Colloids and Surfaces A: Physicochemical and Engineering Aspects, 16 (1993) 65-12 Elsevier Science Publishers B.V., Amsterdam

Xanthate adsorption at PbS surfaces: molecular model and thermodynamic description

Pawel Nowak Polish Academy of Sciences, Institute of Catalysis and Surface Chemistry, ul. Niezapominajek I, 30239 Krakow, Poland

(Received 11 August 1992; accepted 2 December 1992)

Abstract

On the basis of the analysis of IR spectroscopic data it was assumed that the adsorbing entity in the system lead

sulfide-aqueous xanthate solution is lead xanthate in molecular form. Starting from this assumption it was shown that

the quantitative data on the adsorption of xanthate at the PbS surface may be described by “classical” adsorption

isotherms, for example, the Frumkin isotherm.

Keywords: Adsorption; galena; lead sulfide; xanthate.

65

Introduction

There is no doubt that the adsorption of xan- thates (alkyl dithiocarbonates) on a galena (lead sulfide) surface, covered with a layer of oxidation products (lead carbonate, lead thiosulfate), pro- ceeds as the exchange reaction of these oxidation products with xanthate ions from solution. However, the mechanism of xanthate adsorption at the bare (not oxidized) galena surface is still the subject of controversy. Following Woods [ 11, most authors assume that the process is electrochemical in nature and that the first step is the electrosorp- tion of the xanthate radical at the surface, accord- ing to the reaction

R-0-CS; = R-O-C& ads + e- (1)

It was first proposed by Greenler [2] and Poling and Leja [3] that the xanthate radical is attached to the lead atom in the first layer of the crystal

Correspondence to: P. Nowak, Polish Academy of Sciences,

Institute of Catalysis and Surface Chemistry, Ul.

Niezapominajek 1, 30239 Krakow, Poland.

lattice of lead sulfide and that the coordination of xanthate to lead in the adsorption layer is 1: 1 instead of 1: 2 as in lead xanthate PbXz (xanthate radicals will henceforth be denoted X). Such coordi- nation was inferred mainly from analysis of the IR frequency shifts observed in the spectra of mono- layer and submonolayer coverage of xanthates on lead sulfide, in comparison with the spectrum of lead xanthate.

A completely different mechanism was proposed many years ago by Taggart et al. [4]. That mecha- nism assumed an ion exchange reaction between sulfide ions from the lattice and xanthate ions from the solution according to the reaction

PbS+H++2X- =Pb(X),+HS- (2)

However, in view of the very big difference between the solubility product of lead sulfide and lead alkyl xanthates [S], this mechanism was totally neglected for a long time. Unquestionable experimental evi- dence that the adsorption of xanthate on the PbS surface does occur by an exchange mechanism has been supplied recently by Leppinen and co-workers

0927-7757/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved.

66 P. NowaklColloids Surfaces A: Physicochem. Eng. Aspects 76 (1993) 65-72

[6-lo]. According to Leppinen and co-workers,

reaction (2) occurs even at a concentration of

xanthate ion lower than the equilibrium concen-

tration for reaction (2), but in this case it is

restricted to the first monolayer (or eventually first

few monolayers). It was clearly shown that reaction

(2) is reversible and that one sulfide ion is

exchanged by two xanthate ions; this means that

the molecular proportion of xanthate radicals to

lead atoms in the adsorption product is 2 : 1. Strong

support for the mechanism proposed by Leppinen

and co-workers comes from the work of Sun and

co-workers [ 11,121. These authors demonstrated

the feasibility of exchange reactions at the PbS

surface in aqueous environments.

Unfortunately the mechanism proposed by

Leppinen and co-workers has not found common

acceptance. According to the present author, the

reason is the apparent disagreement between the

behavior of the PbS-xanthate system, which may

be expected on the basis of the mechanism pro-

posed by Leppinen and co-workers and the results

of the experiments reported in many publications.

According to the mechanism developed by

Leppinen and co-workers, if the experiment is

performed under conditions in which the S2 - ions

are continuously removed from the solution (by

oxidation with dissolved oxygen, for example), full

monolayer coverage of the surface by adsorbed

xanthate should be quickly attained (even at low

xanthate concentrations); however, this does not

seem to be the case. For example, Finkelstein and

co-workers [13-171, in many experiments with

galena surfaces free of oxidation products and at

pH 8-10 observed, during 1 h, the formation of

approximately 0.2-0.4 monolayer of xanthate at

the surface. Buckley and Woods [18] observed, at

pH 9.2 and a xanthate concentration of lop4 mol

dmm3, the formation of less than 0.4 mono-

layer during the first hour of sorption on freshly

cleaved galena. Similar coverage under comparable

conditions was observed by the present author

c191. The aim of this work is to find a possible

explanation of the apparent disagreement between

the data of Leppinen and co-workers and the data

presented by other authors and to propose another

approach to the thermodynamic description of the

interaction in the PbS-xanthate system.

Methods, techniques and materials studied

The measurements of adsorption of xanthate at

the surface of lead sulfide were performed using

the infra red internal reflection spectroscopy (IR-

IRS) technique [20]. Thin layers (200 nm) of PbS

were deposited on the surface of germanium reflec-

tion elements (angle of refraction 45”, 25 active

reflections) by the chemical bath deposition method

[21]. These layers were highly crystalline, strongly

textured (with the (100) plane oriented parallel to

the surface), nearly stoichiometric and slightly

p-type. The conductivity type was determined by

thermopower measurements. More information on

the preparation procedure and properties of the

PbS layers may be found in previous work (see

Ref. [20] and references cited therein). The mea-

surements were performed simply by dipping the

reflection element covered by the PbS layer in

solution, with free exposure to air. After the pre-

determined time, the reflection element was with-

drawn, washed (if necessary) and placed in the

reflection accessory to measure the spectrum. The

spectra were registered with the Nicolet 800

Fourier transform IR/Raman spectrometer. For

each spectrum, 128 scans were collected and

averaged. Some spectra were also recorded using

the KBr pellet technique. Commercial potassium

ethyl xanthate was purified by crystallization from

acetone. Lead ethyl xanthate was prepared by

precipitation from a solution of lead nitrate by

adding a solution of potassium ethyl xanthate and

further crystallization from acetone. All other re-

agents were of analytical grade purity. Doubly

distilled water was used to prepare the solutions.

X-ray diffraction patterns were obtained on a

DRON2 diffractometer. All experiments were car-

ried out at room temperature.

P. NowakjColloids Surfaces A: Physicochem. Eng. Aspects 76 (1993) 65-72 67

Results and discussion

The identity of the adsorbing species

As already stated, the 1 : 1 coordination in the

adsorbed layer was inferred mainly on the basis of

the observed IR shifts. One of the IR absorption

bands, located in most metal xanthates close to

1200 cm-‘, in the case of lead ethyl xanthate

(PbX,) was observed at a frequency of about

1210cm-‘, but for the product of ethyl xanthate

adsorption on the PbS surface at submonolayer

coverage, this band was observed at 1195 cm- ‘.

This shift was considered as proof that xanthate is

adsorbed in such a way that the xanthate radical

is bound to a lead atom in the first monolayer of

lead sulfide and that the coordination of xanthate

to lead is 1 : 1 [3]. However, careful inspection of

the existing literature on the IR spectrum of lead

xanthates shows [22] that the position of the

absorption band considered depends strongly on

the sample preparation; peak positions between

1220 and 1198 cm-’ have been reported in the

literature [22]. The difference between these two

values (22 cm - ‘) is much higher than the difference

considered as an indication of adsorption [3].

Further examples are given in Fig. 1 (the positions

of the absorption band maxima are given in

Table 1). It may be noted that for all three spectra

of lead ethyl xanthate presented in Fig. 1 the

maximum of the band located close to 1200 cm- ’

occurred at a frequency between 1191 and

1199 cm-‘, in the frequency range which was

TABLE 1

IR band frequencies for the spectra shown in Fig. 1

Spectrum Wavenumber (cm-‘)

A 1212, 1192 1142, 1110 1027, 1019, 994

B 1199 1143,llll 1028, 1018, 995

C 1191 1140,1115 1029, 1000 D 1194 1142, 1114 1024

E 1195 1141,1114 1023 F 1192 1137,1114 1023

1300 1200 I100 1000 WRVENUMBER/C~-~

3 1200 1100 1000 WAVENIJMBER/CI~-~

Fig. 1. IR spectra: A, lead ethyl xanthate, crystallized from acetone (IRS spectrum); B, the same sample as for spectrum A but spectrum

recorded by the KBr pellet technique; C, thin layer of lead ethyl xanthate, obtained by evaporation of its solution in acetone on the

surface of KBr (transmission spectrum); D, PbS surface after 30 min contact with a solution of lead ethyl xanthate in acetone

(concentration 0.001 mol dmm3) and rinsing with acetone; E, PbS surface after 30 min contact with an aqueous solution of potassium

ethyl xanthate (concentration 0.002 mol dmm3; pH, 6.5); F, the same sample as for spectrum E but rinsed three times with acetone.

68 P. NowaklColloids Surfaces A: Physicochem. Eng. Aspects 76 (1993) 65-72

ascribed to adsorbed species [2,3,7,19,21]. Figure 1

shows also the spectra (D-F) of the surface of lead

sulfide after adsorption of xanthate. The maximum

of the absorption band, which in lead xanthate is

located close to 1200 cm- r, in all three samples

occurred at a wavenumber higher than in the case

of the lead xanthate sample presented in Fig. 1

(spectrum C). However, there are some features

which distinguish these spectra from the spectra of

lead xanthate: firstly, the characteristic broadening

of the band, and secondly the disappearance of the

fine structure of the band located at a wavenumber

of about 1020 cm- ‘. Therefore, it can be stated

that the observed frequency shifts may be interpre-

ted neither as an indication of the 1 : 1 coordination

of xanthate to lead nor as proof of the adsorbed

state of xanthate species.

The similarity between the spectrum of lead sul-

fide after sorption from the solution of lead ethyl

xanthate in acetone and the spectrum of lead

sulfide after sorption from aqueous potassium ethyl

xanthate solution is especially remarkable. In the

latter case the mechanism of adsorption according

to reaction (1) is very probable; in the former case,

the simplest mechanism would be the adsorption

of the lead xanthate molecule from the solution on

the lead sulfide surface. Figure 2(a) presents the

hypothetical conformation of the lead xanthate

molecule at the (100) crystal plane of the lead

sulfide surface. This conformation may be obtained

from the conformation of the lead xanthate mole-

cule in the crystal state [23] by rotation around

the bonds, without significant changes in either

bond lengths or bond angles. The following features

of the conformation presented should be noted:

(a) the surface coverage is one xanthate radical for

one surface lead atom in PbS (which was observed

in many works); (b) one molecule of adsorbate is

attached to four atoms in the crystal lattice of PbS,

which should lead to strong adsorption; (c) all

dangling bonds of the PbS surface are saturated,

which should stabilize the adsorption system; (d) all

atoms in the lead xanthate molecule after adsorp-

tion have the same number of bonds as in the case

of the lead xanthate molecule in the crystal state

R-

(b)

Fig. 2. The molecular conformation of the lead xanthate mole-

cule: (a) adsorbed on the surface of PbS ((100) plane); (b) in the

crystal state.

(the conformation of the lead xanthate molecule is

presented in Fig. 2(b)). It should be noted that

the results of IR measurements at least do not

contradict the model presented; also the results of

X-ray photoelectron spectroscopy measurements

[22] were interpreted in accordance with the pre-

sented model of the adsorbed layer. However, the

present author does not suggest that in the case of

the aqueous solution, the PbX, molecule is first

formed in solution and then adsorbed at the sur-

face; in this case the exchange mechanism, as

proposed by Leppinen and co-workers, probably

occurs.

P. NowaklColloids Surfaces A: Physicochem. Erg. Aspects 76 (1993) 65-72 69

Thermodynamic description

In the description of the PbS-xanthate system,

Leppinen and co-workers [6-91 assumed the so-

called “surface phase model”. In this model it is

assumed that the outermost layer of lead sulfide,

partially covered with xanthate, may be treated as

a separate phase composed of PbS and the complex

(PbX),S. (However, no emphasis was placed on

the particular structure of the surface complex and

the thermodynamic description used by Leppinen

and co-workers may be equally well applied to

PbX, as the surface species.) Further, it was

assumed that the chemical potential of both com-

ponents depends on the concentration of the com-

ponent in the surface phase, being equal at the

same time to the chemical potential of the same

component in the aqueous phase. For example, the

chemical potential of PbS in the surface phase was

expressed [669] as

p(PbS,,) = p*(PbS,,) + RT ln[x(Pb”)x(S*-)]

+ RT Inf(PbS) (3)

where x denotes the molar fraction of the species

in the surface phase,fis the activity coefficient and

sf refers to the surface phase.

According to the present author this approach

is incorrect, because as long as lead sulfide exists

in the system as a separate phase, the chemical

potential of that species must be constant in any

phase in the system (including the surface phase)

and equal to the chemical potential of pure PbS.

The alternative proposition is to treat the process

of xanthate sorption at the PbS surface as the

adsorption of PbX, species at the PbS surface and

to try to describe that process by an adsorption

isotherm.

For PbS in equilibrium with aqueous solution

the following equations hold:

PbS(s) = PbS(aq) = Pb2+(aq) + S2 -(as) (4)

C~~Z+~~q~lC~2~~~q~l/C~~~~~~~l = Kids (5)

CPb2’(as)lCs2-(aq)l = Kids CPbWdl = Klsp (6)

Owing to the low value of the second dissociation

constant of H,S, the concentration of S2- ions in

solution is always negligible (except in extremely

alkaline solutions), so the above equations are only

the formal expressions of the equilibrium condi-

tions. A similar set of equations may be obtained

for HS- ions which are the product of PbS dissoci-

ation in neutral and slightly alkaline solutions:

PbS(s) = PbS(aq) + H,O = Pb2+(aq) (4a)

+ HS(aq) + OH-(aq)

CPb2 ‘(4lCHS pWl [OH- WWCPbS@q)l = K;ds

(54

Introducting the second dissociation constant of

H2S

CH’(aq)lCS2-(aq)l/CHS-(aq)l = Ksis (5’4

and the ionic product of water

CH ‘WI [OH -(as)1 = K, (5c)

the solubility product of lead sulfide may be

expressed as

CPb2 ‘(as)lCs2 -(as)1 = CPbWq)l Kids KdK,

= K~sp (64

In acidic solutions, where H,S is the predominating

sulfur species, an analogous set of equations may

also be obtained.

A similar set of equations may also be written

for the precipitated lead ethyl xanthate:

PbX,(s) = PbX,(aq) = Pb2+(aq) + 2X-(aq) (7)

CPb2+(aq)lCX-(aq)12/CPbX2(aq)l = K2ds (8)

Cpb2’WlCx-W12 = K2ds CPbX2(aq)l = Kzsp (9)

where sp denotes solubility product and ds denotes

dissociation.

Thus when both solid phases coexist the

following relationship holds:

C~-(412/CS2-Wl = K&KI~~ = K (10)

If the quotient [X-(aq)]2/[S2p(aq)] is lower than

70 P. NowakjColloids Surfaces A, Physicochem. Eng. Aspects 76 (1993) 65-72

K, lead xanthate does not exist as a separate phase.

In that case the activity of PbX,(aq) species may

be calculated from Eqns (6) and (8):

CPb&Wl = (K,,,IK,,,)CX-(aq)12/CS2-(aq)l (11)

For the sake of brevity, activity coefficients were

neglected in the preceding derivation, but this does

not change the merit of the reasoning.

Most of the isotherms used in the description of

adsorption at the soliddliquid phase boundary may

be expressed in the form

BC =f(O) (12)

where C is the concentration (or activity) of the

adsorbate in solution, B the equilibrium constant

of the adsorption process, 0 the surface coverage

andf(@) is some function of the coverage. Inserting

the expression in Eqn (11) for C into Eqn (12) one

obtains

(BK,,,IK,,,) FW12/CS2-(41 =f(@) (13)

The constants appearing on the left-hand side of

Eqn (13) may be grouped into one constant B’:

B’CX-(aq)12/CS2-(aq)l =A@) (14)

As shown by Leppinen [6], if the pH and the

analytical concentration of the dissolved sulfide

species (H,S + HS- + S2-) are known, one can

always calculate the concentration of S2-. For a

given analytical concentration of dissolved sulfide

species, the concentration of the S2-(aq) ions

depends strongly on the pH of the solution; the

adsorption should also depend on pH accordingly.

If the concentration of xanthate ions in solution

and the surface coverage by adsorbed xanthate are

also known, one may try to fit an adsorption

isotherm to the experimental data. Figure 3 shows

the Frumkin adsorption isotherm (the quotient

[X-(aq)]2/[S2-(aq)] was used instead of concen-

tration)

BC = O/(1 - 0) exp(-2a0) (15)

least-squares fitted to the data of Leppinen [6].

One comment should be made. In his calculations,

Leppinen assumed that the “parking area” of the

8.4

a

B.8 2.5 1.5 6.5 8.5

LOGC CEtX-12/CS-21 1

Fig. 3. The Frumkin adsorption isotherm fitted to the data of

Leppinen 161. Abscissa, the quotient of ethyl xanthate ion and

sulfide ion concentrations; ordinate, surface coverage (see text

for details).

xanthate radical equals 0.35 nm2, which is the area

of one face of the elementary crystal unit of PbS.

However, this face contains two surface lead atoms.

Because the present author assumed that at full

coverage the adsorption density would be one

xanthate radical for one surface lead atom (Fig. 2),

the 0 values given in the work of Leppinen were

divided by two. It may be stated that a quite good

fit is obtained, keeping in mind that both 0 and

concentration values are the products of a rather

complicated analysis of the solution composition.

The constant a in Eqn (15) characterizes the attrac-

tion/repulsion interactions in the adsorbed layer.

In the presented fit, the value a= -4.5 was

obtained, which is characteristic of strong repul-

sion. This is not surprising, because the parking

area of one xanthate radical was assumed to be

0.175 nm2, whereas the cross-sectional area of the

xanthate radical is 0.29 nm’ [24]. However, no

attraction may be expected between the relatively

short alkyl radicals of ethyl xanthate.

The above approach has further consequences.

The effective adsorption equilibrium constant B’

in Eqn (14) is the product of three constants:

adsorption constant B, the solubility product of

lead sulfide, Klsp, and the dissociation constant of

lead xanthate, KZds. The last, concerning only

dissolved species, does not depend on the proper-

P. NowaklColloids Surfaces A: Physicochem. Eng. Aspects 76 (1993) 65-72 71

ties of either the solid phase or the interface.

However, it is to be seen that any change in the

solubility product of lead sulfide is equivalent to a

change in the adsorption constant. The solubility

product of a crystalline material should be a

thermodynamic constant. However, for a real solid,

it does depend on factors such as the degree of

crystallinity or diameter of particles of the solid.

The dependence of the solubility product of a

crystalline solid on the particle diameter has been

known for a long time [25]. A remarkable example

of the dependence of the solubility on the degree

of crystallinity may be found in the work of Landa

and Gast [26]. These authors found very good

agreement between the value of crystallinity calcu-

lated from X-ray diffraction data and the solubility

of the sample for hydrated ferric oxide. Significantly

higher solubility for freshly precipitated metal sul-

fides is reported, for example, by Goerlich [27]

and Wu and Yang [28].

The influence of the value of the apparent solu-

bility product on the course of the adsorption

isotherm is illustrated in Fig. 4. The same isotherm

equation and the same values of all constants as

for the data set from Fig. 3 were assumed for

curve A. For curve B, a ten times lower solubility

product was assumed and for curve C a ten times

higher one (all other constants were kept the same).

Fig. 4. Three hypothetical adsorption isotherms for the adsorp-

tion of ethyl xanthate on the surface of lead sulfide of different

solubility products (see text for details). The vertical portions

of the curves represent precipitation of lead xanthate (PbX,).

It is seen that in the case of curve B, a much higher

value (much lower for curve C) of the quotient

[X-(aq)]‘/[S’-(as)] is required to obtain the same

surface coverage. For all other conditions kept

identical, this means that a proportionally higher

(or lower) concentration of xanthate would be

required to obtain the same surface coverage. For

the case presented in Fig. 4, it was assumed that

precipitation of lead ethyl xanthate starts under

the conditions at which 0 = 1, but this need not

be the case.

In the work of Leppinen, lead sulfide was

obtained by the precipitation from solutions of

sodium sulfide and lead nitrate under oxygen-free

conditions. Such a procedure gives usually a poorly

crystalline solid phase. This was proved by the

present author. A sample of PbS was obtained

following the procedure applied by Leppinen [6].

As a reference sample, lead sulfide obtained by the

thiourea method [21] was used. The latter method,

ensuring slow precipitation, gives PbS with a high

degree of crystallinity. In the diffractogram of PbS

obtained by the thiourea method, all reflections

had their proper positions and relative intensities

[29]. The sample of PbS obtained by precipitation

with Na,S solution, and prepared for X-ray analy-

sis in the same way as the other sample, gave much

weaker reflections (integral intensity about eight

times lower) and at the same time the full widths

at half-maximum for all peaks were 2-3 times

greater. This provides evidence that the sample

obtained by precipitation with Na,S solution was

really poorly crystalline and at least partly com-

posed of extremely small grains. In view of the

preceding discussion this means that the surface

coverages obtained in the experiments reported by

Leppinen were probably greater than the coverages

which one may expect for a highly crystalline

galena under identical conditions.

Conclusions

The mechanism of the adsorption of alkyl xan-

thates at the surface of lead sulfide has been

72 P. NowakjColloids Surfaces A: Physicochem. Eng. Aspects 76 (1993) 65-72

presented on the basis of two assumptions: (1) that

adsorption proceeds as the exchange reaction

between xanthate ion from the solution and the

sulfide ion from the first atomic layer of lead

sulfide, as was shown by Leppinen and co-workers

[6-91, and (2) that the adsorbing entity is lead

alkyl xanthate in the molecular form, and the

adsorption of that species may be described by an

adsorption isotherm. The key conclusion from the

analysis presented is that the surface coverage by

adsorbed xanthate should depend on the apparent

solubility product of lead sulfide which, in turn,

depends on the solid state properties of PbS (the

degree of crystallinity and the diameter of the

grains of the mineral). It predicts that different

samples of lead sulfide may attain different surface

coverages by adsorbed xanthate at the same con-

centration of xanthate in solution and under iden-

tical conditions of the experiment, depending on

the sample properties. The present author believes

that the proposed mechanism may be operative in

many systems (salt type or sulfide mineral-anionic

surfactant) and may be the explanation for the

frequently observed diversity of the behavior of

different samples of the same mineral in flotation

even under identical conditions.

Acknowledgments

The long discussions with Dr. Leppinen from

the University of Turku and Dr. Rastas from

Helsinki University of Technology as well as access

to the unpublished results of Dr. Leppinen [6] are

gratefully acknowledged. However, that acknowl-

edgment does not imply approval of the conclu-

sions of this article by Dr. Leppinen and Dr. Rastas.

The helpful assistance of Mrs. Joanna Krysciak

(Institute of Catalysis and Surface Chemistry) with

the IR measurements and Mrs. Daria Maslowska

(from the same institute) with the X-ray diffraction

measurements is also acknowledged.

References

5

6

I

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

21

28

29

R. Woods, J. Phys. Chem., 75 (1971) 354.

R. Greenler, J. Phys. Chem., 66 (1962) 879.

G.W. Poling and J. Leja, J. Phys. Chem., 67 (1963) 2121.

A.F. Taggart, G.R.M. de1 Giudice and O.A. Ziehl, Trans.

AIME, 112 (1934) 348.

C. Du Rietz, Proc. XI International Mineral Processing

Congress, Istituto di Arte Mineraria, Universita di Cagliari,

Cagliari, 1976, p. 375.

J.O. Leppinen, Ph.D. Thesis, University of Turku,

Finland, 1986.

J.O. Leppinen and J. Mielczarski, Int. J. Miner. Process,

18 (1986) 3.

J.O. Leppinen and J.K. Rastas, Colloids Surfaces, 20 (1986) 221.

J.O. Leppinen and J.K. Rastas, Colloids Surfaces, 29

(1988) 205.

J.K. Rastas, P.M. Sten and J.O. Leppinen, Can. Metall.

Q., 29 (1990) 249.

Z.-X. Sun, W. Forsling, L. Ronngren, S. Sjoberg and P.W.

Schindler, Colloids Surfaces, 59 (1991) 243.

Z.-X. Sun, W. Forsling and S. Sjoberg, Proc. XVII

International Mineral Processing Congress, Dresden,

Preprints Vol. 2, 1991, p. 157.

A.M. Gaudin and N.P. Finkelstein, Nature, 207 (1965) 389.

N.P. Finkelstein, S. Afr. Inst. Metall., Report of

Investigation 527, 1969.

N.P. Finkelstein, Sep. Sci., 5 (1970) 227.

P.J. Harris and N.P. Finkelstein, S. Afr. Inst. Metall.,

Report of Investigation 1414, 1973.

P.J. Harris and N.P. Finkelstein, Int. J. Miner. Process., 2

(1975) 77.

A.N. Buckley and R. Woods, Colloids Surfaces, 53 (1991)

33.

P. Nowak, J. Mielczarski and J. Strojek, Pol. J. Chem., 54

(1980) 517.

K. Laajalehto, P. Nowak, A. Pomianowski and E. Suoninen, Colloids Surfaces, 57 (1991) 319.

J.L. Davies and M.K. Norr, J. Appl. Phys., 37 (1966) 1670.

K. Laajalehto, P. Nowak and E. Suoninen, Int. J. Miner.

Process., 37 (1993) 123.

H. Hagihara and S. Yamashita, Acta Crystallogr., 21 (1966) 350.

A.M. Gaudin and G.S. Preller, Trans. AIME, 169 (1946)

24.

E.K. Rideal, An Introduction to Surface Chemistry, The

University Press, Cambridge, 1939, p. 253.

E.R. Landa and R.G. Gast, Clays Clay Miner., 21 (1973) 121.

Z. Goerlich, Zesz. Nauk. Uniw. Jagiellon., Ser. Nauk

Chem., 7 (1962) 5 (in Polish).

C.-C. Wu and H.-M. Yang, Anal. Chim. Acta, 84 (1976) 385. ASTM Diffraction File 5-592.