756
J. Phys. Chem. 1984,88, 756-759
dicative of an increase in phase homogeneity. Preparations of the mixed composition CdRhl,sFe0,204 were performed by solid-state reaction of the oxides and by a precursor method. X-ray analysis of the products in both cases indicated the formation of a single-phase spinel. The measurement of cell parameters was not attempted, since unsubstituted CdRh204and CdFe204have similar cell parameters at 8.765 (1) and 8.708 (1) A, respectively. The magnetic susceptibility values given in Table I indicate that the precursor method for preparing solid solutions achieves maximum homogeneity. Since the effects of phase homogeneity on the magnetic susceptibilities of both solid solution systems have been established, a comparison with unsubstituted CdFe204is appropriate. Within the limits of the synthetic technique, the samples of C d G a l , s F ~ , 2 0 4 prepared at lo00 "C and C ~ E U I ~ , ~ Fprepared Q ~ O ~ by the precursor method are the most homgeneous for the respective compositions. emu/mol equiv The magnetic susceptibility value of 1.37 X of Fe observed for these samples shows a large increase from the value of 0.96 X emu/mol equiv of Fe for unsubstituted CdFe204. The remaining small deviation from spin-only moment is due to the clustering inherent in a random distribution of 10% iron over the spinel B sites. Statistical analysis for this composition predicts that 53% of the Fe3+ions will be isolated and that 28% will exist in nearest-neighbor pairs, 11% in clusters of three, and a total of 8% in larger clusters. The Curie constant and magnetic susceptibility are the sums of contributions from each Fe3+ion; the amount contributed per ion will depend upon the cluster size. For example, the measured value of 1.37 X emu/mol equiv of Fe could be explained by assigning the spin-only value of 1.50 X to isolated and paired Fe3+ions, and the bulk value of 0.96
X
to clusters of three or more.
Summary and Conclusions The normal spinels CdFe204,CdGal,8Feo,204, and CdRhl,,Feo.204 were prepared, and their magnetic susceptibilities were measured. Unsubstituted CdFe204showed a gcffof 4.72 (5) pB, which is lower than the value 5.92 pB expected for high-spin Fe3+(3d5).The deviation from spin s / 2 behavior is attributed to a hybridization of the 6Sand 4G states resulting from spin-orbit interaction coupled with strong crystal fields possessing trigonal components at the spinel B sites. The magnetic susceptibility of CdGal.sFeo,204 samples was found to increase with the temperature of preparation, which was attributed to an increase in phase homogeneity. Similarly, samples of CdRhl,sFeo,204 prepared by a precursor method were found to be more homogeneous than those prepared directly from the oxides, as determined by magnetic susceptibility. For homogeneous samples of both CdGal,8Feo,204 and CdRh1,sFe0,204, observed magnetic susceptibilities of 0.0137 emu/mol equiv of Fe approach that expected for Fe3+(3ds). The small deviation from ideal spin-only moment is caused by the statistical existence of a few remaining Fe3+ clusters. Acknowledgment. Acknowledgment is made to the Office of Naval Research, Arlington, VA, for the support of Mark Tellefsen and to the National Science Foundation (Grant DMR-82-03667) for the support of Louis Carreiro and Kirby Dwight. Acknowledgment is also made to Brown University's Materials Research Laboratory program which is funded through the National Science Foundation. Registry No. CdFe204,12013-98-8.
Raman Spectra and Force Constants for the Nitric Oxide Dimer and Its Isotopic Species E. M. Nom,+L.-H. Chen, M. M. Strube, and J. Laane* Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received: May 25, 1983)
The Raman spectra of the solid nitric oxide dimer (16014N14N160) and two of its isotopically substituted species (16015NisNi60 and 18015N15N'80) at 12 K have been recorded and analyzed. The observed isotopic shifts demonstrate that fundamental vibrational frequencies for the normal isotopic species are at 1866 (ui), 1762 ( u s ) , 268 ( u 2 ) , 215 ( u 6 ) , and 189 ( u 3 ) cm-'. A band at 97 cm-' may be due to the sixth vibration (v4). The isotopic frequency shifts observed for the 495-cm-I band demonstrate that this is the combination band u2 + Y6 and is not a fundamental. The data for the three isotopic forms of cis-N202made it possible for the first time to calculate a meaningful set of force constants for this molecule. The stretching force constant for the weak N-N bond was calculated to be 0.32 mdyn/A.
Introduction The vibrational spectra of the nitric oxide dimer, cis-ONNO, which is formed upon condensation of nitric oxide, have been studied at least eight times Nonetheless, general agreement on the vibrational assignments has not been reached. Table I summarizes the previous spectroscopic data reported for cis-N202.There is general agreement that bands near 1860,260, and 170 cm-' are the AI modes, but whether 260 or 170 cm-' results from the N-N stretching has remained an open question. The assignment of the antisymmetric stretching v s at 1760 cm-I is secure, but the frequency of the bending motion v6 has not been firmly established. Durig and Griffins assigned a Raman band at 489 cm-I to this mode, but more recent work'sS places it near 'Present address: Department of Chemistry, Zagazig University, Zagazig, Egypt.
0022-3654/84/2088-0756$01.50/0
200 cm-'. However, the band near 490 cm-I has been observed in other studies1.' and its origin is not obvious. Isotopic substitution with ISN has in one case been previously usedS in an attempt to clarify the assignments. The reported frequency shifts for the vI N = O stretching bands were reasonable (-30 cm-I), but those for the 264- and 176-cm-I bands (-2 and (1) A. L. Smith, W. 189 (1951).
E. Keller, and H. L. Johnston, J . Chem. Phys., 18,
( 2 ) W. G. Fateley, H. A. Bent, and B. Crawford, Jr., J . Chem. Phys., 31, 204 (1959).
( 3 ) W. A. Guillory and C. E. Hunter, J . Chem. Phys., 50, 3516 (1969). (4) C. E. Dinerman and G. E. Ewing, J . Chem. Phys., 53, 626 (1970). (5) J. R. Durig and M. G. Griffin, J . Roman Spccfmsc.,5 , 273 (1976). (6) G. R. Smith and W. A. Guillory, J. Mol. Specfrosc.,68, 223 (1977). (7) A. Anderson and 9. Lassier-Govers,Chem. Phys. Left., 50, 124 (1977). (8) J. R. Ohlsen and J. Laane, J . Am. Chem. SOC.,100, 6498 (1978).
0 1984 American Chemical Society
Raman Spectra and Force Constants for cis-N202 - m m O
I:
CQ
N
7
The Journal of Physical Chemistry, Vol. 88, No. 4, 1984 757
+
I
cis-NgO2 at 12 K
I
I
1
W
r-
2
1
2000
1600
I
1
I
I
200
400
1600 600
I 0
Cm-1
Figure 1. Raman spectrum of the solid nitric oxide dimer (cis-O=NN=O) at 12 K. TABLE 11: Raman Spectra (an-')of (NO), at 12 K
I E
E E E
3 m -
?- I
W W m
W
N
W
W W
W r-
N m W
02 rW
i
3
-
3
N
m
> rg
W W #
m
>
m
-
m W
1866 s 1762 vw 491 mw 401 w w 347 vw 266 s 214 w 20 1 w 187 s 97 s 55 s 41 s
m
> r0
- -
r-
1832 1730 480 -394 340 26 1 209 -197 183 95
1783 1682 468 -385 -330 253 205 -193 177 94
v1
VS 2'
+
'6
+
v4
2v4 v2
+
U6
v2 '6
2v4 v3
v4
lattice mode lattice mode
+3 cm-l, respectively) were not. Consequently, the need for more reliable isotopic shift data is clear. Three force constant calculations on cis-N202have been carried out p r e v i o u ~ l y , ~but - ~ Jthese ~ either have been based on unreliable data or have not had the availability of isotopic shift data. Thus, none are meaningful. A theoretical calculation of frequencies for the nitric oxide dimer has also been reported," but the results differ radically from the experimental ones. Frequencies of 1858,635, 439, 190, 1709, and 768 cm-' were calculated for v1 through v6, respectively. The present study focuses then on obtaining reliable Raman spectra for these isotopic forms of the nitric oxide dimer. The measurements of the isotopic shifts will lead to a definitive assignment and also to a meaningful set of force constants. Experimental Section Materials and Preparations. Samples of I4NO (99.0%, Matheson Gas Products), ISNO(99.0%, Stabler Isotopic Chem(99% isotopic purity, Mound Laboratories) were icals), and 15N180 purified (in order to remove NO2) by using trap to trap vacuum distillations and procedures previously described.* The purity of the samples was confirmed spectroscopically. The purified gas samples were deposited as solid films on a polished brass wedge cooled to 12 K by an Air Products CSW-202 closed-cycle helium refrigerator. Spectroscopic Measurements. Raman spectra were recorded with a Cary Model 82 spectrophotometer equipped with a Coherent Radiation Model 53 argon ion laser. The 5145-A line was used (unfocused) for the Raman excitation. The frequency calibration was checked before and after each spectrum by using the Rayleigh line and the 994-cm-' band of Na2S04. Spectral slit widths ranging from 3 to 6 cm-' were used, and the frequency accuracy was estimated to be A1 cm-' for sharp fundamentals but no better than f4 for broad combination bands. (9) D. M. Eshelman, F. J. Torre, and J. Bigeleisen, J . Chem. Phys., 60, 420 (1974). (10) V. Kumon, U.P. Verma, and A. N. Pandey, J. Mol. Struct., 49,411 (19781. (li) S.Skaarup, P. N. Skancke, and J. E. Boggs, J . Am. Chem. Soc., 98, 6106 (1976). \ -
758 The Journal of Physical Chemistry, Vol. 88, No. 4, 1984
TABLE 111: Force Constants for cis-N,O, constant
description thiswork ref 5
N - 0 stretch 14.487 N-N stretch 0.323 ONN bcnd 0.340 f, torsion 0.020 fro, N - 0 , ONN 0.111 f ~ aN-N, ONN 0.149 fa, ONN,ONN 0.171 frr N-0, N - 0 0.778 f~~ N-EU',N-O -0.079 fr
fR fa
14.49 0.59 0.89
0.44 0.83
Nour et al. TABLE 1V: Observed and Calculated Frequencies (cm-') for cis-N,O,
ref 9
ref 10
ref 11
14.51 0.55 0.14 0.5 0.0 0.09 -0.03 -0.10 -0.01 0.75 0.73 0.00 0.00
14.50 2.29 2.17 0.07 0.43 0.82 0.30 1.07 0.99
14.57 0.33 0.29
(NO),
e5~0),
obsd
calcd
obsd
calcd
obsd
calcd
1866 266 187 97 1762 214
1866 266 186 97 1762 214
1832 261 183 95 1730 209
1832 259 184 95 1730 210
1783 253 177 94 1682 205
1783 255 176 93 1683 205
~~
A,
uI u, u3
A,
B,
u4 us
vb
TABLE V: Observed ( t 2 cm") and Calculated Frequency
The units are mdyn/A forf,., f R , f r r , andfRr, mdyn/rad for f r n and fRa.and rndyn .&/rad2 for fa.f,, and fa&. a
Shifts for c i s - N 2 0 2 0 1 5 ~ 1 5 ~ 0
Results The Raman spectrum for (I4NO)2at 12 K is shown in Figure 1, and the spectral frequencies for this isotopic species as well as for (15NO)2and (15N180)2 are tabulated in Table 11. The data for the naturally occurring isotopic form are in good agreement with the literature, especially with the work of Anderson and Lassier-Govers.' In agreement with these workers, we saw no evidence for a band near 176 cm-l, where Durig and GriffenS had assigned a medium-intensity band to u3. Presumably an impurity was responsible for this band. The isotopic data for (ISNO), are in general agreement with the literature except that the frequency shifts of 11 and 5 cm-I for the 491- and 266-cm-l bands, respectively, differ substantially from the values of 5 and 2 cm-' previously reported5. The data for the (15N180)2 isotopic species are very helpful in confirming several assignments. The 491-cm-I band is clearly v2 v6. While the sum of the frequencies v2 Y6 only equals 480 cm-I, the frequency shifts of 11 and 23 cm-l observed for this band agree well with the shifts of 10 and 22 cm-l predicted from the sums of u2 + v6 for the (15N0)2and (1sN180)2 species. Previously, this band had been assignedS erroneously as V6, the antisymmetric angle bending. The frequency shifts for the 401- and 347-cm-' bands confirm these to be 2v4 Y6 and v2 v4, respectively. Each of these three combination bands occurs at least 10 cm-' higher than expected, indicating that there is considerable anharmonic interaction between the different vibrational modes. The assignments shown in Table I1 for the fundamental vibrations, based on the isotopic shifts and confirmed by the force constant calculation (to be discussed), are certainly the correct ones, with the possible exception of the 97-cm-I band as v4, the A2 torsion. It is conceivable that this latter band is a lattice mode, but the fact that the overtone 2v4 and the combination bands u2 u4 and u2 v6 have been observed supports its assignment as a fundamental. There has been no disagreement that bands at 1866 and 1762 cm-' are the u1 and us N=O stretches, and the 260- and 166-cm-' bands, which are polarized in the Raman spectrum of the liquid,' are clearly the AI modes u2 and v3. As will be seen from the force constant calculation, the N-N stretching and the symmetric angle-bending motions are highly coupled. The last vibration, v6, the antisymmetric angle bending, nicely accounts for the Raman band at 214 cm-' and also for the frequency shifts observed upon isotopic substitution.
+
+
VI
V2 u3
v.3 V5 'b
+
+
Force Constant Calculations The normal-coordinate calculation was carried out utilizing a general quadratic force field and the obvious choices for the internal coordinates: R , the N-N stretch; r l and r2, the N=O stretches; a l and a2,the angle bendings; and T,the torsion. All 18 observed frequencies for the three isotopic species were used to determine four principal and five interaction force constants. One interaction constant, frmt, representing the N-0 stretching interaction with the more distant angle bending, was assumed to be negligible and was set equal to 0.0. Table I11 lists the force constants determined from this study and compares them to those reported p r e v i ~ u s l y ~as~well ~ ~ ' as ~ to those from a theoretical calculation." It should be noted that previous calculations did not have the benefit of the isotope shift data and used incomplete or incorrect frequency assignments. Table IV lists the observed
18015N15N180
obsd
calcd
obsd
calcd
34 5 4 2 32 5
34 7 2 2 32 5
83 13 10 3 80 9
83 11 10 4 79 9
TABLE VI: Potential Energy Distributiona for cis-N,O,
u1 u2 V3 u4
+
+
(15~180)~
V5 '6
fR
fr
0 49 87 0 0 0
100 1 0
0 99 0
fa 0 50 13 0 1 100
f, 0 0 0 100 0 0
Normalized to a total of 100 for the diagonal forcc constant distributions. a
and calculated frequencies for all three isotopic species; all calculated values agree within f 2 cm-l, and the average error is less than *0.3%. Table V shows the excellent agreement between the observed and calculated frequency shifts due to isotopic substitution. This lends further support to the reliability of the force constant calculation. Table VI presents the potential energy distribution for each of the vibrations. As can be seen, ul, u4, us, and V 6 are essentially pure modes with each corresponding to a specific symmetry coordinate. The two lower frequency AI modes v2 and u3 are strongly coupled, however, reflecting the fact that there is no "pure" N-N stretching frequency for this molecule. Discussion The use of three isotopic species of the nitric oxide dimer has made it possible to make definitive vibrational assignments for this molecule. The results demonstrate that the 489-cm-l band, previously assigned to a fundamental, is a combination band (u2 4,) whereas the Al fundamentals are at 1866,266, and 187 cm-l. The latter two frequencies represent the N-N stretching and O=N-N angle-bending motions, which are strongly coupled. Thus, there is no clear-cut answer to the controversy as to whether the stretching or bending is at a higher frequency. The other (B,) bending frequency has been assigned at 214 cm-', and the A2 torsion is most probably responsible for the band at 97 cm-'. The observation of two highly coupled totally symmetric vibrations u2 and u3 for cis-N202is very similar to the situation observed for the analogous vibrations for as-N2O3.I2 For dinitrogen trioxide the coupled N-N stretching and bending motions occur at 266 and 205 cm-' (vs. 266 and 187 cm-l for N202). The N-N stretching frequency for N2O4 is 275 cm-I, but this does not appear to be significantly coupled to any other vibration. The force constants determined for the nitric oxide dimer are consistent with the conventional picture of two nitric oxide
+
(12) E. M. Nour, L.-H. Chen, and J. Laane, J . Phys. Chem., 87, 1113 (1983).
J. Phys. Chem. 1984, 88, 159-162 molecules held together by a weak N-N bond. The N=O stretching frequencies (1 866 and 1762 cm-’) and the force constant of 14.49 mdyn/A are only slightly lower than the valued3 for free NO: vNo = 1876 cm-l and f N o = 16.0 mdyn/A. The corresponding frequency and force constant values for as-N203are 1858 cm-’ and 15.04 mdyn/A. The force constant for the weak N-N linkage was calculated to be only 0.32 mdyn/A for N202;for N2O3 this stretching constant is 0.57 mdyn/A. Since each of these values has an uncertainty of about 0.1 mdyn/A, the difference may not be highly significant. Nonetheless, the N-N bond is clearly (13) J. Laane and J. R. Ohlsen, Prog. Inorg. Chem., 27,465 (1980), and refrences therein.
759
extremely weak in both cases. For comparison, the nitrogennitrogen bond in N 2 0 has a force constantI3 of 18.5 mdyn/A, ON=N02- has a force constanti4 of 7.9 mdyn/A, and N2032has a valueI5 of 4.4 mdyn/A. A typical N-N single bond may be expected to have a force constant of about 4 mdyn/A. Acknowledgment. This work was sponsored by the National Science Foundation. Registry No. (I4NO),, 16824-89-8; (”NO)2, 61925-25-5; (‘5N’80)2, 88296-32-6. (14) L.-H. Chen and J. Laane, J . Raman. Specfrosc.,14, 284 (1983). (15) F. T. Bonner, M. J. Akhtar, T.-V. King, L.-H. Chen, andT. Ishida, J . Phys. Chem., 85, 4051 (1981).
Nonexistent Glass Transition for Amorphous Solid Water D. R. MacFarlane and C. A. Angell* Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: August 9, 1983)
In an attempt to characterize the nature of the glass transition in vitreous water we have vapor deposited the amorphous solid directly in a differential scanning pan, and studied its warm-up behavior under high-sensitivity conditions. Notwithstanding the use of many preparation variations and DSC scanning cycles known to maximize the thermal manifestation of the “glass transition”, no transition anywhere in the region expected from binary solution extrapolations has been detected. Rather, the material remains unrelaxed up to the onset of crystallization commencing abruptly in the range 150-162 K depending on deposition conditions. We interpret the observation by reference to known (network glass + “modifier”) system behavior.
Introduction For the frequency with which its experimentally determined behavior confounds the most confident predictions, water is, among known substances, without peer. This contribution documents another in a series of such predictive failures, each of which has in the past led to a new and useful understanding of the nature of this extraordinary substance. We are concerned in this work with the nature of amorphous solid (or vitreous) water (ASW). This material and its relationship to liquid water is currently in focus because of the apparent success that independent laboratories seem to have had recently1i2in suppressing the crystallization phenomenon during ultrafast cooling of initially liquid water samples. The resulting product is an X-ray amorphous form of the substance which shows behavior during subsequent warm-up which is generally, and in some cases exactly, similar to the behavior of the amorphous solid water which is produced by vapor deposition of dilute gas molecules on a cold substrate^.^ That the glassy looking material deposited from the low-pressure vapor is amorphous to X-rays was first shown by Burton and Oliver4 in 1932. In 1966 McMillan and Loss reported a glass transition in such deposits some 20 K below the temperature of crystallization, but the thermal effect was later denied in the work of Ghormley.6 Subsequently, adiabatic calorimetry studies by Sugisaki et al.7 showed an increase in heat capacity, which is ( I ) Brugeller, P.; Mayer, E.Nature (London) 1980, 288, 569. 1980, 288,
characteristic of the glass transition, at a somewhat lower temperature than that of McMillan and Los, but the complete transition could not be observed because of crystallization of the deposit at the low temperature of 136 K. In 1970 Angell and Sares showed that the glass transition temperature predicted by extrapolation of binary solution data on many salt water systems was consistent with the TBreported by McMillan and Los, and this was subsequently supported by extrapolations involving a number of molecular liquids? including some whose glass transition temperatures fell at lower values. Most workers would agree that the extrapolation of these data, to yield Tg(H20) = 139 K as shown in Figure 1, carries conviction. Angell and Sare also showed, using an entropy argument going back to Kauzrnann,lo that the extrapolated glass transition temperature could not be reconciled with the observed heat capacity of liquid water. As a result, they anticipated that, in the supercooled state of water, an anomalous decrease in heat capacity would be encountered. Subsequent experiments’ ‘ - I 3 in the supercooled region revealed, characteristically, an anomaly which ran in the opposite sense. Angell et al.13attempted to rationalize the increase in supercooled water heat capacity by postulating a A-type transition just below the limit of observation. As a result of this the heat capacity, it was asserted, would plunge to a low value thereby postponing the entropy catastrophe to temperatures compatible with McMillan and Los’ glass transition temperature. Johari14subsequently showed that if one accepted the heat capacity rise observed at 132 K by Sugisaki et al.’ as the glass transition
579. (2) (a) Dubochet, J.; McDowell, A. W. J . Microsc. 1981, 124, RP3-RP4. (b) Dubochet, J.; Lepault, J.; Freeman, R. Ibid. 1982, 128, 219. (3) For a complete review see the comprehensive article by M. S.Sceats and S.A. Rice in ’Water, A Comprehensive Treatise”; Franks, F., Ed.; Plenum: New York, 1982; p 115. (4) Burton, E. F.; Oliver, W. F.Proc. R . Soc. (London), Ser. A 1935,153, 166. (5) McMillan, J. A.; Los, S.C. J . Chem. Phys. 1965, 42, 829. (6) Ghormley, J. A. J . Chem. Phys. 1967, 48, 503. (7) Sugisaki, M.; Suga, H.; Seki, S.J . Chem. SOC.Jpn. 1968, 41, 2591.
(8) Angell, C. A.; Sare, E. J. J . Chem. Phys. 1970, 52, 1058. (9) Sare, E. J.; Angell, C. A. J. Solution Chem. 1973, 2, 53. (IO) Kauzmann, W. Chem. Rev. 1948, 43, 219. (11) Rasmussen, D. H.; MacKenzie, A. P.; Tucker, J. C.; Angell, C. A. Science 1973, 18, 4079. (12) Rasmussen, D.H.; MacKenzie, A. P. J . Chem. Phys. 1973,59, 5003. (13) Angell, C. A.; Shuppert, J.; Tucker, J. C. J . Phys. Chem. 1973, 77, 3092. (14) Johari, G. P. Phil. Mag. 1977, 35, 1077
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0 1984 American Chemical Society
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