952
D. E. WOESSNERAND B.S. SNOWDEN, JR.
Temperature-Dependence Studies of Proton and Deuteron Spin-Lattice Relaxation in Ammonium Chloride
by D. E. Woessner and B. S. Snowden, Jr. Mob2 Oil Corpwation, Field Research Laboratory, Dallas, Terns 763.81 (Recsived September $0,1066)
The X transition in ammonium chloride at 242.8"K has been detected by proton spinlattice relaxation temperature-dependence measurements. The temperature trend of the nuclear correlation time ( r c ) is in qualitative agreement with the volume temperature dependence. However, considering the effect of volume change on electrostatic forces, it is evident that a simple change in electrostatic potential cannot account for the quantitative temperature dependence of re. Better quantitative agreement is obtained when the change of the temperature dependence of r c is compared with that of the shear elastic constant, c44. There appears to be an indirect relation between the temperature dependence of roand the degree of order in the crystal lattice in the region of the X transition.
Introduction Detection of the X thermal transition in the ammonia halides by nuclear magnetic resonance (nmr) spinlattice relaxation has been previously as being unsuccessful. I n the present work the transition was clearly observed for solid NH4C1 at 2423°K. This has been reported4 to be an order-disorder transition. The NH4+ions in the CsC1-type lattice are oriented in the unit cell so that the hydrogen atoms point toward the nearest neighbor chloride ion. This gives two possible tetrahedron orientations. If the orientations of the ammonium tetrahedrons in the unit cells are identical, the lattice is in its ordered state. When the orientations of the ammonium tetrahedrons are randomly distributed among the two possible orientations, the lattice is in the completely disordered state. Experimental Results All measurements were made with the standard nuclear resonance pulse apparatus previously described.6 The only significant modification to this experimental apparatus is the use of a fast response probe.6 The TIvalues were obtained in the temperature range from 140 to 373°K by the nmr pulse technique utilizing repeated 180-90" pulse sequences. The deuteron TIvalues were measured at a resonance frequency of 9.5 MHz and those for protons a t resonance The Journal of Physical Chembtry
frequencies of 9.5 and 25 MHz. The NDICl was prepared by successive exchanges of NHICl with DzO. The samples were dried overnight by vacuum pumping and then sealed in Pyrex vials. The TI temperature dependences are shown in Figures 1 and 2. Note that in each instance there is a TIshift of a factor of approximately 2.0 at the X-point transition (249.4'K for ND4C14 and 242.8% for NH4C17). The TIminima are presented in Table I. ~
Table I: TIMinima For ND&l and NH&l
Nucleus
Deuteron
Proton Proton
Resonance frequency, MHa
Min TI value, msec
Temp of TImin, 'K
Calcd TI min values, msec
9.5 9.5 25.0
0.455 1.86 5.05
192 191
0.435 1.77 4.67
200
(1) E. M. Purcell, Phyeica, 17, 282 (1951). (2) A. H,Cooke and L. E. Drain, Proc. Phya. Soc. (London), Ads, 894 (1952). (3) J. E. Anderson and W. P. Slichter, J . Chem. Phys., 44, 1797 (1966). (4) H. A. Levy and 9. W. Peterson, J . Am. Chem. SOC.,7 5 , 1536 (1953). (5) J. C. Buchta, H. 8. Gutowsky, and D. E. Woessner, Rev. SA. Instr., 29, 55 (1958). (6) R. A. McKay and D. E. Woessner, J . Sci. Inatr., 43,838 (1966). (7) F. Simon, Ann. Physik, 68, 241 (1922).
TEMPERATURE DEPENDENCE OF PROTON SPIN-LAITICERELAXATION
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Figure 1. The temperature dependence of the proton TIfor NH&l at 9.5 and 25 MHz.
The Tl values are analyzed by use of the widely known expressions*for protons and deuterons.
for the protons and
for the deuterons, where up2is the second moment of the proton resonance expressed in angular units, (e2qQ)/his the quadrupole coupling constant, q is the asymmetry parameter of the quadrupole interaction, wo is the angular resonance frequency, and rcis the correlation time of the ammonium tetrahedron reorientation. Each 2'1 passes through a minimum value when wort = 0.6158. Using the 78°K value,S up2= 3.54 X 10'0 radians2/sec2,the computed proton minimum Tl value is 4.67 msec at 25 MHz and 1.77 msec at 9.5 MHz. For the deuteron TI, the 119°K values'O (e2q&)/h =
IC
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954
D. E. WOESSNER AND B. S.SNOWDEN, JR.
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roo exp(E,/RT)
(4)
Application of this equation gives an Ea which increases from 4.7 above the X point to 6.9 kcal/mole in the transition region13 below the X point. However, below 195"K, the E, value is 4.7 kcal/mole. The 7,' values are 6 x and 1.7 X 10e16 sec above and below the X transition, respectively. These results for ammonium chloride are consistent with those obtained from similar measurements on several other ammonium ~ a 1 t s . l ~An increase of Ea with a decrease in temperature through the X transition The Journal of Physical Chemistry
1
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'
4.0 1000 T
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-
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Figure 4. The proton T I values near the A point measured a t 25 MHz with the use of a probe designed to minimize temperature variations over the sample.
those of the protons. Above the X point and in the transition region, this ratio is approximately 1.22 and below the transition temperature this ratio is 1.36. Below the transition region there is a small discrepancy between the proton rCvalues calculated a t 9.5 and 25.0 MHz, which causes an uncertainty to the absolute value of this ratio, However, even in this region, the r c values for the deuterons are consistently higher than those for the protons. This is expected since the moment of inertia of the ND4+ion is higher than that of the NH4+ion.11*12 For purely descriptive purposes, the temperature dependence of re may be expressed in terms of the following Arrhenius equation rc =
1 3.5
has been observed for (NH4)$04, (NH&BeF4, and NH4HS04. The ammonium chloride rco values are close to those found for (NH&S04.
Discussion Theoretically, the transition a t the X point should result in a discontinuity of the temperature dependence of T ~ . However, owing to a small temperature gradient in the sample, the discontinuity may be less apparent. The data in Figures 1 and 2 show this effect. Figure 4 shows TI values- measured in the temperature range near the X point a t 25 MHa. These values were obtained with a special probe arrangement'5 which was designed to minimize any possible temperature gradient. The transition is markedly sharper than shown in Figure 1. A sufficiently large temperature gradient could obscure detection of the transition by spin-lattice relaxation measurements. ~-
(11) E. L. Wagner and D. F. Hornig, J. Chem. Phys., 18, 296 (1950). (12) J. S. Waugh and E. I. Fedin, Sovkt Phys. Solid State, 4, 1633 (1963). (13) The temperature range from approximately 195OK to the x
point will be designated as the transition region. (14) S. R . Miller, R. Blinc, M. Brennan, and J. S. Waugh, Phys. Rev., 126, 528 (1962). (15) D. E. Woessner and B. S. Snowden, Jr., in press.
TEMPERATURE DEPENDENCE OF PROTON SPIN-LATTICE RELAXATION
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955
a t frequencies of 390 and 280 cm-l for NH4C1 and NDIC1, respectively. Occasionally, a torsional oscillation causes a complete reorientation of the ammonium ion to another equivalent position.9 Usually12 it is assumed that there is a certain probability that a given oscillation results in such a reorientation. This probability is given by the equation ro =
-e
VdRT
(5)
Wt
where wt is the torsional oscillation frequency in units of radians per second and V Ois the classical barrier to the reorientation. For this equation, the ratio of the deuteron to proton correlation times is approximately the square root of 2, because the moment of inertia of the ND4+ ion is twice that of the NH4+ ion. This relationship is obeyed by the torsional frequencies obtained from infrared spectroscopy. l1 It is
200
Figure 5. The temperature dependence of the relative linear dimension [l L(T)/L(296)]and of the shear elastic constant, cp4, for a single crystal of ammonium chloride. The data are taken from Table I of ref 18.
-
The X transition manifests itself through other crystal properties. This is illustrated in Figure 5. The crystal volume exhibits temperature trends which are in the same direction as those for r, (see Figure 3). It is possible that these quantities are related through the electrostatic interactions in the crystal lattice. However, a specific relationship which connects the temperature, volume, and correlation time by the electrostatic interactions is not known. Also, there may be other lattice parameters which are more closely related to 7-0. Making the assumption that the temperature dependence follows an Arrhenius equation, it is possible to calculate the effect of the change in volume on electrostatic forces of the crystal lattice. Assuming that the lattice expands uniformly, the results of an electrostatic calculationg indicate that the potential energy barrier to rotation of the ammonium ion is inversely proportional t o the fifth power of the linear dimension of the unit cell. By use of thermal expansion data,le one finds that the potential barrier should be only 3.0% greater a t 224°K than it is at 273.2"K. There is an increase in E. of 47% below the X point as compared to the value above the X point. This indicates that the simple electrostatic picture cannot explain the magnitude of the changes of the temperature dependence of 7,.
The ammonium ions undergo torsional oscillations"
to proton correlation times obtained from the 9.5MHz data. However, the values of correlation times deduced from relaxation times are dependent on the details of the reorientation process. These details are not the same for NH4Cl and KD4C1. The proton relaxation depends on reorientation of the protonproton internuclear vector, whereas the deuteron relaxation depends on the nitrogen-deuteron internuclear vector. For this reason we did not attempt a more detailed analysis of the ratio of the correlation times. Below the transition region the temperature dependence of 7, for NH4Cl obeys the simple relation: rc = 4.4 X 10-14e4.7X108/RT. Since the reciprocal of the torsional frequency observed" for the molecule is 1.36 X 10-14 (radian/sec)-' the 7, values obey eq 5 below the transition region. I n the transition region re decreases with increasing temperature faster than this equation predicts. This phenomenon can be attributed t o a decrease in the preexponential factor in eq 4 and a simultaneous increase in E,. However, previous electrostatic arguments suggest that the change in the classical potential energy barrier (Le., V,) is too small to account for the change in r c. Therefore, the change in r, temperature dependence in the transition region must be greatly influenced by a temperature-dependent preexponential factor in eq 4. A similar deviation from electrostatic theory in the transition region is reported for the shear elastic modulus, ~ 4 4 . ~ The ~ 8 ~relaxation ~ times for long-range order~
~~
~
(16) A. W. Lawson, Phys. Rev., 5 7 , 417 (1940). (17) C. W. Garland and C. F. Yarnell, J. Chem. Phys., 44, 3678 (1966). (18) C. W. Garland and R. Renard, ibid., 44, 1130 (1966).
Volume '7'1, Number 4 March 1967
956
ing near the X point have been deduced from ultrasonic attenuation m e a s u r e m e n t ~ and ~ ~ found to be the same order of magnitude as the nuclear correlation times. This indicates a relationship between the ease of ammonium ion reorientation and the elastic properties of the crystals. The temperature dependencels of the shear elastic modulus, cd4 (see Figure 5 ) , shows a close correspondence between c44 and the temperature dependence of rc. This may reflect the variation of the volume with temperature because the value of ck4 varies almost linearly with volume. Elastic constant data far from the transition region can be interpreted in terms of a crystal which is completely ordered or disordered. The temperature dependences of cP4 in the completely ordered and completely disordered temperature regions are essentially the same. It has been suggestedlg that these comparable temperature dependences should exist only if the coupling between the ammonium tetrahedron and the lattice is weak. The lattice energy of the ammonium ions depends only slightly on the anisotropic coupling between neighboring ammonium ions. This coupling is short range and mainly determined by octopolcoctopole interactions.20 As the temperature decreases through the X point, the c44 data exhibit an increased variation with temperature. This behavior is in qualitative agreement with the theory which predicts the effects of ordering for a compressible Ising model lattice. The change of c44 in passing through the X point is about 7%. This is much greater than the change in electrostatic potential barrier and appears to be consistent with twofold change of rc. If eq 4 applies a t the X point and rC0is constant, the change in E, required to this change in rc is 0.335 kcal/mole. This is 7.1% of the E, = 4.7 kcal/mole which describes ro
The Journal of Physical Chemistry
D. E. WOESSNER AND B. S. SNOWDEN, JR.
above the X point. This latter value of Ea agrees with the electrostatic energy barrier.9
Conclusions The above results together with several other factors suggest that in the transition region the temperature dependence of rc is strongly influenced by the degree of order. First, the Ea values above and below the transition region are consistent with the electrostatic energy barrier. This suggests weak coupling between the ammonium ions in these temperature regions. The sizable difference between these E, values and the E, value in the transition region indicates an effect of the changing degree of order. Second, there is the twofold change of rc at the X point. We have also shown that the relative changes of the temperature dependence of rc do not follow a simple electrostatic approach. The connection between rc and the degree of order is apparently indirect in the transition region. It is possible that the elastic constants are related to the T~ values. Possibly similar studies on ammonium bromide will provide insight into this relationship. At the X point the ammonium bromide changes lattice typez1and the volume change is opposite22 to that in ammonium chloride. This study is now in progress. Acknowledgments. The authors wish to thank J. E. Fagan and P. H. Haagen for performing the spinrelaxation measurements and A. C. Hall, W. L. Medlin, and J. R. Zimmerman for their many helpful comments in the preparation of this paper. We also wish to thank the Mobil Oil Gorp. for permission to publish this work. (19) C. W.Garland and R. Renard, J . Chew. Phys., 44, 1120 (1966). (20) C. W.Garland and J. S. Jones, ibid., 41, 1165 (1964). (21) J. A. A. Ketelaar, Nature, 134, 250 (1934). (22) F. Simon and R. Bergmann, Z . Physik. Chem., B8, 255 (1930).
