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Free proton dynamics in coal
PI Ir, A ELSEVIER
Physica B 213&214 (1995) 631 633
Free proton dynamics in coal F. Fillaux a'*, A. Lauti6 a, R. Papoular b, S.M. Bennington c, J. Tomkinson c aLaboratoire de Spectrochimie lnJkarouge et Raman, Centre National de la Recherche Scientifique, 2 rue Henry-Dunant, 94320 Thiais, France b Service d 'Astrophysique, CEN Saclay, 91191 Gif-sur-Yvette. France c Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OXl I OQX, UK
Abstract Inelastic neutron scattering provides a unique method to observe protons in coals. New measurements of the full S(Q, 09) map for a coal sample containing ~ 5 wt % of protons are presented. Peaks of intensity due to vibrations of
protons bound to heavy atoms are clearly observed. Underneath there is a ridge of intensity due to recoil of free protons.
1. Introduction Coal is an extremely complex material which is of great importance for basic research and practical use [1]. This material consists primarily of stacks of a few planar layers containing a limited number of aromatic rings, which form the 'basic structural units'. The remainder of the carbon and other atoms (e.g., O, N, S) form disordered chemical groupings. The inherent properties of coals severely restrict the techniques that can be used for their structural characterisation. Inelastic neutron scattering spectra (INS) provide information which is specific to the proton dynamics in this material. The scattering cross-section of hydrogen atom is more than one order of magnitude greater than those of the other atoms, and, even for concentrations of hydrogenous species as low as ~ 1 wt %, the total crosssection for the matrix is such that it can be regarded as effectively transparent. In this presentation we report new INS spectra of a coal sample and we conclude that there is a significant
*Corresponding author.
quantity of recoiling protons which can be represented as a gas of free particles.
2. Experimental The coal sample from the Gardanne seam was supplied by the Centre d'Etude et de Recherche des Charbonnages de France (reference number 840234). The spectra were obtained with the TFXA and MAR1 spectrometers at the ISIS pulsed neutron source.
3. Bounds and free protons The dynamics of bound protons are well represented as harmonic oscillators, and the scattering law for the 0 --, n transition [2]: (Q2u2)"
S(Q, too) -
~.
,
exp~ - QZuZ)
(1)
where u z = h/2mo9 o is the mean square amplitude in the ground state. The profile in Q at constant energy transfer h~o, provides a direct estimate of the effective oscillator mass (m* ~ 2QZ./hto., with rn* in atomic mass units, he0. in meV and Q, in A 1).
0921-4526/95/$09.50 ~( 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 2 3 3 - 2
632
F. Fillaux et al./Physica B 213&214 (1995) 631 633
The scattering law for a gas of free particles, on the other hand [2] is 1
12
!
h2Q 2
ER =hcoR -
(3)
2m
where ER is the recoil energy. The corresponding map is characterised by a ridge of intensity along the recoil line defined by Eq. (3). The measured S(Q, co) map (Fig. 1) reveals a ridge of intensity which coincides with the recoil line calculated according to Eq. (3) with m = 1.008 amu (solid line in Fig. 1). Therefore, the recoiling particles are bare protons. Rather intense inelastic peaks are superimposed on this ridge at ~ 375 meV/3000cm i (CH stretching), 100-200 m e V / 8 0 0 - 1 6 0 0 c m - 1 (CH bending) and the elastic peak centred at the origin. The intensity maxima also lie close to the recoil line, as anticipated for CH oscillators with effective mass ~ 1 ainu. However, their width at constant energy is greater than for the recoil spectrum, with significant intensity at low Q values due to the pre-exponential factor of Eq.(l). Above
vE
1000 2000 30'00 Enegy transfer (cm-')
4000
Fig. 2. INS spectrum of the same sample at 25 K obtained with the TFXA spectrometer.
400 meV/3200cm 1, overtone and combination bands are anticipated, but hidden by the continuum. These contributions account for the difference between the observed and the theoretical S(Q, co) map for a gas of free protons. There is also a ridge of weaker intensity observed below 100 meV/800 cm i and yet at large momentum transfer. This coincides rather well with the recoil line calculated for aluminum. The recoil of carbon atoms is not observed. The spectrum of the same sample was obtained with the TFXA spectrometer (Fig. 2) which gives a cut of S(Q, ~o) along the line E ~ 2Q 2 (with E and Q in meV and 1 units, respectively) corresponding to the recoil line for particles with mass 1 amu. The broad bands correspond to the vibrations of bound protons. They are superimposed on a c o n t i n u u m of intensity which is the fingerprint of recoiling protons with this spectrometer.
4. The gas of free protons
I--
LU
5
10
15 20 25 30 Momentum Transfer(,&, ')
35
40
Fig. 1. S(Q, ~o} intensity contour map of a coal sample from Gardanne at 2 K. Intensity contours are equally spaced on a linear scale. The recoil lines for proton, carbon and aluminium atoms are superimposed.
The width of the recoil profile provides an estimate of the effective temperature (T*) of the free proton gas. For a sample temperature of 2 K, T* = 950 + 50 K. Therefore, the recoiling protons are not at rest. The kinetic energy distribution corresponds to that of an isotropic harmonic oscillator with proton mass and fundamental frequency 164 4- 9 meV/1320 + 70 cm-1. This rather large kinetic energy could be due to a local potential with only one b o u n d state below the dissociation threshold. However, the TFXA spectrum shows that the continuum of intensity is still observed at very low energy transfer (Fig. 2). Therefore, the protons are effectively free. Equipartition of the energy occurs preferentially between protons, because they have the same mass. The mean frequency for the bound proton modes estimated
F. Fillaux et al./Physica B 213&214 (1995) 631 633 from the TFXA spectrum is 174 meV/1390 cm - 1, which is virtually equal to the kinetic energy estimated above for the free protons. Therefore, the free protons can be seen as being in a box with walls made of bound protons.
5. Conclusion The S(Q, co) map demonstrates the existence of a gas of free protons in coal. The effective mass of these free protons is very close to 1 ainu (bare protons). They correspond to H ÷ entities presumably inserted between graphite-like planes in the basic structural units. The effective mass and the equipartition of the energy between free and bound protons suggest that the influence of the local electric field on the dynamics is negligible. Apparently, there are no significant correlation effects between the free protons and electrons in the conduction band. Free hydrogen atoms would also be consistent with an effective mass of 1 amu. But, although such free atoms
633
should give He molecules very rapidly, the INS spectra provide no support for the presence of hydrogen molecules in coal. The existence of free protons in solids has received but very little attention, so far. To our knowledge, none of the previous studies on coals has been conclusive. The major reason is that they can be characterised unambiguously only with INS. The S(Q, ~o) map presented in this paper illustrates the great interest of this technique for the observation and characterisation of free protons. Beyond this particular case, we believe that this new technique will have a great impact on our knowledge on the dynamics of mobile protons in solids.
References [1] H. Charcosset (ed.), Advanced Methodologies in Coal Characterisation (Elsevier, Amsterdam, 1990). [2] S.W. Lovesey,Theory of Neutron Scattering FromCondensed Matter, Vol. l: Nuclear Scattering (Clarendon, Oxford, 1984).
Physica B 213&214 (1995) 631 633
Free proton dynamics in coal F. Fillaux a'*, A. Lauti6 a, R. Papoular b, S.M. Bennington c, J. Tomkinson c aLaboratoire de Spectrochimie lnJkarouge et Raman, Centre National de la Recherche Scientifique, 2 rue Henry-Dunant, 94320 Thiais, France b Service d 'Astrophysique, CEN Saclay, 91191 Gif-sur-Yvette. France c Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OXl I OQX, UK
Abstract Inelastic neutron scattering provides a unique method to observe protons in coals. New measurements of the full S(Q, 09) map for a coal sample containing ~ 5 wt % of protons are presented. Peaks of intensity due to vibrations of
protons bound to heavy atoms are clearly observed. Underneath there is a ridge of intensity due to recoil of free protons.
1. Introduction Coal is an extremely complex material which is of great importance for basic research and practical use [1]. This material consists primarily of stacks of a few planar layers containing a limited number of aromatic rings, which form the 'basic structural units'. The remainder of the carbon and other atoms (e.g., O, N, S) form disordered chemical groupings. The inherent properties of coals severely restrict the techniques that can be used for their structural characterisation. Inelastic neutron scattering spectra (INS) provide information which is specific to the proton dynamics in this material. The scattering cross-section of hydrogen atom is more than one order of magnitude greater than those of the other atoms, and, even for concentrations of hydrogenous species as low as ~ 1 wt %, the total crosssection for the matrix is such that it can be regarded as effectively transparent. In this presentation we report new INS spectra of a coal sample and we conclude that there is a significant
*Corresponding author.
quantity of recoiling protons which can be represented as a gas of free particles.
2. Experimental The coal sample from the Gardanne seam was supplied by the Centre d'Etude et de Recherche des Charbonnages de France (reference number 840234). The spectra were obtained with the TFXA and MAR1 spectrometers at the ISIS pulsed neutron source.
3. Bounds and free protons The dynamics of bound protons are well represented as harmonic oscillators, and the scattering law for the 0 --, n transition [2]: (Q2u2)"
S(Q, too) -
~.
,
exp~ - QZuZ)
(1)
where u z = h/2mo9 o is the mean square amplitude in the ground state. The profile in Q at constant energy transfer h~o, provides a direct estimate of the effective oscillator mass (m* ~ 2QZ./hto., with rn* in atomic mass units, he0. in meV and Q, in A 1).
0921-4526/95/$09.50 ~( 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 2 3 3 - 2
632
F. Fillaux et al./Physica B 213&214 (1995) 631 633
The scattering law for a gas of free particles, on the other hand [2] is 1
12
!
h2Q 2
ER =hcoR -
(3)
2m
where ER is the recoil energy. The corresponding map is characterised by a ridge of intensity along the recoil line defined by Eq. (3). The measured S(Q, co) map (Fig. 1) reveals a ridge of intensity which coincides with the recoil line calculated according to Eq. (3) with m = 1.008 amu (solid line in Fig. 1). Therefore, the recoiling particles are bare protons. Rather intense inelastic peaks are superimposed on this ridge at ~ 375 meV/3000cm i (CH stretching), 100-200 m e V / 8 0 0 - 1 6 0 0 c m - 1 (CH bending) and the elastic peak centred at the origin. The intensity maxima also lie close to the recoil line, as anticipated for CH oscillators with effective mass ~ 1 ainu. However, their width at constant energy is greater than for the recoil spectrum, with significant intensity at low Q values due to the pre-exponential factor of Eq.(l). Above
vE
1000 2000 30'00 Enegy transfer (cm-')
4000
Fig. 2. INS spectrum of the same sample at 25 K obtained with the TFXA spectrometer.
400 meV/3200cm 1, overtone and combination bands are anticipated, but hidden by the continuum. These contributions account for the difference between the observed and the theoretical S(Q, co) map for a gas of free protons. There is also a ridge of weaker intensity observed below 100 meV/800 cm i and yet at large momentum transfer. This coincides rather well with the recoil line calculated for aluminum. The recoil of carbon atoms is not observed. The spectrum of the same sample was obtained with the TFXA spectrometer (Fig. 2) which gives a cut of S(Q, ~o) along the line E ~ 2Q 2 (with E and Q in meV and 1 units, respectively) corresponding to the recoil line for particles with mass 1 amu. The broad bands correspond to the vibrations of bound protons. They are superimposed on a c o n t i n u u m of intensity which is the fingerprint of recoiling protons with this spectrometer.
4. The gas of free protons
I--
LU
5
10
15 20 25 30 Momentum Transfer(,&, ')
35
40
Fig. 1. S(Q, ~o} intensity contour map of a coal sample from Gardanne at 2 K. Intensity contours are equally spaced on a linear scale. The recoil lines for proton, carbon and aluminium atoms are superimposed.
The width of the recoil profile provides an estimate of the effective temperature (T*) of the free proton gas. For a sample temperature of 2 K, T* = 950 + 50 K. Therefore, the recoiling protons are not at rest. The kinetic energy distribution corresponds to that of an isotropic harmonic oscillator with proton mass and fundamental frequency 164 4- 9 meV/1320 + 70 cm-1. This rather large kinetic energy could be due to a local potential with only one b o u n d state below the dissociation threshold. However, the TFXA spectrum shows that the continuum of intensity is still observed at very low energy transfer (Fig. 2). Therefore, the protons are effectively free. Equipartition of the energy occurs preferentially between protons, because they have the same mass. The mean frequency for the bound proton modes estimated
F. Fillaux et al./Physica B 213&214 (1995) 631 633 from the TFXA spectrum is 174 meV/1390 cm - 1, which is virtually equal to the kinetic energy estimated above for the free protons. Therefore, the free protons can be seen as being in a box with walls made of bound protons.
5. Conclusion The S(Q, co) map demonstrates the existence of a gas of free protons in coal. The effective mass of these free protons is very close to 1 ainu (bare protons). They correspond to H ÷ entities presumably inserted between graphite-like planes in the basic structural units. The effective mass and the equipartition of the energy between free and bound protons suggest that the influence of the local electric field on the dynamics is negligible. Apparently, there are no significant correlation effects between the free protons and electrons in the conduction band. Free hydrogen atoms would also be consistent with an effective mass of 1 amu. But, although such free atoms
633
should give He molecules very rapidly, the INS spectra provide no support for the presence of hydrogen molecules in coal. The existence of free protons in solids has received but very little attention, so far. To our knowledge, none of the previous studies on coals has been conclusive. The major reason is that they can be characterised unambiguously only with INS. The S(Q, ~o) map presented in this paper illustrates the great interest of this technique for the observation and characterisation of free protons. Beyond this particular case, we believe that this new technique will have a great impact on our knowledge on the dynamics of mobile protons in solids.
References [1] H. Charcosset (ed.), Advanced Methodologies in Coal Characterisation (Elsevier, Amsterdam, 1990). [2] S.W. Lovesey,Theory of Neutron Scattering FromCondensed Matter, Vol. l: Nuclear Scattering (Clarendon, Oxford, 1984).