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Neutron diffraction studies of amorphous methyl alcohol
Journal of Non-Crystalline Solids 74 (1985) 303-312 North-Holland, Amsterdam
303
N E U T R O N D I F F R A C T I O N S T U D I E S OF A M O R P H O U S M E T H Y L ALCOHOL D.C. STEYTLER and J.C. D O R E Physics Laboratory, University of Kent, Canterbury, CT2 7NR, England
D.C. M O N T A G U E Willamette University, Salem, Oregon, USA Received 10 August 1984 Revised manuscript received 27 November 1984
A neutron diffraction study has been made of vapour-deposited methyl alcohol, CD3OD. Although some crystalline material was present in the deposit it was possible to obtain the inter-molecular interference function D M(Q) for the amorphous solid over a Q-range extending to 6 A-1. The structural features may be compared with similar data for crystalline and liquid CD3OD. The results demonstrate an intermediate stage in which hydrogen-bonded chains play an important role in the local structure as in the liquid phase but do not possess the long-range order of the crystalline material. Systematic variations in the diffraction patterns for the liquid and amorphous phases of CD3OD, D20 and ND 3 can be correlated and relate to changes resulting from orientational correlations due to hydrogen-bonding.
I. Introduction The network structure of glasses and amorphous materials has received much attention in recent years and the ability to measure pair correlation functions to high precision by X-ray or neutron diffraction has opened up the possibility of providing stringent tests for any model construction. One class of material that is of relatively recent interest occurs in the case of hydrogenbonded molecules. Extensive studies of amorphous ice [1,2] have shown that the strong orientational effects of the hydrogen-bonding interaction leads to a tetrahedral network which resembles that of amorphous silicon or germanium due to the 4-fold nature of the inter-molecular co-ordination. In contrast to this behaviour, amorphous ammonia with an expected six-fold co-ordination appears to have quite different properties [3]. Further studies have now been made for vapour-deposited methyl alcohol in order to investigate a 2-fold co-ordinated system incorporating the apolar methyl head group which does •not participate in the network-bonded structure. Current Monte Carlo simulations of the liquid phase have emphasised the formation of chains by hydrogen-bonding in the hydroxyl group. The structural properties of the amorphous 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
304
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
phase are of particular interest since it would seem that this material would not readily form an inter-connected network. The study of amorphous methanol therefore has relevance to a wide range of organic glass-forming systems and the structural relationship to both the crystalline and liquid phases should give some insight into the geometrical factors which influence its properties.
2. Experimental procedure Although the glassy state of methanol may be formed by supercooling from the liquid phase [4] it was decided to use similar preparative methods to those described in the previous studies of amorphous ice [1] and ammonia [3]. This consisted of vapour deposition onto a cold substrate plate. Fully deuterated methanol CD3OD, with a quoted enrichment of 99% deuterium was obtained
~000I
CD=OD
7000
GO0~5800
~o00-
Intensity
~
Sample
3000 -
200e(Arbitrary units)
i~oo~ @. -
-
30002000-
•_•jJ•j•_
1000-
@,00
13./5
2L5o
,,'.25
~.oo
Crystalline
4 n
~.5o
56,25
112.00
Scattering Angle 0 / degrees Fig. 1. The diffraction pattern for a) vapour-deposited CD3OD; and b) crystalline CD3OD obtained for an an incident neutron wavelength of 1.37 .~.
D.C. Steytler et a L / Neutron diffraction studies of amorphous methyl alcohol
305
from Merck, Sharp and Dohme. The liquid was placed in an isolated tube and degassed by several freeze-pump-thaw cycles. A needle-valve leading into the cryostat was then opened. The methanol vapour was pre-cooled by flowing through a copper tube which had a weak-thermal link to the nitrogen-cooled heat shields. The issuing stream of molecules was directed onto a vanadium substrate plate of 1 mm thickness which was connected to a liquid helium reservoir and maintained at approximately 10 K. Approximately 2 ml of material was deposited over a period of 1 day corresponding to a mean deposition rate of 0.08 ml h r - ] . The diffraction experiment was performed on the Curran diffractometer at the Dido reactor AERE, Harwell. An angular scan of 2-95 ° was made using an incident neutron wavelength of 1.37 A. The results, after correction for scattering from the substrate plate, are shown in fig. 1 indicating that there is a significant proportion ( - 15%) of crystalline methanol in the deposited sample. A separate measurement of the diffraction pattern for crystalline methanol was made by heating the sample above the glass transition and then cooling to 50
l
I
I
i
6
4
x \x
i ] C aOD
amorphous
2
do/dO
I
I
1
i
I
i
6 barnlsterad/mol
4
~x
liquid
o
Q/A-' Fig. 2. The differential cross-section for neutron scattering by a) a-CD3OD (A = 1.37 ,~); and b) liquid CD3OD (X = 0.94 .A0; the solid line is the fl(Q) form-factor for scattering by the isolated molecule.
306
D. C Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
K; these results are also shown in fig. 1. There appears to be little diffraction broadening and the scattering for the amorphous material was obtained by simple subtraction of the scaled crystalline pattern from that of the composite sample. The final results are shown in fig. 2a as a function of the scattering vector, Q.
3. Analysis Structural studies of CD3OD (and CD3OH ) in the liquid phase have been presented elsewhere [5-7] and give the basic formalism for analysis of the diffraction observations. The structure factor, SM(Q) obtained from the intensity profile may be written as
SM(Q)=f,(Q)+ DM(Q) where fl(Q) is a form-factor for
scattering by individual molecules (intramolecular contributions) and DM(Q) arises from the arrangement of the molecules (inter-molecular contributions). The molecular form factor for CD3OD contains eight terms and is much more complicated than that for D20 or N D 3. Using the geometrical parameters obtained from the liquid studies the fl(Q) function may be evaluated and the corresponding cross-section is shown in fig. 2 superimposed on the experimental values. Since the measured intensity is not in absolute units the data have been scaled to give agreement in the overall intensity at high-Q values. The shape of the fl(Q) curve does not follow the observed intensity pattern in the limited Q-range of the present measurements but reference to the measurements on the liquid phase [5] shown in the lower part of fig. 2 indicates that the normalisation of the theoretical curve can be made to an accuracy of approximately 2%. Corresponding results for liquid CD3OD at 293 K are given in the lower curve, fig. 2b. The liquids studies have shown that strong hydrogen-bonding interactions can cause an elongation of the O - D distance in the hydroxyl group but this has a relatively small effect on the fl(Q) curve at low Q-values. The DM(Q) curve obtained for the amorphous solid by subtraction of the molecular contribution, is shown in fig. 3. A similar curve for liquid CD3OD is also shown for comparison. As expected, the results for the amorphous solid exhibit similar general features to those of the liquid but have a larger amplitude. The main diffraction peak for the amorphous solid is displaced to a larger Q-value than that for the liquid phase. This effect is identical to that observed in the comparison of amorphous and liquid N D 3 but it seems that amorphous D20 ice and liquid water exhibit an opposite shift in the peak position. The variation in the peak position is also found to vary systematically as the temperature of the liquid is changed. This feature seems to be particularly characteristic of hydrogen-bonded systems since other liquids studied by neutron diffraction techniques show a negligible shift with temperature variation. This behaviour is partially explained by the larger density variation in
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol I
!
I
i
I
307
I
CD30D 0.2
D (O)
liquid 0
-0.2
,
,
,
o/A-' Fig. 3. The inter-molecular function DM(Q) for the amorphous ( phases of CD3OD.
) and liquid ( - -
--)
hydrogen-bonded liquids but is also a strong indication of structural rearrangement in the molecular orientation of adjacent molecules as the liquid is cooled through its super-cooled phase to form a glass. The variation of the peak position, Qo(T), is shown in fig. 4 with the corresponding density curve, p(T), for each of these three molecular systems. If the change in density leads to a simple scaling of all the intermolecular distances the DM(Q) function would also be scaled without change of shape and Qop1/3 would remain constant. This relation appears to be followed approximately by both CD3OD and ND 3 but not by D20. Since the intermolecular hydrogen-bond distance is expected to remain unchanged by temperature variation it is much more likely that changes in the relative orientational correlation of adjacent molecules are required to accommodate the density difference. The change in the form of DM(Q) therefore gives some indication of structural re-arrangement although it is impossible to deduce any further information from this single set of data. The extrapolation" of the Qo(T) curve for liquid CD3OD past the normal freezing point is consistent with the value for a-CD3OD at the glass transition point; this is quoted as 103 ( + 5) K for CH3OH [8] and is probably a few degrees higher for CD3OD. The behaviour of the corresponding curves for water and amorphous ice exhibit a different functional behaviour. Amorphous H 2 0 ice is unstable above 140 K [9] and the extrapolated liquid curve appears to reach the Q0-value of
308
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol 1.1
1.0
P g'ml-1
0.9
0.8
0.7 N
.J
2.1
~ -...
NHI
j
2.0
Qo/A-'
1.9
1.7
-
I I
I T~
-o-r .......... I 'r, 150
;.
2 .........
2(~0
;.
CDIOD
,'r~
~-I-~.,
"r' TA
250
3()0
360
Temperature / degrees K Fig. 4. Peak position, Q0, and density, p, for hydrogen-bonded systems showing the inter-relation between liquid and amorphous phases; TM is the melting point, Tg, the glass transition temperature and TA, the Angell temperature;? indicates an extrapolation over the super-cooled liquid region.
amorphous ice at a much higher temperature. This is very close to the Angell temperature of 228 K which is characteristic of the anomalous behaviour of various thermophysical properties in the deeply super-cooled region [10]. As water is super-cooled to temperatures - 30°C below the normal freezing point properties such as compressibility, specific heat, diffusion, viscosity, dielectric relaxation etc. show an anomalous behaviour characteristic of the approach to a critical point at 228 K for H20 and 233 K for D20. The nature of the implied transition remains controversial but the experimental evidence suggests that this could be the homogeneous nucleation temperature and therefore represents a metastability limit for the existence of the liquid phase. It is also instructive to compare the data for the amorphous material with that of the crystalline phase, using the data of fig. 1. The main diffraction peak sharpens as the liquid is transformed to a glass but remains much broader than the sharp double Bragg peak exhibited for the crystalline solid. The group of small peaks which cover the angular range of 25-35 ° also correspond well with the positive oscillation at a Q-value o f - 2.8 ,~. This suggests that the essential features of local ordering remain similar in both the solid phases but the amorphous solid lacks the long-range correlations that are present in the
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
309
crystalline lattice. Since the width of the diffraction peak i s - 0.4 A, the presence of significant oscillations in the pair correlation function would not be expected to extend much further than 20 A. The structures of the a and fl phases of the crystalline solid have been investigated by Tauer and Lipscomb [14] using X-rays. In both lattices there is an infinite zigzag chain of hydrogen-bonded molecules. For the higher temperature a-phase, this has a planar form parallel to the (100) face but undergoes a displacement transition to give puckered chains in the lower temperature phase. Krishna Mufti [15] extended the measurements to lower temperatures and observed similar unit cell dimensions but a change in the angle fl of the monoclinic cell. It seems from the discussion of these experimental results that the strong hydrogen-bonding is retained and the phase transformation is primarily influenced b y density considerations. The suggestion that the amorphous solid consists of similar hydrogen-bonded chains with only partially ordered correlation in the azimuthal angles is therefore consistent with the known properties of the crystalline solid.
4. Discussion
The present results for a-CD3OD give a valuable insight into the structural relationships that occur in the molecular arrangement but the restricted range of the data means that a detailed model description of the network cannot be established from this single diffraction measurement. The real-space distribution function, d(r) which is related to the neutron-weighted intermolecular pair-distribution function, g(r) may be evaluated by the usual transform relation
d(r) = 4~rrPM[ g ( r ) -- 1] = 2 fOmaXQDM(Q)M(Q) sin Qr dO, qTJ o
where PM is the molecular number density and M(Q) is a modification function, chosen to reduce truncation errors due to the termination of the data at the value Qm~; in the present case M(Q) is taken to be
sin( ~rQ/Qmax) M(Q)= (~rQ/Qmax) The d(r) function for a-CDaOD is shown in fig. 5 for a Qmax-value of 6.5 A -x and the corresponding function d(r) for the liquid is also given for a similar to truncation point. As the Qma~ is relatively low, the real-space resolution is insufficient to show the detailed features of the local correlations. In the analysis of neutron data for a-D20 [1] it was possible to observe well-resolved peaks at short distances (1.5-2.5 A) and these are probably present d(r) function due to the restricted Q-range and lower weighting function. In the high-resolution analysis of the liquid data for CD3OD [16]
310
D.C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol ,
,
I
1
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i
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0"2I
CD30D /
liquid
//\,-/
d(r)
i
//'
~ ~amorphou$
/
-0.2
-0.4
. . . .
g
. . . .
lb'
'
'
Fig. 5. The real-space correlation function d(r) corresponding to the data given in fig. 3.
some structure on the broad peak from 2-5 A, is also present but much less pronounced than for a-D20. In spite of these restrictions a number of interesting features can be identified in the comparison of the liquid and amorphous phases shown in fig. 5. The broad peak at 3.5-5 A, is due to many contributing terms at intermediate distances, particularly arising from methyl-methyl correlations. Transition from the liquid to the solid phase has little effect on the height of this peak but shows a displacement to shorter distances arising from the increased packing density in the solid phase. The C - C and C - O distances in the crystalline form are 3.6 and 4.2 A in the low-temperature phase which indicates why many partial terms contribute to this peak. The loca configuration due to the hydrogen-bonding is not much affected by the change in temperature except for a closer packing of the individual units. At larger distance (> 6 A) the increased density leads to enhanced correlations due to the static nature of the disordered chains. This behaviour is similar to that seen for a-D20 and presumably results from a more restricted variation of the hydrogen-bond bend angle. The peak positions show a consistent contraction of the length scale by a factor of 0.92 and indicate that significant correlations extend beyond 15 A. This variation is in good agreement with the estimate of the density from the slope of the d(r) curve at low r-values which suggest that the density of the amorphous solid is increased by 25 + 3% over that of the liquid at 293 K. This value is also in satisfactory agreement with the extrapolation of the liquid density line to the glass transition point (fig. 4).
D. C Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
311
The full description of the structure in terms of partial pair-correlation functions requires ten independent terms. It is possible, in principle, to isolate some of these functions by selective H / D substitution of the deuterium atoms in the molecule. This procedure has been used in a detailed investigation of the liquid phase [5] and the results have been compared with a Monte Carlo simulation by Jorgensen [17] using the TIPS potential. Although the full analysis is incomplete the preliminary results give strong support to the model proposed by Jorgensen which predicts the formation of strongly correlated hydrogen-bonded chains which may have occasional branches. The apolar methyl group plays the role of an inert space-filling unit which does not participate in the network. The stereo projections show that there is a considerable space between molecules in the liquid phase and its presumably this volume that is continuously reduced as the temperature is lowered and the density increased.
5. Conclusions The present general features in the a-CD3OD results can be compared with corresponding neutron diffraction data obtained for D20 and ND 3. It is clear that hydrogen-bonding interactions play a major role in defining the structural properties of these materials in both the liquid and amorphous solid phases. In all cases the inter-molecular DM(Q) function can be seen as a natural end product in the extrapolation of trends observed in the temperature variation of data for the liquid phase. The main peak is sharper, showing the increased range of spatial correlation in the amorphous solid. The d(r) functions suggest that local order is very similar in both phases but there is greater orientational correlation in the solid due to the hydrogen-bonding interaction. It is natural to think that this arises from the more restricted range of O - H - - - O angles in the network structure compared with dynamic range represented by the time-averaged structure of the liquid phase. It therefore seems that the continuity of phase between the normal liquid, supercooled liquid and glassy solid is represented by a systematic variation of geometrical arrangement which is primarily influenced by the particular features of the hydrogen-bonding interaction. In the present discussion it has been assumed that the amorphous (vapourdeposited) solid is identical to the glassy solid formed directly from the melt. It would be of interest to verify this assumption by diffraction studies of the super-cooled liquid and solid phases. Corresponding X-ray diffraction data would also be of value in verifying the predictions from the Monte Carlo simulation. Furthermore, it has now been recognised [18] that isotopic substitution of hydrogen and deuterium is not a simple isomorphous replacement. A detailed analysis of neutron data for CD3OH/CD3OD liquid mixtures [5] showed that the partial g(r) distribution functions associated with the H / D atom of the hydroxyl group showed a systematic variation. The results suggest
312
D.C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
that the proton has a wider spatial distribution in real space than the deuteron. The effect is much larger than would be expected from a simple normal-modes analysis of the molecular vibrations with a changed mass and is clearly dependent on the detailed behaviour of the hydrogen-bond interaction. In this context there is increasing speculation about the possibility of proton delocalisation along the hydrogen-bond axis which may arise from quantum effects. Since this effect is likely to be more pronounced in the low-temperature amorphous phase it would be interesting to conduct experiments on aCD3OH/D mixtures in an analogous manner. It is hoped that some of these additional measurements can be made in the 'not-too-distant' future.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
M.R. Chowdhury, J.C. Dore and J.T. Wenzel, J. Non-Cryst. Solids 53 (1982) 247. A.H. Narten, C.G. Venkatesh and S.A. Rice, J. Chem. Phys. 64 (1976) 1106. M.R. Chowdhury, J.C. Dore and P. Chieux, J. Non-Cryst. Solids 43 (1981) 267. M. Sugisaki, H. Suga and S. Seki, Bull, Chem. Soc. Japan 41 (1968) 2586. D.G. Montague, J.C. Dore and S.A. Cummings, Mol. Phys. 53 (1984) 1049. D.G. Montague and J.C. Dore, submitted to Mol. Phys. H. Bertagnolli and H.G. Hertz, Phys. Stat. Sol. 49 (1978) 463. C.A. Angell, J.M. Sare and E.J. Sare, J. Phys. Chem. 82 (1978) 2622. P.V. Hobbs, in: Ice Physics (Clarendon, Oxford, 1974) p. 42. C.A. Angell, in: Water: a Comprehensive Treatise, vol. VII, F. Franks, ed. (Plenum, New York, 1982). H.E. Stanley and J. Teixeira, J. Chem. Phys. 73 (1980) 3404. L. Bosio, J. Teixeira and H.E. Stanley, Phys. Rev. Lett. 46 (1981) 597. L. Bosio, J. Teixeira, J.C. Dore, D.C. Steytler and P. Chieux, Molec. Phys. 50 (1983) 733. K.J. Tauer and W.N. Lipscomb, Act. Cryst. 5 (1952) 606. G.S.R. Krishna Murti, Indian J. Phys. 42 (1959) 458. D.G. Montague, I.P. Gibson and J.C. Dore, Molec. Phys. 44 (1981) 1365. W.L. Jorgensen, J. Am. Chem. Soc. 103 (1981) 341; and private communication. J.C. Dore, in: Proc. ILL Workshop on Water, to be published.
303
N E U T R O N D I F F R A C T I O N S T U D I E S OF A M O R P H O U S M E T H Y L ALCOHOL D.C. STEYTLER and J.C. D O R E Physics Laboratory, University of Kent, Canterbury, CT2 7NR, England
D.C. M O N T A G U E Willamette University, Salem, Oregon, USA Received 10 August 1984 Revised manuscript received 27 November 1984
A neutron diffraction study has been made of vapour-deposited methyl alcohol, CD3OD. Although some crystalline material was present in the deposit it was possible to obtain the inter-molecular interference function D M(Q) for the amorphous solid over a Q-range extending to 6 A-1. The structural features may be compared with similar data for crystalline and liquid CD3OD. The results demonstrate an intermediate stage in which hydrogen-bonded chains play an important role in the local structure as in the liquid phase but do not possess the long-range order of the crystalline material. Systematic variations in the diffraction patterns for the liquid and amorphous phases of CD3OD, D20 and ND 3 can be correlated and relate to changes resulting from orientational correlations due to hydrogen-bonding.
I. Introduction The network structure of glasses and amorphous materials has received much attention in recent years and the ability to measure pair correlation functions to high precision by X-ray or neutron diffraction has opened up the possibility of providing stringent tests for any model construction. One class of material that is of relatively recent interest occurs in the case of hydrogenbonded molecules. Extensive studies of amorphous ice [1,2] have shown that the strong orientational effects of the hydrogen-bonding interaction leads to a tetrahedral network which resembles that of amorphous silicon or germanium due to the 4-fold nature of the inter-molecular co-ordination. In contrast to this behaviour, amorphous ammonia with an expected six-fold co-ordination appears to have quite different properties [3]. Further studies have now been made for vapour-deposited methyl alcohol in order to investigate a 2-fold co-ordinated system incorporating the apolar methyl head group which does •not participate in the network-bonded structure. Current Monte Carlo simulations of the liquid phase have emphasised the formation of chains by hydrogen-bonding in the hydroxyl group. The structural properties of the amorphous 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
304
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
phase are of particular interest since it would seem that this material would not readily form an inter-connected network. The study of amorphous methanol therefore has relevance to a wide range of organic glass-forming systems and the structural relationship to both the crystalline and liquid phases should give some insight into the geometrical factors which influence its properties.
2. Experimental procedure Although the glassy state of methanol may be formed by supercooling from the liquid phase [4] it was decided to use similar preparative methods to those described in the previous studies of amorphous ice [1] and ammonia [3]. This consisted of vapour deposition onto a cold substrate plate. Fully deuterated methanol CD3OD, with a quoted enrichment of 99% deuterium was obtained
~000I
CD=OD
7000
GO0~5800
~o00-
Intensity
~
Sample
3000 -
200e(Arbitrary units)
i~oo~ @. -
-
30002000-
•_•jJ•j•_
1000-
@,00
13./5
2L5o
,,'.25
~.oo
Crystalline
4 n
~.5o
56,25
112.00
Scattering Angle 0 / degrees Fig. 1. The diffraction pattern for a) vapour-deposited CD3OD; and b) crystalline CD3OD obtained for an an incident neutron wavelength of 1.37 .~.
D.C. Steytler et a L / Neutron diffraction studies of amorphous methyl alcohol
305
from Merck, Sharp and Dohme. The liquid was placed in an isolated tube and degassed by several freeze-pump-thaw cycles. A needle-valve leading into the cryostat was then opened. The methanol vapour was pre-cooled by flowing through a copper tube which had a weak-thermal link to the nitrogen-cooled heat shields. The issuing stream of molecules was directed onto a vanadium substrate plate of 1 mm thickness which was connected to a liquid helium reservoir and maintained at approximately 10 K. Approximately 2 ml of material was deposited over a period of 1 day corresponding to a mean deposition rate of 0.08 ml h r - ] . The diffraction experiment was performed on the Curran diffractometer at the Dido reactor AERE, Harwell. An angular scan of 2-95 ° was made using an incident neutron wavelength of 1.37 A. The results, after correction for scattering from the substrate plate, are shown in fig. 1 indicating that there is a significant proportion ( - 15%) of crystalline methanol in the deposited sample. A separate measurement of the diffraction pattern for crystalline methanol was made by heating the sample above the glass transition and then cooling to 50
l
I
I
i
6
4
x \x
i ] C aOD
amorphous
2
do/dO
I
I
1
i
I
i
6 barnlsterad/mol
4
~x
liquid
o
Q/A-' Fig. 2. The differential cross-section for neutron scattering by a) a-CD3OD (A = 1.37 ,~); and b) liquid CD3OD (X = 0.94 .A0; the solid line is the fl(Q) form-factor for scattering by the isolated molecule.
306
D. C Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
K; these results are also shown in fig. 1. There appears to be little diffraction broadening and the scattering for the amorphous material was obtained by simple subtraction of the scaled crystalline pattern from that of the composite sample. The final results are shown in fig. 2a as a function of the scattering vector, Q.
3. Analysis Structural studies of CD3OD (and CD3OH ) in the liquid phase have been presented elsewhere [5-7] and give the basic formalism for analysis of the diffraction observations. The structure factor, SM(Q) obtained from the intensity profile may be written as
SM(Q)=f,(Q)+ DM(Q) where fl(Q) is a form-factor for
scattering by individual molecules (intramolecular contributions) and DM(Q) arises from the arrangement of the molecules (inter-molecular contributions). The molecular form factor for CD3OD contains eight terms and is much more complicated than that for D20 or N D 3. Using the geometrical parameters obtained from the liquid studies the fl(Q) function may be evaluated and the corresponding cross-section is shown in fig. 2 superimposed on the experimental values. Since the measured intensity is not in absolute units the data have been scaled to give agreement in the overall intensity at high-Q values. The shape of the fl(Q) curve does not follow the observed intensity pattern in the limited Q-range of the present measurements but reference to the measurements on the liquid phase [5] shown in the lower part of fig. 2 indicates that the normalisation of the theoretical curve can be made to an accuracy of approximately 2%. Corresponding results for liquid CD3OD at 293 K are given in the lower curve, fig. 2b. The liquids studies have shown that strong hydrogen-bonding interactions can cause an elongation of the O - D distance in the hydroxyl group but this has a relatively small effect on the fl(Q) curve at low Q-values. The DM(Q) curve obtained for the amorphous solid by subtraction of the molecular contribution, is shown in fig. 3. A similar curve for liquid CD3OD is also shown for comparison. As expected, the results for the amorphous solid exhibit similar general features to those of the liquid but have a larger amplitude. The main diffraction peak for the amorphous solid is displaced to a larger Q-value than that for the liquid phase. This effect is identical to that observed in the comparison of amorphous and liquid N D 3 but it seems that amorphous D20 ice and liquid water exhibit an opposite shift in the peak position. The variation in the peak position is also found to vary systematically as the temperature of the liquid is changed. This feature seems to be particularly characteristic of hydrogen-bonded systems since other liquids studied by neutron diffraction techniques show a negligible shift with temperature variation. This behaviour is partially explained by the larger density variation in
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol I
!
I
i
I
307
I
CD30D 0.2
D (O)
liquid 0
-0.2
,
,
,
o/A-' Fig. 3. The inter-molecular function DM(Q) for the amorphous ( phases of CD3OD.
) and liquid ( - -
--)
hydrogen-bonded liquids but is also a strong indication of structural rearrangement in the molecular orientation of adjacent molecules as the liquid is cooled through its super-cooled phase to form a glass. The variation of the peak position, Qo(T), is shown in fig. 4 with the corresponding density curve, p(T), for each of these three molecular systems. If the change in density leads to a simple scaling of all the intermolecular distances the DM(Q) function would also be scaled without change of shape and Qop1/3 would remain constant. This relation appears to be followed approximately by both CD3OD and ND 3 but not by D20. Since the intermolecular hydrogen-bond distance is expected to remain unchanged by temperature variation it is much more likely that changes in the relative orientational correlation of adjacent molecules are required to accommodate the density difference. The change in the form of DM(Q) therefore gives some indication of structural re-arrangement although it is impossible to deduce any further information from this single set of data. The extrapolation" of the Qo(T) curve for liquid CD3OD past the normal freezing point is consistent with the value for a-CD3OD at the glass transition point; this is quoted as 103 ( + 5) K for CH3OH [8] and is probably a few degrees higher for CD3OD. The behaviour of the corresponding curves for water and amorphous ice exhibit a different functional behaviour. Amorphous H 2 0 ice is unstable above 140 K [9] and the extrapolated liquid curve appears to reach the Q0-value of
308
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol 1.1
1.0
P g'ml-1
0.9
0.8
0.7 N
.J
2.1
~ -...
NHI
j
2.0
Qo/A-'
1.9
1.7
-
I I
I T~
-o-r .......... I 'r, 150
;.
2 .........
2(~0
;.
CDIOD
,'r~
~-I-~.,
"r' TA
250
3()0
360
Temperature / degrees K Fig. 4. Peak position, Q0, and density, p, for hydrogen-bonded systems showing the inter-relation between liquid and amorphous phases; TM is the melting point, Tg, the glass transition temperature and TA, the Angell temperature;? indicates an extrapolation over the super-cooled liquid region.
amorphous ice at a much higher temperature. This is very close to the Angell temperature of 228 K which is characteristic of the anomalous behaviour of various thermophysical properties in the deeply super-cooled region [10]. As water is super-cooled to temperatures - 30°C below the normal freezing point properties such as compressibility, specific heat, diffusion, viscosity, dielectric relaxation etc. show an anomalous behaviour characteristic of the approach to a critical point at 228 K for H20 and 233 K for D20. The nature of the implied transition remains controversial but the experimental evidence suggests that this could be the homogeneous nucleation temperature and therefore represents a metastability limit for the existence of the liquid phase. It is also instructive to compare the data for the amorphous material with that of the crystalline phase, using the data of fig. 1. The main diffraction peak sharpens as the liquid is transformed to a glass but remains much broader than the sharp double Bragg peak exhibited for the crystalline solid. The group of small peaks which cover the angular range of 25-35 ° also correspond well with the positive oscillation at a Q-value o f - 2.8 ,~. This suggests that the essential features of local ordering remain similar in both the solid phases but the amorphous solid lacks the long-range correlations that are present in the
D. C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
309
crystalline lattice. Since the width of the diffraction peak i s - 0.4 A, the presence of significant oscillations in the pair correlation function would not be expected to extend much further than 20 A. The structures of the a and fl phases of the crystalline solid have been investigated by Tauer and Lipscomb [14] using X-rays. In both lattices there is an infinite zigzag chain of hydrogen-bonded molecules. For the higher temperature a-phase, this has a planar form parallel to the (100) face but undergoes a displacement transition to give puckered chains in the lower temperature phase. Krishna Mufti [15] extended the measurements to lower temperatures and observed similar unit cell dimensions but a change in the angle fl of the monoclinic cell. It seems from the discussion of these experimental results that the strong hydrogen-bonding is retained and the phase transformation is primarily influenced b y density considerations. The suggestion that the amorphous solid consists of similar hydrogen-bonded chains with only partially ordered correlation in the azimuthal angles is therefore consistent with the known properties of the crystalline solid.
4. Discussion
The present results for a-CD3OD give a valuable insight into the structural relationships that occur in the molecular arrangement but the restricted range of the data means that a detailed model description of the network cannot be established from this single diffraction measurement. The real-space distribution function, d(r) which is related to the neutron-weighted intermolecular pair-distribution function, g(r) may be evaluated by the usual transform relation
d(r) = 4~rrPM[ g ( r ) -- 1] = 2 fOmaXQDM(Q)M(Q) sin Qr dO, qTJ o
where PM is the molecular number density and M(Q) is a modification function, chosen to reduce truncation errors due to the termination of the data at the value Qm~; in the present case M(Q) is taken to be
sin( ~rQ/Qmax) M(Q)= (~rQ/Qmax) The d(r) function for a-CDaOD is shown in fig. 5 for a Qmax-value of 6.5 A -x and the corresponding function d(r) for the liquid is also given for a similar to truncation point. As the Qma~ is relatively low, the real-space resolution is insufficient to show the detailed features of the local correlations. In the analysis of neutron data for a-D20 [1] it was possible to observe well-resolved peaks at short distances (1.5-2.5 A) and these are probably present d(r) function due to the restricted Q-range and lower weighting function. In the high-resolution analysis of the liquid data for CD3OD [16]
310
D.C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol ,
,
I
1
!
i
! - t-- r--T----1
0"2I
CD30D /
liquid
//\,-/
d(r)
i
//'
~ ~amorphou$
/
-0.2
-0.4
. . . .
g
. . . .
lb'
'
'
Fig. 5. The real-space correlation function d(r) corresponding to the data given in fig. 3.
some structure on the broad peak from 2-5 A, is also present but much less pronounced than for a-D20. In spite of these restrictions a number of interesting features can be identified in the comparison of the liquid and amorphous phases shown in fig. 5. The broad peak at 3.5-5 A, is due to many contributing terms at intermediate distances, particularly arising from methyl-methyl correlations. Transition from the liquid to the solid phase has little effect on the height of this peak but shows a displacement to shorter distances arising from the increased packing density in the solid phase. The C - C and C - O distances in the crystalline form are 3.6 and 4.2 A in the low-temperature phase which indicates why many partial terms contribute to this peak. The loca configuration due to the hydrogen-bonding is not much affected by the change in temperature except for a closer packing of the individual units. At larger distance (> 6 A) the increased density leads to enhanced correlations due to the static nature of the disordered chains. This behaviour is similar to that seen for a-D20 and presumably results from a more restricted variation of the hydrogen-bond bend angle. The peak positions show a consistent contraction of the length scale by a factor of 0.92 and indicate that significant correlations extend beyond 15 A. This variation is in good agreement with the estimate of the density from the slope of the d(r) curve at low r-values which suggest that the density of the amorphous solid is increased by 25 + 3% over that of the liquid at 293 K. This value is also in satisfactory agreement with the extrapolation of the liquid density line to the glass transition point (fig. 4).
D. C Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
311
The full description of the structure in terms of partial pair-correlation functions requires ten independent terms. It is possible, in principle, to isolate some of these functions by selective H / D substitution of the deuterium atoms in the molecule. This procedure has been used in a detailed investigation of the liquid phase [5] and the results have been compared with a Monte Carlo simulation by Jorgensen [17] using the TIPS potential. Although the full analysis is incomplete the preliminary results give strong support to the model proposed by Jorgensen which predicts the formation of strongly correlated hydrogen-bonded chains which may have occasional branches. The apolar methyl group plays the role of an inert space-filling unit which does not participate in the network. The stereo projections show that there is a considerable space between molecules in the liquid phase and its presumably this volume that is continuously reduced as the temperature is lowered and the density increased.
5. Conclusions The present general features in the a-CD3OD results can be compared with corresponding neutron diffraction data obtained for D20 and ND 3. It is clear that hydrogen-bonding interactions play a major role in defining the structural properties of these materials in both the liquid and amorphous solid phases. In all cases the inter-molecular DM(Q) function can be seen as a natural end product in the extrapolation of trends observed in the temperature variation of data for the liquid phase. The main peak is sharper, showing the increased range of spatial correlation in the amorphous solid. The d(r) functions suggest that local order is very similar in both phases but there is greater orientational correlation in the solid due to the hydrogen-bonding interaction. It is natural to think that this arises from the more restricted range of O - H - - - O angles in the network structure compared with dynamic range represented by the time-averaged structure of the liquid phase. It therefore seems that the continuity of phase between the normal liquid, supercooled liquid and glassy solid is represented by a systematic variation of geometrical arrangement which is primarily influenced by the particular features of the hydrogen-bonding interaction. In the present discussion it has been assumed that the amorphous (vapourdeposited) solid is identical to the glassy solid formed directly from the melt. It would be of interest to verify this assumption by diffraction studies of the super-cooled liquid and solid phases. Corresponding X-ray diffraction data would also be of value in verifying the predictions from the Monte Carlo simulation. Furthermore, it has now been recognised [18] that isotopic substitution of hydrogen and deuterium is not a simple isomorphous replacement. A detailed analysis of neutron data for CD3OH/CD3OD liquid mixtures [5] showed that the partial g(r) distribution functions associated with the H / D atom of the hydroxyl group showed a systematic variation. The results suggest
312
D.C. Steytler et al. / Neutron diffraction studies of amorphous methyl alcohol
that the proton has a wider spatial distribution in real space than the deuteron. The effect is much larger than would be expected from a simple normal-modes analysis of the molecular vibrations with a changed mass and is clearly dependent on the detailed behaviour of the hydrogen-bond interaction. In this context there is increasing speculation about the possibility of proton delocalisation along the hydrogen-bond axis which may arise from quantum effects. Since this effect is likely to be more pronounced in the low-temperature amorphous phase it would be interesting to conduct experiments on aCD3OH/D mixtures in an analogous manner. It is hoped that some of these additional measurements can be made in the 'not-too-distant' future.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
M.R. Chowdhury, J.C. Dore and J.T. Wenzel, J. Non-Cryst. Solids 53 (1982) 247. A.H. Narten, C.G. Venkatesh and S.A. Rice, J. Chem. Phys. 64 (1976) 1106. M.R. Chowdhury, J.C. Dore and P. Chieux, J. Non-Cryst. Solids 43 (1981) 267. M. Sugisaki, H. Suga and S. Seki, Bull, Chem. Soc. Japan 41 (1968) 2586. D.G. Montague, J.C. Dore and S.A. Cummings, Mol. Phys. 53 (1984) 1049. D.G. Montague and J.C. Dore, submitted to Mol. Phys. H. Bertagnolli and H.G. Hertz, Phys. Stat. Sol. 49 (1978) 463. C.A. Angell, J.M. Sare and E.J. Sare, J. Phys. Chem. 82 (1978) 2622. P.V. Hobbs, in: Ice Physics (Clarendon, Oxford, 1974) p. 42. C.A. Angell, in: Water: a Comprehensive Treatise, vol. VII, F. Franks, ed. (Plenum, New York, 1982). H.E. Stanley and J. Teixeira, J. Chem. Phys. 73 (1980) 3404. L. Bosio, J. Teixeira and H.E. Stanley, Phys. Rev. Lett. 46 (1981) 597. L. Bosio, J. Teixeira, J.C. Dore, D.C. Steytler and P. Chieux, Molec. Phys. 50 (1983) 733. K.J. Tauer and W.N. Lipscomb, Act. Cryst. 5 (1952) 606. G.S.R. Krishna Murti, Indian J. Phys. 42 (1959) 458. D.G. Montague, I.P. Gibson and J.C. Dore, Molec. Phys. 44 (1981) 1365. W.L. Jorgensen, J. Am. Chem. Soc. 103 (1981) 341; and private communication. J.C. Dore, in: Proc. ILL Workshop on Water, to be published.