, it may be difficult to distinguish between adsorption at kinks and surface terrace from the value of the adsorption energy alone. The strongest argument in favour of adsorption at surface terrace is the observation of dead supersaturation zones in which growth is enormously retarded or is entirely blocked (eq. (34), (37) and (40)). In case dead zones are not observed but v(cimp) or R(Cimp) data are avai]able, eqs. (30), (31) and (32) are useful. According to these equations, the estimated value of the radius of the critical two-dimensionM nucleus r~ umst be greater than the nearest neighbour distance a, i.e. 4r2n ..... = l. A good example to distinguish between kink and terrace adsorption mechanisms is the data, reported by Risti~ et al. (1994), of V(Cimp)and v(er) for the {111} faces of NaCIO3 obtained in the presence of

K. Sangwal

32

Table 2. Adsorption mechanism

Bliznakov Cabrera

Values of various parameters of eqs. (25), (26), (26) and (32) for {111} faces of NaC103 in the presence of dithionate ions

Langmuir isotherm Low Cimp K1 AG~ (kJ/mol) 0.041 8.3 0.0146 11.0

High cimp K1 AGed (kJ/mol) 0.0063 13.2 0.0105 11.9

Temkin isotherm Low cimp Co AG~* (k J/tool) 0.316 3.0 0.203 4.14

High ci~p Co AG~o (kJ/mol) 0.0348 8.7

dithionate ions (see Fig. 2). The data do not reveal any dead zones of supersaturation, which suggests that kink adsorption model is more likely. The V(Clmp) data, shown in Fig. 2, is replotted in Figs. 17a and 17b according to eqs. (25) and (30), and eqs. (26) and (32), respectively. Figure 17 clearly shows that the data are best represented by eq. (26) of the kink adsorption model in combination with the Temkin isotherm (Fig. 17b, curve 1). In the case of Langmuir isotherm (Fig. 17a), the plots in fact yield two slopes with intercepts of 2.5 and 1.5 for kink adsorption mechanism (eq. (25)), and 2.2 and 0.8 for surface adsorption mechanism (eq. (30)), rather than 1 expected from the models. The two slopes also correspond to two values of the energy of adsorption below and above cimv ~ 120 ppm, respectively. The values of different parameters estimated from Fig. 17 are listed in Table 2. It should be noted that the above behaviour of adsorption at kinks is very similar in nature to that deduced in the case of KDP (see Fig. 9 and Table l) from the data reported by Bredikhin et al. (1987). However, in the case of KDP, Cabrera- Vernfilyea mechanism holds. It is somewhat difficult to establish the two-dimensional adsorption-layer mechanism from the kinetic data. In order to make a distinction between the kink/terrace adsorption and the two-dimensional adsorption-layer mechanism, we consider the energies of adsorption in the two cases. If CAs is the energy of interaction between the adsorbing particle A and the site of adsorption S on the surface, OAA is the energy of interaction between two nearest adsorbed species, and z is the coordination number in the impurity layer, the total heat of adsorption may be given by AGaa = CAS + ZCAAO/2.

(49)

The factor 2 in the denominator of the second term on the right-hand side of eq. (49) appears I)ecause each atom in the impurity layer is considered twice. In the case of adsorption at a terrace or kink site when Cha = 0, AGed(I) = 4)as. On the other hand, for adsorption by two-dimensional impurity layer when 0 > 1 and (¢AS + ZCAA/2) > ZCAA/2, A G ~ ( I I ) < ZOAA/2. It may therefore he inferred that for terrace/kink adsorption mechanism the heat of adsorption is independent of the surface orientation, whereas that for the surface adsorption layer mechanism the heat of adsorption depends on the coordination number z and hence on the surface orientation. Since the mechanisms of impurity adsorption involving kinks/terrace and two-dimensional surface layer take place at relatively low and high impurity concentrations, respectively, eq. (49) predicts that AGed(I) > A G ~ ( I I ) . Experimental results of several investigations (Bliznakov and Kirkova, 1957, 1969; Davey, 1979; Draganova, 1981; Draganova and Koleva, 1980; Black et al., 1986; Davey, et al., 1986; Chu et al., 1989; Owczarek and Sangwal, 1990a, b; Risti~ et al., 1994; De Vreugd et al., 1994) convincingly demonstrate that growth rates of crystals growing in the presence of impurities invariably always

Effects of Impurities on Crystal Growth Processes Cim p

100 5o 10

33

(ppm)

2o

10

.......

l

a

30

8

] 6;

.,, 20 %

o

!

I ~o

IO

10~'/Cimp

(ppm) "1

Cinm ( ppm ) 5

10

50

100

500 1000

l

i

X 'XX

Q6

"# ->

X

G

O

O4

I %o

:~ O2 :>

|

>~

-

-

i

i

I

2

log [Cimp (ppml]

17.

Data of step velocity v on { l 11 } faces of NaCtOa crystals as a function of cimp of dithionate ions (see fig. 2; Ristid et aI., 1994) replotted in terms of dependences predicted by (a) Langmuir (eqs. (25) and (30)), and (b) Temkin isotherms (eqs. (26) and (32)). (a) Plots of (1) vo/(Vo - v) and (2) {v~/(v~ - 't,~)} 2 against c71 and (b) (1) (v0 - v)/vo and (2) {(v~ - v2)/v~} 2 against 111112, logci~p. In (a) and (b): (1) Bliznakov mechanism and (2) Cabrera-Vermilyea mechanism.

34

K. Sangwal

E

fE -

2

4

-

6

;.

8

z

• !100]

25oC

10-

Cimp (lOamot/t) Fig. 18.

Dependence of growth rates R of the (100) and (111) faces of KC1 crystals at a = 3.6 % on concentration Clmp of CdCI2 at two different temperatures (Draganova and Koleva, 1980). Note that for each face the decrease in R with increasing Cimp is steep below a particular value of clmp typical of a face and temperature, while it is small beyond this particular ci,,p.

decrease with all increase in the impurity concentration. However, in some cases (Draganova, 1981; Draganova and Koleva, 1980), at low impurity concentrations the decrease in growth rate is much larger than that at higher impurity concentrations. Figure 18 shows this type of dependence for the growth rates of the (100) and (111) faces of KC1 crystals growing in the presence of CdCI2 impurity. This example suggests that kink/terrace adsorption and surface-layer adsorption take place in low and high impurity concentration intervals, respectively. It is also found (Draganova, 1981; Draganova and Koleva, 1980) that in the range of low impurity concentration A G ~ for the (100) and (11 l) faces is similar, but that for the layer adsorption mechanism, in agreement with the above inference, AGed is higher for the (111) face. Moreover, the value of AGed corresponding to the former mechanism was found to be higher than that for the latter mechanism.

8. IMPURITY EFFECTS ON SURFACE MICROMORPHOLOGY OF BULK CRYSTALS Effects of impurities at low and high concentrations on the morphology of growing surfaces of bulk single crystals may be distinguished in accordance with the operative mechanism of adsorption. At low concentration of impurities, the effects are reflected by changes in the configuration (overall shape) of growth structures e.g. spirals and hillocks (Dunning and Albon, 1958; Dunning et al., 1965;

Effects of Impurities on Crystal Growth Processes

35

Davey and Mullin, 1974b; Dam and Van Enckevort, 1984; Chernov et al., 1986, 1987; Hottenhuis and Oudenampsen, 1988; Li et al., 1990; Onuma et al., 1990; Shekunov et al., 1992; Gratz and Hillner, 1993; Bikov et al., 1994) and by changes in the thickness of layers composing them (Hottenhuis and Lucasius, 1986; Hottenhuis and Oudenampsen, 1988; Owczarek and Sangwal, 1990a; Gratz and Hillner, 1993; De Vreugd et al., 1994). The effectiveness of different impurities in changing the surface morphology is different (Dunning and Albon, 1958; Dunning et al., 1965; Hottenhuis and Lucasius, 1986; Hottenhuis and Oudenampsen, 1988). Spirals and hillocks are composed of growth layers starting from growth centres, and, consequently, their shapes reflect the shapes of growth layers composing them. Adsorption of impurity particles at kinks in a growth ledge (layer) can (1) reduce the rate of integration of growth units at them, and (2) increase the average distance between kinks if the adsorbed impurity particles -ender them ineffective. The effect of both changes is to increase the polygonization of growth layers. However, in the case of adsorption at surface terrace, the random distribution of impurity species and the curling tendency of layers between two adsorbed particles will lead to a rounding of growth layers. Both polygonization (Hottenhuis and Lucasius, 1986) and rounding, of growth layers (Dunning and Albon, 1958; Dunning et al., 1965; Dam and Van Enckevort, 1984; Li et al., 1990; Gratz and Hillner, 1993) have been observed. In the case of the {010} faces of potassium hydrogen phthalate crystals, adsorption of different impurities at two different types of kinks has also been discerned (Hottenhuis and Oudenampsen, 1988). No observable effect on the morphology has also been found in some cases (Davey and Mullin, 1974b; Chernov and Malkin, 1988). Large aggregates of impurities and other heterogeneities may act as growth centres for the initiation of growth layers on low-index crystal faces (Griffin, 1951, 1952; Sunagawa, 1962, 1968; Joshi and Kotru, 1976; Kotru, 1978; Sangwal and Rodriguez-C, lemente, 1991). Direct observation of changes in the velocity and morphology of monomolecular steps on the (10]-4) face of calcite in the presence of additives by real-time, in situ atomic force microscope has revealed (Cratz and Hillner, 1993) that poisons affect growth rate and step morphology (Fig. 19). This study ha~s also sl,.own the following: (1) The molecules of an additive or related complexes adsorb directly at steps, halting their motion. At high impurity concentrations, the steps appear diffuse, topographic highs due to the amaging of adsorbed poisons (Figs. 19b,c,e). (2) There exists a threshold concentration of the additive when poisoning of steps takes place. This effect is observed for industrial threshold inhibitors like l-hydroxyethylidene-l,l-diphosphonic acid (HEDP), sodium triphosphate (NaTP), and sodium hexametaphosphate (SHMP). (3) For HEDP, SHMP and NaTP, adsorption onto the steps is rapid initially (~ 0..5-2.5% monolayer coverage), followed by its slower uptake by enlargement of the poisoned zones. (4) No threshold additive concentration appear for NaH2PO4, NaC1 and Mg z+ ions. In this case, addition of the former two additives greatly slows the motion of steps, which show pronounced, bulbous step roughening (Fig. 19e). Addition of Mg2+ insignificantly lowers the step velocity but induces changes in step morphology (Fig. 19f). The above observations are not in conflict with the models of adsorption of impurities at kinks and surface terrace. HEDP, SHMP and NaTP additives adsorb according to Cabrera-Vermilyea mechanism (surface terrace), NaH2PO4 and NaCI adsorb according to Bliznakov mechanism (kinks), while Mg 2+ ions probably lead to changes in crystal solubility. However, the observation of the existence of a threshold impurity concentration in the case of HEDP, SHMP and NaTP deserves explanation. It is possible that only above a certain concentration impurity species acquire a chemical

36

K. Sangwal

g

Fig. 19.

Effect of different additives on the morphology of spiral steps on (101-4) surface of calcite: (a,d) no impurity, (b,c) 10 #M HEDP, (e) 10 #M sodium dihydrogen phosphate, and (f) 300 #M MgCl2. Solution supersaturation ratio: (~c) = 1.6, and (d-f) 4.2. Note that the steps are immobile broad and high in (b) and (c), and that the visibility of steps increases with time (compare (b) and (c) with (a)). Image size: (a-c) 1.5/*in, (d,e) 3 #m, and (f) 15 #m. From Gratz and Hillner (1993).

configuration and form (e.g. as aggregates) capable of poisoning the steps. Growth layers emitted by an isolated source show that they are relatively thin and closely-spaced near the source, but that as one goes away from the source their height progressively increases (i.e. the layers become more and more bunched) and the distance between two neighbouring layers increases (Rak and Sangwal, 1983; Van Enckevort and Jetten, 1985; Szurgot and Sangwal, 1986; Sangwal et al., 1986). This type of behaviour of steps (i.e. bunching) results due to deceleration of steps caused by the overlap of their diffusion fields (Chernov, 1961) and/or by the time-dependent adsorption of impurities (Van der Eerden and Miiller-Krumbhaar, 1986). These two processes give different dependences of interstep spacing Ax on distance x from the source; &x
Effects of Impurities on Crystal Growth Processes

37

Adsorption of impurities on the steps of S faces may lead to the formation of bunched layers (called growth striations) (Watanabe and Sunagawa, 1982, 1983; Kanda et al., 1982, 1984; Miyata et al., 1980; Hosaka et al., 1986; Yumoto et al., 1986). These growth striations are very similar to macrosteps on F faces (Sangwal and Rodriguez-Clemente, 1991).

9. GROWTH MORPHODROMS OF ALKALI HALIDES Occurrence of a change in the growth mechanism of a face with a change in the supersaturation used for growth may result in a change in the relative growth rates of different faces appearing in the morphology. Since the overall morphology of a crystal consists of faces growing at the lowest rates, the morphology of a growing crystal may change with a change in the supersaturation. As described above, the presence of an impurity in the growth system can also lead to a change in the growth rates. The alkali halides are well known examples of such changes in growth morphology. The changes in the growth forms of crystals obtained by variation of both a and Cimp are described by (c~,ci,,) curves, called growth morphodroms (Bienfait et al., 196,5; Kern, 1967). In the case of Na('.l, at a supersaturation ~r > 0.23, the growth habit changes from cube with the {100} faces to octahedra with the {111 } faces. Certain impurities significantly lower the values of * necessary for changing the external form (Bienfait et al., 1965). The value of supersaturation at which transition in the growth form takes place depends on the temperature of growth and the chemical properties of an impurity. Tile habit modifying behaviour of impurities in alkali halide crystals is explained in terms of close periodicity between their {111} faces and the simple planes of the three-dimensional crystals of impurities (see fig. 12). The effect of these impurities appears at concentrations much lower than their solubilities. Figure 20 smnmarizes the results of the observation of growth forms and surface morphology of KCI crystals in relation to supersaturation and concentration of Pb 2+ ions. It was suggested ( L i e t al., 1990) that the habit change of KCI crystals from cubic to octahedral is due to the precipitation of Ph 2+ ions as PbC12 crystallites preferentially along the (110) steps of growth layers on the {100} face. Preferential adsorption of PbCl2 crystallites reduces the advancing velocity of the layers in perpendicular directions. The piling up of these {110} steps results in an S-type face, rather than the original K-type face consisting of only kinks. As a result, initially small hoppered { 111 } faces develop in the habit. The {111} faces become wavy as growth proceeds without distinguishable growth steps on it. This is followed by the advancement of layers from the edges or corners of the face. Inhibition of the advancing steps by PbCI2 precipitates, and coverage of the developing face by a PbCI2 film entirely blocks the normal growth of the face. At this stage the character of the face resembles that of an F face. After some time, growth spirals begin to appear from the central portion of the face. (;rowth spirals beconle circular and the step height increases with increasing impurity concentration. As schematically shown in the figure, both {100} and {111} faces become hoppered above certain values of supersaturation but the transition from a flat {111} face to a hoppered one takes place at a Ph 2+ concentration much higher than that for the { 100} face. It is worthwhile to note that the mechanism of poisoning of steps on tile { 100} faces of KC1 crystals hy Pb(',12 impurity is very similar to that observed by atomic force microscope on calcite by HEDP, SHMP and NaTP impurities (see Sec. 8).

K. Sangwal

38

x

A'I"

o"

(%1

('cI

3.0

6.0

2.5

5.0

2.0

4.0

111>>100 \

x x

•

\

~ I O0

~

1.5

3.0

1.0

2.0

0.5

I .0

® ,

\

® I00 • II1

100

0

0

Fig. 20.

pure

IO0

200

400

600

800

I000 2000 Pb c o n c e n t r a t i o n (ppm}

Growth forms and surface morphology of KCI crystals in relation to supersaturation and concentration of Pb 2+ ions (Li et al. (1990).

The growth habit can also be changed when two impurities 1 and 2 are simultaneously used. In such cases, the concentration of one impurity required to bring about the same change in crystal habit decreases at the expense of an increase in the concentration of the other impurity (Bienfait el al., 1965). This behaviour is expected from the model of adsorption of two immobile competing impurities (see Subset. 5.1.2). According to eq. (40), the value of In S=' increases with increase in the concentrations of either of the impurities (see Fig. 6). Therefore, relation (40) shows that, for a constant In S*', in order to bring about a change in the growth rate of a face by increasing the concentration (CA) of one of the impurities, say A, in a mixture of two impurities A and B, the concentration (cB) of the other impurity, say B, should be decreased to bring about the same change.

REFERENCES Addadi, L. Z. Berkovitch-Yellin, I. Weissbuch, J. van Mil, L.J.W. Shimon, M. Lahav and L. beiserowitz (1985). Angew. Chem. Int. Ed. Engl. 24,466. Alexandru, H.V. and C. Berbecarn (1995). Cryst. Res. Tecnol. 30, 307. Antinozzi, P.A., C.M. Brown and D.L. Purich (1992). J. Cryst. Growth 125,215. Aquilano, !)., M. Robbo, G. Vaccari, G. Mantovani and G. Sgualdino, (1984). In: Industrial Crystallization 84 (S.J. Jan~i(: and E.J. de Jong, eds.), p. 91. Elsevier, Amsterdam. Barret, N.rl'., G.M. Lamble, K.J. Roberts, J.N. Sherwood, G.N. Greaves, R.J. Davey, R.J. Oldman and D. Jones (1989). J. Cr.yst. Growth 94, 689. Barsukova, M.I., V.A. Kuznetsov, T.M. Okhrimenko, V.S. Naumov, O.V. Kachalov, A. Yu. Klimova,

Effects of Impurities on Crystal Growth Processes

39

M.I. Kolybaeva and V.I. Salo (1992). Kristallografiya 37, 1003. Beckmann, W. and R. Boistelle (1985). J. Cryst. Growth '/'2, 621. Belyustin, A.V. and A.V. Kolina (1978). Kristallografiya 23, 230. Berkovitch-Yellin, Z., J. van Mil, L. Addadi, M. Lahav and L. Leiserowitz (1985). J. Amer. Chem. Soc. 107, 3111. Berkovitch-Yellin, Z. (1985). J. Amer. Chem. Soc. 107, 8239. Bienfait, M., R. Boistelle and R. Kern (1965). In: Adsorption et Croissance Cristalline (R. Kern, ed.), p. 557. CNRS, Paris. Bikov, A.Z., V.G. Avramov, S.B. Damianova and S.D. Stoichkov (1994). J. Cryst. Growth 140, 100. Black, S.N., R.J. Davey and M. Halcrow (1986). J. Cryst. Growth 79, 785. Bliznakov, G.M. (1954). Bull. Acad. Sci. Bulg. Ser. Phys. 4, 135. Bliznakov, G.M. (1958). Fortschr. Min. 36, 149. Bliznakov, G.M. (1965). In: Adsorption et Croissance Cristalline (R. Kern, ed.), p. 291. CNRS, Paris. Bliznakov, G.M. and E.K. Kirkova (1957). Z. Phys. Chem. 206, 271. Bliznakov, G.M. E.K. Kirkova and R.D. Nikolaeva (1965). Z. Phys. Chem. 228, 23. Bliznakov, G.M. and E.K. Kirkova (1969). Krist. Teeh. 4,331. Boistelle, R. (1976). In: Industrial Crystallization (J.W. Mullin, ed.), p. 169. Plenum, New York. Boistelle, R. and J.P. Astier (1988). J. Cryst. Growth 90, 14. Botsaris, G.D., G.E. Denk and R.A. Shelden (1973). Krist. Tech. 8, 769. Bredikhin, V.I., V.I. Ershov, V.V. Korolikhin, V.N. Lizyakina, S.Yu. Potapenko and N.V. Khlyunev (1987). J. Cryst. Growth 84, 509. -" Buekley, H.E. (1951). Crystal Growth. Wiley, New York. Cabrera, N. and D.A. Vermilyea (1958). In: Growth and Perfection of Crystals (R.H. Doremus, B.W. Roberts and D. Turnbull, eds.), p. 393. Wiley, New York. (Jhernov, A.A. (1961). Uspekhi Fiz. Nauk 73, 277; Engl. Transl.: Soy. Phys. Uspekhi 4, 116. Chernov, A.A. (1984). Modern Crystallography III: Crystal Growth. Springer, Berlin. Chernov, A.I. and A.I. Malkin (1988). J. Cryst. Growth 92, 432. Chernov, A.A., V.F. Parvov, M.O. Kliya, D.V. Kostomarov and Yu.G. Kuznetsov (1981). Kristallografiya 26, 1125. Chernov, A.A., L.N. Rashkovieh and A.A. Mkrtehyan (1987). Kristallografiya 32,737. Chernov, A.A., L.N. Rashkovieh, I.L. Smol'ski, Yu.G. Kuznetsov, A.A. Mkrtchyan and A.I. Malkin (1986). Rost Kristallov, 15, 43. Chu, Y.D., L.D. Shiau and K.A. Berglund (1989). J. Cryst. Growth 97, 689. Clydesdale, G., K.J. Roberts and R. Docherty (1994a). J. Cryst. Growth 135. 331. Clydesdale, G., K.J. Roberts, K. Lewtas and R. Docherty (1994b). J. Cryst. Growth 141,443. Dam, B. and W.J.P van Enckevort (1984). J. Cryst. Growth 69, 306. Davey, R.J. (1974). J. Cryst. Growth 34, 109. Davey, R.J. (1979). ln: Industrial Crystallization 78 (E.J. de Jong and S.J. Jan~id, eds.), p. 169. North-Holland, Amsterdam. Davey, R.J. (1986). J. Cryst. Growth 76, 637. Davey, R.J., S.N. Black, D. Logan and S.J. Maginn (1992). J. Chem. Soc. Faraday Trans. 88, 3461. Davey, R.J., W. Fila and J. Garside (1986). J. Cryst. Growth 79, 607. Davey, R..]. and J.W. Mullin (1974a). J. Cryst. Growth 23, 89. Davey, R.J. and J.W. Mullin (1974b). J. Cryst. Growth 26, 45. Davey, R.J. and J.W. Mullin (1974c). J. Cryst. Growth 29, 45. De Vreugd, C.H., G.J. Witkamp and G.M. van Rosmalen (1994). J. Cryst. Growth 144, 70. Draganova, D. (1981). Izv. Khim. Bulg. Akad. Nauk. 14, 229. Draganova, D. and R. Koleva (1980). Izv. Khim. Bulg. Akad. Nauk. 13, 631. Dugua, J. and B. Simon (1978). J. Cryst. Growth 44, 265.

40

K. Sangwal

Dugua, J. and B. Simon (1978). J. Cryst. Growth 44, 280. Dunning, W.J. and N. Albon (1958). In: Growth and Perfection of Crystals (R.H. Doremus, B.W. Roberts and D. Turnbull, eds.), p. 411. Wiley, New York. Dunning, W.J., R.W. Jackson and D.G. Mead (1965). In: Adsorption et Croissance Cristalline (R. Kern, ed.), p, 303. CNRS, Paris. Eggers, D.F., N.W. Gregory, G.D. Halsey and B.S. Rabinovitch (1964). Physical Chemistry. Chap. 18. Wiley, New York. Fontcuberta, .L, R. Rodriguez and J. Tejada (1978). J. Cryst. Growth 44, 593. Forsythe, E. and M.L. Pusey (1994). J. Cryst. Growth 139, 89. Frank, F.C. (1958). In: Growth and Perfection of Crystals (R.H. Doremus, B.W. Roberts and D. Turnbull, eds.), p. 411. Wiley, New York. Ginde, R.M. and A.S. Myerson (1993). J. Cryst. Growth 126, 216. (hatz, A.J. and P.E. Hillner (1993). J. Cryst. Growth 129, 789. Griffin, L.J. (1951). Phil. May. 42, 1337. Griifin, L.J. (1952). Phil. May. 42,827. Hamza, S.M., A. Abdul-Rahman and G.tl. Nancollas (1985). J. Cryst. Growth 73, 246. Hartman, P. (1973). In: Crystal Growth: an Introduction ( P. Hartman, ed.), p. 367. North-Hollan& Amsterdam. Hartman, P. (1987). In: Morphology of Crystals, (I. Sunagawa, ed.). Part A, Chap. 4. Terrapub, Tokyo. Herden, A., R. Lacmann, Chr. Mayer and W. Schr6der (1993). d. Cryst. Growth 130, 245. Hosaka, M., T. Miyata and S. Taki (1986). J. ('ryst. Crowth 75, 473. Hottenhuis, M.H.J. and C.B. Lucasius (1986). ,l. Cryst. Growth 78, 379. Hottenhuis, M.H.J. and A. Oudenampsen (1988). J. Cryst. Growth 92, 513. •/oshi, M.S. and P.N. Kotru (1976). Krisl. Tech. 11,913. .hdg, A. and B. Deprick (1983). d. Cryst. (;rowth 62,587. I(anda, H., N. Setaka, T. Ohsawa and O. Fukunaga (1982). d. Cryst. Growth 60, 441. Kanda, H., N. Setaka, T. Ohsawa and O. Fnkunaga (1983). Mater. Res. Soc. Syrup. Proc. 22,209 Kern. R. (1.(t67). Rost Kristallov 8, 5. Kern. R. and R. Dassonville (1992). ,l. Cryst. (h'owth 116, 191. Kimura, H., (1985). J. Cryst. Growth 73, 53. Kirkova, E.K. and R.D. Nikolaeva (1971). ffrist. 7)ch. 6, 741. Kirkova, E.K. and R.D. Nikolaeva (1973). Krist. T~'ch. 8, 463. Kotru, P.N. (1978). h'rist. Tcch. 13, 35. Kubota, N., H. Kinno and K. Shimizu (1990). d. (5"yst. Growth 100, 491. Levina, I.M. (1992). Kristallografiya 37, 514. Li, L., K. Tsukamoto and I. Sunagawa (1990)..]. Cryst. Growth 99, 150. Malkin, A.I., A.A. Chernov and I.V. Alexeev (1989). d. Cryst. Growth 97, 765. Miyata, T., M. Kitamura and I. Sunagawa (1980). ,~ci. Rep. Tohoku lh~iv. 14, 191. Monaco, L.A. and F. Rosenberger (1993). J. ('r.i/st. Growth 129, 465. Mullin, .J.W. (1972). Crystallisation, 2nd edition. Butterworths, London. Mullin, J.W., A. Amatavivadha.ma aim M. Chakraborty (1970). ,]. Appl. Chem. 20, 153. Nielsen. A.E. (1984). d. Cryst. Growth 67, 289. Nikolaeva. R.D. and E.K. Kirkova (1975/76). Ann. Univ. 5'ofia: Facult~ (:hem. 70, 223. Ohara, M. and R.C. Reid (1973). Modeling Crystal Growth Rates from Solutions. Prentice-Hall, New .Jersey. Okhrimenko, T.M., S.T. Kozhoeva, V.A. Kuznetsov, Yu.A. Klimova and M.L. Barsukova (1992). KristaIlografiya 37, 1309. Ontlllla, K., K. Tsukamoto and I. Sunagawa (1990). ,l. Cryst. Growth 100, 125. Oicik, J. (1982). Adsorption. PWN, Warsaw.

Effects of Impurities on Crystal Growth Processes

41

Owczarek, I. and K. Sangwal (1990a). d. Cryst. Growth 99, 827. Owczarek, ]. and K. Sangwal (1990b). J. Cryst. Growth 102, 574. Potapenko, S.Yu. (1993a). J. Cryst. Growth 133, 141. Potapenko, S.Yu. (1993b). J. Cryst. Growth 133, 147. Punin, Yu.O. and A.S. Vorob'ev (1978). Kristallografiya 23 168. Rak, M. and K. Sangwal (1983). J. Cryst. Growth 65, 493. Reich, R. and M. Kahlweit (1968). Bet. Bunsenges. Physik. Chem. 72, 66. Riuaudo, C., A.M. Lanfranco and M. Franchini-Angela (1994). J. Cryst. Growth 142, 184. Risti~, R., B.Yu. Shekunov and J.N. Sherwood (1994). J. Cryst. Growth 139,336. Risti~, R. and J.N. Sherwood (1991), J. Phys. D: Appl. Phys. 24, 171. Risti(!, R., J.N. Sherwood and T. Shripathi (1990). J. Cryst. Growth 102, 245. Risti¢<, R., J.N. Sherwood and K. Wojciechowski (1993). J. Phys. Chem. 97, 1074. Roberts, K.J., J.N. Sherwood and A. Stewart (1990). J. Cryst. Growth 102, 419. Sangwal, K. (1987). Etching of Crystals: Theory, Experiment and Application. North-Holland, Amsterdam. Sangwal, K. (1989). J. Cryst. Growth 97, 393. Sangwal, K. (1993). J. Cryst. Growth 128, 1236. Sangwal, K. (1994). In: Elementary Crystal Growth (K. Sangwal, ed.), Chap. 4. Saan, Lublin. Sangwal, K. and K.W. Benz (1995). Impurity striations in crystals. This volume. Sangwal, K. and R. Rodriguez-Clemente (1991). Surface Morphology of Crystalline Solids. Trans Tech, Zurich. Sangwal, K., R. Rodriguez-Clemente and S. Veintemillas-Verdaguer (1986). J. Cryst. Growth 78, 144. Sangwal, K. and S. Veintemitlas-Verdaguer (1994). Cryst. Res. Technol. 29,639. Sano, (~., N. Nagashima, T. Kawakita and Y. Iitaka (1990). J. Cryst. Growth 99, 1070. Sasaki. T. and A. Yokotani (1990). J. Cry.~t. Growth 99, 820. Sears. (;.W. (1958). J, Chem. Phys. 29, 1045. Shekunov. B.Yu., L.N. Rashkovich and I.L. Smol'ski (1992). J. Cryst. Growth 116,340. Shimon, L..J.W., F.C. Wireko, J. Wolf, I. Weissbuch, L. Addadi, Z. Berkovitch-Yellin, M. Lahav and L. Leiserowitz (1986). Mol. Cry,st. Liq. Cryst. 137, 67. Simon, B. and R. Boistelle (1981). J. Cryst. Growth 52, 779. Simon, B., A. Grassi and R. Boistelle (1974). J. Cryst. Growth 26, 90. Sunagawa, I. (1962). Amer. Min. 47, 1139. Sunagawa, 1. (1968). Min. Mag. 36, (1968). SUl'ender, V. and K. Kishan Rao (1993). Bull. Mater. Set. (India) 16, 155. Szurgot, M. and K. Sangwal (1986)..1. Cryst. Growth 79, 829. Tat, (I.Y., C.-S. Cheng and Y.-C. Huang (1992). J. Uryst. Growth 123, 236. Triboulet, P. and M. Cournil (1992). J. Cryst. Growth 118, 231. Troost, S. (1968). J. Cryst. Growth 3/4 340. Troost, S. (1972). J. Cryst. Growth 13/14,449. Van der Eerden, J.P. and H. Miiller-Krumbhaar (1986). Electrochi~nica Acta 31, 1007. Van der Voort, E. and P. Hartman (1990). ,I. ('ryst. Growth 104,450. Van Enckevort, W.J.P. and L.A.M.,]. Jetten (1985). J. Cryst. Growth 60, 275. Van Rosmalen, G.M. and P. Bennema (t990). J. Cryst. Growth 99, 1053. Van Rosmalen, G.M., G.J. Witkamp and C.H. de Vreugd (1989). In: Industrial Crystallization 87 (.1. IN')vlt and S. Jacek, eds.), p. 15. Akademia, Prague. Veilltemillas-Verdaguer, S. and R. Rodriguez-Clemente (1986). J. Cryst. Growth 79 198. Velikhov, Yu.N. (1992). Kristallografiya 37, 540. Velikhov, Yu.N. and O.V. Demirskaya (1993). l(ristallografiya 38,239. Velikhov, Yu.N., O.V. Demirskaya and I.V. Pulyaeva (1992). l(ristallografiya 37, 509.

42

K. Sangwal

Voronkov, V.V. and L.N. Rashkovich (1992). Kristallografiya 37, 559. Voronkov, V.V. and L.N. Rashkovich (1994). J. Cryst. Growth 144, 107. Watanabe, K. and I. Sunagawa (1982). J. Cryst. Growth 57, 367. Watanabe, K. and I. Sunagawa (1983). J. Cryst. Growth 65, 568. Weijnen, M.P.C., M.C. van der Leeden and G.M. van Rosmalen (1987}. In: Geochemistry and Mineral Formation in the Earth Surface (R. Rodriguez-Clemente and Y. Tardy, eds.), p. 753. CSIC, M~uirid. Weijnen, M.P.C. and G.M. van Rosmalen (1984). In: Industrial Crystallization 84 (S.J. Jan~i~ and E.J. de Jong, eds.), p. 61. Elsevier, Amsterdam. Witkamp, G.J. and G.M. van Rosmalen (1991). J. Cryst. Growth 108, 89. Witkamp, G.J., J.P. van der Eerden and G.M. van Rosmalen (1990). J. Cryst. Growth 102, 281. Wojciechowski, K. (1989). Ph.D. Thesis, University of Strathclyde (UK). Yokotani, A., K. Fujioka, Y. Nishida, T. Sa.saki, T. Yamanaka and Y. Yamanaka (1987). J. Cryst Growth 85, 549. Yumoto, H., R.R. Hisiguti and T. Kaneko (1986). J. Cryst. Growth 75, 284. Zipp, G.L. and N. Rodriguez-Hornedo (1992). J. Cryst. Growth 12~1, 247.

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KESHRA

43

SANGWAL

Professor Keshra Sangwal was born and educated in India. He completed his secondary school education in 1962 and BSc in 1965, both in Abohar (Panjab), and received his MSc and PhD degrees from Sardar Patel University (Gujarat) in 1968 and 1972, respectively. After shifting to Poland in 1980, he obtained his "doktor habilitowany" degree in 1985 from the University of Ltd,~, and the national title of Professor of Physical Sciences in 1993. Professor Sangwai worked as lecturer in Sardar Patel University (India), as adjunkt (adjunct professor) in the Technical University of L t d , , and as docent (associate professor) and professor in the Pedagogical University of Cz~stochowa. Since 1991 he has been working as professor of physics in the Technical University of Lublin, where he also heads the Group of Solid State Physics. His research activities deal with elementary processes of growth and dissolution of crystals from solutions, and mechanical properties and real structure of crystals. He has authored two books (Etching of Crystals, North-Holland 1987; and, with R. Rodrigues-Clemente, Surface Morphology of Crystalline Solids, Trans Tech 1991), edited two books (Wzrost Krysztaktw, 1990, in Polish; Elementary Crystal Growth, Saan 1994), authored/coauthored 8 chapters for monographs and books, contributed 8 review ariticles, and has published over ninety original papers in international journals. Professor K. Sangwal is the co-founder of Polish Crystal Growth Society, and currently is its presidentelect for the period 1998-2001. Prof. Sangwal enjoys studying ancient literature on religion and philosophy, listening classical western and oriental music, and reading romantic poetry.