MOTIONS IN A VISCOUS INORGANIC LIQUID : FERROUS ION IN COLD PHOSPHORIC ACID

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MOTIONS IN A VISCOUS INORGANIC LIQUID :

FERROUS ION IN COLD PHOSPHORIC ACID

P. Flinn, B. Zabransky, S. Ruby

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, suppliment au no 12, Tome 37, Dtcembre 1976, page C6-739

MOTIONS IN A VISCOUS INORGANIC LIQUID

:

FERROUS ION IN COLD PHOSPHORIC ACID

(*)

P. A. FLINN

Carnegie-Mellon University, Pittsburgh, Pa. 15313, U. S. A.

B. J. ZABRANSKY and S. L. RUBY

Argonne National Laboratory, Argonne, Illinois 60439, U. S. A.

R6sum6. - Le but de ce travail Btait de dkcider si : a) il y a des effets de relaxation rotationnels quand Ia diffusion devient importante au-dessus de la tempkrature Tg de la transition vitreuse ;

b) on peut expliquer l'absorption Mossbauer dans un modkle de dynamique de solides vitreux et de liquides. Nous montrons qu'on n'observe pas de relaxation rotationnelle, et qu'il y a un accroissement rapide avec la tempkrature, ?L partir de T, des modes mous, ce qui apparait la

fois dans les mesures d'effet Mossbauer et de diffusion Raman.

Abstract.

-

The two main purposes of this work were to decide : a) are there rotational relaxation effects when diffusion becomes important above the glass transition temperature Tg ;

and b) can the intensity of the MB absorption be understood in terms of glass and liquid dynamics ? We report that rotational relaxation is not seen, and that there is a rapid increase in soft modes with temperature beginning at T g seen both by Mossbauer technique and by Raman scattering.

1. Introduction.

-

Since the early work [l, 21 on solutions of iron in glycerine, it has been clear that the Mossbauer effect can be used to obtain valuable information about the dynamics of atoms in cold liquids. The effect has been used to investigate a variety of systems, both organic and inorganic, but in most aqueous systems, observations have been ham- pered by the limited metastability of the supercooled liquid. The system phosphoric acid-water has proved to be especially suitable for study, since it has an extended range of equilibrium liquid where observations can be made, and in the metastable region, crystallization is easily suppressed. The system is also suitable for Raman-effect measurements, which provide valuable additional information, Some results have been reported previously [3, 41.

Previous Mossbauer studies of ions in diffusion have concentrated mainly on the increase in line width with temperature, and have correlated this with the increasing (translational) diffusion constant D. Little attention has been paid to the amplitude f(T). As the line is being rapidly broadened by diffusion, it becomes difficult to follow the intensity (especially without a theory of the line shape). It should be recalled that

(*) By acceptance of this article, the publisher or recipient acknowledges the U. S . Government's right to retain a nonex- clusive, royalty-free license in and to any copyright covering the article.

diffusion alone does not cause a decrease in area, only an increase in line width.

Here the iron atom is caged by the oxygen atoms, and it is not clear what is diffusing [3, 51. The magnitude of the EFG is interpreted as mainly due to the sixth 3d electron in this high-spin ion, but its direction would be due to the deviation from cubicity of the six oxygen neighbors. If the detailed position of these $icker in the liquid state this could well give rise to a quadrupole relaxation effect. Less likely perhaps the iron atom with the nearest six oxygens (hexaquo-ion) might rotate as a whole, giving rise to a similar effect. One of our purposes is to look for effects described by a rotational diffusion constant d.

Thanks first to Tjon and Blume and with important extensions due to Dattagupta [6,7], a simple expression for the MB line shape from an atom vibrating rapidly with

x2,

diffusing translationally with D, and synchro- nously rotating diffusively with d, now exists. A defect of this work is that an independent determination of

QS(T) is not available ; it would be much easier to determine small amounts of rotational collapse of the splitting if the splitting itself were known independently.

2. The phosphoric acid-water system.

-

The phase diagram of the phosphoric acid-water system, plotted from solubility data is shown in figure 1. We investi- gated two compositions : The eutectic composition

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C6-740 P. A. FLINN, B. J. ZABRANSKY AND S. L. RUBY

160

10 20 30 40 50 60 70 80 90 100

MOLE % H3P04

W . 1. - Phase diagram for phosphoric acid-water system.

H3P04

+

3 . H 2 0 (referred to as phos 6), and the

usual commercial form, H3P04 f H 2 0 (phos 2). The glass transitions shown were determined by differen- tial thermal analysis, and for the H3P04

+

H 2 0 , also by measurement of the specific volume as a function of temperature [3]. The specific volume measurement showed that the transition is quite sharp (a range of about 5 degrees), reversible, and independent of heating or cooling rate over a rather wide range. (T, for phos 2 and phos 6 are 155 K and 175 K

respectively).

The Mossbauer sample of the eutectic composition was prepared by dissolving iron metal 92.8

%

enriched in 57Fe in the eutectic acid

-

water mixture to pro- duce an iron content of 3 mg/cm3. The sample was mounted in a plastic cell with a l-mm thick spacer, to provide an absorber thickness of 0.3 mg/cm2 of 57Fe. The sample of composition H3P04

+

3 H 2 0 was prepared similarly, but with an effective thickness of about 0.2 mg/cm2 of 5 7 ~ e . The water-iron atomic concentration ratio was

-

200 in both cases.

3. Some experimental details. - Mossbauer spectra were obtained with a constant acceleration spectro- meter operating vertically. Details of the apparatus are given elsewhere [ 5 ] . The sample temperature was measured with an iron-constantan thermocouple, and controlled to an accuracy of 0.2 K. Measurements on a given sample were taken at various temperatures in random order. No effect of previous thermal history on the spectra was observed. The source used was 57Co in copper.

The earlier data (phos 2) was taken before the importance of a detailed theory of the line shape was realized. Later, special effort was taken experimentally to put the vertical experimental scale into absolute units. This involved measurements of signal and background rates for the detector system as well as finding

f,

for the source. A small fraction of the iron ions (- 2

%)

become

both trivalent and magnetically ordered. At low temperatures this weak impurity spectrum could be seen outside the main absorption. It did not decrease with temperature nearly as fast as the main absorption, and could just barely be seen at temperatures (240 K) where the main absorption had vanished. Appro- priate corrections have been made for this small effect. Also the small amount of absorption due to iron atoms in the beryllium window of the proportional counter have been subtracted.

4. Experimental results.

-

A set of typical spectra for phos 2 is shown in figure 2. At low temperatures

t I I I l ~ ' I I I I - 2 0 -16 -12 -8 -4 0 4 8 12 16 2 0

VELOCITY ( m m / * l

FIG. 2.

-

MB absorption spectra at 78, 209, 220 and 228 K for phos 2. Diffusion broadening is the main effect required to

explain these shapes.

the spectrum is a typical quadrupole split ferrous doublet, with a splitting of about 3.3 mm/s and an isomer shift of about 1.3 mm/s relative to metallic iron at room temperature. The doublet shows a slight, weakly temperature-dependent, broadening toward the center, as seen more clearly in figure 3.

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MOTIONS IN A VISCOUS INORGANIC LIQUID : FERROUS ION I N COLD PHOSPHORIC ACID C6-741 FROZEN GLASS 0.8 1.2 1.6 I VELOCITY ( r n m / s ) -4 -3 -2 - 1 0 1 2 3 4

FIG. 3. - Ferrous hexaquo ion in a crystalline and glass environment. Solid line represents best fit of a symmetric Lorentzian doublet. Using a 8-blurring convolution in addition

allows an excellent fit to the glass data.

5. Data analysis.

-

To extend the measurements as far as possible beyond T,, the absorber thickness no, was chosen rather large (8.5 for phos 6), and at low temperatures there were strong saturation effects. Accordingly the spectrum was calculated for the fitting procedure using a transmission integral convolution 181.

The above-mentioned broadening toward the center required a distribution of quadrupole splittings N(v, vs), not just the usual 6(v - v,). Here e2 qQ/2 =v,. It was found that a distribution of the form

was fully adequate to explain the data at any temperature with only one additional parameter

p.

The temperature dependence of

seems to us quite reasonable. The non-uniform positions of the near neighbors in the glass means

qlattice is not constant, and we interpret the above p-blurring as arising from qion

+

qlattice. In ferrous chloride aqueous solutions where both the glass and crystalline phases are available (see Fig. 3), 8-blurring disappears upon crystallization. At high temperatures, there is no way to see /&blurring ; fortunately, by then it is no longer important to the fits to have an accurate value for

P,

and we have used a reasonable extrapola- tion from lower temperature results. The solid line through the glass points is the result of the fitting procedure before p-blurring (X' = 8 346). After, the line is indistinguishable from the points (X2 = 242). Above the glass.transition it is necessary to include

effects due to diffusive motion of the ferrous ions, and also the possibility of relaxation effects, since the motion of the ions will result in a variation of the electric field gradient with time. The necessary theory for the combined relaxation and diffusion problem has been given by Dattagupta [6, 71. In the first paper, a theroy is given for the case where at every diffusive

c< jump D the direction of the EFG can change ran-

domly. When one goes to frequent small jumps as seems appropriate for liquids [4] (the continuous diffusion limit), this gives too muchrotational narrowing. In the second paper, the line shape is calulated if at each jump the EFG redirects by

+

be. Here A8 is defined through the rotational diffusion constant d. And the line shape becomes :

S @ ) = Real

[----

p + k 2 ~ +d 6

(p+k2 D) (p+k2 D+6 d ) + ( ~ ~ / 2 ) '

1

where p =

-

f(m

-

m,)

+

y/2, k = 2 n/A, and

y = 117, = natural line width. It is couvenient to

write a = 6 d/k2 D to describe the relative importance of rotation and translation.

To observe the rotational narrowing, 6 d must be equal to or greater than y/2. Also, the translational broadening cannot be greater than QS/2. These can be combined to show that a

>

0.04 or so is needed to see rotational relaxation. The whole-ion rotation picture suggests that d = D / U ~ ; this is the classical macroscopic Stolkes law result for spheres of redius a in a diffusing medium. Then as = (614 n2) = 0.10 for 57Fe and a = 1 d;. Roughly put, if Stokes law is numerically correct, rotational narrowing will be hard to see. The picture of flickering nearest neighbors might well allow much larger a, however.

6. Temperature dependance of Mossbauer para-

meters. - a) ISOMER SHIFT.

-

The temperature dependence of the isomer shift is shown in figure 4. The shift is an approximately linear function of temperature, but the slope is

-

4.5 X 10-4 mm/s K,

100 120 140 160 180 2 0 0

TEMP. ( K )

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C6-742 P. A. FLINN, B. J. ZABRANSKY AND S. L. RUBY

substantially less than the classical second-order Doppler shift of

-

7.3 X lOW4 mm/s K. It is unlikely that this discrepancy is due to the quantum corrections, since the first order quantum corrections varies as 1/T [9], which should produce curvature over this temperature range rather than as apparent change of slope. Also, using a Debye model, and a Debye temperature of 180 K estimated from the Debye- Waller factor data, as discussed below, the correction term at 77 K is only 0.015 mm/s.

The difference .between the observed slope and the classical value is probably due to the volume dependence of the isomer shift. We can estimate the order of magnitude of this effect as follows : the pressure dependence of the isomer shift for ferrous compounds is about - 0.003 mm/s kbar [10], the compressibility is of the order of 10-3 kbar-l, and the volume thermal expansion for our material is about 1.6 X 10-4 K-'. Combining these estimates, we obtain a value of 5 X 10-4 mm/s K, which is adequate to explain the discrepancy.

These results for isomer shift are quite similar to those observed for ferrous ions in the quite similar environment provided by the crystalline mineral vivianite, Fe3(P04), 8 H,O 1111. There are two iron sites, each surrounded octahedrally by oxygens : Fe,, with two phosphate oxygens and four water oxygens as neighbors ; and Fe,,, with four phosphate and two water oxygens as neighbors. At 80 K, the isomer shifts are 1.29 mmls for Fe,, and 1.33 mm/s for Fe,,. The increase of isomer shift with phosphate content observed in our glasses is consistent with these results ;

the numerical values suggest that the ferrous ions have a preference for water oxygens rather than phosphate oxygens. In the eutectic, for example, the water/phosphate oxygen ratio is intermediate between the values for the two iron sites, but the isomer shift is smaller for the glass than for either of the crystalline sites. The reduced tempe'rature dependence of the peak shift is also quite similar for vivianite : the difference between the measurements at 80 K and 295 K gives a slope of

-

4 X 10-4 mm/s K for Fe, and

- 5 X 10-4 mm/s K for Fe,,.

In principle, in addition to shifts resulting from chemical isomer shift effects, there will be second- order Doppler shift effects. If the motion of the iron atom is strongly affected by high-energy photons, then at those modest temperatures

<

u2

>

may not yet be the high temperature limit. In such a complicated crystal, this is difficult to judge.

2 W(T). Below the glass transition temperature, the exponent of the Debye-Waller factor shows the usual linear temperature dependence, but in the liquid region the change with temperature is far more rapid, as seen in figure 5. The slope in the solid region corres- ponds to Mossbauer temperature of 180 K.

Above T, in the liquid region, there appears to be an additional contribution which varies approximately as .(T

-

T,)2, where T, is the glass transition tempera-

TEMP. ( K )

FIG. 5. - 2 W for phos 2 and phos 6 vs. temperature.

ture. This additional amplitude of motion can be related to the presence of an approximately linear term in the power spectrum of liquids, as seen in Raman spectra. The extra amplitude of motion determined from the Mossbauer measurements is shown in figure 6.

FIG. 6.

-

Excess A W plotted against T- T,.

7. Quadrupole splitting temperature dependence. -

The previous parameters, isomer shift and 2 W, hardly depend on a, but that is not the case for QS. Roughly, an oversized a causes the fitting program to produce an undersized QS. At higher temperatures, both QS and a cannot be left as free parameters to be fitted without finding minimization difficulties. There- fore a series of values for a were chosen, and fittings for the experimental data were made for each value of a.

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MOTIONS I N A VISCOUS INORGANIC LIQUID : FERROUS ION I N COLD PHOSPHORIC ACID C6-743

V E L O C I T Y ( m m / $ )

FIG. 7.

-

Calculated spectral shapes vs. temperature for a = 0.1 and 1.0.

FIG. 8. - Quadrupole splitting for phos 2 and phos 6 vs. temperature.

-

_'0 \ 3.5-.

-

P V) U 3-3- J _{PHOS 6}

above T, is eliminated, or even reversed. If we knew QS(T) independently, this would determine a rather sharply. The weak temperature dependence of QS(T) as a glass is typical of ferrous compounds, and can be accounted for by thermal population of the excited electronic states [12].

2

3.2- a a 3

8. Diffusion and relaxation effects.

-

In a previous paper [3], the behavior of D for phos 6 has been report- ed assuming a = 0. Including separate macroscopic measurements of 0 at a higher temperature range, log D becomes nearly linear when plotted against 1/T

x PHOS 2

over four orders of magnitude. Somewhat improved plots can be made at the price of introducing a new temperature To, but its physical significance remains nuclear.

Using a

<

0.2, and the value for D at 200 K, 6 d

is found to be

<

8.5 X 106 implying the characteristic time to rotate through a radian is greater than 1OU7 S.

But higher temperatures to speed up this rate cannot be used because A r at this temperature from transla-

tional diffusion is already 1.4 mm/s (cf. 1.6 mm/s for QS12).

9. Conclusions.

-

At temperatures in the glassy region the ferrous ions dissolved in the phosphoric acid water system appear to be surrounded octahedrally by six oxygens in configurations similar to those in crystalline iron phosphate (vivianite). In the glass, however, the distribution of quadrupole splittings indicates the presence of modest variations in the nearest neighbor configurations.

In the liquid region, the local environments remain essentially the same as those in the glass ; the evidence here is the constancy of QS which is very sensitive to nearest neighbor structure.

The absence of rotational narrowing effects means that d is very small and makes the flickering effect quite slow at z E 200 K with S 2 10-l' cm2/s. If the bond-

ing were weaker in the phosphate glass, the bond breaking frequency would be higher, but this increase in Q would probably be matched by an increase in D. It is likely there is not a good physical system to observe rotational diffusion via MB technique.

There is an abrupt and strong increase in

<

x2

>

at T,. In addition to the glass

"x,~

-

an additional b(T - Tg)2 seems to be needed. This is undoubtedly the result of the (( softening >> of the

transverse modes of the glass. It is still a thermal vibration about a solid-like position. Simultaneously D

is increasing as well according to D = Do e-"IkT where E, 0.55 eV. The picture of generating soft modes is supported by preliminary work on Raman scattering from phosphoric acid liquids.

We wish to thank John Love for his help in some parts of this work.

3.1

References

I I I I I I

[l] BUNBURY, D. St. P,, ELLIOT, J. A., HALLAND, H. E., WILLIAMS, J. M., Phys. Lett. 6 (1963) 34.

[2] CRAIG, P. P. and SUTIN, N., Phys. Rev. Lett. 11 (1963) 460.

[3] RUBY, S. L., in Perspectives in Mossbauer Spectroscopy, S. G. Cohen and M. Pasternak, ed. (Plenum, New York) 1973, p. 181.

141 RUBY, S. L., LOVE, J. C., FLINN, P. A. and ZABRANSKY, B. J., Appl. Phys. Lett. 27 (1975) 320.

[5] RUBY, S. L., ZABRANSKY, B. J. and STEVENS, J. G., J. Chem. Phys. 54 (1971) 4559.

161 DATTAGUPTA, S., Phys. Rev. B 12 (1975) 47.

70 90 110 130 150 170 190 210

[7] DATTAGUPTA, S., Phys. Rev. B 14 (1976) 1329.

[8] SHENOY, G. K., FRIEDT, J. M,, MALETTA, H. and RUBY, S. L. in Mossbauer Effect Methodology, Vol. 9, I. J. Gm- verman, C. W. Seidel and DIETERLY, D. K., eds. (Plenum, New York) 1974, p. 277.

[9] MARADUDLN, A. A., -INN, P. A. and RUBY, S. L., Phys. Rev. 126 (1962) 9.

[l01 CHAMPION, A. R., VAUGHAN, R. N. and DRICKAMER, H. G.,

J. Chem. Phys. 47 (1967) 2583.

[l11 GONSER, U. and GRANT, R. W., Phys. Stat. Sol. 21 (1967) 331.