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Dielectric relaxations in partly deuterated ammonium dichromate
Volume 142, number I ,2
CHEMICAL PHYSICS LETTERS
4 December 1987
DIELECTRIC RELAXATIONS IN PARTLY DEUTERATED AMMONIUM DICHROMATE John le G. GILCHRIST Centre de Recherches sur les Tres Basses TempCratures, CNRS, B. P. 166X. 38042 Grenoble Cedex, France
Received 24 August 1987; in final form 25 September 1987
Two dielectric relaxations in partly deuterated ammonium dichromate are attributed to reorientations of mixed-isotope ammonium ions. Loss peaks were observed between 20 and 40 K and obey the Arrhenius law with activation energy 1.5 kcal/mol for the stronger relaxation. The dipole moment is of the order of 0.015 D.
1. Introduction The motions of symmetric groups such as NH: in solids have been studied extensively by neutron scattering and magnetic resonance techniques, while the motions of unsymmetric groups such as OH- (as substitutional impurities in alkali halides) have been extensively studied by thermal, acoustic and dielectric methods. Partial deuteration brings ammonium compounds within the scope of the thermal, acoustic and dielectric methods. In ammonium dichromate the ammonium site lacks tetrahedral symmetry [ l-31 and the rotation barrier is fairly low [4]. Relaxational response to electric and strain tields is to be expected if the ammonium symmetry is broken by partial deuteration.
2. Experiment Ammonium dichromate (Prolabo “pur” 97-99%) was recrystallised from natural water, recrystallised from 5.528 or 60% deuterated water in a dessicator with PzOs, or recrystallised twice from D20 (99.8%) in the dessicator. The samples were estimated to be respectively 0, 5, 25, 55 and 97Ohdeuterated. They were crushed and pressed into pills, squeezed between indium electrodes, cooled in a cryostat tube described previously [ 51 and measured with a transformer capacitance bridge (General Radio 16 16). Pill densities were ~0.8 of X-ray densities and the
Fig. 1. Dielectric loss angle (microradians) or partly deuterated ammonium dichromate at 1.2 kHz minus the loss angle of an undeuterated sample. X, 0, +, l are respectively 5% d, 25% d, 55% d. 97% d.
apparent dielectric constant was 26 at low temperature. The dielectric loss angle of the 0% d sample increased regularly with temperature by 8 urad between 10 and 50 K while remaining below 20 urad in absolute value. The data shown in figs. 1 and 2 are differences between the loss angles of the part-deu-
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
121
Volume 142, number 1,2
CHEMICAL PHYSICS LETTERS
4 December 1987
whole loss curves including both peaks. In a similar experiment with ammonium cerium nitrate, (NH&Ce(NO& (Prolabo “rectapur” 95%) no significant difference was found between the dielectric losses of 0% d and 55% d samples. This corroborates the view of Svare et al. [6] that NH3D+ ions must be essentially locked in this salt, since partdeuteration was surprisingly ineffective in causing proton spin relaxation.
6
(brad3
3. Discussion
lo
20
30
%(lq
50
Fig. 2. Dielectric loss angle of 55% d ammonium dichromate minus the loss angle of an undeuterated sample. X, 0, +, 0 are respectively at 12 Hz, 120 Hz, 1.2kHz, 12 kHz.
terated and undeuterated samples. These two figures show data obtained at different times with different pills of the 55% d sample. The usual speed of cooling from ambient to working temperature was x 200 Wh but the pills featured in fig. 2 were also cooled at z 3000 K/h, and also at z 3 K/h between 150 and 110 K. This made no perceptible difference. In fig. 1 it can be seen that the loss curves scale approximately as x( 1 -x), where x is the deuterium fraction, and shift along the temperature axis with x without significant change in the ratio of the two peaks. From fig. 2 the two apparent relaxation processes obey the Arrhenius law with activation energy of 1.5 kcal/mol for the major peak, 0.9 kcal/mol for the minor, but the latter value is unreliable because the peaks tend to merge at higher frequencies and temperatures. Putting together the data of figs. 1 and 2, and regarding solely the major relaxation process it can be deduced that at 35 K, the 97Ohd sample would relax z 6.5 times more slowly than the 5W d. The rms dipole moment per ammonium ion can be estimated using the Onsager relation with the data of fig. 2 or the corresponding real part of the dielectric susceptibility and is of the order of 0.015 D for the 122
There is little doubt that the relaxations observed here correspond to reorientations of isotopically mixed ammonium ions. The more probable processes are 120” jumps about an NH (or ND) axis involving the cyclic permutation of three hydrogen atoms. The two potentially dielectrically active cases are when the three permuted hydrogens are H2D or HD,. According to the evidence of fig. 1, H2D and HD2 contribute equivalently to the major relaxation process and also to the minor one. Manifestly one peak is not due to H2D and the other to HD2. Though less likely, 180’ jumps about a diad axis are also possible. Then the relaxations of NHSD+, NH2D: and NHD: might have been resolved as three loss peaks, but this was not observed. At room temperature the monoclinic unit cell (space group C$, ) of ammonium dichromate contains eight equivalent (f) ammonium ions [ 11. The normal compound was found to have three secondorder phase changes near 268, 155 and 128 K [ 71. However it has also been reported that phase II (stable between 268 and 155 K) is easily supercooled [ 31. The perdeuterated version has phase changes near 170, 120 and 80 K and possibly also near 140 K [ 31. The structures of the low-temperature phases have not been reported, to our knowledge. The barrier hindering NH: rotation in phase IV of the normal compound (stable below 128 K) has been estimated to be 0.7 kcal/mol at 20 K [ 81, but also possibly 3.76 kcal/mol at 17 K [ 31. On the other hand Svare [ 41 deduced an activation energy of 1.58 kcal/ mol from the variation of the proton spin relaxation time between 85 and 250 K, a range which would span phases IV, III and II. By extrapolation from fig. 2 it appears that at such temperatures the two die-
Volume 142, number I ,2
CHEMICAL PHYSICS LETTERS
lectric relaxations will have coalesced into one, and the activation energy is close enough to allow identification to be made with the process deduced from Svare’s proton spin relaxation times. The agreement ismoreaccurateifthe Eyringlaw holds, viz. rate a TX with exp( -AGIRT), AG independent of temperature. Since the two relaxation processes vary regularly and similarly with x, the x=0 and x= 1 compounds and the intermediate ones are likely to be isostructural around 30 K. Possibly the structure contains two inequivalent ammonium sites, but even if all the sites were equivalent, the two loss peaks could be accounted for by noting that already in the monoclinic room-temperature structure [ 11 one NH,-0 distance is distinctly shorter than the others, which suggests that it corresponds to a stronger N-H...0 hydrogen bond. Possibly the faster (and weaker) relaxation corresponds to reorientation only about this strongly hydrogen-bonded axis and the slower (and stronger) one to reorientations in which D replaces H or vice versa in the strongly hydrogen-bonded position. If the dipole moment were to be regarded as an intrinsic property of the mixed-isotope ammonium groups the faster relaxation would be expected to be twice as strong as the slower on this basis. (This is related to the fact that if 8 is the angle between a strong H-bond axis and the applied field, then for randomly oriented crystals (sin’t?) = 3.) However, the dipole moment perhaps mainly arises from small displacements of the ammonium ions with respect to the surrounding lattice and the ammonium position is likely to be most sensitive to whether H or D forms the strongest hydrogen bond. This would make the slower relaxation the stronger. The change of relaxation rate as a function of x is too big to be explained by the difference in zero-point energy between -NH*D and -NHD2 rotators (assuming 120” jumps). With a threefold sinusoidal potential of 2.0 kcaYmo1 the relevant zero-point energy terms would perhaps be 0.50 and 0.45 kcal/mol respectively [ 41 but to account for a 6.5-fold change in relaxation rate at 35 K a difference in activation energy of 0.12 kcal/mol would be needed. Moreover the loss curve of the 55% d sample cannot be expressed as a linear combination of the 5% d and 97% d curves. Fig. 3 shows an attempt to do so. When -NH,D and -NHD2 are present in nearly equal
0
4 December 1987
A/? lo
1. 20
I
30
1
4oT(K)
50
Fig. 3. Dielectric loss of 55% d ammonium dichromate as in fig. 1, with a linear combination of the 5% d and 97% d data (twice the 5% d curve + five times the 97% d).
numbers the loss curve has the same shape as if only one or the other is present. The shift of relaxation rate with x is therefore mainly a collective effect (lattice or structural parameters or phonon spectrum) and only to a minor degree due to the statistical effect of summing the contributions of the different isotopic ammonium species. The relaxations show no sign of tunnelling. Tunnelling would be revealed by a departure from the Arrhenius law, enhanced loss extending down to below 10 K or possibly by a widening difference between the behaviours of low-x and high-x samples towards the lowest temperatures. A reliable upper limit to the tunnel splitting cannot be given because the relaxation rate in the tunnelling regime also depends on the unknown strain coupling. A dielectric relaxation due to mixed-isotope ammonium ions was recently observed in ammonium hexachlorostannate [ 91, and other ( NH&MX6 antifluorites are currently under study. In these cases the tetrahedral symmetry of the ammonium sites must be broken “accidentally” by imperfections or impurities, and the relaxations tend to be weaker and less readily reproducible. 123
Volume 142, number 1,2
CHEMICAL PHYSICS LETTERS
References [ 1] A. Bystriim and K.-A. Wilhelmi, Acta Chem. Stand. 5 (195 1) 1003.
[ 21 G.A.P. Dalgaard, AC. Hazel1 and R.G. Hazell, Acta Chem. Scand.A28 (1974) 541.
[ 31 C.J.H. Schutte and A.M. Heyns, J. Mol. Struct. 5 (1970) 37. [4] I. Svare, J. Phys. Cl0 (1977) 4137.
124
4 December 1987
[5] J. le G. Gilchrist and R. Isnard, J. Phys. El2 (1979) 28. [6] I. Svare, G. Thorkildsen, HI. Andersson, S.M. Skaeveland and P. Trivijitkasem, J. Phys. Cl 1 (1978) 997. [ 71 J. Jaffray, Compt. Rend. Acad. Sci. 241 (1955) 1114. [ 81 R.E. Richards and T. Schaefer, Trans. Faraday Sot. 57 (1961) 210. [9] J. le G. Gilchrist, J. Odin and J. Peyrard, in: Quantum aspects of molecular motions in solids, ed. A. Heidemann (Springer, Berlin, 1987) p. 118.
CHEMICAL PHYSICS LETTERS
4 December 1987
DIELECTRIC RELAXATIONS IN PARTLY DEUTERATED AMMONIUM DICHROMATE John le G. GILCHRIST Centre de Recherches sur les Tres Basses TempCratures, CNRS, B. P. 166X. 38042 Grenoble Cedex, France
Received 24 August 1987; in final form 25 September 1987
Two dielectric relaxations in partly deuterated ammonium dichromate are attributed to reorientations of mixed-isotope ammonium ions. Loss peaks were observed between 20 and 40 K and obey the Arrhenius law with activation energy 1.5 kcal/mol for the stronger relaxation. The dipole moment is of the order of 0.015 D.
1. Introduction The motions of symmetric groups such as NH: in solids have been studied extensively by neutron scattering and magnetic resonance techniques, while the motions of unsymmetric groups such as OH- (as substitutional impurities in alkali halides) have been extensively studied by thermal, acoustic and dielectric methods. Partial deuteration brings ammonium compounds within the scope of the thermal, acoustic and dielectric methods. In ammonium dichromate the ammonium site lacks tetrahedral symmetry [ l-31 and the rotation barrier is fairly low [4]. Relaxational response to electric and strain tields is to be expected if the ammonium symmetry is broken by partial deuteration.
2. Experiment Ammonium dichromate (Prolabo “pur” 97-99%) was recrystallised from natural water, recrystallised from 5.528 or 60% deuterated water in a dessicator with PzOs, or recrystallised twice from D20 (99.8%) in the dessicator. The samples were estimated to be respectively 0, 5, 25, 55 and 97Ohdeuterated. They were crushed and pressed into pills, squeezed between indium electrodes, cooled in a cryostat tube described previously [ 51 and measured with a transformer capacitance bridge (General Radio 16 16). Pill densities were ~0.8 of X-ray densities and the
Fig. 1. Dielectric loss angle (microradians) or partly deuterated ammonium dichromate at 1.2 kHz minus the loss angle of an undeuterated sample. X, 0, +, l are respectively 5% d, 25% d, 55% d. 97% d.
apparent dielectric constant was 26 at low temperature. The dielectric loss angle of the 0% d sample increased regularly with temperature by 8 urad between 10 and 50 K while remaining below 20 urad in absolute value. The data shown in figs. 1 and 2 are differences between the loss angles of the part-deu-
0 009-2614/87/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
121
Volume 142, number 1,2
CHEMICAL PHYSICS LETTERS
4 December 1987
whole loss curves including both peaks. In a similar experiment with ammonium cerium nitrate, (NH&Ce(NO& (Prolabo “rectapur” 95%) no significant difference was found between the dielectric losses of 0% d and 55% d samples. This corroborates the view of Svare et al. [6] that NH3D+ ions must be essentially locked in this salt, since partdeuteration was surprisingly ineffective in causing proton spin relaxation.
6
(brad3
3. Discussion
lo
20
30
%(lq
50
Fig. 2. Dielectric loss angle of 55% d ammonium dichromate minus the loss angle of an undeuterated sample. X, 0, +, 0 are respectively at 12 Hz, 120 Hz, 1.2kHz, 12 kHz.
terated and undeuterated samples. These two figures show data obtained at different times with different pills of the 55% d sample. The usual speed of cooling from ambient to working temperature was x 200 Wh but the pills featured in fig. 2 were also cooled at z 3000 K/h, and also at z 3 K/h between 150 and 110 K. This made no perceptible difference. In fig. 1 it can be seen that the loss curves scale approximately as x( 1 -x), where x is the deuterium fraction, and shift along the temperature axis with x without significant change in the ratio of the two peaks. From fig. 2 the two apparent relaxation processes obey the Arrhenius law with activation energy of 1.5 kcal/mol for the major peak, 0.9 kcal/mol for the minor, but the latter value is unreliable because the peaks tend to merge at higher frequencies and temperatures. Putting together the data of figs. 1 and 2, and regarding solely the major relaxation process it can be deduced that at 35 K, the 97Ohd sample would relax z 6.5 times more slowly than the 5W d. The rms dipole moment per ammonium ion can be estimated using the Onsager relation with the data of fig. 2 or the corresponding real part of the dielectric susceptibility and is of the order of 0.015 D for the 122
There is little doubt that the relaxations observed here correspond to reorientations of isotopically mixed ammonium ions. The more probable processes are 120” jumps about an NH (or ND) axis involving the cyclic permutation of three hydrogen atoms. The two potentially dielectrically active cases are when the three permuted hydrogens are H2D or HD,. According to the evidence of fig. 1, H2D and HD2 contribute equivalently to the major relaxation process and also to the minor one. Manifestly one peak is not due to H2D and the other to HD2. Though less likely, 180’ jumps about a diad axis are also possible. Then the relaxations of NHSD+, NH2D: and NHD: might have been resolved as three loss peaks, but this was not observed. At room temperature the monoclinic unit cell (space group C$, ) of ammonium dichromate contains eight equivalent (f) ammonium ions [ 11. The normal compound was found to have three secondorder phase changes near 268, 155 and 128 K [ 71. However it has also been reported that phase II (stable between 268 and 155 K) is easily supercooled [ 31. The perdeuterated version has phase changes near 170, 120 and 80 K and possibly also near 140 K [ 31. The structures of the low-temperature phases have not been reported, to our knowledge. The barrier hindering NH: rotation in phase IV of the normal compound (stable below 128 K) has been estimated to be 0.7 kcal/mol at 20 K [ 81, but also possibly 3.76 kcal/mol at 17 K [ 31. On the other hand Svare [ 41 deduced an activation energy of 1.58 kcal/ mol from the variation of the proton spin relaxation time between 85 and 250 K, a range which would span phases IV, III and II. By extrapolation from fig. 2 it appears that at such temperatures the two die-
Volume 142, number I ,2
CHEMICAL PHYSICS LETTERS
lectric relaxations will have coalesced into one, and the activation energy is close enough to allow identification to be made with the process deduced from Svare’s proton spin relaxation times. The agreement ismoreaccurateifthe Eyringlaw holds, viz. rate a TX with exp( -AGIRT), AG independent of temperature. Since the two relaxation processes vary regularly and similarly with x, the x=0 and x= 1 compounds and the intermediate ones are likely to be isostructural around 30 K. Possibly the structure contains two inequivalent ammonium sites, but even if all the sites were equivalent, the two loss peaks could be accounted for by noting that already in the monoclinic room-temperature structure [ 11 one NH,-0 distance is distinctly shorter than the others, which suggests that it corresponds to a stronger N-H...0 hydrogen bond. Possibly the faster (and weaker) relaxation corresponds to reorientation only about this strongly hydrogen-bonded axis and the slower (and stronger) one to reorientations in which D replaces H or vice versa in the strongly hydrogen-bonded position. If the dipole moment were to be regarded as an intrinsic property of the mixed-isotope ammonium groups the faster relaxation would be expected to be twice as strong as the slower on this basis. (This is related to the fact that if 8 is the angle between a strong H-bond axis and the applied field, then for randomly oriented crystals (sin’t?) = 3.) However, the dipole moment perhaps mainly arises from small displacements of the ammonium ions with respect to the surrounding lattice and the ammonium position is likely to be most sensitive to whether H or D forms the strongest hydrogen bond. This would make the slower relaxation the stronger. The change of relaxation rate as a function of x is too big to be explained by the difference in zero-point energy between -NH*D and -NHD2 rotators (assuming 120” jumps). With a threefold sinusoidal potential of 2.0 kcaYmo1 the relevant zero-point energy terms would perhaps be 0.50 and 0.45 kcal/mol respectively [ 41 but to account for a 6.5-fold change in relaxation rate at 35 K a difference in activation energy of 0.12 kcal/mol would be needed. Moreover the loss curve of the 55% d sample cannot be expressed as a linear combination of the 5% d and 97% d curves. Fig. 3 shows an attempt to do so. When -NH,D and -NHD2 are present in nearly equal
0
4 December 1987
A/? lo
1. 20
I
30
1
4oT(K)
50
Fig. 3. Dielectric loss of 55% d ammonium dichromate as in fig. 1, with a linear combination of the 5% d and 97% d data (twice the 5% d curve + five times the 97% d).
numbers the loss curve has the same shape as if only one or the other is present. The shift of relaxation rate with x is therefore mainly a collective effect (lattice or structural parameters or phonon spectrum) and only to a minor degree due to the statistical effect of summing the contributions of the different isotopic ammonium species. The relaxations show no sign of tunnelling. Tunnelling would be revealed by a departure from the Arrhenius law, enhanced loss extending down to below 10 K or possibly by a widening difference between the behaviours of low-x and high-x samples towards the lowest temperatures. A reliable upper limit to the tunnel splitting cannot be given because the relaxation rate in the tunnelling regime also depends on the unknown strain coupling. A dielectric relaxation due to mixed-isotope ammonium ions was recently observed in ammonium hexachlorostannate [ 91, and other ( NH&MX6 antifluorites are currently under study. In these cases the tetrahedral symmetry of the ammonium sites must be broken “accidentally” by imperfections or impurities, and the relaxations tend to be weaker and less readily reproducible. 123
Volume 142, number 1,2
CHEMICAL PHYSICS LETTERS
References [ 1] A. Bystriim and K.-A. Wilhelmi, Acta Chem. Stand. 5 (195 1) 1003.
[ 21 G.A.P. Dalgaard, AC. Hazel1 and R.G. Hazell, Acta Chem. Scand.A28 (1974) 541.
[ 31 C.J.H. Schutte and A.M. Heyns, J. Mol. Struct. 5 (1970) 37. [4] I. Svare, J. Phys. Cl0 (1977) 4137.
124
4 December 1987
[5] J. le G. Gilchrist and R. Isnard, J. Phys. El2 (1979) 28. [6] I. Svare, G. Thorkildsen, HI. Andersson, S.M. Skaeveland and P. Trivijitkasem, J. Phys. Cl 1 (1978) 997. [ 71 J. Jaffray, Compt. Rend. Acad. Sci. 241 (1955) 1114. [ 81 R.E. Richards and T. Schaefer, Trans. Faraday Sot. 57 (1961) 210. [9] J. le G. Gilchrist, J. Odin and J. Peyrard, in: Quantum aspects of molecular motions in solids, ed. A. Heidemann (Springer, Berlin, 1987) p. 118.