periment showed that there was no change in the signalto-noise ratio when the flow rate was increased.
(5) M. D. Levenson, C. Flytzanis, and N. Bioembergen, Phys. Rev. B, 6, 3962 (1972). (6) P. R. Regnier and J. P. E. Taran, Appl. Phys. Lett., 23, 240 (1973). (7) M. D. Levenson, I€€€ J . Quantum Electron., qe-IO,110 (1974). (8) M. D. Levenson and N. Bioembergen, J. Chem. Phys., 60, 1323 (1974). (9) R. F. Begiey, A. B. Harvey, and R. L. Byer, Appl. Phys. Lett., 25,387 (1974). (IO) R. F. Begley, A. B. Harvey, R. L. Byer, and B. S.Hudson, J. Chem. phys., 61,2466 (1974). (11) R. F. Begiey, A. B. Harvey, R. L. Byer, and B. S. Hudson, Am. Lab., 6 ( I I ) , 11 (1974). (12) I.Itzkan and D. A. Leonard, Appl. Phys. Lett., 26. 106 (1975). (13) F. Mova, S.A. J. Druet, and J. P. E.Taran, Opt. Commun., 13, 169 (1975). (14) J. J. Barrett and R. F. Begley, Appl. Phys. Lett., 27, 129 (1975). (15) 1. Chabay, G. K. Klauminzer, and 6. S.Hudson, Appl. Phys. Left., 28, 27 (1976). (16) 8. Hudson, W. Heatherington 111, S. Kramer I.Chabay, and G. K. Klauminzer, Proc. Natl. Acad. Scl., 73,3798 (1976). (17) L. A. Carreira, T. C. Maguire, and T. B. Malioy, Jr., J . Cbem. Phys., (in
CONCLUSIONS The use of the micro optical cell brings the CARS technique into the range of a useful liquid chromatographic detector from the standpoint of the internal volume of the detector and inherent sensitivity. Furthermore, flow has been shown to have no adverse effect on the signal-to-noise ratio. This cell allows for the rapid optical alignment of the laser beams and is relatively inexpensive, even when fused quartz is used so as to permit ultraviolet measurements to be made. This also opens the way for the possibility of applying the CARS technique to (a) photolysis studies (b) kinetic (stop-flow) studies, and (c) molecular excited-state studies. This extension of the CARS technique greatly widens its applicability as a useful spectroscopic tool. LITERATURE CITED J. A. Armstrong, N. Bioembergen, J. Ducuing, and P. S.Pershan, Phys. Rev., 127, 1918 (1962). P. D. Maker and R . W. Terhune, Phys. Rev. A, 137,801 (1965). J. J. Wynne, Phys. Rev. Lett., 29, 650 (1972). E. Yablonovitch, C. Flytzanis, and N. Bloembergen, Phys. Rev. Lett.,
29, 285 (1972).
press).
(18) J. Dillon, A. Spector, and K. Nakaniski, Nature(London), 259,42 (1976).
RECEIVED for review January 10, 1977. Accepted March 2, 1977. The authors gratefully acknowledge financial support given this study by the United States Environmental Protection Agency by Grant No. USEPA R804155010. One of us (T.B.M) would like to thank the Mississippi State University Development Foundation for financial assistance.
Determination of the Composition of Mixtures of Sodium Chromite and Chromic Oxide by Electron Spin Resonance Spectrometry I r a B. Goldberg," Harry R. Crowe, and Wayne M. Robertson Science Center, Rockwell International, Thousand Oaks, California 9 1360
The electron spin resonance (ESR) signals due to the Cr3+ compounds, Cr203and NaCrO,, can be separated as a function of temperature by virtue of their transitions between antiferromagnetic and paramagnetic states. Relative signal amplitudes can be used to determine as little as 0.2 YO to as high as 10 % Cr2O3 in NaCr02, and relative double integrals can be used to determine Cr203over the range of 0.5 to 100%. Absolute determinations based on calibration using pure materials permit ESR to be used to determine the amount of each material with an accuracy of f2%. Absolute determinations utilizing other standards (e.g., MnS04*H20)are subject to a large uncertainty because the Curie temperatures of the chromium compounds are not well deflned.
Electron spin resonance (ESR) has been used for analyses of dilute paramagnetic species in liquid, solid, and gaseous materials. However, the application of ESR to the analysis of concentrated materials or inhomogeneous mixtures has not been considered. Nevertheless magnetic materials can exhibit paramagnetic, ferromagnetic, or antiferromagnetic properties. Each of these properties is characterized by different temperature dependencies of their ESR signal amplitudes, gfactors, and linewidths and by their magnetic susceptibilities. These properties can permit the separation of features due to one or more components of a heterogeneous mixture, and can often permit detection of the presence of homogeneous 962
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7,JUNE 1977
impurities because of their effect on the intrinsic magnetic properties, such as the linewidth or the susceptibility, In addition, ESR provides a rapid analytical technique. We consider here the determination of chromium sesquioxide (Cr203)and sodium chromite (NaCrO,) in mixtures. Both of these materials contain Cr(II1) in similar co-ordination to oxygen, and both exhibit antiferromagnetic properties, However, the transition temperature of NaCrOz to a paramagnetic state occurs at a considerably lower temperature than does Crz03. This feature permits signals due to the two components to be separated. Sodium chromite, NaCr02, forms on chromium-containing alloys, such as stainless steel and Inconel (Ni-Cr-Fe), by reaction of the alloy with trace oxygen in the liquid sodium coolant (1) in nuclear reactors. The layer of sodium chromite which forms on these alloys is thought to act as lubricant for control- and fuel-rod elements. The lubricating properties, which probably result from its layered hexagonal crystal structure ( 2 ) ,have not been investigated. In order to understand these properties, NaCrOz was made by the reactions given in Equation 1 ( 1 ) and Equation 2 (3) Na,CO, t Cr,O,Na,Cr,O,
+
9 0 0 OC --f
PNaCrO, t CO,
900 OC
3H,
--, ZNaCrO, +
3H,O
(2)
It was necessary to be able to ascertain the amount of NaCrO2 in these reaction products, and to be able to distinguish NaCrOz from unreacted Cr203,as well as distinguish
other components in the mixtures. We have found that ESR provides a sensitive technique in which the reaction could be studied and the products analyzed. Signals due to various chromium materials could be easily separated by virtue of their different NBel temperatures. This approach to the analysis of nondilute materials has not previously been utilized.
EXPERIMENTAL Apparatus. The ESR spectrometer consists of a modified V-4502 (Varian) instrument with a 38-cm Magnion magnet, TEIM dual sample cavity, reflection-homodyne bridge with a detector biasing arm, microwave power meter, and Air Products LTD-3-110 temperature controller. The spectrometer is interfaced to a PPPB/M (Digital Equipment Corp.) laboratory computer as described in Ref. 4. Reagents. Two techniques were used for the preparation of sodium chromite. The principal method used is given by Equation 1 (I). Stoichiometric amounts of sodium carbonate and chromium sesquioxide were weighed into lots of about 90 g, mixed by hand using a mortar and pestle, and heated to 900 “C in a molybdenum crucible in argon atmosphere. The mixture was heated for 1 h, ground and remixed, and heated for an additional 8 h. The material was weighed before and after heating and at the end of the third heating was found to have lost essentiallyall the weight required by the loss of COz from Equation 1. Emission spectrographic analysis of the sodium chromite showed impurity levels as follows; silicon 0.031%, iron 0.033%, magnesium 0.0014%, molybdenum 0.61%, copper 0.0028%, calcium 0.0037%. No other impurity elements were detected. X-ray powder patterns of this material exhibited all of the expected lines ( I ) , with no other lines observed. The second method of preparation is given by Equation 2 (3). This reaction was carried out in a platinum boat. An initial heating of an hour was not sufficient to allow the reaction to go to completion. The x-ray powder pattern of a sample revealed several lines in addition to the sodium chromite lines. Further heating in hydrogen caused the reaction to go to completion as determined by x-ray measurements. Reaction 1 was preferred for the preparation since the sodium dichromate used in Equation 2 melts at a low temperature and tends to splatter and run throughout the reaction vessel, while Equation 1 was a much “cleaner” reaction with very little liquid phase appearing during the reaction. Chromium oxide (C.P. Grade) was used as received from Baker Chemical Company. The lot analysis kindly supplied by the J. T. Baker Company, indicated impurities of 0.65% were sulfates and 0.48% were cations not precipitated by NH40H. We msume , therefore that the purity is 98.8%. Manganese sulfate (reagent grade) was obtained from Matheson, Coleman and Bell. A saturated solution was prepared at room temperature, heated to 80 “C, and filtered. The precipitate was dried in flowing nitrogen for 3 days. The water content was 10.62% determined by the weight loss after heating the sample at 325 “C. This is in agreement with 10.66% calculated for MnS04.H20. Procedure. Samples of 1-5 mg were weighed into 3-mm i.d. quartz tubes (wall thickness 0.5 mm). The heights of these samples in the tube were typically less than 2 mm. The sample was placed in the ESR cavity, and the field was set to the peak of the first derivative, and the signal was maximized by moving the sample vertically. Spectra were recorded on the dedicated computer. A total of 2048 data points, at increments of 3.6 G were taken for each sample at each temperature. Scan rates of 30 G/s were utilized and the filtering time constant was 0.32 s. Spectra were doubly integrated and corrections were made for incomplete integration assuming a Lorentzian lineshape. The magnitude of the correction was typically 7%, remaining essentially constant for all samples used for analysis. The spectrometer was calibrated by using a weighed sample of MnS04.H20as a standard. The same procedure was followed as described for the chromium containing samples. RESULTS AND DISCUSSION ESR Absorption. ESR spectra are typically displayed as the derivative of the absorption. Thus, the magnetization of the sample xHo, is directly proproporional to the double
integral of the ESR signal (5-7)
(3) where H , is the modulation amplitude, p is the microwave power incident on the sample Ho is the resonance field, N is the number of paramagnetic ions in the sample, x is the magnetic susceptibility, and K is a constant which will depend upon the instrument and the cavity and sample geometries. Sample Size a n d Geometry. The application of Equation 3 to determine the susceptibility of a paramagnetic sample requires that the geometries of the sample and microwave cavities be identical for each sample. This includes the quartz Dewar, sample position, sample tube sizes and wall thicknesses, and tuning of the cavity. In order to tune the cavity, we find that the most reproducible setting occurs when the cavity is critically coupled to the waveguide (minimum reflected power when the sample is not at resonance) and microwave power in phase with the reflected signal a t resonance added to bias the detector. Provided that identical sample tubes are used for all samples, the diameter of the sample will be kept the same. In these measurements the sample diameter is 3 mm. Since these samples do not exhibit a particularly large dielectric constant or loss tangent, and also because these samples are kept in a region of low oscillating electric field intensity, the effect on the cavity tuning is not significantly dependent upon the sample size. However, the signal strength is dependent upon the length of the sample. For a point sample, which can be moved along the axis of a TEloz microwave cavity a t the position of the maximum oscillating magnetic field, the signal (S) will be approximated by Equation 4
-S- - cos
SO
(4)
2(7)
where z is the axial position of the sample measured from the center of the cavity, L is the length of the cavity, and So is the signal for a sample concentrated a t the cavity center. In practice, non-uniform magnetic field modulation will cause a sharper decrease of S/So as the sample is moved from the cavity center (8,9). However, Equation 4 is adequate for the purposes of this discussion. We now allow the sample to be uniformly distributed along a finite length ls< L centered at the cavity center. The signal relative to one in which the entire sample is concentrated a t the cavity center is given by
2
Thus in order to maintain a value of S/Sowithin 0.99, the maximum value of l,/L must be smaller than 0.113 for a rectangular TEIMcavity (9.54 GHz unloaded), where L = 2.24 cm. The maximum sample length may be 0.25 cm, which is within the range of those used in these measurements. The absorption of power on a reflection type ESR spectrometer is determined by the change in the cavity Q-factor (AQ) during resonance. The change in the Q-factor is given by Equation 6 (10)
where 7 is the filling factor, and x’’ is the imaginary part of the magnetic susceptibility. For a small sample centered in a TE104 cavity, 7 2Vs/Vc, where V, is the sample volume
-
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
963
14
Table I. Magnetic Parameters of Cr,O, and NaCrO,
,
,
I
,
,
,
,
I
,
,
,
,
,
,
k
Cr,O,
NaCrO,
temperature, K Curie temperature, K
306-312 ( 1 3 - 1 8 )
48
-1070 ( 1 7 )
-322 ( 2 3 ) -400
g-Factor
-680-400 ( 1 9 - 2 2 ) -485' 1.97 ( 1 4 ) 1.982 * O.OOla 3.73* 3.54-4.12 ( 1 9 - 2 2 )
Nee1
(P,f f 1" a
i:
-
12
3 (3, 23)
i:
30 ( 3 )
1.979 i: 0.003 (3) 1.984 i: 0.002= 3.70 ( 2 3 ) 3.60 + 0.05 ( 3 )
This work. Best value, Ref. 21. Theoreticalvalue + l)]"' = 3.873 for g = 2. for e = -485 K.
*t
g[s(S
I
and V , is the cavity volume (11). The value of qx" a t the resonance maximum is given by Equation 7 ~ X " m a x=
2nfoTz
(OK)
Temperature dependence of the double integral of samples of NaCrO, and Cr2O3: (A)Cr2O3, ( 0 )NaCrO,, (0)NaCrO, prepared from Cr,O3 containing 0.6 X stochiometric amount of Na2C03,(0) NaCrO, prepared by heating Na2Cr207in H, Figure 1.
g2pzHoS(St l ) N 3k(T- @)V,
(7)
where g is the spectroscopic splitting factor, /3 is the Bohr magneton, S is the electron spin, k is the Boltzman constant, T is the absolute temperature, O is the Curie temperature of the sample, fo is the resonant frequency. For NaCr02,Ho is about 3.3 KG, and 8 = -322 K. Assuming a Q of 6500, if a nonlinearity of 1%for the value of AQ/Q is permitted, then the maximum number of paramagnetic ions permitted is approximately 3.5 X 10". The largest sample used here consists of approximately 2.7 X lo1' ions of Cr3+. This would imply a nonlinearity of about 0.8% at the absorption maximum. The double integral is perturbed to a smaller degree. Analysis of Mixtures. Antiferromagnetic materials exhibit two distinct temperature regions. At low temperatures, the materials are antiferromagnetic, i.e., they exhibit an anomalously low magnetic susceptibility due to antiparallel coupling of spins. In this region, the magnetic susceptibility is strongly orientation dependent, and resonance can only be observed in the THz frequency range for small applied fields. As the temperature increases, the susceptibility will also increase. At the NBel temperature, ON, the material undergoes a transition to a paramagnetic state. 8 N is usually very near the temperature maximum of the magnetic susceptibility. At higher temperatures, T > O N , the magnetic susceptibility approaches the value given by the Curie-Weiss law. At temperatures only slightly greater than ON, the ESR linewidth has been shown to decrease rapidly. Typically the half-width a t half height is proportional to (1- ~ N / T ' - where ~, p 0.75 (12). In addition, the NBel temperature of polycrystalline Cr203has been shown to be slightly sensitive to the size and shape of the particles (13). Thus, quantitative measurements should not be carried out within a few degrees of the NBel temperature, because of large linewidth variations with temperature, sensitivity of O N to particle geometry, and because the Curie-Weiss law is not obeyed. However, these properties suggest that various components in a mixture might be determined independently by virtue of the temperature dependence of their ESR signals. Since antiferromagnetic materials a t T < 0~ do not exhibit a conventional ESR signal, the composition of the material may be determined by measurements in the paramagnetic region of each component, but below the NBel temperature of each of the successive components. ESR and magnetic properties of Cr203have been extensively studied (14-22). Parameters are given in Table I. Although g and 8 N are well documented, values of the Curie temperature show considerable scatter (13,19-22). The value of 0 appears to depend upon the method of preparation and on the handling of the sample (20,21), including the amount
-
964
TEMPERATURE
i
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
700 800
100 3
i
1
,
1
I
I 1
K
/
120
'
"
160
"
'
200
'
1
I
240
TEYPERATURE
I
1
280
320
360
(OK)
Figure 2. Temperature dependence of the peak-to-peak linewidth of samples of NaCrO, and Cr,03; (A) Cr,03, ( 0 )NaCrO,, (0)NaCrO, prepared by incomplete reaction of CrzO3 and Na2C03,( 0 )NaCrO, prepared by heating NapCr,07in H2
of absorbed O2 (21) even though samples may appear to be chemically equivalent (20). Regardless of the magnetic moment, and the Curie temperature, the reciprocal of the susceptibility of Cr2O3 is linear with temperature above 320 K (13, 19, 21). Sodium chromite has not been so extensively studied. Magnetic parameters are listed in Table I (3, 23). The variation of the Curie temperature with sample preparation has not been studied. Figure 1shows the temperature dependence of the double integral of the ESR signal of several samples of NaCrOz and Crz03. Note that a t 300 K, the double integral of the Cr203 signal is essentially zero and increases rapidly at 305 K. However, the double integral of the ESR signal of NaCrOz decreases slowly in that region. A sample of NaCrOz which contains Crz03 due to incomplete reaction with Na2C03, shows a rapid increase of the double integral a t about 305 K. The linewidths of NaCrOz and CrzO3 are shown in Figure 2. Note that the linewidth of NaCrOz decreases more slowly with temperature than predicted, and that at 330 K, the linewidth
1,5
Table 11. Dependence of the Amplitudes of the ESR Spectra on the Composition of NaCr0,-Cr,O, Mixtures Fraction NaCrO, 1,000 0.990 0.979 0.958 0.923 0.834 0.675
Amplitude 300K 3.66 4.03 5.47 4.91 5.67 4.93 4.43
Amplitude 330K
Ratio
3.83 4.28 5.87 5.41 6.60 6.30 7.78
1.045 1.062 1.073 1.102 1.164 1.278 1.792
Omitted from mean. weighing uncertainty,
Amplitude (330 K)/ w t NaCrOZb
1.4
1.494 1.444 1.499 1.481 1.460 1.467 1.31ga 1.474 u 0.021 % 1.4
3 1,1 b
/I
v/ 1
t
Include a 0.5% (i.0.02 mg)
a
c
3 9 h
1
1
8330
--
s300
-_
A330 - g 3 3 0
A 3 0 0
+A300
where A and B are the signals per unit weight of the NaCrOz and Crz03at the respective temperatures, and f is the weight of NaCrOz divided by the sum of the weights of NaCrOz and Cr203. S may either be the amplitude or double integral of the ESR spectra. Data for mixtures of NaCrOz and Crz03are shown in Figure 3. Note that the double integral is linear with l/f,but that the peak-to-peak amplitude is only linear above about 90% NaCrOz. As Crz03 is added to NaCrOz, the
1
1
,
1
1
ti 1>
~
linewidth increases, and thus the amplitude becomes nonlinear. The values of A330/A300 determined from the graph are 1.046 for the peak-to-peak amplitudes and 0.974 for the double integrals. These compare to values extrapolated from the temperature dependencies between 220 and 300 K, which are 1.045 f 0.002 and 0.972 f 0.004, respectively. The standard deviation off was 0.0025 for values off between 0.9 and 1.0 using relative peak-to-peak amplitudes, and 0.008 for values off between 0.1 and 1.0, using relative double integrals. Data for these measurements and for the ratio of the peak-to-peak amplitude and double integrals divided by the weight of each component is given in Tables I1 and 111. Note that the amplitude at 300 K divided by the weight of NaCrOz is constant with a standard deviation of 1.4%. The corresponding standard deviation for the double integral ( D ) is 2.6%. These contain a weight error of about f0.5%. The results of the calculation 0 3 3 0
- 0.974
0 3 0 0
WCr,O,
(8)
f
,
12 13 14 RECI?%oWL SF EI3T F#CTlQi F: z C
Figure 3. Ratio of peak-to-peak amplitudes and double integrals of the ESR signal at 330 K to that at 300 K
Q=
. -1
I
11
13
of NaCrOz is 2 / 3 of that of Cr203. The linewidth and double integral of a sample of NaCrz07 reduced in hydrogen is also shown in Figures 1 and 2. This sample contained residual dichromate, and was incompletely reduced. At about 250 K, a rapid increase of the double integral is observed. This suggests the presence of an antiferromagnetic component with a NBel temperature near 255 K. This may be due to an intermediate valence state of Cr, either as an oxide or oxy-anion. Cr(V1) is diamagnetic, and CrOz is ferromagnetic. Crz05exhibits a NBel temperature lower than 100 K (24). Numerous chromium oxides of compositions Cr02.25to Cr02.67exhibit paramagnetic susceptibilities a t room temperature (25) suggesting NBel temperatures below 290 K. At low temperatures, a sharper line is observed for NaCrOz than would be expected for the pure material. Above 320 K the double integral and linewidth again seem to rise, suggesting additional antiferromagnetic components in the material. If a signal S is assumed which at 300 K is due to NaCrOz, and a t 330 K is due to the sum of both NaCrOz and Cr203, then the ratio of these can be shown to be given by Equation 8
fi
are also given in Table 11. Values of Q are constant to within 5% at compositions between 1 and 100% Crz03. The agreement a t 1 and 2% levels of Cr203is fortuitous because the double integrals are only reproducible to *0.2%, and a t 1% of Cr203,the differences between values of the double integral are accurate to f 15%. The limits of detection of Crz03in NaCrOz is about 0.5% Cr203by weight utilizing the relative double integral values, and about 0.25% utilizing the relative peak-to-peak ampli-
Table 111. Composition of Mixtures of NaCrO, and Cr,O, and the Double Integrals of the ESR Spectra at 300 K and 330 K Fraction NaCrO, 1.000 0.9902 0.9792 0.9580 0.9230 0.8341 0.6752 0.0000
wta
NaCrO,, mg 2.45 2.79 3.65 3.315 3.885 3.36 3.29 0.00
wt Crz03,mg 0.000
0.0277 0.0780 0.145 0.324 0.669 1.58 3.38
Double integralsb 300 K 0.513 0.584 0.737 0.677 0.819 0.704 0.645 0.000
330 K 0.500 0.574 0.734 0.68 5 0.864 0.815 0.949 0.647
Ratio of integrals 0.974 0.983 0.996 1.012 1.055 1.158 1.472 m
av U
% a
The total weight includes an uncertainty of *0.02 mg or 0.4 to 0.8%.
D 30n)/wt D ( 3 0 0-) 0.974
PfaCrO, 0.2094 0.2093 0.2020 0.2042 0.2108 0.2095 0.1960
...
0.2059 0.0054 2.6
~ ( , , , ) / w tCr,O,
...
0.187 0.207 0.177 0.205 0.193 0.203 0.192 0.195 0.011 5.6
Arbitrary units.
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
965
Table IV. Determinations of Cr,O,
Material
OW)
MnSO,.H, 0
- 26 - 26
Cr,O,
-485a - 600 - 400 -400 - 322 - 200
NaCrO,
a
Recommended value of
a n d NaCrO,
Based on MnSO,.H,O
T(K) 300 330 330 330 330 300 300 300
N observed, mol
4.61 x 5.25 x 4.12 x 3.23 x 2.87 x 2.29 x
N predicted
Error, % 0.0
7.10 X 7.10 X
10-5 10-5 10-5 10-5 10-5 10-5
4.45 x 4.45 x 4.45 x 2.29 x 2.29 x 2.29 x
0.7
+ 3.6
10-5
10-5 10-5 10-5 10-5 10-5
14.
- 10. 41. 25.
assumed
O,
tudes. The latter technique can only be used up to about 10% CrzO3 while the double integral ratios can be used over the full range of composition. Absolute Composition. Based on the data shown in Tables I1 and 111,if the peak-to-peak amplitude is calibrated at 300 K, the amount can be determined to within about &2%, as indicated by the constancy of the amplitude divided by the weight. Considering the noise level of the instrument, we place the limit of detection at about 3 fig. Similarly the double integral can be used for this determination, although a slightly larger error is incurred. However, the detection limit is considerably smaller because of the noise reduction due to the integration process (26). A similar argument is also applicable to Cr203, but here the accuracy of the determination will depend upon the amount of NaCrO2 present since the amount is proportional to the difference between two values. An alternative method of determining the amount of a paramagnetic material is to relate the double integral to that of a standard. We have utilized MnSO4-HZ0to calibrate the ESR spectrometer. Determinations of the amount of NaCrOz and CrzO3 are shown in Table IV. 8 for MnS04 has been determined to be -26 K (27). Utilizing a Curie temperature of -485 K gives reasonable agreement between the predicted and observed amounts of Crz03. However, Curie temperatures between -400 to -600 K have been reported, which would reflect an error of between -10 and +14%. The best value of 8 for NaCrO2 appears to be -322 K (23) since it was determined over a wider temperature range than was the value of -400 (3). Nevertheless, both of these values indicate a larger amount of NaCr02 than the sample contains. A value of 8 = -200 K results in good agreement. Based on observations of Cr203@ I ) , the Curie temperature may be in error by this amount. It is also evident from the magnetic susceptibility measurements that the value p e f fwhich , is equivalent to [g2S(S + l)]l’zis considerably different from the theoretical values. For CrzO3, with 8 = -485 K, the value of p e f fis 3.73 rather than 3.84 based on the g-factor. Similarly for NaCrOz, peff 3.65. If these values were utilized in Equation 2 rather than the values determined from the ESR measurements, the calculated amounts of each material would be larger. A t present the source of this discrepancy is not understood. Since the Curie temperatures of Crz03and NaCrOz may depend on the handling and preparation, the analysis based on calibration by a different paramagnetic standard is unreliable. Homogeneous Mixtures. Several stoichiometric mixtures of NaZCO3and CrzO3 were incompletely reacted. Linewidths of NaCrOz in the paramagnetic region were equal to those of the pure material. This suggests that NaCr02 forms without inclusions at up to about 10% excess CrzO3. A mixture of
-
966
7.10 X 7.15 X
ANALYTICAL CHEMISTRY, VOL. 49, NO. 7, JUNE 1977
Crz03with 0.500 times the stoichiometric NaZCO3was also reacted to completion. The relative double integrals indicated that the ratio of the weights of CrzO3 to NaCrOz is 0.385, or a molar ratio of 0.546 as opposed to the expected value of 0.500. This discrepancy was accompanied by a peak-to-peak linewidth of 216 G instead of 255 G at 300 K. Thus the linewidth may provide an indication of the homogeneous purity of the material. This has not been investigated. ACKNOWLEDGMENT We thank David Lind for carrying out x-ray crystallographic measurements on these samples. LITERATURE CITED P. Chiotti, P. C. S.Wu, and R. W. Flsher, J. Nucl. Mater., 38, 260 (1971). W. Rudorff and H. Becker, Z . Naturforsch. B., 9, 614 (1954). P. R. Elliston, F. Habbal, N. Saleh, G. E. Watson, K. W. Blazey, and H. Rohrer, J. Phys. Chem. Solids, 36, 877 (1975). I. 6 . Goldberg, H. R. Crowe, and R. S.Carpenter 11, J . Magn. Reson., 18, 84 (1975). G. E. Pake, “Paramagnetic Resonance”, W. A. Benjamin, Inc., New York. 1962, Chapter 2. J. E. Wectz and J. R. Bolton, ‘‘Eleckon Spin Resonance: Elementary Thmy and Practical Application”, McGraw-Hill, New York, 1972, pp 462-464. I. 8. Goldberg, and A. J. Bard, “Analytical Applications of Electron Spin Resonance” In “Treatise on Anawical Chemistry: Magnetic and Related Methods,” I. M. Kolthoff, P. J. Elving, E. B. Sandell, and M. M. Bursey, Ed., 2nd ed, John Wiley, New York, in press. Operating Manual for Varlan V-4502 or E-Llne ESR Spectrometers. I. B. Goldberg and G. R. Schneider, J. Chem. Phys.. 65, 147 (1976). B. Vigouroux, J. C. Gordon, P.Lopez, and J. Pescia, J. Phys. E, 6 , 557 (1973). C. P. Poole, “Electron Spin Resonance,” John Wiley, New York, 1967, pp 291-307. H. Mor1 and K. Kawasaki, Progr. Theor. Phys., 28, 971 (1962). W. Gunsser, W. Hllle, and A. Knappwost, Z . Naturforsch. A , 2 3 , 781 (1968). T. R. McGuire, E. I. Scott, and F. Grannis, Phys. Rev., 102, 1000 (1956). L. R. Maxwell, Am. J. Phys., 2 0 , 80 (1952). L. R. Maxwell and T. R. McGuire, Rev. Mod. Phys., 25, 279 (1953). E. P. Trounson, D. F. Bleii, R. K. Wangsness, and L. R. Maxwell, Phys. Rev., 79, 542 (1950). S. A. Angelov and D. R. Mechandjiev, C. R . Acad. Bulg. Sci., 26, 1213 (1973). K. Honda and T. Sone, Sci. Rep. Tohoku Imp. Univ., 2, 1 (1913). C. J. Gorter, W. J. de Haas, and J. van den Handel, Proc. Acad. Sci. Amsterdam, 36, 168 (1 933). S. S.Bhatnagar. A. Cameron, E. H. Harbard, P. L. Kapur, A. King, and B. Prakash, J. Chem. SOC.,1433 (1939). G. Foex and M. Graff, C. R. HeM. Seances Acad. Sci., 209, 160 (1939). A. Apostolov and R. Ch. Bois, C. R . Acad. Bulg. Sci., 22, 527 (1969). E. Hirota and B. Kubota, J. Phys. SOC. Jpn., 1 5 , 1715 (1960). W. H. Albrecht and E. Wederkind, 2.Anorg. Chem., 210, 105 (1933); 0. Glemser, U. Hauschild, and F. Trupel, ibid., 277, 113 (1954). D. W. Posener, J. Magn. Reson., 14, 129 (1974). Y. Allain, J. P. Krebs, and J. de Gunzbourg, J. Appl. Phys., 39, 1124 (1968).
RECEIVED for review December 27,1976. Accepted March 17, 1977. This work was supported by the Westinghouse Hanford Company, Richland, Wash., under contract Y6W-S44-37399. Computer programs for control and analysis of data were developed under support of the Office of Naval Research.
