3462
The Journal of Physical Chemistv, Vol. 83, No. 26, 1979
when excess Zn(I1) is present, OH- reacts with Zn(ITP)2in the same way to form a high relaxivity Zn(I1) environment. However, because the same reaction is also found with Zn(ATP)2-,the presence of an oxygen in the 6 position of either inosine tautomer is clearly no longer deemed necessary. It is not clear why the low pH hydrolysis of Zn(I1) and accompanying formation of high relaxivity species does not occur for Zn(CTP)2-, Zn(CDP)-, or Zn(UTP)2- systems. We can only speculate that the formation of high relaxivity species at low pH is related to the more favorable stacking interactions possible with purine nucleotides than with pyrimidines. It is worth noting that a similar low pH hydrolysis of Zn(I1) has been reported for two purine type nucleotide monophosphate complexes, namely, those with 5'-GMP and with 2'-AMP.I3 In these instances there was no indication that the 1:l complexes were characterized by planar stacking of the bases. The ZnADP system was not really an exception even though no proton loss could be seen by 36ClNMR over the pH 6.0-7.0 pH range. This is a favorable case for stacking interactions and high relaxivity species equivalent to those for ZnATP and the inosine nucleotides form even below pH 6.0, apparently without the need for a hydrolysis type reaction.
References and Notes (1) Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore Laboratory under contract W-7405ENG-48. (2) R. Phillips, Chem. Rev., 66, 501 (1966). (3) R. M. Izatt, J. J. Christensen, and J. H. Rytting, Chem. Rev., 71, 439 (1971).
Uchida, Isoya, and Weil (4) M. Cohn and T. R. Hughes, J . Biol. Chem., 237, 176 (1962). (5) G. G. Hammes, G. E. Maciel, and J. S. Waugh, J . Am. Chem. Soc., 83, 2394 (1961). (6) G. G. Hammes and D. L. Miller, J . Chem. Phys., 48, 1533 (1967). (7) J. A. Happe and M. Morales, J . Am. Chem. SOC.,88, 2072 (1966). (8) P. W. Schneider, H. Brintzinger, and H. Erlenmeyer, Helv. Chim. Acta, 47, 1717 (1964). (9) H. Sternlicht, R. G. Shulman, and E. W. Anderson, J. Chem. Phys., 43, 3133 (1965). (10) H. Sternlicht, D. E. Jones, and K. Kustin, J . Am. Chem. Soc., 90, 7110 (1968). (11) V. Wee, I. Feldrnan, P. Rose, and S. Gross, J . Am. Chem. Soc., 96, 103 (1974). (12) T. A. Glassman, C. Copper, L. W. Harrison, and T. J. Swift, Biochemistry, 10, 843 (1971). (13) J. M. Rifkind and G. L. Eichhorn, J. Am. Chem. Soc., 94, 6526 (1972). (14) T. A. Glassman, C. Cooper, G. P. P. Kuntz, and T. J. Swift, FEBS Lett., 39, 73 (1974). (15) J. A. Happe and R. L. Ward, J. Am. Chem. Soc., 91, 4906 (1969). (16) J. A. Happe, J. Am. Chem. Soc., 95, 6232 (1973). (17) A. Abragam and R. V. Pound, Phys. Rev., 92, 943 (1953). (18) T. E. Bull, J. Andrasko, E. Chiancone, and S. Forsen, J . Mol. Biol., 73, 251 (1973). (19) C. F. Springgate, A. S. Mildvan, R. Abramson, J. L. Engle, and L. A. Loeb, J . Biol. Chem., 248, 5987 (1973). (20) C. D. Jardetzky and 0. Jardetzky, J. Am. Chem. W.,82,222 (1960). (21) S. S. Danvluk and F. E. Hruska. Biochemistrv. 7. 1038 11968). (22) M. P. Schweizer, A. D. Broom, P. 0. P. Ts'o, andD. P. Hollis, >. A h . Chem. Soc., 90, 1042 (1968). (23) J. A. Happe, unpublished results. (24) C. E. Johnson, Jr., and F. A. Bovey, J. Chem. Fhys., 29, 1012 (1958). (25) J. Kraut and L. H. Jensen, Acta Crystallogr., 16, 79 (1963). (26) The K 2 protons of AMP2-and AMPH- have the same chemical shift." This suggests that the dominant conformation is the same for both. (27) S. M. Wang and N. C. Li, J. Am. Chem. Soc., 88, 4592 (1966). (28) C. Giessner-Prettre and B. Pullman, J. Theor. Biol., 27, 87 (1970). (29) M. P. Schweizer, S. I. Chan, and P. 0. P. Ts'o, J . Am. Chem. SOC., 87, 5241 (1965). (30) A. D. Broom, M. P. Schweizer, and P. 0. P. Ts'o, J . Am. Chem. Soc., 89, 3612 (1967). (31) P. 0. P. Ts'o and S. I. Chan, J. Am. Chem. Soc., 86, 4176 (1964).
Dynamic Interchange among Three States of Phosphorus 4+ in a-Quartz Y. Uchlda,+J. Isoya, and J. A. Well" Department of Chemistry and Chemical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, S7N OW0 Canada (Received September 4, 1979) Publication costs assisted by the Department of Chemistry and Chemical Engineering, University of Saskatchewan
Dynamic averaging due to electron jumping among three states with different sp hybrid directions in the P4+ center [PO4l0in a-quartz has been studied by single-crystal electron paramagnetic resonance. The spinHamiltonian matrices g and Aslp for low temperature (i.e., C140 K) spectra P(1) and P(I1) and for high temperature spectrum P(A) are reported. For each crystal site, the line positions of P(A) agree well with those derived from the matrices measured for the three states. i.e., with weighted averages including P(1) and the two symmetry-related P(I1) spectra.
Introduction Phosphorus and germanium can replace silicon within the [Si04]0tetrahedra in a-quartz. The free ion configuration of both P4+and Ge3+is (nsl),with n = 3 for P4+and n = 4 for Ge3+. Recently, room temperature electron paramagnetic resonance (EPR) of the P4+center [PO4l0 in a-quartz was described,l and dynamic averaging among three states of Ge3+was observed2 in [GeOJ by use of EPR. The present work reports observations of dynamic effects in [PO4l0similar to those exhibited by [Ge04]-. Thus two energetically inequivalent species, P(1) and P(II), were observable at low temperatures as separate EPR signals. The present results indicate the following: (i) P(I) +National Institute for Researches in Inorganic Materials, 1-1 Namiki, Sakura-Mura, Niihari-Gun, Ibaraki, 300-31 Japan. 0022-3654/79/2083-3462$01 .OO/O
represents the ground state of [PO4l0and P(I1) the first excited state, which is doubly-degenerate in the absence of an external magnetic field B but gives_riseto separate EPR signals for general directions of B. (ii) Dynamic averaging occurs between these three states, which correspond to occupation by the unpaired electron of phosphorus sp hybrid orbitals along three different directions in the PO4 unit.
Experimental Section Incorporation of impurity ions into the a-quartz lattice is effectively controlled by the pH value of the aqueous solution used in hydrothermal g r ~ w t h .Phosphorus-doped ~ a-quartz crystals were grown by using alkali hydrogen phosphate solutions in an internally heated vessel, with argon gas as the pressure medium. The crystals, as used 0 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979 3463
Dynamic Interchange among P4+ Centers in a-Quartz 120 K P
(I)
P
(I) I
I
A 1.0 m T P(A)
290 K
P(A)
, , y h , , , , . / /
Figure 1. EPR spectra of the [PO,]' center taken with the magnetic field along the c axis. Species P(1) and P(I1) are separately observed in the low temperature spectrum (- 120 K, Y = 9.96 GHz). Averaged form P(A) is observed in the high temperature spectrum (-290 K, v = 9.99 GHz).
for our EPR studies, had nearly rhombohedral shape [long edge along one (I Zl)of the three symmetry-equivalent twofold axes; a pair of faces perpendicular to c']. The sample was characterized to be right (P3,21) quartz. We use, as a crystal coordinate system, a right-handed Cartesian axis set in which the z axis is the crystallographic threefold screw axis (Z) and the x axis is parallel to GI. The positive end of the 3c axis develops negative charge on compression along x . The sample was X irradiated at room temperature by use of a Machlett AEG-50s tube with tungsten target and a beryllium window (50 kV, 50 mA, 1 h). Details about the spectrometer and the variable temperature system were described elsewhere.2 I t should be noted that a GaAs FET microwave amplifier, inserted in front of the diode detector in the microwave bridge, was very effective in enabling measurement of the weak signals of the excited state P(I1) of the P4+center.
Results The P4+center [PO,]O is created in phosphorus-doped a-quartz by X irradiation at room temperat~re.~ The EPR spectra of [PO4l0are anisotropic and consist of pairs of hyperfine lines due to 31P (I = natural abundance 100%) with large spacings (-110 mT). Thermal Behavior. When the magnetic field is parallel to the c axis, all symmetry-related sites are magnetically equivalent. Therefore, the thermal behavior of the [PO4l0 center was studied primarily through observation of c axis spectra (BlIZ). The room temperature (-290 K) c axis spectrum of P(A) is shown in Figure 1. The hyperfine splitting is 108.63 mT at 9.993 GHz. The first-derivative peak-to-peak line width ABFp is 0.119 mT for the low-field line and 0.045 mT for the high-field line. When the crystal was cooled to -40 K, a new doublet P(1)of hyperfine lines (splitting 110.57 mT at 10.023 GHz; AB,, 0.010 m T for both low-field and high-field lines) was observed in place of P(A). Additional, relatively weak hyperfine doublets (splitting 0.16 mT) centered around each primary P(1) line were observed. From the observed peak-heights ratio of -0.05, these lines are assignable as arising from two equivalent 29Sinuclei ( I = natural abundance 4.7%). When the crystal was warmed to above -40 K, new hyperfine doublets P(I1) began to be observable at -80 K, in addition to P(1). The c axis spectrum a t -120 K is shown in Figure 1. At this temperature, the hyperfine
splittings of P(1) and of P(I1) are 110.76 and 104.77 mT, respectively (9.957 GHz); the line width AB is 0.012 m T and & P(I1). for both low-field and high-field lines of I!? At higher gain, four pairs of weak hyperfine doublets (splitting 0.69, 0.42, 0.38, and 0.12 mT, respectively), centered around each primary line of P(II), were observed. From the observed peak-heights ratio of -0.025, each of the four pairs are assignable to occupation by 29Siof one of four inequivalent silicon neighbor sites. The intensity of P(I1) relative to P(1) increases as the temperature is increased (the ratio P(II)/P(I) is 0.01 at -80 K and 0.07 at -120 K). With further temperature increase, line broadening occurs first in P(I1) (AB is 0.023 mT at -140 K, 0.15 mT at N 160 K, and not oglervable above 170 K) and then in P(1) (AB,-,is 0.013 mT at -140 K and 0.14 mT at 180 K). The hyperfine splitting of P(1) and P(I1) varies only slightly within this temperature range. At 195 K, the splitting of the signal assigned to P(1) a t lower temperatures begins to decrease appreciably. At -205 K, the spectrum is assignable to P(A) (splitting 110.23 m T at 9.981 GHz, AB, is 0.78 mT for the low-field line and 0.46 mT for the high-field line). The hyperfine splitting of P(A) decreases as temperature increases (109.15 mT at 9.982 GHz at -230 K and 108.81 mT at 9.984 GHz at -255 K). The line widths of P(A), unequal for the low-field and high-field lines, decrease as temperature increases. The complete sequence of the thermal EPR phenomena described above is reversible. EPR Parameters o f P ( I ) ,P(IT),and P(A). EPR spectra were recorded a t 10' angular intervals with the crystal rotated around Gl,with B l & , at three different temperatures: -40, -120, and -290 K. The spin-Hamiltonian matrices g and A31p of P(1)a t both -40 and 120 K, of P(I1) at -120 K, and of P(A) at -290 K were calculated by fitting observed field strengths and microwave frequencies to the spin-Hamiltonian 7fB= pe9.g.i5 4- 9 . A 3 I P . 1 - pn1.ghp.i5 (1) where electron spin S = 1 / 2 and 31Pnuclear spin I = 1/2. All matrices in 7fs were assumed to be symmetric; the nuclear Zeeman matrix was taken as isotropic (g31p = 2.2610).5 Some details of the calculation have been described elsewhere.2i6 The matrices obtained are given in Table I. Here the hyperfine parameters are expressed in magnetic field units (i.e., energy divided by go& where go = 2.002319).7 The principal values and directions associated with the matrices g and A 3 1 P are given in Table 11. The set of matrices presented is the one assigned to one particular site, to be called site The sets corresponding to the other sites are obtainable from this set by the symmetry operations of group D3. The principal values of g and A3iP of P(A) agree well with the room temperature data reported in ref 1 (2.0025, 2.0011, and 2.0003 for g; 113.9, 112.2, and 105.8 mT for A31p). Unfortunately, the x axis nominally defined as x 11 +al had been utilized as 3c Il-al therein; after suitable correction, the principal direction reported in ref 1agree with those of our present matrices. Dynamical Averaging. In a-quartz, there are three magnetically distinguishable orientations of the Si04tetrahedra. The [PO4l0centers are observed to substitute with equal abundance into the three types of Si04 tetrahedra. These symmetry-related sites will be denoted as sites 1, 2, and 3, respectively (Figure 2). Site i is any Si04 site centered on axis Zt; here i = 1, 2, 3. The species corresponding to the P(1) spectrum and averaged form P(A), both of which exhibit Cz symmetry about the crystal twofold axis on which the P4+ion is located, occur in three symmetry-related sites, to be labeled as sites 1, 2, and 3.
-
-
-
-
3464
and A31n(in mT) in the Crystal Coordinate System for Site 1of P(I), P(II), and P(A)
TABLE I: Matrices
temp, K
species
P
g
120
-120
P(W
-
0
0
108.313
0.456 107.560
0
0
2.0025
0.0016 1.9998 0 0.462 107.701
122.893
0 108.469
g
2.0012
0.0004 2.0013
g
0.0021
0.005
72
0.005
94
0.004
70
0.020
0.0000
101.901
0.362 115.589
2.0012 0.594 -2.281 102.218
2.0010
0
0
2.0020
0.0009 2.0007
0
0 112.041
113.902
&lP
64
0.0016 1.9999
A31p
-
290
122.795 2.0012
&Ip
P(A)
0
0 2.0025
2.0012
A31p
-
rms no. of deviation, line positions mT
matrixa
-
-40
P(I)
a
Uchida, Isoya, and Well
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979
-0.600 105.837
AJlPin units of mT.
TABLE 11: Principal Values and Directions of Matrices g and Tialp for Site 1 of P(I), P(II), and P(A) species
temp, K
P(I)
40
~I
-
matrix €? 1
A31p
-120
g
A3IP
P(II)
-120
g
A3Ip
P(A)
-290
g
ANp
a
principal valuesa 2.0012 2.0032 1.9991 122.7 96 108.528 107.345 2.0012 2.0032 1.9991 122.893 108.68 6 107.484 2.0013 2.0034 1.9991 115.972 102.514 101.222 2.0010 2.0025 2.0003 113.902 112.099 105.779
principal directions Y
X
0.0
1.0 0.0 0.0
-0.0186 0.7099 0.7041 0.0185 0.7224 0.6912
1.o 0.0 0.0 1.0 0.0 0.0
deg
0.9052 -0.4249
0.4249 0.9052
0.9813 0.1481 -0.1233 0.9865 0.0994 -0.1303
-0.1918 0.6886 -0.6993 -0.1628 0.6843 -0.7108
101.1 46.5 134.4 99.4 46.8 135.3
0.0 0.8947 -0.4467 0.0 0.9954 -0.0954
0.0 0.4467 0.8947 0.0 -0.0954 - 0.9954
90.0 63.5 26.5 90.0 95.5 174.5
0.0 0.9047 -0.4261
0.0 0.9056 -0.4242
0.0
1.0 0.0 0.0
0.0
8,
90.0 64.8 25.2 90.0 64.8 25.2 90.0 64.9 25.1 90.0 64.9 25.1
0.9046 -0.4262
1.0
0.0 0.0 1.o 0.0 0.0
2
0.4262 0.9046 0.0 0.4261 0.9047
0.0 0.4242 0.9056
0.0
@,deg 0.0 90.0 270.0 0.0 90.0 270.0
0.0 90.0 270.0
0.0 90.0 270.0 91.1 11.8 350.1 88.9 7.8 349.3
0.0 90.0 270.0
0.0 90.0 270.0
A3,p in units of mT.
The species P(II),which does not have this C2 symmetry, occurs in six symmetry-related sites, to be labeled as sites 1, 1', 2, 2', 3, and 3'. We define site i of P(I),sites (i, )'i of P(I1) and site i of P(A) as arising from site i of the [PO4l0 center. We assume that the averaging to produce site i of P(A) occurs between site i of P(1) and sites (i, i') of P(I1). Then, the line positions of P(A) can be formulated as a weighted average of corresponding line positions of P(1) and P(I1): B(ed)P(A),site i
= fIB(e,d')P(I),site
(1/2)fIIB(e,d')P(II),site c
c + + ( l / 2 ) f I I B ( e , d ' ) P ( , , ) , s i ~ i' (2)
where the relative unpaired electron residence times in P(1) and P(I1) are expressed respectively as mole fractions f~ and fII (with f I + fII = 1). Here 8 and 4 specify the applied magnetic field directions.2 Using (2), we can calculate the mole fractions at -290 K from the measured line positions of P(A) and line positions of P(1) and P(I1) calculated for -290 K. The latter, which would be observed as distinct signals instead of P(A) if no dynamic process occurred, can be estimated by using the matrices g and A31p of P(1) and P(I1) obtained at 120 K. We included corrections for the temperature dependence of the spin-Hamiltonian parameters, obtained
-
The Journal of Physlcal Chemistry, Vol. 83, No. 26, 1979 3485
Dynamic Interchange among P4+ Centers in a-Quartz
412
A
t"
a2
I..-
+IZ
II-1,
r 410
II
'
:,011X -
0: s i
( P )
c
408
1
404
c
(?:o
/
1'
\
A-1
/ /
\
-4
Flgure 2. The three sites of [PO,]' in relation to the three sites of SiO, (indicated by silicon atom i , where i = 1, 2, 3). The three sites of P(1) and the six sites of P(I1) are indicated by their unique hyperfine axis directions. Atomic positions of silicon and oxygen atoms in a-quartz (fight P3*21) are shown as a projection on (0001). The crystal coordinate system (xyz, right-handed, z axis up) is also shown. r
402
\
-
L
d 0
L 30
90
60
120
150
180
e,deg
Flgure 4. The EPR line positions of the high-field hyperfine member of P(A) (site 1, C#J = 90°, v = 10.05 GHz) at -290 K, derived by dynamic averaging among three states: site 1 of P(1) and sites (1, 1') of P(I1).
-
296
A-
1
\
298
-
288
r
E-
2 , 3'
n
/
290
288 i
0
30
90
60
120
150
180
e-
-
' L
--A 0
&.,
Figure 3. The EPR line positions of the low-field hyperfine member of P(A) (site 1 , d = 90°, v = 10.05 GHz) at ~ 2 9 K0 derived by dynamic averaging among three states: site 1 of P(1) and sites (1, 1') of P(I1). The heavy curve shows the positions calculated by eq (2) with mole fraction f , = 0.552 and corrections for temperature dependence of Amp, bA = 0.370 mT, and 6, = -0.199 mT. The circles indicate the observed line positions at -290 K. Also shown are the curves for !(I) and P(I1) line positions as calculated from 12_0K matrices g and h i p with corrections and 6,. In this rotation (BLif,), sites (1, 1') of P(I1) are magnetically equivalent.
-
by comparing the matrices g and A31p of P(1) measured at -40 and -120 K (Tables I and 11); we notice a small temperature dependence, mainly in the principal values of Anp. The three principal values of A q are expressed in terms of the isotropic part Aiso,anisotropic part b, and deviation C from uniaxiality as Aiso+ 2b, Ak0 - b + C, Ak0 - b - C, respectively. Ai, is taken to be positive, consistent with the positive sign of g31p. We assumed that the temperature dependence is appreciable only in Ak0q d b; thus the matrix g and the principal directions of A31p were treated as independent of temperature. The corrections to be applied additively to Aiso and b are termed gA and 6 b , respectively. We further assumed that the same set of
30
60
90
e
--
120
150
180
ideg I
Figure 5. The EPR line positions of the low-field hyperfine member of P(A) (sites 2 and 3, 6 = 90°, u = 10.05 GHz) at -290 K, derived by dynamic averaging among three states; site i o f P(1) and sites ( i , i')of P(I1) (here i= 2, 3, respectively). For PJI) and P(A), sites (2, 3) are magnetically equivalent in this rotation ( B Iif,).
corrections are applicable to both P(1) and P(I1). The field positions of P(1) and P(I1) at -290 K were calculated for the microwave frequencies of the observed P(A) signals by using the -120 K matrices corrected by use of bA and 66. The mole fractions, as well as these corrections, were obtained by least-squares fitting. The values f I = 0.552, = 0.370 mT, and = -0.199 mT fit the 70 measured line positions of P(A) with a,root-mean-square deviation of 0.049 mTe9 The good agreement between the calculated and observed line positions of P(A) is illustrated in Figures 3-6. The mole fraction was obtained by using the line positions of all sites in both low- and high-fields simultaneously; however, for simplicity, these line positions are illustrated in separate figures. The microwave frequency for the observed line positions varied somewhat; the observed field strengths in these figures were corrected to
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979
3466
412
1-2,
~
Uchida, Isoya, and Weil V'
3
9
-
410
L I
y A-2,
B
I 406 -
ImT
-
404 r
t
1607;
3
i j""l-I-"e__
I6071
I I -n2 , 2',3' 3
b I v
402
Flgure 7. Si04 unit (site 1) including the neighboring silicon atoms. The notation for the oxygen atoms and the 0-Si-0 angle bisectors is shown. In the distorted tetrahedron of Si04 in the low symmetry lattice of a-quartz, none of the bisector directions fu, v , v', w , and d a r e (electrically) identical. In the [PO,]' center, the P4+ ion substitutes for Si4+, presumably with some further alteration of the geometry.
-u I 0
30
120
90
60
180
150
edeg
)
Figure 6. The EPR line positions of the high-field hyperfine member of P(A) (sites 2 and 3, 4 = 90°, v = 10.05 GHz) at -290 K, derived by dynamic averaging among three states: site i o f P(1) and sites ( i , i f ) of P(I1) (here i = 2, 3, respectively).
TABLE 111: Hyperfine and Orbital Parametersa for P4+in a-Quartz species
temp, K
Aiso, mT
b, mT
up,:
P(1) P(I1)
-120 -120
113.021 106.569
4.936 4.702
0.28 0.27
apAD2
u
0.45 0.43
u'
a single fixed microwave frequency. It is to be noted that single unique values of f I and fII can describe the whole rotation. Note also that the line positions of P(A) depend quite strongly on temperature, since the mole fractions do.
Discussion In both P(1)and P(II), the matrices g and A3ip are nearly coaxial (Table 11). One principal value of A 3 9 is considerably larger than the other two, but the deviation from uniaxiality exceeds the experimental error. The wave function for the unpaired electron is tentatively described by the LCAO 4
2=1
* '
(3)
The first two coefficients can be estimated by utilizing the values of l'k3s(0)12 and ( given by Watkins and Corbett.1° The phosphorus coefficients, and the hyperfine parameters Aivoand b used to estimate them, are listed in Table 111. We note that, to a first approximation, the unpaired electron is in a 3s + 3p orbital on the phosphorus ion, with appreciable spin density also on the neighboring oxygen ions. The principal direction for the largest principal value of A31p is, herein, termed the unique axis. It is likely that the unique axes of P(1) and P(I1) indicate the direction, in each, of the phosphorus 3p orbital involved in the sp hybrid orbital in eq 3. We shall now compare the unique axes with the directions in site 1 of the normal Si04unit (Table IV, Figure 7).11 There are six 0-Si-0 angles in
r3c3)
bisector direction u -u
a The orbital parameters were estimated by using wave functions for neutral phosphorus atoms.'O With numerical Hartree-Fock wave functions for free Pzt [ c. FroeseFischer, Comput. Phys. Commun., 4, 1 0 7 (1972)], one finds a J S za, J P 2for P(1) and P(II), respectively, t o be 0.26, 0.33 and 0.24, 0.32.
$ = aPg$P3s + aP3plc/P3p+ Cao,$o, + *
TABLE IV: Room Temperature Directions of the Site 1 SiO, Unit in @-Quartz(Right. P3-21)
w w'
angle 0(3)-Si-0(4) 0(1)-Si-0(2) O(l)-Si-0(3) 0(2)-Si-0(4) 0(2)-Si-0(3) O(l)-Si-O(4)
atom-atom direction
deg (=109.6) (=109.1) (=108.7) (=108.7) (=110.4) (=110.4) 8 , deg
deg 90.0 90.0 163.9 16.1 106.3 73.7
0,
Q, deg 0.0 180.0 269.4 90.6 90.2 269.8
Q, deg
the unit, which has Cz symmetry; O(l)-Si-0(3) and 0(2)-Si-0(4) are related by Cz rotation about til, and so are 0(2)-Si-0(3) and O(l)-Si-O(4). However, the bisectors u, u'and w, w'of the two angles in each pair are not parallel. The bisectors u and u' (= -u) of 0(3)-Si-0(4) and 0(1)-Si-0(2) are along +dl and -til, respectively. In site 1of P(I),the unique axis coincides with fZl, and thus with bisectors fu. In site 1 of P(II), the unique axis is close (7.1') to bisector w of angle 0(2)-Si-0(3); the unique axis of site 1' of P(I1) is close (7.1') to bisector w' of angle O(l)-Si-0(4). Thus it seems reasonable to conclude that the three states involved in the averaging process correspond to occupation of phosphorus sp orbitals along bisectors fu,w ,and w', respectively. In P(I),the other two principal directions of A31p are close (3.1, 4.3') to the interatomic directions O(3)-O(4) and O(1)-0(2), respectively. In P(II),the other two principal directions are close (4.2, 5.7') to O(2)-0(3) and 0(1)-0(4),respectively. These good correlations between the principal directions and the axes of the Si04 unit in the crystal provide strong evidence that the [PO4l0center occurs substitutionally for SiOa. Site 1 of P(1) has C2 symmetry about Zl, whereas sites (1,l')of P(I1) are symmetry related by Cz rotation about Zl. As a result of averaging among these, with equal participation of the two P(I1) sites (1, 19,site 1 of P(A) exhibits Cz symmetry about til, i.e., one principal direction of P(A) agrees with Zl. The above discussion of averaging in site 1 of the [PO4l0center applies of course also to the other two sites. The relation among the sites of P(I),P(II),and
Dynamic Interchange among P4+ Centers in a-Quartz
P(A) is illustrated in Figure 2. The averaging process is caused by rapid (on the EPR time scale) electron jumping between sp hybrid orbitals associated with the three different directions. Occurrence of the sp orbital nearly perpendicular to Zlimplies distortion from C2 symmetry in P(I1). As discussed in the previous paper,2 the jumping of the electron is likely to be associated with appreciable nuclear displacements. With sp hybridization, the electron density along the p-orbital axis is much larger on one side of the phosphorus nucleus than on the other. The two possible site 1configurations of P(II), in which the side with greater electron density lies within the respective angles 0(2)-P(Si)-0(3) and O(l)-P(Si)-O(4), may be designated by the bisectors w and w’, respectively (see Figure 7). As discussed in ref 2 , the assignment of the sp orbital in site 1 of P(I1) (or Ge(1)) to either w or w’(--w) is not obvious. In P(1) (and Ge(II)), assignment of the greater electron-density side to +u or to -u is also not trivial.12 We depict in Figure 2 the assignment for both P(1) and P(I1) deemed from a simple crystal field approach2 to be the more appropriate. In the [Ge04]- center, occupancy of the germanium sp orbitals along (w,w? give the ground state configurations Ge(I), and that along fu gives the excited state Ge(II).2 Thus the configurations that give ground and excited states are, respectively, opposite for the [PO4l0 and [Ge04]centers. In both centers, the energy difference between the ground and excited states is of a magnitude such that the temperature dependence of the population ratio is observable even below room temperature. Thus the difference, as measured on the energy scale, between corresponding states of the two centers seems to be small. The differences between the two centers are presumably related to the following factors: (i) The center [PO4l0is effectively neutral in the lattice of [SiO4l0units, whereas the center [Ge04]-is effectively negative. (ii) The principal quantum numbers n of the valence electron of P4+and Ge3+ions are 3 and 4, respectively. Hence the electron, a t least in the free ion, is more extended spatially in Ge3+than in P4+. Studies of the electron jump rate by analysis of EPR line widths are in progress, and will be published elsewhere. The energy difference between P(1) and P(I1) will be determined from detailed analysis of the temperature de-
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979 3467
pendence of the mole fraction. We plan to incorporate other S = 1 / 2 paramagnetic ions into the a-quartz lattice for further studies of deformations of the tetroxide tetrahedra in this material.
Acknowledgment. The authors are greatly indebted to Dr. K. Hirota (National Institute for Researches in Inorganic Materials, Japan) for his help in growing the phosphorus-doped quartz crystals. The research reported here was supported by the Natural Sciences and Engineering Research Council of Canada. References and Notes (1) Y. Uchida, J . Phys. SOC.Jpn., 42, 1937 (1977). (2) J. Isoya, J. A. Weil, and R. F. C. Claridge, J . Chem. Phys., 69,4876 (1978). (3) K. Hirota and Y. Uchida, Proceedings of the ACSICSJ Chemical Congress, INOR 371,Hawaii, 1979. (4) The charge state, pt or P5+, before irradiation was not determined. When the crystal was irradiated at 77 K and transferred to our cryogenic EPR system without warm-up, P(1) was the only phosphorus-related spectrum observed at -40 K. No evidence for charge-compensating ions, which might have existed in the neighborhood of the phosphorus before irradiation, was found. (5) “Magnetic Properties I”, tandolt-Bornstein Tables, 6th ed, Vol. 2, Part 9,Sprlnger, West Berlin, 1962,pp 7-73. (6) H. Rinneberg and J. A. Weil, J . Chem. Phys., 56, 2019 (1972). (7) E. R. Cohen and B. N. Taylor, “Atomic Masses and Fundamental Constants, Proceedings of the International Conference (4th)”, 1971, J. H. Sanders, Ed., Plenum, New York, 1973,p 543. (8) Assignment of the EPR signals to the appropriate sites was carried out as follows. For the P(1) and P(A) spectra, which exhibit C2 symmetry about the crystaltwofold axes, sites (2,3)are magnetically equivalent in the rotation 5 1 a’,. Two signals with an intensity ratio of 1:2 were observed for both the low-field and high-fleld members of the hyperfine doublet. Thus, assignment of site 1 is simple. In P(II), pairs (14l’),(2,37,and (3,2’)are magneticallyequivalent in the rotation 5 Ia’,; the spectrum consists of low-field three lines L,, L, L3 and high-field three lines HI, H, Ha. Our assignment of L, and H, to site 1 is confirmed by observing the line width of site 1 of P(A) as a function of line separation between P(1) and P(I1). The assignment of site 2 to (L2, H,) and site 3 to (La, H3) is not trlvial. However, when we made the assignment of site 2 to (L,, H3)and site 3 to (L3, H,), the matrices g and A31p calculated were far from coaxial. (9) With SA = S, =: 0, the mole fraction f , = 0.584,with a rootmean-square deviation 0.194 mT, was obtained. (10)G. D. Watkins and J. W. Corbett, Phys. Rev. A , 134, 1359 (1964). (11) Based on the room temperature crystal structure data by Y. LePage and G. Donnay, Acta Crysfallogr., Sect. 5 , 32, 2456 (1976). (12) To solve this problem, we are planning experiments utilizing electric field effects. It may also be solvable by sufficiently detailed interpretation of the matrix g.
