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Measurement of kinetics of solid-solid phase transformation by pulse NMR
JOURNAL
OF MAGNETIC
Measurement
33, 2 11-2 14 (1979)
RESONANCE
of Kinetics of Solid-Solid Pulse NMR
Phase Transformation
by
Recently, Ross and Strange (1) have used the pulse NMR technique to determine the phase diagrams of plastic crystals. In that study, the abrupt changes in Ti or TZ at the phase transition provide the means of detecting the precise phase-transition pressure. In this communication we report an NMR relaxation study of the kinetics of the plastic phase transition in adamantane. The high-pressure phase transition of adamantane has been shown (2) to be structurally analogous to the lowtemperature transition at one bar. The use of pressure as an experimental variable allows us to rapidly bring the sample to a nonequilibrium state to drive the phase transition towards completion. At the phase-transition pressure, the Tl of adamantane decreases abruptly (3) by a factor of about 40 in passing from the plastic (CX) phase to the brittle (0) phase. This large discontinuity allows us to monitor the NMR signal during the phase transition and separate the contributions from each phase as a function of time, since one may write Mobs
= UK
[II
+X&&s,
where Mi are the magnetizations, and xi are the mole fractions of each phase contributing to the observed magnetization at any time. For the inversion-recovery pulse sequence used, M(r) = M,,(l-2 exp(-r/Ti)), El where 7 is the time between the 180” inversion pulse and the 90” sampling pulse. the equilibrium magnetization MO is the same for both the pure a and the pure p phases. Combining the above equations leads to the relationship for x,(t) xc2(t) =
R (6 T) - exp(-r/ TIP) exp(-r/ T,,) - exp(-T/ T,,)’
where x, + x8 = 1, and the quantity R = (MO- M(7))/2Mo depends on T and on the time t since the phase transition was initiated. In this experiment, each x, value is the measured average of one MO and three M(T) values. For comparable sensitivity during the phase transition, the T values chosen are Tl
=
Tla
ln(%
72 =
%TI,
+
73
Tl,d
h(2),
141
= Tlo ln(2).
For adamantane, this four-pulse sequence takes from 2 to 4 sec. An equilibration period of ~TI, is allowed between each magnetization measurement to avoid saturation of the more slowly relaxing plastic phase signal. Even during the fastest 211
0022-2364/79/010211-04$02.00/0 Copyright 0 1979 by Academic Press. Inc. All rights of reproduction in any form reserved. Printed in Great Britain
COMMUNICATIONS
212
0.05
0
2
3
(kbar) FIG. 1. Pressure dependence of r1 for adamantane dispersion in D20 at 0” for compression (0) and decompression (0) measurements. Dashed lines represent the !inear extrapolation of r, into the phase-transition region. P
transitions, the duration of this sequence represents a phase change of less than 5 mole %. The standard deviation of the three averaged x, values is typically *3 mole% during the fast, initial portion of the phase transition and drops to *l mole% as the rate of change of x, decreases. The linear pressure dependence of Tl in the pure (Y and p phases (3) is measured for each sample and extrapolated into the phase-transition region as illustrated in Fig. 1 to provide the values of Tl, and TIP. This measurement also allows the determination of the equilibrium transition pressures POfor the forward (a + p) and the reverse transitions. This is important since small sample- and cell-dependent variations in PO have been noted (4). The sample cell consists of a polychlorotrifluoroethylene (Kel-F) cylinder with a Kel-F piston in each end to transmit the pressure to the sample. Each piston has two rubber O-rings to effect a seal against the pressurizing fluid, carbon disulfide. Adamantane was obtained from Eastman Kodak Co. (Rochester, New York) and from Aldrich Chemical Co., Inc. (Milwaukee, Wisconsin). All samples were purified by vacuum trap-to-trap sublimation; in addition, some samples were first recrystallized from a filtered solution of spectroscopic grade carbon disulfide. The powdered adamantane was loaded into the cell in argon atmosphere dry box. Details of the
213
COMMUNICATIONS
pulse spectrometer and pressure generating system are available in the literature (5,6). For the kinetic measurements, to ensure that each transition starts from a pure parent phase, the forward transitions are approached from an initial pressure of 1 bar and the reverse transitions are approached from 5 kbar. From this initial point, the pressure is brought stepwise over 30 to 90 min to an equilibration pressure Peg, which is typically within 50 bar of the equilibrium transition pressure PO. After spending 15 to 30 min at PCs,the pressure is rapidly (less than 10 set) changed to the nonequilibrium, driving pressure, PO+ AP, at which the kinetic measurement is to be made. This pressure is carefully maintained within 5 bar over the duration of the measurement. The difference between Peg and Po+AP in these experiments ranges from 75 to 400 bar. This rapid compression or decompression causes a temperature change in the pressurizing fluid. However, the largest observed fluctuation was 0.6”C for a 400-bar pressure drop and in all cases, the temperature of the fluid returns to within I
1.0
0.0
0
I
I
I
I
I
I
I
I
I
I
I
2
4
6
8
IO
12
I
I
I
IO
I2
14
t(min) I
I
I
0.8
0.6 2 0.4
i 2
4
6
8
I‘
t (min)
FIG. 2. Growth curves for the mole fraction of the plastic phase of adamantane dispersion in D20 at 0” at various pressures. Pressures shown are in bar.
214
COMMUNICATIONS
O.l”C of the nominal temperature within 1 min following the pressure change. Hence, it is reasonable to neglect the thermal effect in the observed kinetics. The periodic measurement of x, begins immediately before the pressure is changed. The time dependence of x, at 0°C for a number of driving pressures PO+ AP is shown in Fig. 2. Each curve is reproducible within 5 mole% over the entire time range after the pressure has stabilized (less than 1 min). In this example, the equilibrium phase transition occurs at 3475 bar for the forward (a-+@) transition and at 3400 bar for the reverse (P+(Y) transition. The sample is surrounded within the cell by D20 as an internal pressure medium to ensure hydrostatic pressure and to ensure that the phase transition goes to completion (4). It is clear that, as AP increases, the transition proceeds at a much faster rate. In an analogous study, Mnyukh et al. (7) found that the rate of growth of the daughter phase in other systems increases as AT = To- T increases, where T is the ambient temperature at which a phase change is being observed, and To and AT are analogous to POand AP. Furthermore, the qualitative features of the curves in Fig. 2 are predicted by the kinetic order-disorder phase-transition theory of Honig (8). In particular, the transition rate undergoes a sharp decrease as the phase change approaches completion and, in addition, the nature of the transformation (growth) curves changes from exponential to sigmoidal as AP decreases for transitions in both directions. We have demonstrated the applicability of the pulse NMR technique to the measurement of the kinetics of phase transition in plastic crystals. The present method requires that the T1 exhibits a large discontinuity at the phase transition, and that the rate of phase change be slow compared to the longer T1 of the two phases involved. A detailed analysis of these and other results will be published elsewhere. ACKNOWLEDGMENI This work was supported by the Department of Energy under Contract DOE-1198.. REFERENCES 1. S. M. Ross AND J. H. STRANGE, Mol. Crysr. Liq. Crysr. 36,321 (1976). 2. T. ITO, Acra Crystallogr. B29, 364 (1973). 3. N. LIU AND J. JONAS, Chem. Phys. Lett. 14, 555 (1972). 4. M. FURY, Ph.D. Thesis, University of Illinois (1978). -5. J. JONAS, Rev. Sci. Znstrum. 43,643 (1972). 6. D. M. CANTOR AND J. JONAS, 1. Mugn. Reson. 28, 157 (1977). 7. Yu.V.MNYUKH,N. A.PANFILOVNA,N.N.PETROPAVLOV, AND N.S.UCHVATOVA,J. phys. Chem. Solids 36, 127 (1975). 8. J. M. HONIG, in “Kinetics of High Temperature Processes” (W. D. Kingery, Ed.), Chap. 25, Technology Press/Wiley, New York, 1959. M. FURY S. G. HUANG J. JONAS Department of Chemistry and Materials Research Laboratory University of Illinois Urbana, Illinois 61801 Received
August
7, 1978
OF MAGNETIC
Measurement
33, 2 11-2 14 (1979)
RESONANCE
of Kinetics of Solid-Solid Pulse NMR
Phase Transformation
by
Recently, Ross and Strange (1) have used the pulse NMR technique to determine the phase diagrams of plastic crystals. In that study, the abrupt changes in Ti or TZ at the phase transition provide the means of detecting the precise phase-transition pressure. In this communication we report an NMR relaxation study of the kinetics of the plastic phase transition in adamantane. The high-pressure phase transition of adamantane has been shown (2) to be structurally analogous to the lowtemperature transition at one bar. The use of pressure as an experimental variable allows us to rapidly bring the sample to a nonequilibrium state to drive the phase transition towards completion. At the phase-transition pressure, the Tl of adamantane decreases abruptly (3) by a factor of about 40 in passing from the plastic (CX) phase to the brittle (0) phase. This large discontinuity allows us to monitor the NMR signal during the phase transition and separate the contributions from each phase as a function of time, since one may write Mobs
= UK
[II
+X&&s,
where Mi are the magnetizations, and xi are the mole fractions of each phase contributing to the observed magnetization at any time. For the inversion-recovery pulse sequence used, M(r) = M,,(l-2 exp(-r/Ti)), El where 7 is the time between the 180” inversion pulse and the 90” sampling pulse. the equilibrium magnetization MO is the same for both the pure a and the pure p phases. Combining the above equations leads to the relationship for x,(t) xc2(t) =
R (6 T) - exp(-r/ TIP) exp(-r/ T,,) - exp(-T/ T,,)’
where x, + x8 = 1, and the quantity R = (MO- M(7))/2Mo depends on T and on the time t since the phase transition was initiated. In this experiment, each x, value is the measured average of one MO and three M(T) values. For comparable sensitivity during the phase transition, the T values chosen are Tl
=
Tla
ln(%
72 =
%TI,
+
73
Tl,d
h(2),
141
= Tlo ln(2).
For adamantane, this four-pulse sequence takes from 2 to 4 sec. An equilibration period of ~TI, is allowed between each magnetization measurement to avoid saturation of the more slowly relaxing plastic phase signal. Even during the fastest 211
0022-2364/79/010211-04$02.00/0 Copyright 0 1979 by Academic Press. Inc. All rights of reproduction in any form reserved. Printed in Great Britain
COMMUNICATIONS
212
0.05
0
2
3
(kbar) FIG. 1. Pressure dependence of r1 for adamantane dispersion in D20 at 0” for compression (0) and decompression (0) measurements. Dashed lines represent the !inear extrapolation of r, into the phase-transition region. P
transitions, the duration of this sequence represents a phase change of less than 5 mole %. The standard deviation of the three averaged x, values is typically *3 mole% during the fast, initial portion of the phase transition and drops to *l mole% as the rate of change of x, decreases. The linear pressure dependence of Tl in the pure (Y and p phases (3) is measured for each sample and extrapolated into the phase-transition region as illustrated in Fig. 1 to provide the values of Tl, and TIP. This measurement also allows the determination of the equilibrium transition pressures POfor the forward (a + p) and the reverse transitions. This is important since small sample- and cell-dependent variations in PO have been noted (4). The sample cell consists of a polychlorotrifluoroethylene (Kel-F) cylinder with a Kel-F piston in each end to transmit the pressure to the sample. Each piston has two rubber O-rings to effect a seal against the pressurizing fluid, carbon disulfide. Adamantane was obtained from Eastman Kodak Co. (Rochester, New York) and from Aldrich Chemical Co., Inc. (Milwaukee, Wisconsin). All samples were purified by vacuum trap-to-trap sublimation; in addition, some samples were first recrystallized from a filtered solution of spectroscopic grade carbon disulfide. The powdered adamantane was loaded into the cell in argon atmosphere dry box. Details of the
213
COMMUNICATIONS
pulse spectrometer and pressure generating system are available in the literature (5,6). For the kinetic measurements, to ensure that each transition starts from a pure parent phase, the forward transitions are approached from an initial pressure of 1 bar and the reverse transitions are approached from 5 kbar. From this initial point, the pressure is brought stepwise over 30 to 90 min to an equilibration pressure Peg, which is typically within 50 bar of the equilibrium transition pressure PO. After spending 15 to 30 min at PCs,the pressure is rapidly (less than 10 set) changed to the nonequilibrium, driving pressure, PO+ AP, at which the kinetic measurement is to be made. This pressure is carefully maintained within 5 bar over the duration of the measurement. The difference between Peg and Po+AP in these experiments ranges from 75 to 400 bar. This rapid compression or decompression causes a temperature change in the pressurizing fluid. However, the largest observed fluctuation was 0.6”C for a 400-bar pressure drop and in all cases, the temperature of the fluid returns to within I
1.0
0.0
0
I
I
I
I
I
I
I
I
I
I
I
2
4
6
8
IO
12
I
I
I
IO
I2
14
t(min) I
I
I
0.8
0.6 2 0.4
i 2
4
6
8
I‘
t (min)
FIG. 2. Growth curves for the mole fraction of the plastic phase of adamantane dispersion in D20 at 0” at various pressures. Pressures shown are in bar.
214
COMMUNICATIONS
O.l”C of the nominal temperature within 1 min following the pressure change. Hence, it is reasonable to neglect the thermal effect in the observed kinetics. The periodic measurement of x, begins immediately before the pressure is changed. The time dependence of x, at 0°C for a number of driving pressures PO+ AP is shown in Fig. 2. Each curve is reproducible within 5 mole% over the entire time range after the pressure has stabilized (less than 1 min). In this example, the equilibrium phase transition occurs at 3475 bar for the forward (a-+@) transition and at 3400 bar for the reverse (P+(Y) transition. The sample is surrounded within the cell by D20 as an internal pressure medium to ensure hydrostatic pressure and to ensure that the phase transition goes to completion (4). It is clear that, as AP increases, the transition proceeds at a much faster rate. In an analogous study, Mnyukh et al. (7) found that the rate of growth of the daughter phase in other systems increases as AT = To- T increases, where T is the ambient temperature at which a phase change is being observed, and To and AT are analogous to POand AP. Furthermore, the qualitative features of the curves in Fig. 2 are predicted by the kinetic order-disorder phase-transition theory of Honig (8). In particular, the transition rate undergoes a sharp decrease as the phase change approaches completion and, in addition, the nature of the transformation (growth) curves changes from exponential to sigmoidal as AP decreases for transitions in both directions. We have demonstrated the applicability of the pulse NMR technique to the measurement of the kinetics of phase transition in plastic crystals. The present method requires that the T1 exhibits a large discontinuity at the phase transition, and that the rate of phase change be slow compared to the longer T1 of the two phases involved. A detailed analysis of these and other results will be published elsewhere. ACKNOWLEDGMENI This work was supported by the Department of Energy under Contract DOE-1198.. REFERENCES 1. S. M. Ross AND J. H. STRANGE, Mol. Crysr. Liq. Crysr. 36,321 (1976). 2. T. ITO, Acra Crystallogr. B29, 364 (1973). 3. N. LIU AND J. JONAS, Chem. Phys. Lett. 14, 555 (1972). 4. M. FURY, Ph.D. Thesis, University of Illinois (1978). -5. J. JONAS, Rev. Sci. Znstrum. 43,643 (1972). 6. D. M. CANTOR AND J. JONAS, 1. Mugn. Reson. 28, 157 (1977). 7. Yu.V.MNYUKH,N. A.PANFILOVNA,N.N.PETROPAVLOV, AND N.S.UCHVATOVA,J. phys. Chem. Solids 36, 127 (1975). 8. J. M. HONIG, in “Kinetics of High Temperature Processes” (W. D. Kingery, Ed.), Chap. 25, Technology Press/Wiley, New York, 1959. M. FURY S. G. HUANG J. JONAS Department of Chemistry and Materials Research Laboratory University of Illinois Urbana, Illinois 61801 Received
August
7, 1978