The Trace-Component Trapping Effect: Experimental Evidence, Theoretical Interpretation, and Geochemical Applications

Geochimica et Cosmochimica Acta, Vol. 62, No. 7, pp. 1233–1240, 1998 Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/98 $19.00 1 .00

Pergamon

PII S0016-7037(98)00071-4

The trace-component trapping effect: Experimental evidence, theoretical interpretation, and geochemical applications VADIM S. URUSOV* and VALENTINA B. DUDNIKOVA Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Kosygin Street, 19, 117975, Moscow, Russia (Received December 17, 1996; accepted in revised form December 11, 1997)

Abstract—Experimental data indicating increase of crystal-melt (fluid) partition coefficients in the range of microconcentrations of trace elements are reviewed and analyzed in detail. This concentration dependence of partition coefficients has been referred to as either deviations from Henry’s law or the trace-component trapping effect. A critical review of a variety of models proposed to explain this phenomenon is also given. It is shown that the most reasonable and developed of these models relate changes in trace element partition coefficient at low concentrations to interactions between the trace element ions and metastable lattice defects (i.e., linear and planar defects) at low temperatures or intrinsic point defects of thermal origin at higher temperatures. The mechanism of interaction between trace element substituent atoms and intrinsic defects is considered in detail, with particular consideration given to the creation of pair associates, coupled substitutions, and the influence of other impurities on the trace element dissolution. The models developed are fit to the available experimental data to provide descriptions of the dependence of partition coefficients on composition and to estimate the concentrations and free energies of formation of the intrinsic defects (i.e., vacancies and interstitial atoms) in a matrix crystal. Some probable geochemical applications and manifestations of the trapping effect are discussed. This leads to the conclusion that there is an urgent need for further consideration of the problem. Copyright © 1998 Elsevier Science Ltd experimental data showing this behaviour were obtained in both directed growth of single crystals and crystallization of silicate melts. Observations of increasing D at ppm levels have been obtained by several different analytical techniques such as radioactive-tracer analysis (e.g., Iiyama, 1974a; Kirgintsev et al., 1977; Grigorash et al., 1981), betha-track autoradiography (e.g., Mysen, 1978a,b; Harrison and Wood, 1980), atomic absorption spectrometry (e.g., Dudnikova et al. 1983; Dudnikova and Urusov, 1986), neutron activation analysis (e.g., Kobayashi and Takei, 1977; Dudnikova et al. 1990), X-ray fluorescent and emission spectroscopy (Nassau, 1963), precision flotation measurements of the relative density of single crystals (Andreev, 1965; Andreev and Bureyko, 1967), and measurements of resistance (Lyubalin et al., 1976). Some examples are given in Figs. 2– 6. However, Beattie (1993a,b,c,d; 1994) has cast doubt on the existence of this phenomenon in silicate systems. In particular, he found that at least some of the data produced by optical b-track autoradiography of the rare earths partitioning between garnet and glass and olivine and glass are in error and that analyses by a secondary ion mass spectrometry technique do not show an increase in D at low concentration. Beattie (1993a) suggested that non-Henry’s law behaviour may be an artifact of the analytical technique. The question as to whether or not Henry’s law behaviour is satisfied over the whole range of trace concentrations is of significance for geochemical modeling and for producing high purity inorganic materials. Therefore, we reevaluate evidence in favor of a trace-component trapping effect. The terminology and definitions in this paper are given, whenever possible, in accordance with the recent recommendations (Beattie et al., 1993). Several explanations have been offered for an increase in D

1. INTRODUCTION

Conflicting evidence has accumulated in the last few decades in regard to Henry’s law behavior at very low trace element (TE) concentrations (1024–1021%) in crystal/melt (fluid) systems. More precisely, an increase of the partition coefficients (D) between crystal and melt (or fluid) is often observed experimentally at the ppm level of TE, whereas the D values remain nearly constant at the higher concentrations of this component up to the percent levels. Typical examples are shown in Fig. 1. As is seen, three regions of D as a function of TE content can be distinguished. There is an initial region (I) of a constant value of D, which is often referred to as low-concentration Henry’s law behaviour, and this is followed by a region (II) of strongly decreasing D as the TE content increases. The third region (III), where D is nearly independent of the TE content, is usually referred to as high-concentration Henry’s law behaviour. The relatively high D values at very low concentration are not predicted from conventional thermodynamic considerations, and this behavior is known as the trace-component trapping effect (Urusov and Kravchuk, 1978). To our knowledge, Kelting and Witt (1949) first observed an increase in D values of alkaline earth ions in KCl single crystals. Subsequent examples are alkali halides (e.g., NaClCs1, Ca21), nitrates (e.g., NaNO3-Sr21), tungstates (e.g., CaWO4-REE31), fluorides of alkaline earths (CaF2-Ba21, BaF2-Ca21), many silicates (e.g., alkali and alkali earths in feldspars, REE in forsterite), semiconductors (e.g., Sb, Ga in Ge) (see references in Dudnikova and Urusov, 1992b; Urusov and Dudnikova, 1993; Dudnikova et al., 1993). Numerous * Author to whom ([email protected]).

correspondence

should

be

addressed 1233

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Fig. 1. Partition coefficients D as a function of TE content in melt during the directed crystallization of single crystals (Kirgintsev et al., 1977). (a) CsI-Na1; (b) NaNO3-Sr21. The results of experiment replicates are marked by different symbols. The contents of Na (a) and Sr (b) were determined by the use of radioactive-tracers.

at low concentration levels: (1) Incomplete equilibration between the crystal and melt. When equilibrium is not attained, the absolute D values may increase substantially with the crystal growth rate increase (Lyubalin et al., 1976), or if the run time in experiments with small phenocrysts immersed in a glass matrix is shortened (Drake and Holloway, 1978; Leeman and Lindstrom, 1978). However, in most experiments under consideration achievement of equilibrium is evaluated by examining the dependence of D on the crystal growth rate (Kirgintsev et al., 1977; Andreev, 1965) or using reversal experiments

Fig. 2. Concentration dependences of D during the directed crystallization of melts: (1) CaWO4-Nd31 (Nassau, 1963). Neodymium content was obtained by the use of X-ray fluorescent and emission spectroscopy; (2) KCl-Ba21 (Dudnikova et al., 1983), (3) KCl-Pb21 (Dudnikova and Urusov, 1986), and (4) KCl-Mg21 (Dudnikova and Urusov, 1987). The contents of Ba (2), Pb (3), and Mg (4) were determined by atomic absorption spectroscopy. The curves were fitted to the experimental data by Eqn. 6.

Fig. 3. Concentration dependences of DCa for single crystals of NaCl against Ca level in melts: circles denote the data obtained by the use of radioactive-tracer analysis (Kirgintsev et al., 1977); crosses denote the data obtained by precision flotation measurements of relative density of single crystals (Andreev, 1965). Solid lines are results of fitting by Eqn. 6 (curve 1) and by Eqn. 12 (curve 2). Dashed line 3 shows the estimated fraction p of associated pairs.

(Mysen, 1978b; Harrison and Wood, 1980). We assume that departures from equilibrium may not be the mechanism explaining the trapping effect. (2) Iiyama (1974b) and Iiyama and Volfinger (1976) hypothesized that forbinden zones around impurity atoms are avoided by other impurity atoms. Some aspects of this model are questionable and contradictory (Navrotsky, 1978). Indeed, most solid solutions of interest tend to form point defect clusters which when stacked together can form embryonic nuclei for a new phase. (3) Interaction of a trace-component with linear and planar metastable defects (Navrotsky, 1978) involves the assumption that TE at ppm levels is mainly incorporated at dislocations and block boundaries, and after these are saturated, a substitution mechanism is dominant and results in a reduction of D values. A quantitative evaluation of dislocation influence on TE solubilities was made by Abramovich and Shmakin (1986), Abramovich et al. (1989;

Fig. 4. Concentration dependences of D for Ba and Ca in fluoritebased single crystals grown by the directed crystallization of melt (Grigorash et al., 1981). Crosses: BaF2-Ca21; triangles: CaF2-Ba21. The contents of Ca and Ba were determined by radioactive-tracer analysis. Curves 1 and 2 were obtained by the use of Eqn. 20. Curve 3 shows the estimated fractions p of associated pairs in BaF2-Ca21 system.

Trace-component trapping effect

Fig. 5. Concentration dependences of DSm in orthopyroxene (a) and forsterite (b): a,1,2-Opx-Sm. Phenocrysts immersed in glass matrix: 1-1075°C, 10 kbar; 2-1075°C, 20 kbar; (Mysen, 1977, 1978b). b,1,2Fo-Sm. Phenocrysts immersed in glass matrix: 1-1075°C, 20 kbar (Mysen, 1977, 1978b). Sm contents were determined by the use of b-autoradiography. b,3-Fo-Sm. Single crystals of Fo were grown by Czochralski method at 1890°C and 1 bar (Dudnikova and Urusov, 1993). Samarium contents were determined by neutron activation analysis.

1990), Tauson et al. (1989). The model is realistic because the interaction of impurities with linear and planar defects is well known. However, this model does not explain the agreement between forward and reversal experiments, because concentrations of dislocations and block boundaries are very much dependent on the synthesis conditions. (4) Trace-component interaction with point defects of a crystal may be the most realistic approach for describing the concentration dependence of D during crystallization from high-temperature melts. In fact, this model has been proposed to explain behaviour of TE heterovalent substitutions at low concentrations (Kelting and Witt, 1949; Wagner, 1953; Nassau, 1963; Andreev and Bureyko, 1967; Wood, 1976; Harrison and Wood, 1980; Urusov and Kravchuk, 1978; Morlotti and Ottonello, 1982; Watson, 1985; Dudnikova and Urusov, 1992b; Urusov and Dudnikova, 1993; Dudnikova et al., 1993). We consider this model in detail.

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tions. Clustering generally reduces the energy of dissolution, i.e., the cluster is more stable than the isolated defects. We shall restrict our consideration to the simplest type of the clusters, the associated pairs of the TE substitutional cation and next nearest-neighbour cation vacancy or interstitial anion. The extended defect clusters or aggregations of the point defects form at high density of TE and can be ignored in this consideration. An examination of the process occuring in the system is made to define the change in the amount of substituent dissolved in the crystal as a result of its interaction with intrinsic defects. The processes under consideration can be represented as independent of one another and described by reactions which follow the law of mass action and satisfy electroneutrality and material balance equations. Solving of the resulting simultaneous equations makes it possible to determine the relative concentrations of all forms of defects, including the dissolved TE at low concentrations. Heterovalent substitutions are accompanied by the production of vacancies V or interstitials I in the matrix lattice, which compensate for the excess or deficient charge of the substituent. For instance, the dissolution of an atom B with valence n 1 1 in an ionic crystal AX, where A is an ion of valence n, is described by the reaction

2. TRACE-COMPONENT INTERACTION WITH POINT DEFECTS OF A CRYSTAL 2.1. Heterovalent Substitutions

Introducing an excess charge to the matrix crystal, the heterovalent substituent violates electroneutrality balance, whereupon the concentration of other charged defects changes in order to maintain the overall electrical neutrality. What is important, primary point defects produced thermally are involved in the charge equalization process. Two main modes of TE substitution can be distinguished. The first mode refers to truly isolated point defects of both types, substitutional and thermal. It is highly plausible for the dilute solution case in which the defects are well separated and noninteracting. However, an alternative should be also taken into account. This mode of TE substitution can be ascribed to defect interactions and formation of clusters of impurities and charge compensating defects assuming they are placed together on nearest-neighbour and next-nearest-neighbour lattice posi-

Fig. 6. Concentration dependences of DTu,Sm for phenocrysts of garnets immersed in silicate hydrous glass (Harrison and Wood, 1980; Harrison, 1981). (a) Gros-Tu; 1300°C, 30 kbar. (b) Pyr-Tu; 1300°C, 30 kbar (solid circles). Pyr-Sm; 1500°C, 30 kbar (open circles). TE contents were determined by b-autoradiography analysis. R denotes the reversal experiment. Solid curves show the results of fitting by Eqn. 14. Dashed line indicates fitting by Eqn. 6.

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V. S. Urusov and V. B. Dudnikova

BnL 1 1 1

n11 x n 1 1 n1 1 AA i AL 1 BzA 1 Vn9 n n n A

(1)

with equilibrium constant Ks K s5@B zA# @V n9 A#

/@B ~n11!1 #. L

1/n

(2)

Here and below, the brackets denote concentration, the subscripts denote the position in the crystal (A) or presence in the melt (L); a superscript denotes the charge (more strictly and generally, valence): (9) - excess negative, ( z ) - excess positive, and (x) - neutral relative to the charge of the atom in its regular position (A or X), in accordance with conventional designations of the solid state chemistry (Kro¨ger, 1964). For the sake of simplicity assume that the crystal contains only one basic type of intrinsic defects, e.g., Schottky defects VA and VX nz 0 i V n9 A 1V X

(3)

with the equilibrium constant of the reaction of formation of intrinsic defects nz K d5@V n9 A # @V X #.

(4)

The product of the solubility of the intrinsic defects remains constant even when other defects are present in the crystal (Kro¨ger, 1964). To be more exact, Ks and Kd are the reduced equilibrium constants, i.e., they are related to true equilibrium constants by the ratio or product of the activity coefficients: Ks 5 K*s g2/g1, Kd 5 K*d/gVAgVX, where K*s and K*d are the true equilibrium constants of reactions 1 and 3, g1 and g2 are the activity coefficients of the TE in crystal and melt, and gVA and gVX are the activity coefficients of the defects. It is quite reasonable to assume that all activity coefficients are nearly constant at low concentration of TE, and, therefore, the Ks and Kd values are proportional to the corresponding thermodynamic quantities. The crystal electroneutrality condition is nz z @V n9 A # 5 @V X # 1 (1/n) @BA#.

(5)

From the simultaneous solution of Eqns. 2, 4, and 5 we obtain an expression for the partition coefficient D 5 [BAz ]/[BL] on the assumption of a constant relation between the reduced and true equilibrium constants of reactions 1 and 3 z A

z A

1/2 21/n

D 5 K s$~@B #/2n! 1 @~@B #/2n! 1 K d# % 2

.

(6)

Equations relating D to the TE level in the melt previously derived (Kelting and Witt, 1949; Andreev and Bureyko, 1967; Nassau, 1963) are particular cases of Eqn. 6 with n 5 1 or n 5 2. Equation 6 is also distinct in form from the solutions for special cases (Harrison, 1981; Morlotti and Ottonello, 1982; Watson, 1985). This equation leads to the following limiting cases: (1) If [BAz ] ! K1/2 then D 5 Ks/K1/2n , i.e., if the TE d d concentration is substantially less than that of the intrinsic defects, the D value tends to be constant. The constancy of D in this region agrees with some observations (region I in Fig. z 1/n 1); (2) If [BAz ] @ K1/2 , so that in this d then D 5 Ks/([BA ]/n) region D should decrease continuously as the TE content increases. The existence of region III (higher-concentration Hen-

ry’s law behaviour) does not involve the intrinsic defects of a crystal. Placement of other substituents on the same sites of a lattice, provided that they introduce an excess charge too, disturbs the electroneutrality balance again and, therefore, affects the concentration dependence of the partition coefficient of the TE under study. The B partitioning upon the addition of another component M with an excess positive (m z ) or negative (m9) charge relative to the matrix ion A is described by D 5 K s $@~@BzA# 6 m@MA#!/2n# 1 @~~@BzA# 6 m@MA#!/2n!2 1 K d#1/2%21/n

(7)

z where m[MA] is taken with a positive sign for Mm and with A m9 a negative sign for MA . All TE having the same excess charge relative to the matrix as the BAz will produce a suppressing effect on its dissolution. TE with a smaller charge than that of the host ion will act as charge compensators and increase the solubility of BAz . Formation of substituent-vacancy (interstitial) associated pairs becomes significant in regions of higher TE contents. Experimental data confirm the existence of associated pairs between the cationic substituent and a cation vacancy at high density of the heterovalent TE (e.g., Lidiard, 1957). To allow for this form of interaction, the reactions of formation of intrinsic defects (3) and TE substitution (1) should be complemented with a reaction for associated pairs (BAVA) formation (n21)9 BzA 1 V n9 A i (BAV A)

(8)

The electroneutrality condition changes when the charged associated pairs form. We denote the total TE concentration by c and introduce the degree of association p 5 [BAVA]/c, whereupon the amount of isolated trace atoms is equal to c(1 2 p). Accordingly, the equilibrium constants of reaction 8, (Kp), and of reaction 1, (Ks), are rewritten as follows K p 5 cp/c(1 2 p) @V n9 A #; 1/n K s 5 c(1 2 p) @V n9 A # /BL

(9) (10)

and the electroneutrality equation becomes nz cp(n 2 1) 1 n @V n9 A # 5 n @V X # 1 c(1 2 p).

(11)

The simultaneous solution of Eqns. 4, 9, 10, and 11 for substitution of an univalent ion with a divalent ion (n 5 1) gives the following expression for D 5 c/BL: D 5 K s/(K d 1 K sBL)1/2 1 K sK p.

(12)

The initial Eqn. 1 characterizes equilibrium between the TE in the melt and that in isolated form in the crystal. When associated pairs form, the concentration of the isolated substituents decreases, and additional TE must be supplied from an external source (melt, fluid) if equilibrium is to be maintained in the crystal. The interaction of the substituent atoms with thermal vacancies results in the formation of a certain fraction of the associated pairs and thus increases the TE content in the crystal. In multisite solid solutions such as garnets, spinels, pyroxenes, etc., substitution and charge compensation can occur in nonequivalent structural positions. Self-compensation of the

Trace-component trapping effect

excess charge is ensured by coupled substitution in chargecompensating proportions besides the vacancy-compensating mode above described. The excess charge that arises when An1 is substituted by B(n11)1 compensates the deficient charge stemming from substitution of Zm1 in another sublattice by a lower charged ion Y(m21)1 A 1Z 1B x A

x Z

(n11)1 L

1Y

(m21)1 L

z A

9 Z

iB 1Y 1Z

m1 L

1A . n1 L

(13)

The use of Eqn. 13 along with Eqns. 2, 4, and 5 enables us to find an expression of D for the coupled heterovalent substitution in the form D 5 K s $~@BzA#/2n! 1 @~@BzA#/2n!2 1 K d#1/2%21/n 1 S

(14)

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true equilibrium constants do not vary with the TE concentration. The electroneutrality requirement is ensured when @V nzX# 1 [(BAV X)nz] 5 @V n9 A# or, in the notations adopted here, @V nzX# 1 cp 5 @V n9 A #.

(19)

Solving simultaneously Eqns. 4, 17, 18, and 19 makes it possible to determine the defect concentration and to obtain an analytical expression relating the partition coefficient D 5 c/BL to the TE concentration D 5 K s $1 1 @K dK 2p/(1 1 BLK sK p)#1/2%.

(20)

where S 5 K13/DY, K13 is the equilibrium constant of reaction 13; DY is the partition coefficient of Y. Assuming that Y partitioning obeys Henry’s law, S is very likely to be constant. Then at higher concentrations D 3 S (Figs. 6 a,b).

Note that Eqns. 6, 12, 14, and 20 are, in principle, common to different types of intrinsic defects and associated pairs (Dudnikova and Urusov, 1992b; Urusov and Dudnikova, 1993).

2.2. Isovalent Substitutions

2.3 Experimental Data Fitting

Under isovalent substitution no excess charges are introduced in the crystal and substituent-vacancy associated pairs become the only type of TE interaction with intrinsic defects. If for heterovalent systems the formation of associated pairs results from electrostatic interactions, in the case of isovalent systems, evidently, an important role is played by elastic interactions which manifest themselves when substituent and host ions differ substantially in size. If the crystal strain decreases because the substituent is incorporated into regions already distorted by intrinsic defects, the dissolution of the TE is facilitated. An additional decrease in the energy of cluster dissolution in relation to isolated substituents may be due to the polarization and vibrational effects (Kro¨ger, 1964). The passage of an isovalent TE B with charge n1 from the melt into the crystal is represented as the simple exchange reaction

The curves shown as solid lines on Figs. 2– 6 present the results of fitting Eqns. 6, 12, 14, and 20 to the available experimental data. It has been done by means of the computer code written by V. S. Rusakov (Moscow University). The problem of finding the optimum values of the fitting parameters was solved within the framework of the method of least squares. For convenience, the concentration of TE in a crystal (BA) is expressed as a fraction of the positions occupied by B atoms of the total amount of A sites in a given crystal lattice. As is seen in Figs. 2 and 5, Eqn. 6 provides very satisfactory fits to the experimental partition coefficients as a function of TE concentrations for heterovalent systems CaWO4-Nd31, KCl(Ba21, Pb21, Mg21), Opx-Sm, Fo-Sm. Formation of the substituent-vacancy associated pairs should be taken into account for NaCl-Ca21: experimental results for this system are adequately described by Eqn. 12 (Fig. 3, line 2) but not by Eqn. 6 (Fig. 3, line 1). It follows that in such different matrices as alkali halides, forsterite, orthopyroxene, and the charge compensation attendant on heterovalent substitution is affected by vacancies or interstitials formation in the same or similar positions. Sometimes it is even possible using Egns. 10 –12 to estimate the fraction p of the associated pairs as a function of composition (Fig. 3, dashed line). However, it is not the case for the concentration dependence of DREE in garnets (Fig. 6a, dashed line). The garnets as well as a majority of rock-forming minerals are multisite solid solutions in which the charge compensation mechanism is likely to be by the so-called coupled substitutions, for instance,

n1 x AxA 1 Bn1 L i AL 1 BA.

(15)

We assume again that Schottky defects are the main form of defects in the crystal, and the associations of cationic substituent with the nearest-neighbour anion vacancy are produced by the reaction V nzX 1 BxA i (BAV X)nz.

(16)

The total TE content c in the crystal is determined by the sum of the associated and isolated forms: c 5 [BxA] 1 [(BAVX)n z ]. If we denote the degree of association p 5 [(BAVX)n z ]/c, then the amount of associated pairs is c(1 2 p). In this notation, the equilibrium constants Ks and Kp of reactions 15 and 16 take the forms K s 5 c(1 2 p)/[BL],

(17)

K p 5 p/(1 2 p) @V nzX#.

(18)

Ca21 1 Si41 i REE31 1 Al31, 2Ca21 i REE31 1 Na1, K1, etc.

As before, Kd, Ks, and Kp are the reduced equilibrium constants Kd 5 K*d/gVAgVX; Ks 5 K*sg2/g1; Kp 5 K*pgVXg1/g(BAVX) and K*d, K*s, K*p are the true equilibrium constants of reactions 3, 15, and 16; g(BAVX) is the activity coefficient of the associated pairs. Once again we assume that the ratios between the reduced and

In particular, the latter substitutions were studied experimentally and theoretically for the sheelite CaWO4 (Nassau, 1963). It seems reasonable, therefore, that Eqn. 14 can be appropriate for such cases. Indeed, as is shown on Fig. 6a,b, Eqn. 14 describes the observed behaviour of DREE for the systems Gros-REE and Pyr-REE under the assumption of coupled

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V. S. Urusov and V. B. Dudnikova

substitution. Note that this type of charge compensation does not forbid partition coefficients from increasing at low TE concentrations, contrary to statements by Harrison and Wood, (1980), Harrison (1981), and Beattie (1994). One can make the estimates of Ks, Kd, S, and Kp values by fitting Eqns. 6, 12, 14, and 20 to the observed data. As follows from the model background outlined above, at least a part of the fitting parameters may possess a certain physical meaning. In particular, Kd values refer to the concentration of intrinsic defects through the definition 4, so that the content of the Schottky (or Frenkel) defects will be, within the approximation that K*d ' Kd, equal to n/N 5 K1/2 d . The estimates of these quantities were performed and compared, whenever possible, with similar data found by means of independent approaches (Dudnikova and Urusov, 1992b; Urusov and Dudnikova, 1993; Dudnikova et al., 1993). For instance, the similar thermal defect concentrations are found for a given crystal with different TE: pyrope: (1–3) z 1027 and grossular: (3– 6) z 1027 at 1300°C (Dudnikova and Urusov, 1992b). The free energy of formation of these defects (g) was derived from the Boltzmann’s equation (n/N)2 5 exp(2g/kT), where k is Boltzmann’s constant, and T is the temperature (K). Our estimates of g values for garnets, orthopyroxene, and forsterite comprise 3.2– 4.6 eV (Dudnikova and Urusov, 1992b). 3. DISCUSSION

In his recent investigation Beattie (1993a) has questioned the occurrence of non-Henry’s law behaviour in the experimental REE partitioning studies for olivine-melt and garnet-melt systems by the use of the optical b-track autoradiography (Mysen, 1976, 1977, 1978a,b; Wood, 1976; Harrison, 1978, 1981; Harrison and Wood, 1980). His remeasurements by secondary ion mass spectrometry of Sm partitioning between grossular and melt at 1300°C and 30 kbars for the experiments performed by Harrison (1978) show no deviations from Henry’s law behaviour. Beattie concluded that the optical autoradiography technique produced a spurious doubling of REE partitioning coefficient at low concentrations and, therefore, the earlier observed deviations may be an artefact of this analytical technique. However, it must be emphasized that the increase of Sm and Nd partition coefficients at low concentrations in forsterite-melt equilibria were also observed using quite a different method of crystal growth and analytical technique. In particular, the single crystals of forsterite had been grown by the use of normal directed crystallization from melt (Czochralski method) and the content of TE had been determined by neutron activation analysis (Dudnikova et al., 1990; Dudnikova and Urusov, 1993). It is seen in Fig. 5b that the trapping effect of Sm partitioning between forsterite single crystal and its melt exists as well as between forsterite phenocrysts and glass produced by quenching the system Mg2SiO4-SiO2-H2O fused at about 1000°C and 10 –20 kbar. It can be added in proof that very similar behaviour of DLa for forsterite grown by the Czochralski method had been established by Kobayashi and Takei (1977) by neutron activation analysis. However recent determination of rareearths (Y, La, Ce, Pr, Sm, Tb, Ho, Yb) partitioning in forsteriteglass pairs using the secondary ion mass spectrometry show no deviations from Henry’s law (Beattie, 1994). Although the

concentrations of the light rare-earth elements (La, Ce, Pr) in crystals were low enough (0.1– 0.4 ppm), the total concentrations of REE, up to 100 –200 ppm, and the total concentrations of all trivalent elements were quite high as much as 1022. As shown by Harrison and Wood (1980) and Harrison (1981), the partitioning of Ce, Sm, and Tm between garnet and hydrous silicate liquid (30 kbar, 1300 and 1500°C) is a function of the total REE concentration in the crystals. For instance, DSm varies from 0.234 6 0.009 with S REE 5 9 ppm to 0.160 6 0.007 with S REE .20 ppm in the garnet crystals. This latter value corresponds to DSm characteristic of higher concentration region at which the trapping effect becomes negligible. It would be interesting to note that Cr did not affect DSm because it is very likely that Cr31 enters the garnet structure by an isovalent (charge-balanced) substitution for Al31. Moreover, recent experimental and theoretical study (Dudnikova and Urusov, 1992c) supports the mutual influence of different TE on the concentration dependence of partition coefficient; for example, DSm for forsterite single crystal-melt system is lowered from 0.014 6 0.001 when the crystal contains only Sm (0.07 ppm) to 0.007 6 0.001 when there are also other TE (La, Ga, Sc, Nd, Lu, Gd; S TE .3 ppm) in the crystal. Note that Eqn. 7 predicts the reduction of DSm from 0.014 to 0.008, which fits the measured value (0.007 6 0.001) within the experimental error bars. Thus, with the total concentration of trivalent TE as much as 3 ppm DSm is halved and takes the value characteristic of higher Sm contents (Dudnikova and Urusov, 1992a). Figure 4 demonstrates a satisfactory description by Eqn. 20 of the observed concentration dependence of partition coefficients in several isovalent systems. It must be emphasized that the trapping effect in such systems is repeatedly observed but only when the crystal chemical properties of a major and trace-components are strongly different, so that the size parameter d 5 (r2 2 r1)/R, (r2 and r1 are the ionic radii of trace and major elements, correspondingly, R is the average interatomic distance) of the solid solution is large (Urusov, 1992). Indeed, in systems NaCl-Br2, CsI-Tl1, NaCl-K1 (Kirgintsev et al., 1977), CaF2-Sr21 (Grigorash et al., 1981), in which the squares of the size parameter d2 do not exceed 1%, no trapping effects were observed. The same is true for such silicate solid solutions as muscovite with trace amount of Rb (Volfinger, 1969), anorthite with Sr (Iiyama, 1974a), leucite with Na (Roux et al., 1971). However, if d2 . 1–3%, then the trapping effects may be significant: NaCl-I2, NaCl-Rb1 (Kirgintsev et al., 1977), BaF2-Ca21, CaF2-Ba21 (Grigorash et al., 1981), Cs in orthoclase (Roux et al., 1971), Rb in albite (Roux, 1971), Cs in muscovite (Volfinger, 1976). Note that in the system CaF2Ba21, with d2 5 1.6%, the trapping effect is higher than in the system BaF2-Ca21 with d2 5 1.2% (Fig. 4). The trapping effect becomes very pronounced at d2 $ 3–5%: CsI-Na1 (Kirgintsev et al., 1977; Fig. 1), Cs in albite (Roux, 1971), Li in sanidine, phlogopite, and muscovite (Iiyama and Volfinger, 1976). From these facts it transpires that the increase of partition coefficient at low concentrations is very important at least in purifying and doping of inorganic materials. More precisely, this effect hinders the production of very pure substances, since fractional (or directed) crystallization methods become ineffi-

Trace-component trapping effect

cient in the later stages of purification when very low concentrations are obtained. Although the geochemical significance of the trapping effect requires further investigation, many geochemical observations show the probable importance of this effect. For example, Urusov and Kravchuk (1978) noticed that the partitioning of some elements between phenocrysts and groundmass of various effusive rocks exhibits behaviour corresponding to the trapping effect. Namely, as is known, the so-called Onuma’s diagrams show smooth parabolic dependence of Di on the radii of i-elements (Onuma et al., 1968). However, the experimental data for most imcompatible elements (K in bronzite, Ba in augite, Cs in biotite and plagioclase; Jensen, 1973) reveal sharp deviations from the values expected from the extrapolation of the curves Di (ri). Very similar behaviour of DCs in plagioclase phenocrysts from Kamchatka basalts has been observed somewhat later (Kravchuk et al., 1981); the DCs is larger by about 2 orders of magnitude than the extrapolated value. A probable explanation of these deviations could be imperfect phase separation, i.e., contamination of crystal by a small amount of glass during the analysis of the crystal, as proposed by McKay (1986). This possibility must not be ruled out, but calculations show that the apparent partition coefficients, if the crystals were contaminated by 1% and 0.3% glass inclusions, form another curve Di (ri) without any well-pronounced minimum. In this context we note that in all graphs showing the partitioning of divalent elements between olivine and melt against ionic radii (Fig. 4 in Beattie, 1994) DBa (1025–1026) deviates from the expected values (1027–1028). Beattie (1994) stated that the effects of contamination of crystals during polishing and sputtering of peripheral glass in the course of SIMS analysis changes the measured partition coefficients by less than 3 z 1025 in these experiments. Therefore, we infer that at least to some extent the observed drastic increase of D values for the most imcompatible cations is due to the trapping effect. In general, an important condition of the trapping effect manifestation is sufficiently large difference of crystal chemical properties of major and trace elements. For isovalent substitutions this condition is necessary and many evidences of the validity of that were discussed above. However, the same is likely to be true for heterovalent substitutions too. In particular, this prediction can be verified by a comparative investigation of the trapping effect for REE of different size, as was shown by Harrison and Wood (1981). From the above discussion it is evident that partition coefficients related to non-Henry’s law behaviour may vary no more than an order of magnitude. This is comparable to variations of D values associated with the natural bulk composition range and corresponding temperature of crystallization. Moreover, in natural systems simultaneous presence of several trace elements may decrease or even eliminate the trapping effect of individual trace elements. Some speculations in the field of probable geochemical consequences of the trapping effect have been recently published (Urusov et al., 1997). Nevertheless, the geochemical significance of the trapping effect remains in question.

1239 4. CONCLUDING REMARKS

In conclusion we argue that the phenomenon of increasing partition coefficient at very low TE concentration (the TE trapping effect) is quite realistic. This result has been found in various experiments using different analytical techniques. A reasonable explanation of the trapping effect is the interaction between small amounts of the TE and the intrinsic and extrinsic defects of a crystal. In the special case of higher temperatures (melt crystallization) it is possible to describe the trapping effect in terms of equilibrium interaction between intrinsic defects (Schottky and Frenkel defects) and substituent atoms. Although we believe this effect occurs, more information is needed about is role in silicate-melt systems. There is an urgent need for measurements of the same samples by several different analytical techniques, including modern approaches such as SIMS. Acknowledgements—The authors wish to thank A. B. Bykov for Chockralski growth of the olivine single crystals, G. M. Kolesov for the neutron activation analysis of the rare-earth elements, and V. S. Rusakov for the help in mathematical treatment of the experimental data. The authors wish to thank F. A. Frey for his well-meaning comments and corrections in the course of editing the manuscript, B. O. Mysen, and P. D. Beattie for critical reviews and many helpful suggestions. REFERENCES Abramovich M. G. and Shmakin B. M. (1986) Abnormal solubility of impurities in inhomogeneous crystals and its geochemical role. Dokl. Akad. Nauk USSR 288, 1216 –1220 (in Russian). Abramovich M. G., Tauson V. L. and Akimov V. V. (1989) Fractionation of microadmixtures into mineral crystals with defect structure. Dokl. Akad. Nauk USSR 309, 438 – 442 (in Russian). Abramovich M. G., Shmakin B. M., Tauson V. L. and Akimov V. V. (1990) Abnormal concentrations of impurities in solid solutions of defect structure. Zap. Vses. Mineral. Ob., Part 199, 1, 13–22 (in Russian). Andreev G. (1965) Partitioning divalent elements between NaCl single crystals and melt. Fiz. Tverd. Tela (Leningrad) 7, 1653–1656 (in Russian). Andreev G. and Bureyko S. F. (1967) Partitioning divalent elements between KCl single crystals and melt. Fiz. Tverd. Tela (Leningrad) 9, 79 – 82 (in Russian). Beattie P. (1993a) On the occurrence of apparent non-Henry’s Law behaviour in experimental partitioning studies. Geochim. Cosmohim. Acta 57, 47–55. Beattie P. (1993b) Olivine-melt and orthopyroxene-melt equilibria. Contrib. Mineral. Petrol. 115, 103–111. Beattie P. (1993c) Uranium-thorium disequilibria and partitioning on melting of garnet peridotite. Nature 363, 63– 65. Beattie P. (1993d) The generation of uranium series disequilibria by partial melting of spinel peridotite: Constraints from partitioning studies. Earth Planet. Sci. Lett. 117, 379 –391. Beattie P. (1994) Systematics and energetics of trace-element partitioning between olivine and silicate melts: Implications for the nature of mineral/melt partitioning. Chem. Geol. 117, 57–71. Beattie P., et al. (1993) Terminology for trace-element partitioning. Geochim. Cosmochim. Acta 57, 1605–1606. Drake H. J. and Holloway J. R. (1978) Henry law behaviour of Samarium in natural plagioclase/melt system: Importance of experimental procedure. Geochim. Cosmochim. Acta 42, 679 – 683. Dudnikova V. B., Urusov V. S., and Bannykh L. N. (1983) Solvus of KCl:Ba21 solid solution from flotation measurements of single crystal density. Phys. Stat. Sol.(a) 80, 399 – 402. Dudnikova V. B. and Urusov V. S. (1986) Solvus of KCl:Pb21 solid solution from flotation measurements of single crystal density. Cryst. Res. Technol. 21, 361–366. Dudnikova V. B. and Urusov V. S. (1987) Decomposition of solid

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