Download observation of longitudinal acoustic phonons in layer

Clay Minerals (1982) 17,195-200.
OBSERVATION
OF LONGITUDINAL
ACOUSTIC
PHONONS
IN LAYER-SILICATES
BY N E U T R O N
INELASTIC
SCATTERING
D. J. C E B U L A * $ , M. C. O W E N t , C. S K I N N E R t ,
W. G. S T I R L I N G * AND R. K. T H O M A S t
*Institut Laue-Langevin, 156X Centre de Tri, 38042 Grenoble, France, and ~Physical Chemistry Laboratory,
South Parks Road, Oxford, UK
(Received 14 September 1981)
A BST R A C T: The techniqueof neutron inelastic scattering has demonstrated the presenceof
longitudinal acoustic phonons in two layer-silicate minerals. Values of the elastic constants
determinedfrom the dispersioncurveshave establishedthe validityof the techniquefor this class
of materials.
INTRODUCTION
Forces between colloidal particles have always been difficult to measure, especially at
small separations. The forces are generally considered to be of five types: (i) long-range
attractive van der Waals, (ii) long-range repulsion arising from overlapping electrical
double layers, (iii) medium-range repulsion arising from overlap of adsorbed polymers, (iv)
short-range hydration forces arising from perturbation of solvent structure, and (v) very
short-range exchange repulsion. The short-range forces are both difficult to measure
and not at all well understood.
Certain clay-water systems are suitable models for studying colloidal forces because the
particles occur as flat plates (~ 10 A thick and up to ~ 104 A in diameter). Much work has
been carried out using compression methods to measure the force between particles as a
function of separation of the surfaces (Israelachvili & Adams, 1978; C allaghan & Ottewill,
1974). These show that at moderate separations the forces are well described by the
DLVO (Derjaguin, Landau, Verwey and Overbeek) (Verwey & Overbeek, 1948) theory of
lyophobic colloid stability, but at short distances the forces become much more repulsive.
Energies involved in increasing the layer separation of clays have been the subject of
computer calculations (Giese, 1978).
An alternative method of determining the forces at small separations is to measure the
normal vibrational modes ('phonons') which propagate through the system. For forces
between layers, the phonons travelling in a direction perpendicular to the layers yield the
appropriate information. Phonon frequencies can be measured by the method of neutron
coherent inelastic scattering (Cochran, 1973).
The ideal experiment would be to measure the longitudinal acoustic phonon dispersion
relation of a clay single crystal as a function of water-layer thickness. The difficulty is that,
whereas it is easy to obtain good single crystals with low mosaic spreads of many types of
On secondmentfrom: Rutherford& Appleton Laboratories(SRC), Chilton, Didcot, Oxfordshire,UK.
9 1982 The MineralogicalSociety
196
D.J. Cebula et al.
clay containing one or two molecular layers of water, well-oriented samples of swollen
clays can only be prepared with difficulty.
This paper describes an experiment in which the presence of longitudinal acoustic
phonons in crystals of hydrobiotite and muscovite was clearly demonstrated. It serves to
establish the method of obtaining elastic constants for such materials from the
measurement of phonon frequencies.
EXPERIMENTAL
Hydrobiotite
The sample used in this study was a crystal of hydrobiotite from Palabora, South Africa
in which the vermiculite fraction contained two molecular sheets of water between silicate
layers; the c lattice spacing (= d(001)) was 14.2 A. The size of the crystal was (~7 • ~5
x ~0.1) cm 3. Examination of the (00l) neutron diffraction pattern clearly showed the
presence of at least one other series of reflections originating from material in the sample
having repeat spacings of other than 14.2 A. These extra reflections were relatively weak
in comparison to the main (00/) series (which was attributed to the vermiculite) and it was
considered that any effects which could arise therefrom in the neutron scattering would be
small and thus could be neglected. The intrinsic mosaic width of the sample measured from
the rocking curve across a Bragg peak was ~3 ~ full width at half maximum (fwhm).
Muscovite
The sample of muscovite used contained no water layers between silicate layers and the
c lattice spacing (= d(001)) was 9.99 A. The size of the sample was (~5 • ~5 • ~0.2)
cm 3 and it gave a good diffraction pattern showing a single (00l) series of peaks. The
mosaic spread measured from a rocking curve was found to be slightly better than 3 ~
fwhm.
Neutron scattering experiment
For both samples, measurements were made at room temperature and in ambient
relative humidities of the acoustic phonons propagating in the (00~ reciprocal space
direction. This notation implies that the Brillouin zone boundary occurs at (0,0,1/2).
The IN3 triple-axis crystal spectrometer at the High-Flux Reactor of the Institut
Laue-Langevin, Grenoble (Institut Laue-Langevin, 1981) was used for measurements on
the hydrobiotite sample. The crystal was mounted on the spectrometer with its c* axis in
the horizontal scattering plane. The frequency of the incoming neutron beam was 3.55
THz, corresponding to a neutron wavelength of 20 = 2.36 A and energy of 14.7 meV.
Both monochromator and analyser crystals were of pyrolytic graphite ((002) reflecting
planes). A pyrolytic graphite filter was employed to minimise 20/2 contamination in the
incident beam.
The technique of constant incident energy was used and energy transfer scans were
performed at given constant values of phonon wavevector, q, and momentum transfer, Q,
of the scattered neutrons. The intensity of neutrons scattered by phonons is related to the
intensity of Bragg peaks in the same vicinity of reciprocal space. As the very strong (001)
Phonons in clays
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reflection of the hydrobiotite occurred at only very small scattering angles, the region in
reciprocal space around the next strongest reflection, the (004), was explored. In this way
the phonon dispersion relation, co(q), could be measured.
Very distinct phonon groups were observed at small values of the phonon wavevector.
Examples are shown in Fig. 1, where the solid lines through the data points are the results
o f least-squares fitting of a Gaussian function to the peak (allowing for a curved sloping
background). Closer to the zone boundary, as q --, zc/c, the signals became much less clear.
This m a y be attributed to two effects. First, the neutron cross-section contains a 1/co
factor resulting in a decrease of the scattered intensity with increasing q and co. The second
effect is one of absorption of the incident and scattered neutron beams by the sample itself.
In the most unfavourable cases (typically for q --, n / c and co(q) ~ ~2 THz) the sample is
oriented with its plane very nearly parallel to the scattered beam. In this case the path
length of the neutron through the sample is particularly long, with the inevitable result of
loss of intensity. This problem of absorption in the sample has been treated for the case of
neutron diffraction from clay-water samples (Cebula et al., 1979).
For measurements on the muscovite sample, the triple-axis spectrometer of the D I D O
reactor at A E R E , Harwell (Baston & Harris, 1978) was employed. Techniques similar to
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solid lines represent calculations using a simple model for the forces between nearest neighbours
in a one-dimensional crystal. The error bars on the measured points are taken as the full width at
half maximum of the gaussians fitted to the data in Fig. 1.
Phonons in clays
199
those just described were used, except that in this case the monochromator was A1 (111),
giving v0 = 7.44 THz (~.0 = 1.63 A, E 0 = 30-78 meV); pyrolytic graphite was used as the
analyser. For muscovite, phonon frequencies were measured in the vicinity of the (003)
reflection. Some examples are shown in Fig. 1.
RESULTS
The dispersion curves deduced from the fitted peak positions in the constant Q scans for
both samples are shown in Fig. 2. The velocities of sound, vg, for both materials were
derived from the initial slopes, these being 4466 + 200 and 5027 + 200 ms -~ for the
hydrobiotite and muscovite, respectively.
The corresponding elastic constants, C33, are given by the equation
Vg = (C331P) 1/2
where p is the density of the material concerned (2.13 g cm -3 for hydrobiotite and 2.79 g
cm -3 for muscovite). The values for Cs3 were 4.25 • 10 l~ Nm -2 for hydrobiotite and 7.05
x 10 l~ N m -2 for muscovite.
DISCUSSION
In terms of sound velocities a distinct difference exists between values for the two-layer
and the zero water layer systems. The values are in general agreement with the value
obtained for 'clay rock' (C.R.C., 1977-1978) of 3480 ms -1 and much greater than that of
water (~ 1500 ms-l), as might be anticipated in view of the likelihood of water structuring
at the clay-water interfaces. The relative values of the force constants for the hydrobiotite
and the muscovite are in the order expected. The structure of muscovite suggests that the
layers are closely packed with strong attractions. The interlayer space in hydrobiotite,
however, is less well defined, as indicated by the ability of the cations to diffuse out and the
limited swelling properties of this mineral.
Interlayer force constants reflect the curvature, d2U/dx 2, of the potential energy
function at its minimum at a given equilibrium separation of the layers. From the swelling
behaviour of clays it would be expected that the potential energy curve would have an
oscillatory form due to solvent structure (Horn & I sraelachvili, 1980) at separations of the
order of the size of the solvent molecules, i.e. the water and the cations. It is clear from
these measurements that force constants can be determined by neutron inelastic scattering
over a wide range of water content. The application of this technique to examine the
potential will be of particular use when applied to continuously swelling samples. In
addition to a simple determination of the force constant, a more sophisticated analysis of
the dispersion curves, taking into account the influence of interactions extending further
than those of simple nearest neighbours, will be performed when more experimental data
are available. In this context, the measurement of transverse acoustic phonons will help to
elucidate the degree of anisotropy in the structures at a microscopic level.
ACKNOWLEDGEMENTS
We thank the ILL, Grenoble, and AERE, Harwell, for the use of neutron beam research facilities and the SRC
for financial support. We are indebted to Dr. A. Leach of I.C.I. Ltd., Mond Division, for supplyingthe sample
of hydrobiotite.
200
D . J . Cebula et al.
REFERENCES
BASTON A.H. & HARRIS D.H.C. (1978) Neutron Beam Instruments at HarwelL Report AERE-R 9278,
H.M.S.O., London.
CALLAGHANI.C. & OTTEWILL R.H. (1974) Interparticle forces in montmorillonite gels. Faraday Disc. Chem.
Soe. 57, 110-118.
CEm~LA D.J., THOMAS R.K, MIDOLETON S., OTTEWILL R.H. & WHITE J.W. (1979) Neutron diffraction from
clay-water systems. Clays Clay Min. 27, 39-52.
COCHRANW. (1973) The Dynamics of A toms in Crystals. Edward Arnold, London.
C.R.C. (1977-78) Handbook of Chemistry and Physics, 58th Edn., table E-47. C.R.C. Press Inc., Florida.
GIESE R.F. (1978) The electrostatic interlayer forces in layer-structure minerals, Clays Clay Miner. 26, 51-57.
HORN R.G. & ISRAELACHVILIJ.N. (1980) Direct measurement of forces due to solvent structure. Chem. Phys.
Lett. 71, 192-194.
INSTITUT LAUE-LANGEWN (1981) Neutron Beam Facilities at the HFR Available for Users. Institut
Laue-Langevin, Grenoble.
ISRAELACHVILI J.N. & ADAMS G.E. (1978) Measurement of forces between two mica surfaces in aqueous
electrolyte solutions in the range 0-100 nm. J.C.S. Faraday I, 74, 975-1001.
VERWEYE.J.W. & OVERBEEKJ.TH.G. (1948) Theory of Stability of Lyophobie Colloids. Elsevier, Amsterdam.
R E S U M E : On a appliqu6 la m&hode de diffusion in61astique des neutrons pour d6montrer
rexistence des phonons acoustiques et longitudinaux dans deux esp&es de silicates en feuillets.
D'apr& les courbes de dispersion on a obtenu des constantes 61astiques &ablissant ainsi la
m&hode pour cette cat6gorie de mat6riaux.
K U RZ RE F E R A T: Die Technik der inelastischen Neutronenbeugung zeigte die Anwesenheit
longitudinaler akustischer Phononen in Zweischichtsilikaten. Die aus den Beugungskurven
bestimmten Werte f/Jr die Elastizitfitskon-stanten haben die Giiltigkeit dieser Technik f/Jr
derartige Materialien nachgewiesen.
R E S U M E N : Se ha aplicado la t&nica de Difusi6n Inelfistica de Neutrones, para demostrar la
presencia de fonones acfisticos longitudinales en dos silicatos laminares. Los valores de las
constantes elfisticas determinadas a partir de las curvas de dispersion, han establecido la validez
de la t6cnica para esta clase de minerales.