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Some studies of defects in calcium oxide-I. Impurity effects
J. Phys. Chem. Solids
Pergamon
Press
1969. Vol. 30, pp. 1793-1799.
Printed
in Great
Britain.
SOME STUDIES OF DEFECTS IN CALCIUM OXIDE-I. IMPURITY EFFECTS A. C. TOMLINSON Physics
Department.
(Received
and B. HENDERSON
Keele University,
16 September
Keele, Staffordshire,
1968; in revisedform
16 December
England 1968)
Abstract- In some CaO crystals grown by the arc fusion technique, paramagnetic resonance lines due to impurity ions are considerably narrower than have usually been reported. Thus it has been possible to resolve the hypertine structure from the nuclei rssGd and r5rGd associated with the Gd3+ electron spin resonance spectrum. An isotropic g-shift of order 0.00008 between the 47Ti and 49Ti hypertine lines in a spectrum due to octahedrally co-ordinated Ti+ ions is also apparent. In annealed and quenched crystals these linewidths are noticeably increased as a result of the lattice disorder present after quenching. Pairs of sharp lines in the electron spin resonance spectrum of Mnp+ are assigned to the doublequantum transitions between pairs of non-adjacent levels. In the absence of strain, the levels involved are unequally spaced and double quantum transitions are not observed. A range of internal distortions in the crystals yields equality of spacing between the levels for some ions, so that AM, = 2 transitions may occur with simultaneous absorption of two microwave photons of identical frequency. 1. INTRODUCTION
available single crystals of calcium oxide contain significant concentrations of transition metal impurities substituted on cation sites. Electron spin resonance studies show that the symmetry around these ions is accurately cubic despite considerable dislocation structure consequent upon the growth process. The valencies of these ions may be varied by annealing the crystals in vacuum or in oxidising atmospheres. The ease with which the valency changes may be effected depends upon the degree of misfit between the impurity ion and the matrix. and upon the need to maintain electrostatic neutrality in the lattice through the incorporation of charge compensating vacancies. Valency changes are also produced by ionising radiation, in which case charge compensation is achieved through electron or hole trapping elsewhere in the lattice. Since numerous impurity ions occur in the trivalent state, cation vacancies are favoured. Holes formed during irradiation are trapped preferentially on the oxygen ions near these vacancies and may be observed by electron COMMERCIALLY
spin resonance. Trapped electron centres are less easily produced in calcium oxide since there are very few anion vacancies in thermodynamic equilibrium, and also because the binding energy of the divalent host lattice precludes the possibility of ionic displacement by ionizing radiation. Anion vacancies are, however, present in crystals which have been subjected to either heavy particle irradiation or to annealing treatment at high temperatures in several atmospheres of calcium vapour. The present crystals were selected from regions of the melt closest to the electrodes since they had been electrolytically coloured during the growth process. The crystals were coloured dark brown, suggesting the presence of colloidal metal particles in addition to the single anion vacancies. In Part I we discuss some interesting features of the impurity spectra of these electrolytically coloured samples. 2. EXPERIMENTAL
PROCEDURE
The calcium oxide crystals were grown by Muscle Shoals Inc., Tuscumbia, Alabama, U.S.A. and had been accidentally electroly1793
1794
A. C. TOMLINSON
tically coloured during the growth process. The crystals were not chemically analysed but concentrations of 1014- 10’” cm-” of paramagnetic ions were detected. Most crystals were examined in the as-received condition, but a few were annealed in oxidising atmospheres by suspending them from platinum wires in air inside an electric furnace. Preliminary electron spin resonance measurements were made with a simple spectrometer which used a helix in place of the more familiar resonant cavity. For more quantitative measurements a Varian V4502 superheterodyne spectrometer with facilities for 100 kHz and audio frequency field modulation was used. The magnetic field was produced by a 9” magnet on a rotatable base and controlled with the Varian Fieldial device. The microwave frequency was measured with a Hewlett Packard 524C frequency counter by zero beating against a S40B transfer oscillator. The field could then be accurately calibrated over a wide range, since the Hamiltonian parameters of such impurities as Mn2+ are well established. Irradiation was accomplished with a high pressure mercury lamp through precisely machined slots in the end wall of a rectangular H,,,, cavity. Paramagnetic resonance measurements were made at 290”. 77” and 4°K. using cold finger dewars when required. At 4°K and using the lowest possible power on the superheterodyne spectrometer commensurate with good sensitivity, no transitions were observed. Presumably this indicates that for all ions the relaxation times are very long: rapid cross-relaxation via other impurities seems to be unimportant compared with the same ions in MgO. 3. RESULTS
AND DISCUSSION
Although nominally ‘undoped’, all crystals showed resonance absorption from Gd”+, Mn’+, Fe”+, Cr”+. Vz+; the linewidths (Table I) for these ions were much smaller than has previously been reported. This emphasises the accurate cubic symmetry around the
and B. HENDERSON
Table 1. Parrrmrrgnetic resonunce 1inen~idth.s in calcium oxide single crystals. Deriwtiw pt’rrk-to-perrk width in gtruss As grown
Annealed
300°K
77°K
0.8 0.6
o- I 0. I
1-o I4
I4
V’t
8 P.I5 0.15
Ti+ F’ centres V centres
I.0 0.02 *
0.1.5 0.02
*
C;d:‘+ Mn’+ Fe” /
Cr”i
:‘Defect measure.
not
detected
and quenched
300°K
0.X
0.X I4
0.7
I2 0.7
/
/ ./ I4
I .o or
_
77°K
spectrum
too
broad
to
ions and the absence of line broadening by lattice defects or by magnetic hyperfine interaction with nuclei of the host lattice. The increased linewidths in quenched crystals are a consequence of the increased disorder present in such crystals. Quenching tends to retain the high temperature concentration of vacancies and also produces significant plastic deformation as a result of the thermal stresses: both these effects will broaden the lines inhomogeneously as a result of the distortions of the cubic crystal field [I]. 3.1 The Gd hypetfine
structurr
The fine structure spectrum of the Y&2 ground state of Cd”+ in calcium oxide has been reported previously both by Shuskus[21 and Low and Rubins[3]. The fine structure parameters measured in the present experiments are in good agreement with those already reported. No evidence was obtained for AM, > 1 forbidden transitions of Cd”+. nor of axially symmetric spectra consequent upon the localization of a charge compensating vacancy near the Gd”+ ion. However, the electron spin resonance linewidths reported earlier are almost two orders of magnitude greater than those reported here. The lines in the previous work were probably inhomogeneously broadened by interaction with
DEFECTS
IN
CALCIUM
lattice defects, although we have noted that they are also quite sensitive to the microwave power level. Consequently Shuskus [2] and Low and Rubins[3] failed to detect the hyperfine structure of the Gd”+ ion in calcium oxide. Figure 1 shows the hyperfine structure associated with the AM, = + f * -3 transition at 77°K. The nuclei involved in this structure have nuclear spin I = # and are associated
OXIDE-I
I795
with 157Gd and 155Gd, which have 15.64 and 14.68 per cent isotopic abundance respectively. Hyperfine structure parameters for these two nuclei in calcium oxide and some other solids are compared in Table 2. The classical contribution to magnetic hyperfine interaction arises from electronic orbital motion, electron spin magnetization outside the nucleus and spin magnetization at the nucleus. Relativistic effects may contribute to all three interactions but unlike core polarization do not contribute to a hyperfine anomaly. This is because a hyperfine anomaly may arise from a non-uniform distribution of unpaired electron spin density over the volume occupied by the nuclear magnetization. The hyperfine anomaly can then be determined from
155($) 157(F) = ] +A
“‘Gd
‘=Gd
I I
I
I
I
I I
I
Fig. I. The ‘jsGd and 15’Gd hyperfine structure attendant upon the M, = f ++ -+ transition for GdY+ ions at 77°K.
where the nuclear g-values and hyperfine constants are to be determined for Gd3+ in the oxide. Usually, and for the systems noted in Table 2, this has not been the adopted procedure. In the absence of ENDOR measurements, the nuclear g-values used have been those determined optically for Gd4 atoms or from NMR measurements on GdN [5]. Using this method we determine A for Gd”+ in CaO to be about I a2 per cent, which is within the range of values reported for other solids. However, it is realised that this is not conclusive evidence for the presence of a hyperfine anomaly, since the nuclear g-values should be measured directly using ENDOR.
Tuble 2. Hyperfine pcwrrmeters in guuss for Gd3+ and Gd IS?A
Crystal Free Atom Bi,Mg,(NO:,),, SrS ThO, CaWO, CaO
. 24H,O
4.0t 0.3 3.68 k 0.06 4.2550.15 4.45 k 0.02 3.97-+0.10
5.34kO.17 5.OkO.05 5.7350.12 5.84kO.02 5.19-t-0.10
I%A,157A 0.80 +- 0.02 0.75’0.07 0.73 +- 0.03 0.744 k 0.0007 0.763 f 0.0006 0.767kO.010
Reference [41 :;3
[sl [91 This paper
I796
A. C. TOMI,INSON
and B. HENDERSON
oxide, since no charge compensation is required and little elastic distortion results Prolonged irradiation at 77°K of the electrolytically coloured crystals revealed a from the small ionic size. Ti”+ is a 3d’ ion. new spectrum, the central component of and although other 3d2 ions (V:%+)exist in which is essentially isotropic, indicating that calcium oxide they may have not been the defect responsible is present in sites of detected using electron spin resonance. There cubic symmetry. The spectrum was somewhat is not (I priori reason why Tip+ should be broadened at 300°K. After production at detected. In addition electron spin resonance spectra from Ti’.+ (3d’) and Ti:‘t(3d’) in 77°K it decayed to half the intensity at room temperature in a few hours. Irradiation at octahedral coordination are unlikely to have room temperature produced the spectrum the properties reported for this spectrum [ 121. transiently~ decay to undete~tably low Ti’+ has been observed substituting for Ca”’ in calcium fIuoride[ 131. where the eightfold intensities occurring within tens of seconds after the cessation of irradiation. Figure 2 cubic coordination reverses the order of the levels relative to that of the octahedral coshows the isotropic hype&e structure associated with this spectrum to consist of ordination. The magnetic resonance spectrum is readily observable in that case. eight lines, the inner six of which almost The Tit ion is isoelectronic with V” _ .A+ overlap a second set of six lines. Consequently ’ . , I In o&rhedral cr$il . isotopes with nuclear spins I = 2 and I =$ are and Mn”+, whrch fields have the orbital singlet state 4A,, involved, with the latter the less abundant. This indicates that the spectrum is due to lowest. Thus in a magnetic field the transitions titanium, for which the abundance of *7Ti between the t$ and ~tf levels are isotropic and coincide precisely. The isotropic g-value is 7.75 per cent and 4Ti is S.SI per cent. of 14866 is consistent with this, and an The spectrum is centred at g = I.9866 (&04OS) and we observe 47A = @A = IO.8 appr~~priately simple spin Hamiltonian includx IO-* cm-‘. A shift of 130 mG is observed ing only the effects of isotropic Zeeman and for the -‘!yTi components relative to -‘TTi, hyperfine interactions may be used to describe corresponding to a difference in g-value of the present results. ‘The g-value in the Zeeman term is given as: 0.00008 for these isotopes. No such isotopic g-shift has been previously reported, although g r= 2.0023 45 an isotopic change in D-value of CT:‘+ in axially symmetric sites in magnesium oxide where A’ is the spin-orbit coupling constant was reported [ 101. We assign this spectrum to Ti+ ions in and A the splitting between the ‘A,, ground term and the .rT,, excited state. Thus the substitutional cation sites. Wertz et a/.[1 I] isotropic g-shift is derived from the quotient have suggested that Ti*+ is stable in magnesh’jh. The two isotopes will have different ium oxide and that Ti:$+ in axially symmetric vibrational frequencies associated with their sites may be detected after X-irradiation. The different masses: this causes the admixture ionic radii of the various titanium ions are Ti3+. 0.68 A: Ti”+, 0.76 A; Ti2+, 0*90A and of other excited state wavefunctions into the Tis, 0.96 A while the radius for Cax+ is 0.99 A “T,, level to differ for the two isotopes. Thus Ti,*+ and Ti”+ are very small relative to Ca2+ the orbital angular momentum generated in the ground state by mixing of the ?A,, and and are unlikely candidates for a substitutional site in calcium oxide. The presence of F+- “T,, levels due to the spin-orbit coupling operator hl,.S will also differ for the two centres in the crystals may bias them against isotopes. The effect is usually negligibly the formation of such ions. Intuitively, theresmall, and in the present case bg = O.OOOOg. fore, one expects Ti”+ to exist in calcium
Fig. 2. The
I
I I
I
H-
inmaing
paramagnetic resonance spectrum of TI‘+ in calcium oxide. This spectrum at 77°K. The shift of only I30 mg between the hyperfine components
I
4gTi
1
I
4’Ti
:
I, I
I
I I
is observed after irradiation with light in the F-band of”‘Ti and’!‘Ti is clearly discernible.
J
I
(3.1 eV)
I
179x
A. C. TOMLINSON
The appearance of the Ti+ spectrum during irradiation is apparently due to electron trapping by Ti’+ ions. The stability of the spectrum evidently depends on the irradiation temperature. and this is most probably due to different defect centres acting as electron donors in the different temperature ranges. At room temperature the F+ spectrum increases transiently with irradiation up to sevenfold, due to liberation of electrons from F-centresf 131. At 77°K this process is less efficient, but Fe”+ and Cr:‘+ ions are formed from the divalent ions. and their stability is similar to that of the Ti” centre formed at this temperature. 3.3 Double sptvtrr4m
quuntum
transitions
in the Mn’+
In as-received crystals the spectrum from MP ions is always present. Transitions other than those corresponding to AM, = + t ++ -1
Pig. 3. Double
and
B. HENDERSON
are considerably broadened especially after quenching, when a new twelve line spectrum is observed. This spectrum, which is enhanced following ultra violet irradiation at 77°K. consists of 6 pairs of sharp lines each centred on one of the principal manganese AM, =++t-,--k]ines. The similarities of this spectrum with those reported earlier by Auzins and Wertz[ 141 for the double-quantum transitions of the Fe”+ and Mn2i in magnesium oxide have prompted further comparison. The nonadjacent t~dnsitions +$ + -4 and i-4 -+ -+ $ as well as -$+-$ and +)++$ occur with simultaneous absorption of two quanta. Equality of spacing between the two sets of levels for each pair is produced by a small tetragonal distortion of the cubic symmetry, which introduces a D-term into the spin Hamiltonian. To first order in perturbation theory, the -S$ levels are shifted by 2D and
qu~~nturn transitions in the e.p.r. spectrum of MnZ+ in CaO: shown is for the m, = ) pentad with H along the principal axis.
the spectrum
DEFECTS
IN
CALCIUM
the *$ levels by 6D compared with the +3 levels. The value of D necessary in the case of Mn*+ in CaO is only 0.55 G. The resonance condition for double quantum transitions to be observed from suitably distorted Mn”+ ions occurs when the separation between the - 4 --, - 4 and the + %+ + 4 lines is subdivided by 2D and 4D[14]. In the case of manganese the energy level scheme is complicated by a large hyperfine interaction, and the fine structure splittings consequently vary for each of the six hyperfine pentads. In Fig. 3 the double quantum transitions are shown for the m, = 8 pentad along a principal axis, where the usual fine structure positions are reversed, i.e. in this case the +$-+ ?j transitions lie outside the ?+ + &$ transitions. The measured line positions are within one gauss of the predicted positions for double quantum transitions, taking into account second-order effects from fine and hyperfine splittings. A further check was made by measuring the increase in line intensity as a function of the microwave magnetic field vector H, at the sample, keeping crystal bias current constant. At low power levels the twelve line spectrum increased more than linearly with HI, consistent with double quantum transitions. The effect of quenching the crystals clearly introduces the distortions necessary for the resonance condition for double quantum transitions to be satisfied. The spectrum was considerably stronger at 77°K than at room temperature, in contrast to the case for Mn2+ in MgO, for which the intensity of the lines
1799
OXIDE-I
increased with increasing m, value [ 141. The mechanism coupling the intermediate states of the double quantum transitions is not understood. If the coupling between the states is phonon assisted, it is not surprising that the temperature dependence of the intensity of the double quantum lines for Mn2+ should be different in calcium oxide than in magnesium oxide. Acknowledgements-The authors are indebted to the United Kingdom Atomic Energy Authority, Harwell, and the Science Research Council for support of the experimental programme. Informative discussions with Professor D.J.E. Ingram and Dr. M. J. Baker were much appreciated. REFERENCES M. A., U.K.A.E.A. Res. Rep. RS530 I. STONEHAM (1967). 7 A. J.. Phys. Rev. 127,2022 (1962). -. SHUSKUS 3. LOW W. and RUBINS R. S., Proc. 1st Int. Conf. Paramagnetic Res. 1,?9 (1962). 4. SPECK D. R., Phys. Rev. 101, 1725 (I 956). R. J., Phys. Rev. Letr. 5. BOYD C. A. and GAMBINO 12,20 ( 1964). 6. LOW W., Phys. Rev. 103, 1309 ( 1956). A. A. and PROKHOROV A. M., I. MANENKOV Soviet Phys. JETP 6,860 (1958). 8. LOW W. and SHALTIEL D., J. Phys. Chem. Solids 6,315 (1958). 9. HEMPSTEAD C. F. and BOWERS K. D., Phys. Rev. 118, 13 1 ( 1960). S. A., HODGES J. A. and SERWAY 10. MARSHALL R. A.. Phys. Rev. 136, A1024 (1964). 1I. WERTZ J. E.. SAVILLE G. S., HALL L. and Auzins P., Proc. Br. ceram. Sot. I,59 (1963). 12. ZARIPOV M. M. KROPOTOV V. S., LIVANOVA L. D. and STEPANOV V. G.. Soviet Phys. solid St. 9,992 (1967). 13. KEMP J. C., ZINIKER W. and HENSLEY E. B., Phys. Left. 25A, 43 (I 967). 14. AUZINS P. V. and WERTZ J. E., J. phys. Chem. 71.2 I I ( 1967).
Pergamon
Press
1969. Vol. 30, pp. 1793-1799.
Printed
in Great
Britain.
SOME STUDIES OF DEFECTS IN CALCIUM OXIDE-I. IMPURITY EFFECTS A. C. TOMLINSON Physics
Department.
(Received
and B. HENDERSON
Keele University,
16 September
Keele, Staffordshire,
1968; in revisedform
16 December
England 1968)
Abstract- In some CaO crystals grown by the arc fusion technique, paramagnetic resonance lines due to impurity ions are considerably narrower than have usually been reported. Thus it has been possible to resolve the hypertine structure from the nuclei rssGd and r5rGd associated with the Gd3+ electron spin resonance spectrum. An isotropic g-shift of order 0.00008 between the 47Ti and 49Ti hypertine lines in a spectrum due to octahedrally co-ordinated Ti+ ions is also apparent. In annealed and quenched crystals these linewidths are noticeably increased as a result of the lattice disorder present after quenching. Pairs of sharp lines in the electron spin resonance spectrum of Mnp+ are assigned to the doublequantum transitions between pairs of non-adjacent levels. In the absence of strain, the levels involved are unequally spaced and double quantum transitions are not observed. A range of internal distortions in the crystals yields equality of spacing between the levels for some ions, so that AM, = 2 transitions may occur with simultaneous absorption of two microwave photons of identical frequency. 1. INTRODUCTION
available single crystals of calcium oxide contain significant concentrations of transition metal impurities substituted on cation sites. Electron spin resonance studies show that the symmetry around these ions is accurately cubic despite considerable dislocation structure consequent upon the growth process. The valencies of these ions may be varied by annealing the crystals in vacuum or in oxidising atmospheres. The ease with which the valency changes may be effected depends upon the degree of misfit between the impurity ion and the matrix. and upon the need to maintain electrostatic neutrality in the lattice through the incorporation of charge compensating vacancies. Valency changes are also produced by ionising radiation, in which case charge compensation is achieved through electron or hole trapping elsewhere in the lattice. Since numerous impurity ions occur in the trivalent state, cation vacancies are favoured. Holes formed during irradiation are trapped preferentially on the oxygen ions near these vacancies and may be observed by electron COMMERCIALLY
spin resonance. Trapped electron centres are less easily produced in calcium oxide since there are very few anion vacancies in thermodynamic equilibrium, and also because the binding energy of the divalent host lattice precludes the possibility of ionic displacement by ionizing radiation. Anion vacancies are, however, present in crystals which have been subjected to either heavy particle irradiation or to annealing treatment at high temperatures in several atmospheres of calcium vapour. The present crystals were selected from regions of the melt closest to the electrodes since they had been electrolytically coloured during the growth process. The crystals were coloured dark brown, suggesting the presence of colloidal metal particles in addition to the single anion vacancies. In Part I we discuss some interesting features of the impurity spectra of these electrolytically coloured samples. 2. EXPERIMENTAL
PROCEDURE
The calcium oxide crystals were grown by Muscle Shoals Inc., Tuscumbia, Alabama, U.S.A. and had been accidentally electroly1793
1794
A. C. TOMLINSON
tically coloured during the growth process. The crystals were not chemically analysed but concentrations of 1014- 10’” cm-” of paramagnetic ions were detected. Most crystals were examined in the as-received condition, but a few were annealed in oxidising atmospheres by suspending them from platinum wires in air inside an electric furnace. Preliminary electron spin resonance measurements were made with a simple spectrometer which used a helix in place of the more familiar resonant cavity. For more quantitative measurements a Varian V4502 superheterodyne spectrometer with facilities for 100 kHz and audio frequency field modulation was used. The magnetic field was produced by a 9” magnet on a rotatable base and controlled with the Varian Fieldial device. The microwave frequency was measured with a Hewlett Packard 524C frequency counter by zero beating against a S40B transfer oscillator. The field could then be accurately calibrated over a wide range, since the Hamiltonian parameters of such impurities as Mn2+ are well established. Irradiation was accomplished with a high pressure mercury lamp through precisely machined slots in the end wall of a rectangular H,,,, cavity. Paramagnetic resonance measurements were made at 290”. 77” and 4°K. using cold finger dewars when required. At 4°K and using the lowest possible power on the superheterodyne spectrometer commensurate with good sensitivity, no transitions were observed. Presumably this indicates that for all ions the relaxation times are very long: rapid cross-relaxation via other impurities seems to be unimportant compared with the same ions in MgO. 3. RESULTS
AND DISCUSSION
Although nominally ‘undoped’, all crystals showed resonance absorption from Gd”+, Mn’+, Fe”+, Cr”+. Vz+; the linewidths (Table I) for these ions were much smaller than has previously been reported. This emphasises the accurate cubic symmetry around the
and B. HENDERSON
Table 1. Parrrmrrgnetic resonunce 1inen~idth.s in calcium oxide single crystals. Deriwtiw pt’rrk-to-perrk width in gtruss As grown
Annealed
300°K
77°K
0.8 0.6
o- I 0. I
1-o I4
I4
V’t
8 P.I5 0.15
Ti+ F’ centres V centres
I.0 0.02 *
0.1.5 0.02
*
C;d:‘+ Mn’+ Fe” /
Cr”i
:‘Defect measure.
not
detected
and quenched
300°K
0.X
0.X I4
0.7
I2 0.7
/
/ ./ I4
I .o or
_
77°K
spectrum
too
broad
to
ions and the absence of line broadening by lattice defects or by magnetic hyperfine interaction with nuclei of the host lattice. The increased linewidths in quenched crystals are a consequence of the increased disorder present in such crystals. Quenching tends to retain the high temperature concentration of vacancies and also produces significant plastic deformation as a result of the thermal stresses: both these effects will broaden the lines inhomogeneously as a result of the distortions of the cubic crystal field [I]. 3.1 The Gd hypetfine
structurr
The fine structure spectrum of the Y&2 ground state of Cd”+ in calcium oxide has been reported previously both by Shuskus[21 and Low and Rubins[3]. The fine structure parameters measured in the present experiments are in good agreement with those already reported. No evidence was obtained for AM, > 1 forbidden transitions of Cd”+. nor of axially symmetric spectra consequent upon the localization of a charge compensating vacancy near the Gd”+ ion. However, the electron spin resonance linewidths reported earlier are almost two orders of magnitude greater than those reported here. The lines in the previous work were probably inhomogeneously broadened by interaction with
DEFECTS
IN
CALCIUM
lattice defects, although we have noted that they are also quite sensitive to the microwave power level. Consequently Shuskus [2] and Low and Rubins[3] failed to detect the hyperfine structure of the Gd”+ ion in calcium oxide. Figure 1 shows the hyperfine structure associated with the AM, = + f * -3 transition at 77°K. The nuclei involved in this structure have nuclear spin I = # and are associated
OXIDE-I
I795
with 157Gd and 155Gd, which have 15.64 and 14.68 per cent isotopic abundance respectively. Hyperfine structure parameters for these two nuclei in calcium oxide and some other solids are compared in Table 2. The classical contribution to magnetic hyperfine interaction arises from electronic orbital motion, electron spin magnetization outside the nucleus and spin magnetization at the nucleus. Relativistic effects may contribute to all three interactions but unlike core polarization do not contribute to a hyperfine anomaly. This is because a hyperfine anomaly may arise from a non-uniform distribution of unpaired electron spin density over the volume occupied by the nuclear magnetization. The hyperfine anomaly can then be determined from
155($) 157(F) = ] +A
“‘Gd
‘=Gd
I I
I
I
I
I I
I
Fig. I. The ‘jsGd and 15’Gd hyperfine structure attendant upon the M, = f ++ -+ transition for GdY+ ions at 77°K.
where the nuclear g-values and hyperfine constants are to be determined for Gd3+ in the oxide. Usually, and for the systems noted in Table 2, this has not been the adopted procedure. In the absence of ENDOR measurements, the nuclear g-values used have been those determined optically for Gd4 atoms or from NMR measurements on GdN [5]. Using this method we determine A for Gd”+ in CaO to be about I a2 per cent, which is within the range of values reported for other solids. However, it is realised that this is not conclusive evidence for the presence of a hyperfine anomaly, since the nuclear g-values should be measured directly using ENDOR.
Tuble 2. Hyperfine pcwrrmeters in guuss for Gd3+ and Gd IS?A
Crystal Free Atom Bi,Mg,(NO:,),, SrS ThO, CaWO, CaO
. 24H,O
4.0t 0.3 3.68 k 0.06 4.2550.15 4.45 k 0.02 3.97-+0.10
5.34kO.17 5.OkO.05 5.7350.12 5.84kO.02 5.19-t-0.10
I%A,157A 0.80 +- 0.02 0.75’0.07 0.73 +- 0.03 0.744 k 0.0007 0.763 f 0.0006 0.767kO.010
Reference [41 :;3
[sl [91 This paper
I796
A. C. TOMI,INSON
and B. HENDERSON
oxide, since no charge compensation is required and little elastic distortion results Prolonged irradiation at 77°K of the electrolytically coloured crystals revealed a from the small ionic size. Ti”+ is a 3d’ ion. new spectrum, the central component of and although other 3d2 ions (V:%+)exist in which is essentially isotropic, indicating that calcium oxide they may have not been the defect responsible is present in sites of detected using electron spin resonance. There cubic symmetry. The spectrum was somewhat is not (I priori reason why Tip+ should be broadened at 300°K. After production at detected. In addition electron spin resonance spectra from Ti’.+ (3d’) and Ti:‘t(3d’) in 77°K it decayed to half the intensity at room temperature in a few hours. Irradiation at octahedral coordination are unlikely to have room temperature produced the spectrum the properties reported for this spectrum [ 121. transiently~ decay to undete~tably low Ti’+ has been observed substituting for Ca”’ in calcium fIuoride[ 131. where the eightfold intensities occurring within tens of seconds after the cessation of irradiation. Figure 2 cubic coordination reverses the order of the levels relative to that of the octahedral coshows the isotropic hype&e structure associated with this spectrum to consist of ordination. The magnetic resonance spectrum is readily observable in that case. eight lines, the inner six of which almost The Tit ion is isoelectronic with V” _ .A+ overlap a second set of six lines. Consequently ’ . , I In o&rhedral cr$il . isotopes with nuclear spins I = 2 and I =$ are and Mn”+, whrch fields have the orbital singlet state 4A,, involved, with the latter the less abundant. This indicates that the spectrum is due to lowest. Thus in a magnetic field the transitions titanium, for which the abundance of *7Ti between the t$ and ~tf levels are isotropic and coincide precisely. The isotropic g-value is 7.75 per cent and 4Ti is S.SI per cent. of 14866 is consistent with this, and an The spectrum is centred at g = I.9866 (&04OS) and we observe 47A = @A = IO.8 appr~~priately simple spin Hamiltonian includx IO-* cm-‘. A shift of 130 mG is observed ing only the effects of isotropic Zeeman and for the -‘!yTi components relative to -‘TTi, hyperfine interactions may be used to describe corresponding to a difference in g-value of the present results. ‘The g-value in the Zeeman term is given as: 0.00008 for these isotopes. No such isotopic g-shift has been previously reported, although g r= 2.0023 45 an isotopic change in D-value of CT:‘+ in axially symmetric sites in magnesium oxide where A’ is the spin-orbit coupling constant was reported [ 101. We assign this spectrum to Ti+ ions in and A the splitting between the ‘A,, ground term and the .rT,, excited state. Thus the substitutional cation sites. Wertz et a/.[1 I] isotropic g-shift is derived from the quotient have suggested that Ti*+ is stable in magnesh’jh. The two isotopes will have different ium oxide and that Ti:$+ in axially symmetric vibrational frequencies associated with their sites may be detected after X-irradiation. The different masses: this causes the admixture ionic radii of the various titanium ions are Ti3+. 0.68 A: Ti”+, 0.76 A; Ti2+, 0*90A and of other excited state wavefunctions into the Tis, 0.96 A while the radius for Cax+ is 0.99 A “T,, level to differ for the two isotopes. Thus Ti,*+ and Ti”+ are very small relative to Ca2+ the orbital angular momentum generated in the ground state by mixing of the ?A,, and and are unlikely candidates for a substitutional site in calcium oxide. The presence of F+- “T,, levels due to the spin-orbit coupling operator hl,.S will also differ for the two centres in the crystals may bias them against isotopes. The effect is usually negligibly the formation of such ions. Intuitively, theresmall, and in the present case bg = O.OOOOg. fore, one expects Ti”+ to exist in calcium
Fig. 2. The
I
I I
I
H-
inmaing
paramagnetic resonance spectrum of TI‘+ in calcium oxide. This spectrum at 77°K. The shift of only I30 mg between the hyperfine components
I
4gTi
1
I
4’Ti
:
I, I
I
I I
is observed after irradiation with light in the F-band of”‘Ti and’!‘Ti is clearly discernible.
J
I
(3.1 eV)
I
179x
A. C. TOMLINSON
The appearance of the Ti+ spectrum during irradiation is apparently due to electron trapping by Ti’+ ions. The stability of the spectrum evidently depends on the irradiation temperature. and this is most probably due to different defect centres acting as electron donors in the different temperature ranges. At room temperature the F+ spectrum increases transiently with irradiation up to sevenfold, due to liberation of electrons from F-centresf 131. At 77°K this process is less efficient, but Fe”+ and Cr:‘+ ions are formed from the divalent ions. and their stability is similar to that of the Ti” centre formed at this temperature. 3.3 Double sptvtrr4m
quuntum
transitions
in the Mn’+
In as-received crystals the spectrum from MP ions is always present. Transitions other than those corresponding to AM, = + t ++ -1
Pig. 3. Double
and
B. HENDERSON
are considerably broadened especially after quenching, when a new twelve line spectrum is observed. This spectrum, which is enhanced following ultra violet irradiation at 77°K. consists of 6 pairs of sharp lines each centred on one of the principal manganese AM, =++t-,--k]ines. The similarities of this spectrum with those reported earlier by Auzins and Wertz[ 141 for the double-quantum transitions of the Fe”+ and Mn2i in magnesium oxide have prompted further comparison. The nonadjacent t~dnsitions +$ + -4 and i-4 -+ -+ $ as well as -$+-$ and +)++$ occur with simultaneous absorption of two quanta. Equality of spacing between the two sets of levels for each pair is produced by a small tetragonal distortion of the cubic symmetry, which introduces a D-term into the spin Hamiltonian. To first order in perturbation theory, the -S$ levels are shifted by 2D and
qu~~nturn transitions in the e.p.r. spectrum of MnZ+ in CaO: shown is for the m, = ) pentad with H along the principal axis.
the spectrum
DEFECTS
IN
CALCIUM
the *$ levels by 6D compared with the +3 levels. The value of D necessary in the case of Mn*+ in CaO is only 0.55 G. The resonance condition for double quantum transitions to be observed from suitably distorted Mn”+ ions occurs when the separation between the - 4 --, - 4 and the + %+ + 4 lines is subdivided by 2D and 4D[14]. In the case of manganese the energy level scheme is complicated by a large hyperfine interaction, and the fine structure splittings consequently vary for each of the six hyperfine pentads. In Fig. 3 the double quantum transitions are shown for the m, = 8 pentad along a principal axis, where the usual fine structure positions are reversed, i.e. in this case the +$-+ ?j transitions lie outside the ?+ + &$ transitions. The measured line positions are within one gauss of the predicted positions for double quantum transitions, taking into account second-order effects from fine and hyperfine splittings. A further check was made by measuring the increase in line intensity as a function of the microwave magnetic field vector H, at the sample, keeping crystal bias current constant. At low power levels the twelve line spectrum increased more than linearly with HI, consistent with double quantum transitions. The effect of quenching the crystals clearly introduces the distortions necessary for the resonance condition for double quantum transitions to be satisfied. The spectrum was considerably stronger at 77°K than at room temperature, in contrast to the case for Mn2+ in MgO, for which the intensity of the lines
1799
OXIDE-I
increased with increasing m, value [ 141. The mechanism coupling the intermediate states of the double quantum transitions is not understood. If the coupling between the states is phonon assisted, it is not surprising that the temperature dependence of the intensity of the double quantum lines for Mn2+ should be different in calcium oxide than in magnesium oxide. Acknowledgements-The authors are indebted to the United Kingdom Atomic Energy Authority, Harwell, and the Science Research Council for support of the experimental programme. Informative discussions with Professor D.J.E. Ingram and Dr. M. J. Baker were much appreciated. REFERENCES M. A., U.K.A.E.A. Res. Rep. RS530 I. STONEHAM (1967). 7 A. J.. Phys. Rev. 127,2022 (1962). -. SHUSKUS 3. LOW W. and RUBINS R. S., Proc. 1st Int. Conf. Paramagnetic Res. 1,?9 (1962). 4. SPECK D. R., Phys. Rev. 101, 1725 (I 956). R. J., Phys. Rev. Letr. 5. BOYD C. A. and GAMBINO 12,20 ( 1964). 6. LOW W., Phys. Rev. 103, 1309 ( 1956). A. A. and PROKHOROV A. M., I. MANENKOV Soviet Phys. JETP 6,860 (1958). 8. LOW W. and SHALTIEL D., J. Phys. Chem. Solids 6,315 (1958). 9. HEMPSTEAD C. F. and BOWERS K. D., Phys. Rev. 118, 13 1 ( 1960). S. A., HODGES J. A. and SERWAY 10. MARSHALL R. A.. Phys. Rev. 136, A1024 (1964). 1I. WERTZ J. E.. SAVILLE G. S., HALL L. and Auzins P., Proc. Br. ceram. Sot. I,59 (1963). 12. ZARIPOV M. M. KROPOTOV V. S., LIVANOVA L. D. and STEPANOV V. G.. Soviet Phys. solid St. 9,992 (1967). 13. KEMP J. C., ZINIKER W. and HENSLEY E. B., Phys. Left. 25A, 43 (I 967). 14. AUZINS P. V. and WERTZ J. E., J. phys. Chem. 71.2 I I ( 1967).