The Journal of Physical Chemistry, Vol. 83, No. 76, 1979
14NNQR of Urea in a Cu(II) Salt
NaP
*l2O3
Figure 3. Crystallization field of the system Na20/SiO2/Al,O3/H2O, showing the regions where types A, X, Y, and P, and hydroxysodalite HS crystallize. The line indicates mother gels of composition Si/AI = 1.0,the points correspond to samples selected from Table I. The crystallization field was taken from ref 12.
gives NMR-two-phase behavior below and single-phase behavior above the same temperature of about 300 K, there is probably Al(OH), or a similar compound in the a cages of type A zeolite. From P B it follows that this amounts to 1A1 in every a cage of Na-A(1) and respectively 0.5 in Na-A(4). Comparing results for the various samples, we found that there is a clear influence of the concentration of NaOH during crystallization upon the amount of OH groups, probably A1(OH)3, in the a cages. This dependence is nearly linear. The amount inside the /3 cages, however, does not vary, within the limits of experimental error. Moreover, the fast exchange in Na-A (1)indicates that the integrity of the cubooctahedra is not perfect if grown in high OH- concentrations. Both are not seen in X-ray
2151
powder patterns and weakly in sorption capacity. An inspection of Table I and Figure 3 shows that there is no preparation method, producing an Na-A zeolite, that contains aluminum in the zeolite lattice only, since the part of the crystallization field that can be expected to represent the samples poorest in aluminum is well covered by our 31 Na-A preparations investigated. The results cannot be explained by admixture of other types of zeolites, since most of the samples were pure Na-A. The influence of trace amounts of zeolite P was below the limits of detection. Even the addition of much greater amounts of zeolite P did not measurably change the NMR signal. Consequently our results imply that every zeolite A synthesized by the methods known today is impure in a crystallographic sense and contains varying amounts of occluded aluminum compounds. These cannot be specified by our study. This seems to be a specific property of zeolite A, since the same type of alumosilicate framework with a higher Si/A1 ratio, i.e. Na-a, does not show the pecularities presented above.13 References and Notes (1) J. S. Murday, R. L. Patterson, H. A. Resing, J. K. Thompson, and N. H. Turner, J. Pbys. Cbem., 79,2674 (1975). (2) H. Pfeifer, Surface Sci., 52, 434 (1975). (3) W. D. Basler, H. Lechert, and H. Kacirek, Ber. Bunsenges. Phys. Cbem., 80,451 (1976). (4) W. D. Basler, J. Phys. Chem., 81,2102 (1977). (5) H. Pfeifer, A. Gutsze, and S.P. Zhdanov, J. Coiioidhterface Sci., in press. (6) W. D. Basler, ACS Symp. Ser., No. 34 (1976). (7) J. R. Zimmerman, W. E. Britten, J . Phys. Cbem., 81, 1238 (1957). (8) D. E. Woessner, and J. R. Zimmerman, J. Pbys. Cbem., 67,1590
(1963). (9) Loewenstein, Am. Mineral., 39,92 (1954). (IO)J. F. Charnel J . Cryst. Growth, 8, 291 (1971). (1 1) W. D. Basler and W. Maiwald, manuscript in preparation. (12)D. W. Breck, "Zeolite Molecular Sieves", Wiley, New York, 1974. (13) W. D. Basler and W. Maiwald, to be presented at The Second International Symposium on Magnetic Resonance in Colloid and Interface Science at Menton, France, 1979.
Nitrogen-14 Nuclear Quadrupole Resonance in Antiferromagnetic CU(HCOO)~*~(NH~)~CO.~H~O Tetsuo Asaji, Ryuichl Ikeda, and Daiyu Nakamura" Depattment of Chemistry, Nagoya University, Chikusa, Nagoya 464, Japan (Received Mar& 7, 1979)
The temperature dependence of I4N NQR frequencies was determined for CU(HCOO)~.~(NH~)~CO.~H~O in the temperature range 2-90 K. Two sets of V I and vII lines of 14NNQR frequencies were detected at the various temperatures studied, indicating that there exist two different kinds of nitrogen sites in the crystal in agreement with the crystal structure determined at room temperature. An anomalous frequency shift attributable to Zeeman interaction was observed for all the lines detected in the antiferromagneticphase below 16 K. The spin structure of the ordered state and the internal field at the two different nitrogen sites were deduced from the shift of the resonance frequencies.
Introduction ordered state have been extensively i n ~ e s t i g a t e d . ~ - ~ Copper(I1) formate tetrahydrate, C U ( H C O O ) ~ . ~ H ~ O , Recently, Kiriyama and Kitahama8 carried out an X-ray forms crystals having a planar network of copper(I1) crystal analysis on copper(I1) formate diurea dihydrate, formalel and is known as a typical example of the twoC U ( H C O O ) ~ . ~ ( N H ~ ) ~ C Oand . ~ Hfound ~ O , that the diurea dimensional Heisenberg spin systems2 The antiferrodihydrate has a layer structure of copper(I1) formate quite magnetic phase transition temperature of this compound similar to that of the tetrahydrate. In crystals of diurea was found at about 17 K by measurements of proton dihydrate, urea and water molecules situated between the magnetic resonance3 (lH NMR), and thereafter, the layers form complex hydrogen-bond networks with one magnetic properties of the tetrahydrate mainly in the another as well as with formate ions. It is anticipated from 0022-3654/79/2083-2151$01 .OO/O
0 1979 American Chemical Society
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The Journal of Physical Chemistry, Vol. 83,No. 16, 1979
/,/,
2954
..
2848 2846
1
b
-
1 kHz
-
2952
freq. l o w e r i n g
....... .. . .
2250
T. Asaji, R. Ikeda, and D. Nakamura
4
5
IO
15
20
25
I2250 30
T/K Figure 1. Temperature dependence of I4NNQR frequencies observed . ~ H ~ O30 K. for C U ( H C O O ) ~ . ~ ( N H ~ ) ~ C Obelow
the structure that interlayer magnetic interaction is weakened to some extent by inserting large urea molecules between the layers of copper(I1) formate. In other words, the diurea dihydrate will provide a better example for the two-dimensional spin system than the tetrahydrate. Haseda et al.9 studied the magnetic susceptibility of the former compound and found a magnetic phase transition at 15.5 K showing a slight anomaly of heat capacity. They suggested the existence of an antiferromagnetic longrange-ordered state similar to that of the tetrahydrate. The present investigation has been undertaken in order to confirm it by observing 14NNQR at lower temperatures, and to obtain information about the spin structure below the phase transition.
N N Ln
i.
Figure 2. Derivative curve of the v;' absorption of Cu(HCOO),-2(NH2),CO.2HZO recorded at liquid helium temperature.
onance frequency yielded an anomaly at 16 K as shown in Figure 1. Although no discontinuity of resonance frequencies could be detected for each line, the temperature coefficient, dv/dT, abruptly changed at the anomaly point. All of the resonance absorptions observed below 16 K were two or three times broader than those recorded above this temperature. When the temperature was slowly raised, the four lines became gradually weak until strong and narrow lines appeared at 16 K. The intensity and line width of these absorptions changed so rapidly near this temperature that we could not determine in a strict sense whether or not the change is discontinuous. With heating further, the intensity of the four lines decreased monotonously and no anomalous behavior was observed up to 90 K. Although the resonance frequency of the lines except the lowest-frequency one decreased with increasing temperature, the lowest-frequency line yielded a positive temperature coefficient even in the paramagnetic phase. It is noteworthy that the lowest-frequency line clearly shows a structure only below 16 K as reproduced in Figure 2 . For the other lines, no well-resolved structure could be recorded. Although saturation of resonance absorptions is quite common for diamagnetic compounds a t lower temperatures, no indication of saturation was observed for the present compound even at liquid helium temperature.
Discussion Experimental Section Assignment of Observed Resonance Frequencies. Since Polycrystalline copper(I1) formate diurea dihydrate was 14N has a nuclear spin I equal to unity, each of crystalobtained by evaporation from an aqueous solution conlographically nonequivalent nitrogen atoms usually yields taining copper(I1) formate, twice the stoichiometric the following three resonance frequencies if the asymmetry amount of urea, and a small quantity of formic acid.1° parameter 17 is finite: Large crystals separated were identified by conventional chemical analysis. V I = (3/4h)eQq(l + 17/3) Anal. Calcd for CU(HCO~)~.~(NH,)~CO~~H~O: Cu, vI1 = (3/4h)eQq(l - q/3) (1) 20.52; C, 15.5; N, 18.1;H, 4.6. Found: Cu, 20.50; C, 15.5; N, 17.5; H , 4.4. vlI1 = (p/2h)eQq = V I - vlI Pulverized crystals were sealed in a sample tube after Here, eQq denotes the quadrupole coupling constant of replacing ambient air with helium. nitrogen. The resonance frequencies of the high- and Nitrogen-14 NQR was observed by means of a modified low-frequency pairs of lines are close to the reported V I and Pound-Watkins type spectrometer,ll employing frequency vn frequencies of urea, re~pectively.'~ Therefore, the higher modulation in the temperature range 2-90 K. Temperand lower pairs of lines can be assigned to V I and VI' lines, atures above 4.2 K were obtained by permitting the sample respectively. Since both V I and vlI consist of two lines, an to warm from liquid helium temperature, The sample ambiguity in the assignment still remains as to whether temperature was observed to increase at a rate of about V I of lower frequency should be combined with vrl of lower 3 K / h around 17 K. A gold (0.03% iron) vs. chrome1 frequency or whether the alternative correspondence thermocouple calibrated by measuring 14N NQR freshould be made. To settle this choice, we have observed quencies in hexamethylenetetramine12 was always used in vlI1 signals. The results are 589.6 and 567.6 kHz at about the present work for the determination of temperature. 19 and 25 K, respectively. Accordingly, the correspondence The observed temperature was estimated to be accurate between V I and vI1 frequencies is definitely determined as within fl K. given in Table I. The quadrupole parameters, eQq/h and Results 7, evaluated at various temperatures are also included in Table I. Four I4N NQR frequencies were observed for copper(I1) Two sets of the quadrupole parameters obtained indicate formate diurea dihydrate over the whole temperature range the existence of two crystallographically nonequivalent investigated. The temperature dependence of each res-
The Journal of Physical Chemistry, Vol. 83, No. IS, 1979
I4N NQR of Urea in a Cu(I1) Salt
TABLE I: I4N NQR Frequencies and Quadrupole Parameters of Cu(HCOO), *2(NH,), C 0 . 2 H 2 0 at Various Temperatures freq, kHz 2 4.2 10.5
17 19 34.5
77 89 2 4.2
10 17 21.5 38
77 89.5
,I
VI1
2955.1 2954.7 2953.0 2948.9 2948.9 2948.1 2942.5 2940.8
2378.8 2379.0 2379.6 2381.2 2381.2 2380.8 2377.4 2376.2
a a
2846.8 2846.8 2846.0 2843.7 2843.7 2843.4 2842.0 2841.4
2251.1 2251.3 2252.1 2254.2 2254.2 2254.3 2255.6 2256.2
a a
a
0.3195 0.3195 0.3194 0.3187 0.3185
b b b b b b b b
3398.6 3398.6 3398.5 3398.4 3398.4
0.3469 0.3469 0.3467 0.3451 0.3444
a a
I
3550
3553.4 3553.4 3552.6 3546.6 3544.7
a
z t.".. r
nitrogen atoms in crystals. According to X-ray crystal analysis,8 one knows that the crystal is monoclinic, P2,/c, with lattice parameters a = 8.275 A, b = 8.346 A, c = 8.018 A, /3 = 96.36", and Z = 2. Although four urea molecules in a unit cell are crystallographically equivalent, two nitrogen atoms in a urea molecule are nonequivalent in the crystal. This agrees well with the present NQR results. Therefore, it is concluded that two nitrogen atoms of a urea molecule in the crystal have different quadrupole parameters. Hereafter, nitrogen atoms yielding the higher and the lower values of eQq/hare referred to as those in sites a and b, respectively. Figure 3 shows the temperature dependence of eQq/h observed for the compound in the paramagnetic phase. Nitrogen atoms on site a show a quite normal temperature variation of eQq/h, but those on site b yield an eQq/h value almost independent of temperature. This unusual behavior for the temperature dependence of eQq/h is attributable to the formation of strong hydrogen bonds involving the NH2 group in question.14 Negita et al.15 studied the 14N NQR of urea in several molecular complexes, and found that the value of eQq/h decreases and 17, on the other hand, increases with increasing the strength of hydrogen bonds formed by the NH2 groups of urea. The hydrogen bonding strength can be estimated from internuclear distances. In the present compound, X-ray crystal analysis8revealed that one NH2 group of urea forms hydrogen bonds with an oxygen atom in a formate ion and with oxygen in a neighboring urea molecule, the N-0 distances of which are 2.979 and 2.861 A, respectively. On the other hand, another NH2 group in the urea molecule forms hydrogen bonds with another oxygen atom of the formate ion and with oxygen in a neighboring water molecule, the N-0 distances being 3.108 and 3.040 A, respectively. Accordingly, the former NH2 group participating in stronger hydrogen bonds and the latter one in weaker hydrogen bonds can be assigned to those having nitrogen atoms at sites b and a, respectively. NQR in the AntiferromagneticPhase. The temperature dependence of the observed resonance frequencies shows an anomaly at 16 K, which agrees well with the magnetic phase transition temperature TN previously r e p ~ r t e d . ~ Therefore, the unusual shift of the resonance frequencies observed below TN is attributable to the Zeeman effect of 14NNQR lines due to an internal magnetic field induced as a result of spontaneous magnetic ordering. The presence of the internal field is confirmed by the facts that the resonance lines recorded below TN are broader than
0.345 0.320
. . ..
t
'
a.
tt
0.318 I
2153
0 0
,t
'la I
20
40
I
I
80
60 T/ I(
Figure 3. Temperature dependence of the quadrupole parameters, eQqlh and 9 of nitrogen atoms at sites a ( 0 )and b (0)in the diurea dihydrate crystal.
those above TN,and the line v i 1 clearly shows structure. The magnetic dipolar interaction between a nitrogen nucleus and two protons in an NH2 group is quenched in the paramagnetic phase owing to the large asymmetry pararneter.l6 This is the reason why the lines observed above TN are sharp. In the presence of a magnetic field, however, the dipolar interaction is operative regardless of the value of 7, causing resonance lines to be broad or sometimes split. By use of the atomic arrangement of an NH2 group determined by the X-ray analysis,8 we have roughly estimated the dipolar splittings of the 14NNQR line. The direction of the internal field experienced by the three nuclei was assumed to be identical. These results show the line is splitted into a quartet, two outer components of which are separated from one another by about 4.5 kHz. This agrees well with the observed splitting of about 2 kHz of the vdl line given in Figure 2. Since the number of the resonance lines observed above and below TN was unchanged, the magnitude of the internal magnetic field should be the same at all of the crystallographically equivalent sites of nitrogen. By applying the method reported by Brown and Parker,17 the magnitude of the internal field and also a partial information about the field direction can be obtained. When both nuclear quadrupole and nuclear Zeeman interactions are taken into consideration, the interaction energy of 14N splits into three sublevels denoted by F1,F2,and F3 because of the nuclear spin equal to unity. Brown and Parker derived the following relations among the three energy levels: 3
CF, = 0 i=1
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The Journal of Physical Chemistry, Vol. 83,No. 16, 1979
T. Asaji, R. Ikeda, and D. Nakamura
-
0 E3
2
8.
I
z
a
200
1
0
100
-1 10
"0
T/ K
20
20
0
Figure 4. Temperature dependence of the magnitude of internal field produced at sites a (0)and b (0).
40
80
60
B/degree Flgure 6. G(6',c$)at c$ = 0, f90, and f180' calculated for sites a (solid curve) and b (dashed curve). Curves of G(B,c$)for an arbitrary angle c$ are between the two extreme curves of the respective site. a
0.4
e-" p o p(pop
1
1
c
!I
a
4
&T *i.---; 13
I.
I
'
I
1
i
~~
b
1.0 T/TN Figure 5. Reduced internal field vs. reduced temperature. Dots and open circles indicate values calculated from the internal field observed at sites a and b, respectively. A Brillouin curve for the spin 112 is also indicated by the dashed line.
0.0
0.2
0.4
0.6
0.8
Here, VQ and vo represent eQq/h and yNH/2a,respectively, and G(6',4) = 3 cos2 6' - 1 + 7 sin2 6' cos 24
(3)
In these equations, the direction of the internal field H is given by the polar coordinate (6',4)defined with respect to the principal axes of the EFG tensor, and Y~ is the gyromagnetic ratio of 14N. The values of F1,F2, and F3 at a given temperature can be obtained from the V I and v*I frequencies observed. Since the observed resonance frequencies in the paramagnetic phase are almost independent of temperature below 20 K, we assumed that the quadrupole parameters are independent of temperature in the antiferromagnetic phase, and calculated the magnitude of internal field by using the values of VQ and 7 determined just above TN. From the calculation, the absolute value of the internal field can be determined as a function of temperature as shown in Figure 4. The extrapolated values of the internal field to absolute zero, H(O), are 250 f 20 and 150 f 20 Oe for sites a and b, respectively. Since the internal field induced at nitrogen nuclei is proportional to the spontaneous magnetization M(7') of the antiferromagnet, the reduced field, H(T)/H(O), a t a given temperature should be identical for both sites a and b. In fact the same temperature dependence curve of H(T)/H(O)is obtained for both sites as given in Figure 5. A theoretical curve of M(T)/M(O)calculated by use of the molecular field approximation1*for the case of S = 1 / 2 is added in Figure 5 for comparison. The values of G(6',4) determined are almost independent of temperature and are 0.3 f 0.1 and 1.8 f 0.1 for sites a and b, respectively. Although G(6',4) is a function of both 6' and 4, it is nearly independent of 4 in the present system
b
Flgure 7. Arrangement of magnetic Cu(I1) ions in the ordered state of CU(HCOO),~~(NH,),CO~~H,O. Solid and open circles Indicate up and down spins, respectively, in the four-sublattice model (left) and the two-sublattice model (right).
as shown in Figure 6. Therefore, one can graphically evaluate the permissible values of 8, which are 49 f 6 and 131 f 6" for site a, and 15 f 5 and 165 f 5" for site b. Spin Structure. The arrangement of magnetic Cu(I1) ions in the ordered state of the diurea dihydrate is shown in Figure 7. For the tetrahydrate, both two- and foursublattice models have been taken into consideration to interpret its magnetic structure in the antiferromagnetic statee2t6 For the present compound, the spin structure based on the four-sublattice model will be discussed with a brief comment about the propriety of the two-sublattice model. The internal field, H(",acting on the ith nitrogen atom in the antiferromagnetic phase of the diurea dihydrate can be calculated approximately by use of the following dipolar field originating from electron spins situated on Cu(I1) ions:
(5) where ( S , ) is the average value of the nth electron spin on the Cu(I1) ion at a distance of r,, from the ith resonant nitrogen, g, denotes the g tensor of the nth electron spin, and the summation of n is extended over all the Cu(I1) ions in the crystal. Yamagata et al. determined the g tensor of this compound from ESR experirnents.lg In the Cartesian coordinate system taking the crystallographic a, b, and c* axes as x , y, and z axes, the g tensor can be given by 2.35 g = 0.0 0.07
(
::I1
:::7)
0.0
2.10
(6)
We assume in the subsequent discussion that all of electron
14N NQR
The Journal of Physical Chemistty, Vol. 83, No. 16, 1979
of Urea in a Cu(I1) Salt
2155
a
c3 c u o
c
O N
0 0
0 Hz0 Flgure 8. Two possible directions for the vector to the averaged electron spin.
k which is parallel
spins have this g tensor, although magnetically nonequivalent sites may carry slightly different g tensor values from each other. If we ignore the effect of spin canting in the present system, the magnitude and the orientation of the averaged spin ( S , ) are independent of n. Then, we introduce a vector k to represent (S,} as CSn) = ank (7) where a , takes either +1 and -1 for up and down spins, respectively. Using eq 7 , we can express eq 5 as
IIb)= P(Ca,D,(c))gk n
(8)
D)= Ca,D,(b) n
(9)
m)= p@)gk
(10)
Let
then or
gk = (po’z))-l@ (11) The tensor D ( [ can ) be calculated numerically by taking the sum over the lattice. Therefore, if one knows the value of H(”, the direction and magnitude of the averaged electron spin on a Cu(I1) ion can be evaluated. Although the magnitude of H ( l )and one of its polar coordinates in the EFG coordinate system have been estimated in the in the crystalpresent NQR study, the direction of lographic coordinate system still remains unknown. However, we can estimate it by considering the symmetry of the crystallographically equivalent nitrogen sites in the ordered state. The results are given in the next section. By use of these values obtained for site b, we can estimate the direction and magnitude of vector k. Since we have two possible directions for the internal field by disregarding the sense of these directions, we also have two possible directions for the vector k , namely, kb’and kLf as given in Figure 8. They are in the ac plane and have the same absolute value of 0.31. It is difficult to determine which direction is more probable between kb’and kb”because both directions are close to each other. When 0 changes by some degrees within *5O from the most probable value of 15a (or 165O), the vectors, k( and kbf’vary only within f 5 O in their direction and fO.O1 in their magnitude. This means that the vector k at site b can be definitely determined t o a certain degree. On the other hand, vector k of site a varies greatly in its direction as well as its magnitude with the changing value of 8. Therefore, we calculated the internal field induced at site a by using eq 10 with kbfand kb” determined for site b, in order to confirm the adequacy of the vectors obtained. The magnitude of the internal field and the angle between the internal field and the z axis of the EFG tensor thus cal-
Figure 9. Atomic arrangement in the crystallographic unit cell of CU(HC~O)~*~(NH~)~CO*~H~O.
culated for site a are 223 Oe and 44 and 136’ by using k i , and 230 Oe and 44 and 136’ by using kb”. These results are in fairly good agreement with the experimental ones if one considers the uncertainty of the 8 value and the assumptions laid on the process of the calculation. The average value of the electron spin of the Cu(I1) ions , be estimated to be 0.31, which at absolute zero, ( S ) ocan gives the zero-point spin deviation defined by {1/2 - (S),) equal to 0.19. This agrees well with the theoretical spin deviation of 0.197 estimated for the two-dimensional Heisenberg antiferromagnet with spin 1/2.20 Accordingly, the point dipole approximation employed seems to give satisfactory results for the evaluation of the internal field produced at the nitrogen sites in the present compound. Orientation of Internal Field H ( i )in Crystal Lattices. In both paramagnetic and antiferromagnetic phases of copper(I1) formate diurea dihydrate, the same number of the NQR frequencies was observed. This implies that the magnitude of the internal field and also the function G(0,$) given by eq 3 are identical for all of the crystallographically equivalent nitrogen sites, if the crystal structure remains unchanged at the Nee1 point. Four urea molecules in a crystallographic unit cell can be mutually superposed by applying symmetry operations generated by an inversion center and screw diad axes shown in Figure 9. In the four-sublattice structure, we have one more symmetry element to be duly considered, which translates the four urea molecules in the crystallographic unit cell into the adjacent one along the a axis, because the size of the magnetic unit cell in this structure is double the crystallographic one. Since the symmetry operations of inversion and translation affect the transformation property of the tensor D(i’and of each EFG coordinate system of nitrogen to a minor extent, only the screw diad axes will afford possible information about the direction of the internal field in the crystallographic coordinate system. By assuming the four-sublattice model, we have examined the geometrical relationship between two internal field vectors produced at the nitrogen sites bl and b2 which are able to be superposed by the operation due to the screw diad axes as shown in Figure 9. When a unit vector (xl,y l , zl)is defined parallel to the can be expressed as internal field H(l) at site bl,
where the Cartesian coordinate axes x,y , and z are taken along the crystallographic axes a , b, and c*, respectively. If a unit vector pointing along the z axis of the EFG tensor at site bl is denoted by {(l), and the angle between {(I) and H(’)by 0, one has
2156
The Journal of Physical Chemistry, Vol. 83, No.
IS, 1979
In a similar manner, we define the unit vectors, (xz, y2,z2) and {(2), at site b2. Since the screw diad axis is parallel to the b =is (y axis) { (2) = -{ (1) { (2) = { (1) and { (2) = -3;(1). 9 x X ' Y Y ' Since (14)
A. J. Kresge and Y. C. Tang
perpendicular to the molecular plane of urea determined by the X-ray analysisa8From eq 13,15, and 19-21, we can obtain permissible values for the components of the unit vectors, (xl, yl, zl) and (xz,yz, zz). Substituting these values into eq 12, the possible directions of the internal field at site bl can be obtained as = "b(l)
( ::::)
or
-0.57 -{x(1)x2
+ ry(1)y2- 3;(?z2 = *cos
6'
(15)
Here, f signs correspond to the choice of the angles 6' and 7r - 8,which give two possible directions of From eq 11, one obtains (D1))-1@) = (D(2))-1H(2)
(16)
If (D(l))-lis expressed as (D(1))-1=
(3 5
(17)
Since the experimental results require that HCl) = Ht2),one obtains the following equations by substituting eq 12, 14, 17, and 18 into eq 16: A(xi - 9 ~ 2 )+ D(yi + y2) + F(z1- 22) = O (19)
+ W Y 1 - Yz) + JWl+ 22) = 0 + E(Y1 + Yz) + C(Z1- 22) = 0
-0.71
where the + and - signs correspond to the cases of 6' equal to 15 and 165', respectively. As for the two-sublattice model, we have also tried to get probable directions for the internal field, but no set yl, zl) and ( x 2 , yz, z2), satisfying eq 13, 15, of vectors, (q, and 19-21 was obtained for site b. Thus the possibility of a two-sublattice model can be excluded.
References and Notes
then (D@))-l can be written by considering the symmetry property of the four-sublattice model as
D(x1 + x 2 )
?H~(1)(-o.oo6) 0.64 (22)
(20) (21)
F(x1- x2) The numerical components of the tensor were evaluated by summing up contributions from all the Cu(I1) ions in a sphere of 400 8, around a resonant nitrogen nucleus by use of the lattice parameters determined at room temperature.8 The calculation was carried out by means of a FACOM 230-60 computer at Nagoya University. Since the molecular structure of urea is almost planar in crystals,8,21the directions of {(i) are taken to be
(1) R. Kiriyama, H. Ibamoto, and K. Matsuo, Acta Crystallogr., 7, 482 (1954). (2) H. Kobayashi and T. Haseda, J. fbys. Soc. Jpn., 18, 541 (1963). (3) J. Itoh and Y. Kamiya, J. phys. SOC.Jpn., 17, Suppl. B-I, 512 (1962). (4) R. B. Fllppen and S. A. Friedberg, J . Cbem. fbys., 38, 2652 (1963). (5) A. Dupas and J.-P. Renard, Pbys. Left. A., 33, 470 (1970). (6) A. Dupas and J.-P. Renard, C. R. Acad. Sci. Paris, Ser W , 271, 154 (1970). (7) M. S. Seehra and T. G. Castner, Jr., Pbys. Rev. 6 ,1, 2289 (1970). (8) H. Kiriyama and K. Kitahama, Acta Crystallogr., Sect. B , 32, 330 (1976). (9) Y. Yamamoto, M. Matsuura, and T. Haseda, J . fbys. Soc. Jpn., 40, 1300 (1976). (10) M. Kishita, Nippon Kagaku Zassbi, 83, 264 (1962). (11) R. Ikeda, D. Nakamura, and M. Kubo, J. fbys. Chem., 70, 3626 (1966). (12) G. A. Matzkanin, T. N. O'Neal, and T. A. Scott, J . Cbem. Pbys., 44, 4171 (1966). (13) M. Minematsu, J. fbys. SOC.Jpn., 14, 1030 (1959). (14) D. Nakamura, R. Ikeda, and M. Kubo, Coord. Cbem. Rev., 17, 281 (1975). (15) H. Negita, T. Kubo, and M. Maekawa, Bull. Cbem. SOC.Jpn., 50, 2215 (1977). (16) G. W. Leppelmeier and E. L. Hahn, fbys. Rev., 141, 724 (1966). (17) L. C. Brown and P. M. Parker, fbys. Rev., 100, 1764 (1955). (18) C. Kittel, "Introduction to Solid State Physics", 4th ed, Wiley, New York, 1971, p 529. (19) K. Yamagata, Y. Kozuka, E. Masai, M. Taniguchi, T. Sakai, and I. Takata, J . fbys. SOC.Jpn., 44, 139 (1978). (20) M. E. Lines, J . fbys. Cbem. Solids, 31, 101 (1970). (21) A. W. Pryor and P. L. Sanger, Acta Crystallogr., Sect. A, 26, 543 (1970).
Hydrogen Isotope Fractionation between Water and Aqueous Mono- and Dihydrogen Phosphate Ions A. J. Kresge" and Y. C. Tang Department of Chemistry, University of Toronto, Scarborough College, West Hill, Ontario M 1C 1A4, Canada (Received November 7, 1978; Revised Manuscript Received April 23, 1979)
The NMR method of determining H-D isotopic fractionation factors for rapidly exchanging solutes in protic solvents was extended to multicomponent systems and was then applied to aqueous L2P04-/LP042-buffer solutions (L = H or D). The results obtained, 4(L2PO4-)= 1.03 and +(LP042-)= 0.91, give an isotope effect on the ionization of L2P04-,KH/KD= 3.54, which is in excellent agreement with the directly measured value, KH f KD = 3.43. Isotopic fractionation factors provide a method of analyzing hydrogen isotope effects which has proved to be especially effective in dealing with solvent isotope effects on reactions catalyzed by acids and bases in aqueous 0022-3654/79/2083-2 156$01.OO/O
so1ution.l This application requires knowledge of the fractionation factors for the acid and base species involved, and, since monohydrogen phosphate-dihydrogen phosphate buffers are frequently used in studies of acid-base
0 1979 American Chemical
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