1232
BRUCER. MCGARVEY
Vol. 61
e.u., roughly of the entropy of vaporization, over direct measurements of rates of vaporization indicating considerable freedom of motion of mole- into high vacuum by minimizing the surface temcules in the surface layer. perature and area uncertainties. It is apparent Although there is no pronounced change in the that the method is not well-suited for determining molecular nature of iodine in the vaporization proc- coefficients near unity; it may also be unsuitable ess, the internuclear distance is reduced appre- in cases where a is very small as the area problem ciably, 2.65 A. in the vapor as compared with 2.70 is then likely t o be troublesome even within the A. in the solid. This may be responsible in part cells.19 We wish to acknowledge with thanks support for the small value of a. Whereas the effusion method does not give con- received for this research from the Research Cordensation coefficients with high precision for io- poration. dine, it appears to offer considerable advantage (19) L. Brewer and J. S. Kane, THIS JOURNAL, 69, 105 (1955).
LINE WIDTHS I N THE PARAMAGNETIC RESONANCE OF TRANSITION IONS I N SOLUTION BYBRUCER. MCGARVEYI Department of Chemistry and Chemical Engineering, University of California, Berkeley 4, Catifornia Received May 10, 1067
The line widths for the paramagnetic resonances of solutions containing the ions Ti+*, Ve4, Mn+6, Mn+*, FA+*, Crfa, Co+*, Ni+z and C U +or ~ various complexes of these ions are re orted and iaterpreted in terms of various broadening mechanisms. It is shown that the widths are adequately accounteffor by assuming the inn is preeent in a small microcrystal formed from solvent molecules or complexing groups and that this microcrystal possesses a spin Hamiltonian similar to that observed in solid crystals. The width is found to depend on the symmetry of the electric field generated bv the oomplexing groups and some deductions about these symmetries are made from the experimental widths. I n addition, a change in width dun to corn lex formation is made use of in the case of manganous ion to measure the complexing constants of manganous ion with pyri&ne. A etudy of the width of the manganous ion resonance in alcohol-water mixtures is also ~. reported.
Introduction McConnel12 recently has proposed an explanation for the dependence of line width upon I , observed in the hyperfine spectra of copper compounds in s o l u t i ~ n . ~His , ~ theory, employing the methods of Bloembergen, Purcell and Pound,4 is based on a microcrystalline model in which the rotation of the microcrystalline unit involving the ion is not sufficient to average out completely the anisotropy of the crystalline resonance. The purpose of this paper is to extend McConnell’s treatment to other ions in the first transition group and to discuss the observed line widths of these ions and their complexes with respect t o this theory. Sources of Line Broadening There are several varieties of interaction which influence the line vldth of paramagnetic ionsin solution. One of these is the broadening resulting from the magnetic dipolar interaction between ions which has been treated by Bloembergen, Purcell and Pound.4 This will not be important for the solutions used in this work as the concentration of most of the solutions was such as to make the contribution to the width from this interaction negligible. Further the concentrations were small enough so that we can disregard the “exchange narrowing” effect observed in highly concentrated solutions. If we consider the ion in solution to be part of a small microcrystal involving solvated molecules or (1) Kalamaroo College, Kalamaaoo, Michigan. (2) H. M. McConnell, J . Chem. Phya., 26, 709 (1956). (3) B. R. McGarvey, THIEJOURNAL, 60, 71 (1966). (4) N.Bloembergen, E. M. Purcell and R. V. Pound, Phya. Reva., 73, 679 (1948).
complexing groups and that this microcrystal moves and tumbles as a unit in the solution maintaining its structure in a time long cgmpared to its rate of tumbling, then there is the possibility of attributing the observed line width to two other mechanisms. One mechanism is important in the spectra of crystals themselves and involves an interaction between the ground state and a nearby excited state limiting the lifetime of the ground state and leading to indeterminancy broadening. Van Vleck6 has considered this mechanism and found that the spin lattice relaxation time T1is dependent to a marked extent on the energy separation between the ground state and the first Stark excited state as well as on the temperature, Thus we can expect appreciable broadening from this mechanism when the symmetry of the electric field about the ion is such as to allow a crystalline field level to lie close to the ground level, but a negligible broadening when the electric field yields a large splitting between the ground state and all crystalline field states. Thus, contributions from this mechanism to the width of the resonance line will be a function of the nature of the ground state of the ion and the symmetry of the electric field about the ion in the microcrystal. If there is any anisotropy in the crystalline resonance of the ion we can expect some broadening of the resonance line, due to the tumbling of the microcrystal in the solution. The extent of the broadening will be determined by the rate of tumbling and the size of the anisotropy in the resonance. The contribution to the width from this mechanism (6)
J. € Van I .Vleck, ibid., 67, 426 (1940).
LINE WIDTHSIN PARAMAGNETIC RESONANCE OF TRANSITION IONS
Sept., 1957
may be estimated by assuming a spin Hamiltonian for the microcrystal similar to that observed experimentally for the crystalline ion and employing the methods of Bloembergen, Purcell and Pound4to calculate the values of T1 and T,’for the resonances. It is interesting to note that although this mechanism predicts a dependence of width upon the symmetry of the electric field just as the other mechanism mentioned above, the dependence is inversed. Lines broadened by the interaction with excited states should become narrower as the symmetry is decreased since the number of degeneracies or near degeneracies becomes less as the symmetry becomes less, while lines broadened by the anisotropy in the resonance should become broader with decreasing symmetry due to the increase of the anisotropy. Experimental Equipment and Procedures The equipment and procedures are the same as those used in an earlier work.* For experimental convenience the width of the line is defined as the EeparatiOn between the maximum and minimum points on the derivative of the absorption curve.
Cu+2.-The spin Hamiltonian for C U + with ~ a spin of is = B[g,,H.S.
+ 91
( H Z S Z
+
+ + B(I,Sn +
HYSYN
AIh’z
IySy)
(1)
where the z-axis is the symmetry axis of the microcrystalline ion and S and I are electron and nuclear spin operators in units of A, respectively. McConne112 has shown that this Hamiltonian gives for TI and 57,’ TI
=
r$)
(AgBHo
+ b I . ) % - * ~ ~ / (+l 4 ~ 2 ~ ~ %(2)2 )
where Ag = 911
- 91; b = A - B
r0=
4mros/3LT
(4) (5)
T,, is the correlation time for fluctuations of the microcrystalline ion, Y O is resonance frequency, ro is the radius of the microcrystal, and q is the vixosity coefficient between the ion and the solvent. The exact relationship between the experimental line width and 1/T1 plus l / T i depends on the shape of the absorption curve, but we can approximate it with the equation
line width S l/rT*’
+ I/2rTl
(6)
This is the line width due to the tumbling motion alone and may not be the observed width if other broadening mechanisms are important. The ground state of C U + in ~ a cubic electric field is doubly degenerate. This degeneracy is not present in an actual case since the electric field is distorted from the cubic field, but in the case of the hydrated ion in crystals, CU(H*O)~+~, the distortion is small so that there is a low lying excited state which limits the life time of the ground state and broadens the resonance lines. I n crystals this mechanism is effective enough to erase the hyperfine structure in the room temperature spectrum.* Thus the lack of ~ in water hyperfine structure for the C U +resonance (6) D. M. 8. Bagguley and J. H. E. Gri5ths, Proc. Phys. SOC. (London), A M , 594 (1952).
1233
solution is probably due to a combination of broadening by interaction with a low lying excited state and broadening caused by slow tumbling of the hydrated ion. We can check eqs. 2 and 3 for the case of copper acetylacetonate in dioxane because for this complex, studies of the crystal spectra have determined the constants in the spin Hamiltonian and have shown that the crystalline electric field is so far from cubical that there are no low lying states to contribute to the width of the observed resonance^.^ Taking ro = 4 A., q = 0.002 poises, Ag = 0.209 and b/h = 559 Mc./s. we obtain for the widths of the four lines the values: 0.84, 0.41, 0.13 and 0.06 X lo8 c./s. Experimentally the widths are 0.44, 0.21, 0.17, 0.13 X lo8 c./s.~ This must be considered as good agreement as far as magnitude is concerned. The ratio of widths is in somewhat greater disagreement since this depends very little on the value assumed for rC. However, the lesser dependence of the experimental lines on I, readily can be accounted for as resulting from: (1) Ag and b are different in dioxane due to solvent interaction,2 the change being in the proper direction to give a lower dependence on I , and (2) the experimental widths have contributions from other broadening mechanisms not dependent upon I,. The agreement is such, however, to indicate that the mechanism proposed by McConnell is the chief one in this case. Ti+3,V+4 and Mn+B.-These three ions are isoelectronic, having one electron in the 3d shell and possessing a spin of l/z. Their spin Hamiltonian is similar to that of C U +but ~ they differ from C U + ~ in that their ground state is triply degenerate in a cubic field and the degeneracy can only be removed by a greater degree of asymmetry in the field than is required for C U + ~ . Thus for Ti+Sand Mn+6, which occur mainly in crystals giving cubical fields about the ion, Tl’s are very short and resonances are detected only a t very low temperatures. Attempts were made to detect the resonance of Ti+3in water solutions of TiCla and of Mn+‘ in alkaline water solutions of K2Mn04but with no success. The electrical fields about the ions are apparently too near cubical to give narrow enough lines for detection. The experimental limit for a detectable line width was approximately 1500 to 2000 gauss so we can say the line widths of Ti+3and Mn+‘ in these solutions were greater than this. Joness has reported detecting the Ti+8resonance in a “green” solution of TiCls prepared by reducing Tic&in acid solution with Zn. The normal color for Ti+3in water is violet. This resonance was 25 gauss wide and appeared also when Ticla was dried and then dissolved in 95% alcohol. This author has as yet been unable to prepare this “green” solution to check the results but it seems possible that Jones was able to prepare some complex of Ti+8 whose symmetry was so low that the excited states of the ion were too far removed from the ground level to be effective in limiting the lifetime. That narrow resonances will result from this ground state when the ion is in a highly asymmetric field is demonstrated in the case of V+4. Pake and (71 A. H. Mski and B. R. McGarvey, to be published.
(8) R. V. Jones, private communication.
BRUCER. MCGARVEY
1234
Sandsg have observed the V+4 resonance in a variety of solutions and have observed the widths of the lines to be both narrow and dependent upon I,. The narrowness can be explained by a large asymmetry resulting from the ion being really the VO+2 ion and in fact the narrowness of the lines must be taken as good evidence for the existence of the VO+2 ion. The resonance disappears when the solution is made alkaline due to the formation of complex ions in which the field about the V+4 ion is more symmetrical. Since the spin Hamiltonian is identical in form to that of C U + ~the , dependence of the line width of the eight hyperfine lines upon I, is adequately explained by the mechanism proposed by McConnell for the Cuf2 ion. Cr+3.-For Cr+3 the spin Hamiltonian for a spin of 3/2 is found to be X = 6gH.S
+ D [ S 2 - (1/3)S(S+ 1)J
(7)
This is for a cylindrically symmetrical electric field, the z-axis being the axis of symmetry. For cubic fields D should be zero while for fields of lesser symmetry an additional term involving S, and S, must be added but this term is normally of smaller magnitude than the axial term and we shall neglect it. Normally g is isotropic with a value near 1.98. Since the symmetry axis of the ion will be tumbling with respect to the magnetic field, it is convenient to recast eq. 7 into a coordinate system where the z-axis coincides with the magnetic field Ho. This gives
+
-
+
X = BgHoSz (3/2)D[S2 (1/3)S(S 111 (cosa e - 1/3) (1/2)0 sin e cos e [(S,S+ S+S,)e-is (S,SS-S,)ei4] (1/4)0 sin2 B[S2+e-ai@ S_2e*i@] (8)
+
+ +
+
+
+
where 6 and 4 are the polar angles for the symmetry axis with reference to the laboratory coordinate system and S+ and S- are the operators (S, is,)and (S, - iS,),respectively. The crystalline spectra of Cr+3 consist of three lines all having the same center of gravity, while the solution spectra consist of only one line. Thus in using eq. 8, are we to calculate an average 1/T1 and 1/T; for the three lines and assign these to the one line observed in solution or are we only seeing the center line which has little anisotropy and just failing to see the other two lines due to their broadness? This can be answered by experimentally comparing the intensities of the solution resonances. In doing this for various Cr+3 complexes it was found that in each case the one resonance observed contained all three resonance transitions. Thus we should use (8) to calculate average values for l/T1 and l/Tz'. Using the same methods employed by Bloembergen, Purcell and Pound4 with the spin Hamiltonian given in eq. 8, it is established readily that
+
(9) T~ and vo have the same definition given for eq. 2 and 3 for copper. (S) Q. E. Pake and R. H.Elan&, B d l , Amsr. Phya. Soc., 89, No. 8, i 8 (1914).
Vol. 61
Cr+*ion has a 4F ground state which gives a singlet ground state in the presence of a cubic electric field, so that broadening due to an interaction with a low lying excited level is generally negligible for the ion. We can, therefore, expect most of the observed broadening in solution to be due to the tumbling motion of the microcrystal. For the Cr(HaO)a+3ion reasonable values for TO and 9 would be 3.8 X 10-8 cm. and 0.00855 poises, respectively, and these would give for T~ the value 4.7 X sec. In crystals containing this ion the D term has values from 0.06 crn.-' a t room temperatures to 0.02 cm.-l at much lower temperatures, but it is not certain how much of this results from anisotropies in the electric field of the water molecules. If we take D to be 0.06 cm.-l then eq. 9 and 10 give l/T1 = 1.5 X 109 sec.-l and l/Tz' = 3.8 X lo9sec.-l which in turn give with eq. 6 a line width of 520 gauss. If we take D to be 0.02 cm.-l then we would obtain l/Tl = 1.8 X los sec.-l and 1/T; = 4.6 X 108 sec.-l giving a line width of 60 gauss. We see that for the value of T,, used, the main contribution to the width comes from T?' rather than TI. The width of the line is more sensitive to the value chosen for D than the value for T~ since in this region of T ~ T1 , and Ta' vary in OPposite directions with T ~ . Thus for D = 0.06 cm.-' the line width only changes from 520 to 260 gauss when the value of T~ is reduced by one fourth. Experimental line widths of various complexes of Cr+* are given in Table I. For a value of T~ 4.7 X 10-l' sec. the line width of Cr(HzO)a+a1s consistent with a value of D = 0.04 cm.-l which would seem to indicate that in the crystal the D term arises mainly from polarization of the ion by the electric field generated by the water molecules surrounding the ion and that the average value of this field does not possess cubic symmetry. Thus the resonance data indicate that the water molecules about the Cr+3ion are not in a perfect octahedral structure but rather in some distorted structure. TheOeffect of increasing the distortion is noted in the resonance of the ion Cr [(H20)~Cl2]+'.This ion should certainly possess a larger value for D and hence should give a broader resonance. The exact width of the resonance could not be determined since the ion slowly converts to the hexahydrate, but it is certainly greater than the 390 gauss observed ten minutes after the solution was made up. The slow conversion to the hexahydrate with the narrower resonance is shown very nicely by the time dependence of the line width given in Table I. The effect of extremely large D values is shown by the work of Singerlo who found for the acetylacetonate that D = 0.592 cm.-l and that the solution resonance is identical with the powder resonance. I n this case the tumbling rate is too slow to reduce l/Tz' appreciably below that observed in the powder. The narrower resonances in CrF,-a and Cr( N H ~ ) G indicate +~ a greater symmetry about the Cr+3 ion than in the case of the hydrated ion, although some of the narrowness should probably be (10)
L. 8. Singer, J . Chem. Phya., 28, 379
(1955).
LINE WIDTHSIN PARAMAGNETIC RESONANCE OF TRANSITION IONS
‘Sept., 1957
1235
attributed to smaller T,,’s due to smaller viscous interaction between ion and solvent. TABLE I LINEWIDTHSOF Cr +3 COMPLEXES
where
Line width Solution
Complex ion
(gauss)
0.2 M CrK(b04)2.12H~0C I - ( H ~ O ) ~ + ~ 210 0.2 M C ~ [ ( H Z O ) ~ C ~ ~ ]Cr[(H~O)&l~jfl CI (10 min.) 390“ (25 min.) 280“ (1 day) 200“ 0.1 M (NH&CrF, CrF6-a 80 Cr(NHs)a+3 34 0.1 M CrINH&(NOs)a 0.01 A4 Cr(NH&(NOa)3 Cr(NH8)6+a 33 a Time is approximate time spectrum was run after preparation of solution.
TABLE I1 LINEWIDTHS OF Fe+8 AND Mn+2 COMPLEXES Solution
0.001 M MnCl2 10.1 M MnClz ‘0.06 M MnClz in pyridine 0.1 M MnClz in C2H50H
+ +
Complex ion
Mn(Hz0)8+2 Mn(HzO)6+z Mn(py)z+z
...
Line width
(gauss)
26 31 610 510
~
0.3 M Fe( ClO& 0.4 N HClOd Fe(HzO)s+S 1200 0.5 M Fe(N03)3 f 2.0 N H N 0 3 Fe(HzO)6+3 1100 0.1 M Fe(NOa)3 2.0 N HCI04 Fe(H20)a+3 1100 0.50 M Fe(NO& 0.50 M K F 0.34 A l a FeF+2 1100 0.50 M Fe(N0313 1.00 Jf K F 0.3 MaFeFz+l 420 0.50M Fe(Pu’03)3f 1.48 N KF 0.3 M a FeF3 330 a Concentrations of complexes estimated from data of R. E. Connick, L. G. Heplei, Z. Z. Hugus, Jr., J . W. Kury, W. M. Latimer and Riaak Sang TYL~O, J . A m . Chem. Sac., 78, 1827 (1956).
+ +
Mn+2 and Fe-t3.-For and Fe+3 with spin of 5/2 the spin Hamiltonian is the same as given for Cr+3 in eq. 7 except for an additional cubic term
+ + 82‘ -
(1/6)~[S.z~ Su4
(1/5)S(S
+ 1)(3S2 + 3X - 1)J
(11)
not present for Cr+3. For Mn+2 there is an adlditional interaction between the nuclear and electron spins, but since i t is normally isotropic and will not contribute to the line width we shall neglect it in our considerations. The normal ground state for the Mn+2 and Be+3ions is sS which has no degeneracy and therefore no nearby excited states to contribute to the line width. Thus any width in the resonance lines should be due primarily to any anisotropy in the resonance. The crystalline spectra of these ions consist of five lines while the solution spectra consist of one line (not counting hyperfine splittings in Mnf2). Thus as in the case of Cr+3we must determine whether the one solution resonance contains all five lines or only the center one of the crystalline spectra. Comparison of intensities again showed that the solution resonance contained all five resonance lines. Therefore proceeding in a similar manner to that used for C r f 3 we can obtain for l/T1 and 1/!Pz’
T ~ ’ =
(3/10)~~
(14)
The contribution of the cubic term to 1/T1 has not been calculated since the contribution of this term to the line width is too small to justify the work necessary for the calculation. In fact as will appear below the contribution of the cubic term to l/Tz’ is also negligible in most c&ses, The Mn+a resonance in water solution has heed studied by several workersii who have found I t t o possess a narrow line width of 30-40 gauss. Fe+3 on the other hand has a width of 1100 auss in water solution. At first glance it seems tgha t this large difference in width can be ascribed t o the fact that the cubic term for Fe+3 is about 20 times as large as the one for Mn+Z. Calculations using eq, 12 and 13 fail to bear this out, For most cr atals D = 0.02 cm.-l for both Fe+3 and Mn+2 w ile d = 0.01 cm.-l for Fe+3and 0.0005 cm.-l for Mnfz. Using eq. 12 and 13 we find for Mnf2, assuming TO = 4.0 A. and 7 = 0.00855 poises, that 1/T1 = 0.85 X 109 see.-’ and l/Tz’ = 1.6 X logsee.-’ giving a line width of 230 gauss. The a term in this case makes a negligible contribution of 1.5 X lo6 sec.-l to l/T9’. For Fe+a, using the same values for T O and q , we obtain exactly the same values, as the cubic term is still negligible, contributing only 5.9 X lo7 sec.-l to l/Tz’. In order that a make a significant contribution to the line width when D = 0.02 em.-’, a must be about 0.05 em.-’ which is much larger than any a values found in crystalline spectra. Thus it appears that even for Fe+S the cubic term does not contribute significantly to the line width and certainly cannot explain the difference in width between Mn+2and Fe+3. Line widths for various complexes of Mn+2 and Fe+3are given in Table 11. The striking difference in width between the hydrated complex of the two ions has been mentioned above. The Mn(HzO)a+2 width is consistent with a value of D = 0.005 cm.-’ which is considerably smaller than that observed in crystal spectra indicating that either the water molecules in the hydrated ion are more nearly cubic in their arrangement in solution than in the crystal or that the D term in the crystal arises primarily from fields generated outside the hydrated ion. The width observed for Fe(HzO)B+a can only be consistent with values of D in excess of 0.04 em.-‘ even allowing for the larger T~ which could result from formation of an iceberg sort of microcrystal. This value for D is much larger than those observed in crystal spectra and is difficult to explain. One is tempted to explain it in terms of a complex of Fe+3 with OH- or some other ions although it is generally believed that no such complex exists with the ions and acidity present in the solutions measured. It is interesting to note, however, that the width of the complex FeF+2
K
(11) M. Finkham, R. Weinstein and A. F. Kip, Phys. Revs., 8 4 , 845 (1951); M. A. Garstens and 8. H. Liebaon, J . Chem. Phya., 2 0 , 1647 (1952); 6. E, Geusic and D. Williama, Phys. Reus., 99, 612 (1955).
1236
BRUCER. MCGARVEY
Vol. 61
The effect of decreasing the symmetry about the ion is most marked in Mn+2 where the resonance literally disappears when a complexing group is added. This effect was first observed by Cohn and Townsend12 in water solutions of Mn+2when complexing groups such as ethylenediaminetetraacetic acid were added. The value for D in these complexes should be about 0.02 em. --I leading t o widths of 230 gauss for each of the hyperfine lines which, however, are only separated by 100 gauss. Thus the resultant resonance is over 500 gauss wide and is normally not observable a t the concentrations and experimental conditions which give easily detectable signals from the narrow Mn+2resonance. -2.0 I I I 1 A more detailed study of the complex fornied be-4.0 -3.0 -2.0 -1.0 tween Mn+2 and pyridine was undertaken to eslog,o xpy. tablish further the broadening mechanism and to Fig. 1.-Plot of logarithm of ratio of complexed to un- show the use to which this broadening could be put complexed manganous ion vs. logarithm of mole fraction of in determining the complexing constants for manpyridine. ganous ion. First it was established that the broadening was not due to a change to a ground I t state of lower multiplicity wherein a low lying excited state could give rise to the broadening. This does happen in the case of the ferricyanide ion which gives too broad a line to detect in water solution. That the complex possesses the same multiplicity can be checked by a measurement of the magnetic susceptibility of the solid complex. Mellor and Coryel113 found the compound Mn(py)lClz t o have a susceptibility of 5.97 Bohr magnetons per manganese which agrees with measurements made by this author. Further the broad resonance of this complex was detected in a 0.06 molar solution of Mn(p,v)zClain pyridine and was found t o be 610 gauss wide. If the complex gives broad lines which are not detectable under conditions used to detect the narrow lines, we can measure the concentration of the uncomplexed Mn+2 by measuring the intensity of the narrow resonance. In the concentration range Fig. 2.-Spectra for 0.2 M MnClz in alcohol-water mix- of 0.001 to 0.01 M used in the measurements, we tures. The mole fraction of water is (1) 1.0; (2) 0.78; (3) can measure the intensity simply by measuring the 0.3; (4) 0.1. height of the derivative curve peaks, since no measurable change in line width occurs in this region. That this can be done was checked by using pure water solutions of MnClz of varying concentrations with the result that in this concentration range the peak heights varied linearly with concentration. d The solutions studied were made up to have the 100 bo same concentration of manganese, which was 0.009 .9 80: M , and varying concentrations of pyridine, the concentration of pyridine varying from zero to 2 molar. The intensities of the resonances were used to obtain the ratio of uncomplexed to complexed manganous ion. The study of this complexing system is quite simple since we are not bothered particularly with ionic strength or pH problems which are so com0.0 0.2 0.4 0.6 0.8 1.00 mon to most complexing studies, If we consider the equilibrium to be of the form Mole fraction of water.
I
Fig. 3.-Line width of hyperfine line of manganous ion in alcohol-water mixtures of 0.2 M MnC12.
is identical with that observed for the hydrated ion i t d f and that the width decreases markedly with the logp sf higher symmetry FeF2+and FeFs.
Mn+1
+ npy = Mn(py),+Z
(12) M. Cohn and J. Townsend, Nature (London], 178, 1090 (1964). (13) D. P. Mellor and C . D. Coryell, J . Am. CAem. Soc., 60, I786
(1938).
THECRYSTAL STRUCTURE OF YTTRIUM NITRIDE
Sept., 1957
1237
then we can write for the thermodynamic equilibrium constant
indicate several species of intermediate widths since the width of the resonances varies gradually as the proportion of alcohol increases until no hyperfine lines are resolvable in the pure alcohol. Representative spectra are given in Fig. 2 for different prowhere X,, is the mole fraction of pyridine. The portions of alcohol. From the shape of the hyperapproximations in (15) should be good ones. The fine envelope, the individual widths of the hyperfine maximum value for X,, is 0.04 in the measurements lines can be estimated. A plot of this width us. so that the activity of pyridine should equal the mole fraction of water is given in Fig. 3. From this mole fraction and the activity of water should be we can estimate the width of an individual hyperapproximately one. Further the charge on the fine line in absolute alcohol t o be about 120 gauss complex ion and the uncomplexed ion are the same which,is consist,ent with a value for D of about 0.01 so that the ionic strength is a constant and the ratio cm. -l. of concentrations should equal the ratio of activities Other Transition Ions for the two ions. If eq. 15 is valid, then a plot of Most ions in the first transition group not yet log,, [Mr~(py).+~]/ [Mn+2]versus loglo X,, should give a straight line of slope n. Such a plot is given mentioned have rather large asymmetries in their in Fig. 1. The straight line obtained gives the spin Hamiltonian and will give lines too broad t o values of n = 1.06 and K = 130 indicating the be detected easily. Attempts t o detect the resopredominant species in these solutions is Mn- nance line in 1M solutions of X C l 2were unsuccess( p ~ ) + ~If. we assume the difference of n from ful, I n crystals containing the hydrated nickel ion unity to be significant and due to the existence of R the axial spin-spin term is rather large with D 2 This is too large ever to be averaged out second smaller complexing constant for M n ( ~ y ) ~ cm.-*. +~ we can estimate from the data values for the first so it is not difficult to understand why no resoand second complexing constants. These values nance was found. Similarily, large anisotropy in the gyromagnetic areK1 = 90 10andKz = 4 2. A similar study was made using ethyl alcohol in ratio yields resonance lines too broad for detection place of the pyridine. In this case the resonances in the case of Fe+2and Co+'.
-
*
*
THE CRYSTAL STRUCTURE OF YTTRIUM NITRIDE BY CHARLES P. KEMPTER, N. H. KRIKORIAN AND JOSEPH C. MCGUIRE Los Alamos Scienti$c Laboratory, llniversitl~of California, Los t l l a m o s , New Mexico Received May d d , lQ67
Pttrium nitride was prepared by converting yttrium met8alto YH? and then to YN. The polycrystalline YN was examined by X-ray diffraction, using both photographic and diffractometric methods. Ytt.rium nitride has space group Oh6-Fm3m (NaC1 structure-type) nnd 4 (YNJ per unit cell. The lattice constant is 4.877 0.006 A. at 23' and :he calThe culated density is 5.89 i 0.02 g./cm.a at 23 ; the pycnomatric density was found to be 5.60 i 0.05 gJcm.3 at 20 melting point of YN is 22670' in the presence of one atmosphere of nitrogen.
*
Introduction Of the Group I11 transition metal nitrides, structural data have been published for ScN and LaN. Becker and Ebertl re orted a rock salt structure for ScN with a = 4.44 , and a calculated density of 4.21 g./cc. at room temperature. Iandelli and Botti2 reported an NaC1-type structure for LaN with a = 5.275 A. More recently Young and ZieglerSfound a lattice constant of 5.295 ==! 0.004 A. for LaN, and concluded that the lattice was the NaCl type. For the lattice constants reported in references 1, 2 and 3, we calculated room temperature densities of 4.47, 6.92 and 6.84 g./cm.a, respectively. Experimental
H
Yttrium sawings were obtained with a small circular saw using anhydrous ethanol as a coolant. First attempts to prepare YN by heating yttrium sawings in nitrogen yielded only 9% YN in 24 hours a t 900'; therefore, two variations (1) K. Becker and F. Ebert, Z.Physik, 81, 268 (1925). (2) A. Iandelli and E. Botti, Atti. accad. Lincei, CEassa sei. fis., mat. nat., %6, 129 (1937). (3) R. A. Young and W. T. Ziegler, J . Am. Chsm. Soc., 74, 5251 (1952).
.
of the method demihed by Eick, Baenziger and Evring' were used. The yt8triummetal chips were first converted to YH2 by reaction with hydrogen at 550' in a quartz tube. The material was then heated to 900' in the presence of a measured quantity of spectro nitrogen. At this temperature the hydride had an observed decomposition pressure of 25 mm. The gas mixture was circulated over the hydride by means of an automatic Toepler pump, and over activated uranium turnings a t 200' where the evolved hvdrogen was continuallv removed. This process was cont
