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Linear crystal-field terms and the 5Do - 7Fo transition of the Eu3+ ion
Solid State Communications Vol. 4, PP.22 7-229, 1966. Pergamon Press Ltd. Printed in Great Britain.
LINEAR CRYSTAL-FIELD TERMS AND THE 5D 3~ ION OF THE Eu W. C. Nieuwpoort and G. B]asse
-
‘F 0 TRANSITION
Philips Research Laboratories, N. V. Philips’ Gloeilampenfabrieken, Eindhoven, Nether]ands (Received 25 March 1966 by G.W. Rathenau)
Experimental and theoretical evidence is presented in favour of admitting linear terms in crystal-field expansions whenever the site symmetry is appropriate.
IT IS customary in crystal-field expansions to exclude terms varying linearly with electron distance. For example, when the potential V~ a-
the site symmetry of the activator (from crystallographic data, see Ref. 4) and the ratio of the integrated emission intensity of the 5D 5D 0 — ‘F0 5D transition to that of the 0 — ‘F1 and 0 ‘F3 transitions summed over their respective crystal-field components. The former ratio is probably the more6Duseful one to look at since the intensity of the 0 ‘F1 transition, as a primarily magnetic dipole transition, is not expected to vary 5D as strongly with the surroundings as the 0 ‘F2 intensity. ‘
round a crystal site is assumed to obey Laplace’s equation ~ V~’ = 0 terms with 2 = I are omitted in the expression vcr (~)= ~ E A2m 2 m2
T2
-‘
-
Y’~(e, cp),
-
even when such terms are “formally” allowedby the site symmetry 1’2(C5, that C~, theseCnv). termsIt must has been be exstated repeatedly cluded because they would yield a net force onthe central nucleus and hence one would not be dealing with an equilibrium situation.
These data show that within the5D indicated accuracy line appears of the always measurements whenever itthe is allowed 0 ‘F0 by the observed site symmetry. Clearly it is also for these symmetries that a linear term is possible but this in Itself does not yet make the term necessary. However, it is known that a theory based on (4f)11 wave functions which are corrected to first order for the effects of both spin-orbit interaction and odd-parity crystal -
Recently, however, Kiss and Weakliem3 found it necessary to include a linear terip in order to explain the observed Stark shifts of lines associated with the 5D 5D 0 ‘F0 and 0 ‘F1 transitions of Sm~in BaC1F (site symmetry C4, ). In this note we present new evidence for the admission of linear terms based on intensities of 6D the 0 ‘F0 3~ (4f8) transition in mixed observed metal in oxides. the fluoresSubcence of Eu sequently we discuss the theoretical argument -
field terms with 2 ~ 3 accounts reasonably well for the absor~xionand emission intensities of those f-f transitions for which a 2 = 1 term is not essential. ~ ~ Our results 5D now contain a number is of theof same casesorder where of magnitude the 0 ‘F0 as that intensity of the ‘F 6D 1 and 0 ‘F3 transitions. 5D Notably in ~r3TiO4 It is 1.65 times that of 0 ‘F1. This would be difficult to understand if the bD0 of a first order theory to the oneinJust -‘F0 intensities could similar not be explained terms mentioned and this requires the presence of a linear term in the crystal field expansion. A similar argument was used by Kiss and Weakliem
-
-
-
-
-
against these terms referred to above and condude that it is invalid. 3~activated phosphors were prepared and the powders Eu measured as described elsewhere. ~ Table 1 presents a summary of the results. We have tabulated the composition of the phosphor,
-
227
228
LINEAR CRYSTAL-FIELD TERMS
Vol. 4, No. 5
TABLE I Intensity ratios of some lines of the Eu~emission in several phosphors
Phosphor
Site symmetry activator
5D
7F 0
-
~,
o
6D 0
7 ~. Li
0 5,-., 110
-
‘F0
Ref.
, t. —
Ba3GdNbO6: Eu
O~
0. 00
0. 00
*
Gd2T13O, : Eu
D3d
0. 00
0. 00
*
Eu(C3H~SO4)3.9H3O
C~
0. 00
0. 00
1
LaC13: Eu
C3~
0. 00
0. 00
8
LaMgA111O19: Eu
D3h
0. 00
0. 00
*
YVO4: Eu
D~
0. 00
0. 00
9
Gd303 : Eu
S~and C2,
0.25
0. 03
10
Sr3TIO4:Eu
C4,
1.65
0.48
*
SrLa.A104: Eu
C1,
0. 09
0. 02
*
Gd8WO6: Eu
C4,
0. 68
0. 05
*
Sr3LaA1O~:Eu
Ca and C1,
0. 16
0. 05
*
Ba3Gd8WO9: Eu
C3,
0.72
0.45
*
GdTISbO6: Eu
C2,
0.04
0.02
*
LiGdO3: Eu
C1
0. 08
0. 04
*
*Thjs work. 2~transiin their workabove, on the Stark shifts of Sm tions quoted The “non-equilibrium” argument used to exdude such terms is not valid in our opinion. It implies that the usual crystal-field model, in addition to providing a convenient formalism to describe and parameterize part of the electronic states of the system, also describes the actual forces operating on the nuclei. That this is not so can be seen already in the familiar, more symmetrical surroundings (e. g. °h’ Td) where the disturbing linear terms are not encountered. In the purely ionic model, for example, the central positive ion in an octahedron of negative ions never occupies a position of minimum energy
with respect to the classical electrostatic forces alone. This is remedied by introducing nonclassical Born-Mayer repulsion forces but these are and there is nothing against this left out of consideration when writing down an effective crystal potential for e. g. the f-electrons. Quite generally there is no reason to r~quirean effective potential used to describe the motion of a particular set of electrons to be identical with the potential from which the forces on the nuclei can be derived. The use of a linear term when allowed by symmetry is not more formal than the crystal-field expansion itself. -
-
It is of interest to note that, as Judd has recently pointed out, ~ linear crystal-field terms
Vol. 4, No. 5
LINEAR CRYSTAL-FIELD TERMS
229
of certain lines in rare-earth ion solution spectra.2
may also be the source of the “hypersensitivity”
References 1.
AXE J.D.,
J. Chem. Phys. 39,
2.
JØRGENSEN C.K. and JUDD B.R., Mol. Phys.
3.
KISS Z.J. and WEAKLIEM H.A.,
4.
BLASSE G., BRIL A. and NIEUWPOORT W. C., Int. Conf. on Luminescence, Budapest (1966); BLASSE G., Philips Res. Repts, (to be published).
5.
JUDD B.R.,
6.
OFELT G.S.,
7.
JUDD B.R.,
8.
SHAZER L.G. DEandDIEKE G.H. ,J. Chem. Phys. 38, 2190 (1963).
9.
BRIL A.,
Phys. Rev. 127,
1154 (1963). 8, 281 (1964).
Phys. Rev. Letters 15, 457 (1965).
750 (1962).
J. Chem. Phys. 37, 511 (1962). J. Chem. Phys. 44,
839 (1966).
WANMAKER W. L. and BROOS J.,
J. Chem. Phys. 43, 311 (1965).
10. BRIL A. and WANMAKER W. L., J. Electrochem. Soc. 111, 1363 (1964).
Es werden experimentelle mid theoretische Argumente ins Feld geft(hrt, weiche zeigen dass auch lineare Terme in Krista]feldentwicklungen zugelassen worden mtlssen wenn die Punktsymmetrie dazu geeignet ist.
LINEAR CRYSTAL-FIELD TERMS AND THE 5D 3~ ION OF THE Eu W. C. Nieuwpoort and G. B]asse
-
‘F 0 TRANSITION
Philips Research Laboratories, N. V. Philips’ Gloeilampenfabrieken, Eindhoven, Nether]ands (Received 25 March 1966 by G.W. Rathenau)
Experimental and theoretical evidence is presented in favour of admitting linear terms in crystal-field expansions whenever the site symmetry is appropriate.
IT IS customary in crystal-field expansions to exclude terms varying linearly with electron distance. For example, when the potential V~ a-
the site symmetry of the activator (from crystallographic data, see Ref. 4) and the ratio of the integrated emission intensity of the 5D 5D 0 — ‘F0 5D transition to that of the 0 — ‘F1 and 0 ‘F3 transitions summed over their respective crystal-field components. The former ratio is probably the more6Duseful one to look at since the intensity of the 0 ‘F1 transition, as a primarily magnetic dipole transition, is not expected to vary 5D as strongly with the surroundings as the 0 ‘F2 intensity. ‘
round a crystal site is assumed to obey Laplace’s equation ~ V~’ = 0 terms with 2 = I are omitted in the expression vcr (~)= ~ E A2m 2 m2
T2
-‘
-
Y’~(e, cp),
-
even when such terms are “formally” allowedby the site symmetry 1’2(C5, that C~, theseCnv). termsIt must has been be exstated repeatedly cluded because they would yield a net force onthe central nucleus and hence one would not be dealing with an equilibrium situation.
These data show that within the5D indicated accuracy line appears of the always measurements whenever itthe is allowed 0 ‘F0 by the observed site symmetry. Clearly it is also for these symmetries that a linear term is possible but this in Itself does not yet make the term necessary. However, it is known that a theory based on (4f)11 wave functions which are corrected to first order for the effects of both spin-orbit interaction and odd-parity crystal -
Recently, however, Kiss and Weakliem3 found it necessary to include a linear terip in order to explain the observed Stark shifts of lines associated with the 5D 5D 0 ‘F0 and 0 ‘F1 transitions of Sm~in BaC1F (site symmetry C4, ). In this note we present new evidence for the admission of linear terms based on intensities of 6D the 0 ‘F0 3~ (4f8) transition in mixed observed metal in oxides. the fluoresSubcence of Eu sequently we discuss the theoretical argument -
field terms with 2 ~ 3 accounts reasonably well for the absor~xionand emission intensities of those f-f transitions for which a 2 = 1 term is not essential. ~ ~ Our results 5D now contain a number is of theof same casesorder where of magnitude the 0 ‘F0 as that intensity of the ‘F 6D 1 and 0 ‘F3 transitions. 5D Notably in ~r3TiO4 It is 1.65 times that of 0 ‘F1. This would be difficult to understand if the bD0 of a first order theory to the oneinJust -‘F0 intensities could similar not be explained terms mentioned and this requires the presence of a linear term in the crystal field expansion. A similar argument was used by Kiss and Weakliem
-
-
-
-
-
against these terms referred to above and condude that it is invalid. 3~activated phosphors were prepared and the powders Eu measured as described elsewhere. ~ Table 1 presents a summary of the results. We have tabulated the composition of the phosphor,
-
227
228
LINEAR CRYSTAL-FIELD TERMS
Vol. 4, No. 5
TABLE I Intensity ratios of some lines of the Eu~emission in several phosphors
Phosphor
Site symmetry activator
5D
7F 0
-
~,
o
6D 0
7 ~. Li
0 5,-., 110
-
‘F0
Ref.
, t. —
Ba3GdNbO6: Eu
O~
0. 00
0. 00
*
Gd2T13O, : Eu
D3d
0. 00
0. 00
*
Eu(C3H~SO4)3.9H3O
C~
0. 00
0. 00
1
LaC13: Eu
C3~
0. 00
0. 00
8
LaMgA111O19: Eu
D3h
0. 00
0. 00
*
YVO4: Eu
D~
0. 00
0. 00
9
Gd303 : Eu
S~and C2,
0.25
0. 03
10
Sr3TIO4:Eu
C4,
1.65
0.48
*
SrLa.A104: Eu
C1,
0. 09
0. 02
*
Gd8WO6: Eu
C4,
0. 68
0. 05
*
Sr3LaA1O~:Eu
Ca and C1,
0. 16
0. 05
*
Ba3Gd8WO9: Eu
C3,
0.72
0.45
*
GdTISbO6: Eu
C2,
0.04
0.02
*
LiGdO3: Eu
C1
0. 08
0. 04
*
*Thjs work. 2~transiin their workabove, on the Stark shifts of Sm tions quoted The “non-equilibrium” argument used to exdude such terms is not valid in our opinion. It implies that the usual crystal-field model, in addition to providing a convenient formalism to describe and parameterize part of the electronic states of the system, also describes the actual forces operating on the nuclei. That this is not so can be seen already in the familiar, more symmetrical surroundings (e. g. °h’ Td) where the disturbing linear terms are not encountered. In the purely ionic model, for example, the central positive ion in an octahedron of negative ions never occupies a position of minimum energy
with respect to the classical electrostatic forces alone. This is remedied by introducing nonclassical Born-Mayer repulsion forces but these are and there is nothing against this left out of consideration when writing down an effective crystal potential for e. g. the f-electrons. Quite generally there is no reason to r~quirean effective potential used to describe the motion of a particular set of electrons to be identical with the potential from which the forces on the nuclei can be derived. The use of a linear term when allowed by symmetry is not more formal than the crystal-field expansion itself. -
-
It is of interest to note that, as Judd has recently pointed out, ~ linear crystal-field terms
Vol. 4, No. 5
LINEAR CRYSTAL-FIELD TERMS
229
of certain lines in rare-earth ion solution spectra.2
may also be the source of the “hypersensitivity”
References 1.
AXE J.D.,
J. Chem. Phys. 39,
2.
JØRGENSEN C.K. and JUDD B.R., Mol. Phys.
3.
KISS Z.J. and WEAKLIEM H.A.,
4.
BLASSE G., BRIL A. and NIEUWPOORT W. C., Int. Conf. on Luminescence, Budapest (1966); BLASSE G., Philips Res. Repts, (to be published).
5.
JUDD B.R.,
6.
OFELT G.S.,
7.
JUDD B.R.,
8.
SHAZER L.G. DEandDIEKE G.H. ,J. Chem. Phys. 38, 2190 (1963).
9.
BRIL A.,
Phys. Rev. 127,
1154 (1963). 8, 281 (1964).
Phys. Rev. Letters 15, 457 (1965).
750 (1962).
J. Chem. Phys. 37, 511 (1962). J. Chem. Phys. 44,
839 (1966).
WANMAKER W. L. and BROOS J.,
J. Chem. Phys. 43, 311 (1965).
10. BRIL A. and WANMAKER W. L., J. Electrochem. Soc. 111, 1363 (1964).
Es werden experimentelle mid theoretische Argumente ins Feld geft(hrt, weiche zeigen dass auch lineare Terme in Krista]feldentwicklungen zugelassen worden mtlssen wenn die Punktsymmetrie dazu geeignet ist.