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Fast hydrogen ion diffusion in solid hydrogen uranyl phosphate (HUP)
Solid State Communications, Vol. 31, pp. 995-997. Pergamon Press Ltd. 1979. Printed in Great Britain. FAST HYDROGEN ION DIFFUSION IN SOLID HYDROGEN URANYL PHOSPHATE (HUP) R.E. Gordon and J.H. Strange Physics Laboratory, The University, Canterbury, Kent CT2 7NR, England and T.K. Halstead Department of Chemistry, University of York, Heslington, York YO1 5DD, England (Received 28 April 1979 by A.R. Miedema)
NMR relaxation time measurements and pulsed field gradient diffusion measurements have been made for I H in hydrogen uranyl phosphate (HUP). The results confirm that for T ~ 274 K HUP is a fast proton conductor exhibiting self-diffusion coefficients greater than I0 -11 m 2 s -I . 1. INTRODUCTION
movement between particles are unlikely to influence the measurements, wheareas such effects can strongly affect the conductivity measurements. NMR relaxation and diffusion will be affected by anisotropic motion which will only be observable in single crystal studies. The theory of nuclear relaxation due to the modu. lation of the nuclear dipolar interaction by self-diffusion is well established. The relevant expressions for T~ and /'2 have been quoted previously [1]. If the nuclear relaxation is dominated by self-diffusion then for a suitable model of self-diffusion in a crystal lattice the dipolar correlation time, To, Can be evaluated and may be identified with the mean residence time, r, for an atom on a normal lattice site. For a diffusion mechanism involving a jump distance ~ then for two dimensional diffusion D is given by
IN A RECENT nuclear magnetic resonance study [1 ] of hydrogen uranyl phosphate, H(UO2PO4)4H20 (I/UP), IH relaxation times were measured to investigate the nature of the self-diffusion of hydrogen in HUP which had been inferred from previous proton conductivity measurements [2]. HUP is a layered hydrate which exists in at least two phases ([, II) the transition temperature between the phases being 274 K [2]. The high temperature phase (I) is of particular interest because of the current need to find materials that are capable of sustaining fast proton transport at temperatures below about 600 K. The ~H relaxation time measurements [1] in HUP (I) are consistent with a transport process whereby the protons of the water molecules undergo two-dimensional self-diffusion. The lack of detailed knowledge about the self-diffusion mechanism makes it difficult to interpret the relaxation times in terms of an appropriate model where (X2) is the mean square jump distance and f i s the and thereby obtain a precise value for the self-diffusion relevant geometrical correlation factor. coefficient D. Childs etaI. [1] have calculated D for An alternative NMR approach under favourable HUP (I) using a simple random walk model. The comexperimental conditions is to use the pulsed field parison of these results with the diffusion data derived gradient technique [3] in which diffusion can be from conductivity measurements [2] must be viewed measured directly. The relevant theory for this techwith some caution since NMR and conductivity technique is to be found in the literature [3]. The basic niques measure different aspects of translational motion. 9 0 ° t 1 8 0 ° spin-echo sequence is modified by the Conductivity is a bulk property which measures charged addition of suitable magnetic field gradient pulses. For defect motion averaged over many jumps whereas the spins undergoing unrestricted diffusion it has been NMR relaxation times provide a measure of motion on a shown [3] that the spin echo attenuation is given by microscopic scale via a correlation time for atomic jumping. Furthermore, the different activation energies in [A(2t)*/A(2t)] = -- 7292D62(A -- ~8) (2) reported for HUP (I) by the two techniques suggest that where A(2t)* and A(2t) are the respective spin-echo translational seif-diffusion and charge transport may not amplitudes at time 2t in the presence and absence of the be determined by the same processes. Since N-MR relaxgradient pulses of amplitude g, duration 8 and separation ation measurements are governed by motion on a local A. scale, powder effects, such as grain boundaries and 995
HYDROGEN ION DIFFUSION IN HYDROGEN URANYL PHOSPHATE
996
104 345,
323 .
.
T(K) .
303 ,
266 ,
=
.
1 0 -I
;0 x
I"-..,...O ~
.~Z
IO
7 ~'~" .~..%,.
i1'1
U-
N d. . J u.I
I
I
3.0
I
I
I
_1000 (K-l) T
I
I
3.5
,
i.to-~
Fig. 1. Temperature dependence of the tH relaxation times obtained at 10 MHz in powder samples of HUP (I): o, Tx; e, 7"2. The lines denote the relaxation times obtained at 16MHz in [1]: - , Tt; . . . . ,7"2. The corresponding time scale is shown on the right. The tH selfdiffusion coefficients obtained by the pulsed field gradient technique are shown, o, and those derived from the NMR relaxation times [1], =. The scale for these points is shown on the left. The purpose of this paper is to report further relaxation time and pulsed field gradient diffusion measurements that have been carried out on HUP (I). 2. MATERIALS AND METHODS Powder samples of HUP prepared from the same batch used by Childs et el. [1 ] were used and sealed in silica tubes at S.T.P. TI and 7'2 were measured to an accuracy of ± 10% at coo = 2u x 107 red s -1 using standard pulse techniques in the temperature range 2 9 3 343 K. The temperature, T, was maintained constant to within 0.5 K by an automatic proportional regulating loop. The proton diffusion coefficient D has been measured using PFG apparatus previously described [4]. 3. RESULTS AND DISCUSSION The results of the relaxation time measurements are shown in Fig. 1. No measurements were made for T > 343 K to avoid any dehydration of the sample. The lines indicate the previous relaxation measurements at co o = 2*t x 1.6 x 1 0 7 r a d s -t [ 1 ] .
For nuclear relaxation dominated by serf-diffusion and assuming ¢0o¢c < 1 then it would be expected that TI = 7"2. The results of both sets of measurements indicate that Ta > / ' 2 with T t / T 2 --~ 1.5 which is believed
Vol. 3 l, No. 12
to be a consequence of the two-dimensional (2-D) nature of the diffusion mechanism. This type of behaviour has already been observed for 7Li relaxation in the onedimensional fast ion conductor Li2Ti307 [5, 6] and was attributed there to a highly correlated 1-D diffusion mechanism. At temperatures above 323 K the results are frequency independent consistent with the nuclear relaxation regime corresponding to ~Oorc < 1. At temperatures below 323 K however there is an increasing dis. crepancy between the results at each frequency. This may be due to the approaching presence of the TI minimum for the higher frequency measurements. Such a frequency dependence would be in contrast to results reported for a l-D conductor [5, 6]. The activation energy for the Tt and T2 data obtained at l0 MHz corresponds to 24.6 ± 1.9 kJ mole -1 which is comparable to the 20 kJ mole -~ measured at 16 MHz. Equation (2) can only be strictly applied for systems where the diffusion is isotropic and unrestricted. In HUP (I) the diffusion is believed to be laminar in nature and equation (2) must be modified accordingly. The relevant theory has boon derived by Stejskal and Tanner [7]. For unrestricted diffusion between two infinite, parallel barriers separated b y a distance d then, r
In [A(2t)*/A(2t)] = -- 7 2 g ~ 2&D [2{1 L
-F 4(7~g±d) 2
exp
\
d
CO8
('y*gie)}
(7~gld) 2
]
{1 --(-- 1)_n cos (78g±d)} [
x
{.rSgj,O~_(n,0~} ~ j
(3)
where gu and g± are the components of the field gradient parallel and perpendicular to the barriers. In HUP (I) the distance between the barriers is "~ 8 A [8]. For the experimental conditions used here 78g±d ~ 10 -4 and equation (3) reduces to In [A(2t)*/A(2t)] = -- 72g~83AD.
(4)
High resolution spectra provide evidence of anisotropic chemical shielding [9]. It is therefore reasonable to assume that crystallites are large enough to permit unbounded diffusion within the layer structure and that inter-crystallite diffusion may be ignored for the purposes of ~terpreting the NMR relaxation data. In a powder the crystallites are randomly oriented with respect to the field gradient g so that for each erystaUite gu = g sin 0 where 0 is the angle between g and the normal to the HUP (I) layers. The powder average for the quantity g~ is g2/3 which on substitution in equation (4) gives, ha [A(2t)*lA(2t)]
= -- {72K262&D
(5)
where D is now taken to be the self-diffusion coefficient along the layers.
Vol. 31, No. 12
HYDROGEN ION DIFFUSION IN HYDROGEN URANYL PHOSPHATE
The values of D measured by the pulsed field gradient technique are also shown in Fig. 1. D = 6 x 10 -11 m 2 s -1 corresponds to the lower limit of measurement for the apparatus in this material. These results confirm that the protons are in a state of rapid translational diffusion. In the absence of adequate structural information for HUP (I) Childs et al. [1 ] have evaluated ¢ at T = 300 K assuming a simple BPP model and obtained a value f o r D = 2 x 10 -11 m 2 s -1 which is in reasonable agreement with the pulsed field gradient values. Despite the approximations inherent in the BPP model whereby the effects of correlated motion in solids are neglected the level of agreement strongly suggests that diffusion is the mechanism controlling the nuclear relaxation behaviour. The results emphasise that the self-diffusion in HUP (I) can be investigated by NMR techniques and that single crystal studies should be capable of yielding much more detailed information on the mechanism and any anisotropic behaviour characteristic of the diffusion process.
997
Acknowledgements - The authors gratefully acknowledge the SRC for a fellowship for one (REG) of us. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
P.E. Childs, T.K. Halstead, A.T. Howe & M.G. Shilton, Mat. Res. Bull. 13,609 (1978). M.G. Shilton & A.T. Howe, Mat. Res. Bull. 12, 701 (1977). E.O. Stejskal & J.E. Tanner, J. Phys. Chem. 42, 288 (1965). R.E. Gordon, J.H. Strange & J.B.W. Webher, J. Phys. E11,1051 (1978). B.A. Huberman & J.B. Boyce, Solid State Commun. 25,759 (1978). J.B. Boyce & J.C. Mikkelson, Jr., Bull Am. Phys. Soc., Series 11 21,285 (1976). J.E. Tanner & E.O. Stejskal, J. Chem. Phys. 49, 1768 (1968). B. Morosin, Phys. Lett. 65A, 53 (1978). T.K. Halstead (private communication).
NMR relaxation time measurements and pulsed field gradient diffusion measurements have been made for I H in hydrogen uranyl phosphate (HUP). The results confirm that for T ~ 274 K HUP is a fast proton conductor exhibiting self-diffusion coefficients greater than I0 -11 m 2 s -I . 1. INTRODUCTION
movement between particles are unlikely to influence the measurements, wheareas such effects can strongly affect the conductivity measurements. NMR relaxation and diffusion will be affected by anisotropic motion which will only be observable in single crystal studies. The theory of nuclear relaxation due to the modu. lation of the nuclear dipolar interaction by self-diffusion is well established. The relevant expressions for T~ and /'2 have been quoted previously [1]. If the nuclear relaxation is dominated by self-diffusion then for a suitable model of self-diffusion in a crystal lattice the dipolar correlation time, To, Can be evaluated and may be identified with the mean residence time, r, for an atom on a normal lattice site. For a diffusion mechanism involving a jump distance ~ then for two dimensional diffusion D is given by
IN A RECENT nuclear magnetic resonance study [1 ] of hydrogen uranyl phosphate, H(UO2PO4)4H20 (I/UP), IH relaxation times were measured to investigate the nature of the self-diffusion of hydrogen in HUP which had been inferred from previous proton conductivity measurements [2]. HUP is a layered hydrate which exists in at least two phases ([, II) the transition temperature between the phases being 274 K [2]. The high temperature phase (I) is of particular interest because of the current need to find materials that are capable of sustaining fast proton transport at temperatures below about 600 K. The ~H relaxation time measurements [1] in HUP (I) are consistent with a transport process whereby the protons of the water molecules undergo two-dimensional self-diffusion. The lack of detailed knowledge about the self-diffusion mechanism makes it difficult to interpret the relaxation times in terms of an appropriate model where (X2) is the mean square jump distance and f i s the and thereby obtain a precise value for the self-diffusion relevant geometrical correlation factor. coefficient D. Childs etaI. [1] have calculated D for An alternative NMR approach under favourable HUP (I) using a simple random walk model. The comexperimental conditions is to use the pulsed field parison of these results with the diffusion data derived gradient technique [3] in which diffusion can be from conductivity measurements [2] must be viewed measured directly. The relevant theory for this techwith some caution since NMR and conductivity technique is to be found in the literature [3]. The basic niques measure different aspects of translational motion. 9 0 ° t 1 8 0 ° spin-echo sequence is modified by the Conductivity is a bulk property which measures charged addition of suitable magnetic field gradient pulses. For defect motion averaged over many jumps whereas the spins undergoing unrestricted diffusion it has been NMR relaxation times provide a measure of motion on a shown [3] that the spin echo attenuation is given by microscopic scale via a correlation time for atomic jumping. Furthermore, the different activation energies in [A(2t)*/A(2t)] = -- 7292D62(A -- ~8) (2) reported for HUP (I) by the two techniques suggest that where A(2t)* and A(2t) are the respective spin-echo translational seif-diffusion and charge transport may not amplitudes at time 2t in the presence and absence of the be determined by the same processes. Since N-MR relaxgradient pulses of amplitude g, duration 8 and separation ation measurements are governed by motion on a local A. scale, powder effects, such as grain boundaries and 995
HYDROGEN ION DIFFUSION IN HYDROGEN URANYL PHOSPHATE
996
104 345,
323 .
.
T(K) .
303 ,
266 ,
=
.
1 0 -I
;0 x
I"-..,...O ~
.~Z
IO
7 ~'~" .~..%,.
i1'1
U-
N d. . J u.I
I
I
3.0
I
I
I
_1000 (K-l) T
I
I
3.5
,
i.to-~
Fig. 1. Temperature dependence of the tH relaxation times obtained at 10 MHz in powder samples of HUP (I): o, Tx; e, 7"2. The lines denote the relaxation times obtained at 16MHz in [1]: - , Tt; . . . . ,7"2. The corresponding time scale is shown on the right. The tH selfdiffusion coefficients obtained by the pulsed field gradient technique are shown, o, and those derived from the NMR relaxation times [1], =. The scale for these points is shown on the left. The purpose of this paper is to report further relaxation time and pulsed field gradient diffusion measurements that have been carried out on HUP (I). 2. MATERIALS AND METHODS Powder samples of HUP prepared from the same batch used by Childs et el. [1 ] were used and sealed in silica tubes at S.T.P. TI and 7'2 were measured to an accuracy of ± 10% at coo = 2u x 107 red s -1 using standard pulse techniques in the temperature range 2 9 3 343 K. The temperature, T, was maintained constant to within 0.5 K by an automatic proportional regulating loop. The proton diffusion coefficient D has been measured using PFG apparatus previously described [4]. 3. RESULTS AND DISCUSSION The results of the relaxation time measurements are shown in Fig. 1. No measurements were made for T > 343 K to avoid any dehydration of the sample. The lines indicate the previous relaxation measurements at co o = 2*t x 1.6 x 1 0 7 r a d s -t [ 1 ] .
For nuclear relaxation dominated by serf-diffusion and assuming ¢0o¢c < 1 then it would be expected that TI = 7"2. The results of both sets of measurements indicate that Ta > / ' 2 with T t / T 2 --~ 1.5 which is believed
Vol. 3 l, No. 12
to be a consequence of the two-dimensional (2-D) nature of the diffusion mechanism. This type of behaviour has already been observed for 7Li relaxation in the onedimensional fast ion conductor Li2Ti307 [5, 6] and was attributed there to a highly correlated 1-D diffusion mechanism. At temperatures above 323 K the results are frequency independent consistent with the nuclear relaxation regime corresponding to ~Oorc < 1. At temperatures below 323 K however there is an increasing dis. crepancy between the results at each frequency. This may be due to the approaching presence of the TI minimum for the higher frequency measurements. Such a frequency dependence would be in contrast to results reported for a l-D conductor [5, 6]. The activation energy for the Tt and T2 data obtained at l0 MHz corresponds to 24.6 ± 1.9 kJ mole -1 which is comparable to the 20 kJ mole -~ measured at 16 MHz. Equation (2) can only be strictly applied for systems where the diffusion is isotropic and unrestricted. In HUP (I) the diffusion is believed to be laminar in nature and equation (2) must be modified accordingly. The relevant theory has boon derived by Stejskal and Tanner [7]. For unrestricted diffusion between two infinite, parallel barriers separated b y a distance d then, r
In [A(2t)*/A(2t)] = -- 7 2 g ~ 2&D [2{1 L
-F 4(7~g±d) 2
exp
\
d
CO8
('y*gie)}
(7~gld) 2
]
{1 --(-- 1)_n cos (78g±d)} [
x
{.rSgj,O~_(n,0~} ~ j
(3)
where gu and g± are the components of the field gradient parallel and perpendicular to the barriers. In HUP (I) the distance between the barriers is "~ 8 A [8]. For the experimental conditions used here 78g±d ~ 10 -4 and equation (3) reduces to In [A(2t)*/A(2t)] = -- 72g~83AD.
(4)
High resolution spectra provide evidence of anisotropic chemical shielding [9]. It is therefore reasonable to assume that crystallites are large enough to permit unbounded diffusion within the layer structure and that inter-crystallite diffusion may be ignored for the purposes of ~terpreting the NMR relaxation data. In a powder the crystallites are randomly oriented with respect to the field gradient g so that for each erystaUite gu = g sin 0 where 0 is the angle between g and the normal to the HUP (I) layers. The powder average for the quantity g~ is g2/3 which on substitution in equation (4) gives, ha [A(2t)*lA(2t)]
= -- {72K262&D
(5)
where D is now taken to be the self-diffusion coefficient along the layers.
Vol. 31, No. 12
HYDROGEN ION DIFFUSION IN HYDROGEN URANYL PHOSPHATE
The values of D measured by the pulsed field gradient technique are also shown in Fig. 1. D = 6 x 10 -11 m 2 s -1 corresponds to the lower limit of measurement for the apparatus in this material. These results confirm that the protons are in a state of rapid translational diffusion. In the absence of adequate structural information for HUP (I) Childs et al. [1 ] have evaluated ¢ at T = 300 K assuming a simple BPP model and obtained a value f o r D = 2 x 10 -11 m 2 s -1 which is in reasonable agreement with the pulsed field gradient values. Despite the approximations inherent in the BPP model whereby the effects of correlated motion in solids are neglected the level of agreement strongly suggests that diffusion is the mechanism controlling the nuclear relaxation behaviour. The results emphasise that the self-diffusion in HUP (I) can be investigated by NMR techniques and that single crystal studies should be capable of yielding much more detailed information on the mechanism and any anisotropic behaviour characteristic of the diffusion process.
997
Acknowledgements - The authors gratefully acknowledge the SRC for a fellowship for one (REG) of us. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
P.E. Childs, T.K. Halstead, A.T. Howe & M.G. Shilton, Mat. Res. Bull. 13,609 (1978). M.G. Shilton & A.T. Howe, Mat. Res. Bull. 12, 701 (1977). E.O. Stejskal & J.E. Tanner, J. Phys. Chem. 42, 288 (1965). R.E. Gordon, J.H. Strange & J.B.W. Webher, J. Phys. E11,1051 (1978). B.A. Huberman & J.B. Boyce, Solid State Commun. 25,759 (1978). J.B. Boyce & J.C. Mikkelson, Jr., Bull Am. Phys. Soc., Series 11 21,285 (1976). J.E. Tanner & E.O. Stejskal, J. Chem. Phys. 49, 1768 (1968). B. Morosin, Phys. Lett. 65A, 53 (1978). T.K. Halstead (private communication).