Powder ESR spectra of paramagnetic impurities in axial symmetry sites

JOURNAL

OF MAGNETIC

RESONANCE

53,462-472

(1983)

Powder ESR Spectra of ParamagneticImpurities in Axial Symmetry Sites RONALD~

S. DE BIASI AND J. A. M. MENDONCA

Centro de Pesquisa de Materiais, Institute Militar de Engenharia, 22290 Rio de Janeiro, Brazil Received January 14, 1983 The resonance fields and amplitudes of the powder ESR spectra of paramagnetic impurities in axial symmetry sites have been computed as functions of the zero-field splitting parameter D for an effective spin S in the range 1 d S < 72. The results, which are presented in graphical form, may be used for the interpretation of powder spectra.

The interpretation of powder ESR data is often hard, due to the fact that the spectrum is the sum of the spectra for paramagnetic centers in all orientations relative to the applied magnetic field. To overcome this difficulty van Reijen (I) has developed a graphical method for S = ‘/2 in which the resonance condition is plotted as a function of reduced magnetic field and crystal field parameters. The same method was used by Barry (2) to generate graphs for S = ‘/2. Although extremely useful, these graphs have some limitations: not all high-amplitude peaks in the powder spectrum are included, since graphs are given only for the x, y, and z crystal orientations and for 5

2

1

NORMALIZED FIG.

forS=

FIELD,

H/Ho

1. Normalized microwave energy W/D as a function of normalized magnetic field H/H,. Transitions 1.

0022-2364183 $3.00 Copyright 0 1983 by Academic Press, Inc. All rights of reproduction in any form reserved.

462

POWDER

ESR SPECTRA FOR AXIAL

463

SITES

a” 1.0

”

I

z

NORMALIZED FIG.

s-

5

ENERGY,

4

5

W/D

2. Positive peak amplitude A, as a function of normalized microwave energy W/D. Transitions for

1.

transitions between adjacent energy levels; the peak amplitudes are not always correctly represented, since they are expressed only in terms of the transition probabilities for particular orientations of the microwave field relative to the symmetry axes of the paramagnetic center; no account is taken of the finite linewidth of the singlecrystal spectrum of each particle.

1.2 c

I

l1 0.6

0 0

1

2

NORMALIZED E‘lc.

forS=

3

ENERGY,

4

5

W/D

3. Negative peak amplitude A. as a function of normalized microwave energy W/D. Transitions 1.

464

DE BIAS1 AND MENDONCA

FIG.

s=

4. Amplitude

ratio A&4. as a function of normalized microwave energy W/D. Transitions for

1.

In the present work, a recently developed computer program (3) was used to generate a similar set of graphs where the limitations mentioned above have been largely corrected. This set should be useful for the interpretation of the powder spectrum of paramagnetic impurities in axial symmetry sites with an effective spin in the range 1
0

1

NORMALIZED FIG.

forS=%.

2

FIELD,

3

H/Ho

5. Normalized microwave energy W/D as a function of normalized magnetic field H/H,.

Transitions

POWDER

ESR SPECTRA FOR AXIAL

465

SITES

. x 1 l?

0.8

$ a

0.6

2

1

NORMALIZED

3

ENERGY,

4

5

W/D

FIG. 6. Positive peak amplitude A, as a function of normalized microwave energy W/D. Transitions for s = 312.

METHOD

OF CALCULATION

The powder spectra used to generate the graphs are computed in the following way. Single-crystal spectra are calculated exactly for a large number of orientations (typically 90), assuming a Hamiltonian, exactly valid for S < 2, of the form 1.2

S= 312

0

1

2

NORMALIZED FIG.

forS=

3

ENERGY,

4

5

W/D

7. Negative peak amplitude A. as a function of normalized microwave energy W/D. ‘12.

Transitions

466

DE BIAS1 AND 5.0

5

4.0

A?

P

3.0

s

x

2.0

2 Ii

a!k

1.0

0

MENDONCA

L

C

1

D

S = 3/2

B

Illllllllllllllll,l1,11/,

0

1

,,,,,,,,I 2

NORMALIZED

FIG. 8. Amplitude s = ‘12*

,,,,I,,,,

3

ENERGY,

4

ratio Ad.4. as a function of normalized microwave energy W/D.

X = ggHs, + (l/2)0(3

5

W/D Transitions for

cos’ t9 - l)[S: - S(S + 1)/3] + D sin 6 cos O[S,S, + S,&] + (l/2)0

sin2 e[Sf - $1

[l]

where g is the g factor, B is the Bohr magneton, H is the applied magnetic field, D is the zero-field splitting parameter, S is the electronic spin, S,, S,,, and S, are the

0

2

NORMALIZED

FfELD,

H/Ho

FIG. 9. Normalized microwave energy W/D as a function of normalized magnetic field H/Ho. for S = 2.

Transitions

POWDER

ESR

SPECTRA

FOR

AXIAL

467

SITES

LL I

2

1.0 L s=2

J s

0.8 t

1

0

2

NORMALIZED FIG. 10. Positive for s = 2.

peak

amplitude

A, as a function

3

ENERGY, of normalized

4

5

WI D microwave

energy

W/D.

Transitions

x, y, and z components of the electron spin operator, and 19is the angle between the applied magnetic field and the axial symmetry axis of the paramagnetic species. The individual single-crystal spectra are then convoluted with a first-derivative lineshape function and added directly to yield the powder spectrum. Details of the calculations are given elsewhere (3).

$

0.4

\

5 ii a

0.2 11 OLLLLL

”

1

3

NORMALIZED FIG. 1 I. Negative for s = 2.

peak amplitude

A. as a function

ENERGY, of normalized

4

5

W/ D microwave

energy

W/D.

Transitions

468

DE BIAS1 AND MENDONCA

d\ a"

4.0

0

1

2

3

NORMALIZED FIG.

s=

12. Amplitude

ratio AJAn

ENERGY,

4

5

W/D

as a function of normalized microwave energy W/D.

Transitions for

2.

GRAPHICAL

PRESENTATION

The computer powder spectra were used to generate a series of graphs (Figs. l16). For each value of the electronic spin S these graphs show (a) the normalized microwave energy, W/D = hu/D, as a function of the normalized magnetic field, H/HO = gflH/hu; (b) the amplitude of the positive peaks in the powder spectrum A,

S = 5/2

0

2

NORMALIZED

FIELD,

H/H,

FIG. 13. Normalized microwave energy W/D as a function of normalized magnetic field, H/Ho. sitions for S = ‘/*.

Tran-

POWDER

ESR SPECTRA FOR AXIAL

469

SITES

D

2

1.0

w >

0.4 -

5 Iii

0.2 -

a OLLJ-LLU 0

1

2

NORMALIZED

3

ENERGY,

4

W/D

FIG. 14. Positive peak amplitude A,, as a function of normalized microwave energy W/D. Transitions forS=5fz.

as a function of W/D; (c) the amplitude of the negative peaks in the powder spectrum A, as a function of W/D, (d) the ratio A&4, for each peak as a function of W/D. A single-crystal linewidth A&, = 8 mT was assumed in all computations. THE POWDER

ESR SPECTRUM

OF CT’+ IN A1203

As an illustration, the graphs presented in the preceding section will be used to study the spectrum of Clj’ in polycrystalline A1203.

-1

02-

0

1

2

NORMALIZED

3

ENERGY,

4

5

W/D

FIG. 15. Negative peak amplitude A. as a function of normalized microwave energy W/D. Transitions for S = %.

470

DE BIAS1 AND MENDONCA

0

1

2

3

NORMALIZED FIG. 16. Amplitude s = 512.

ENERGY,

4

5

W/D

ratio AJAn as a function of normalized microwave energy W/D.

Transitions for

The powder sample used in this work was prepared from pure oxides which were carefully ground together and then fired for 96 hr at 1350°C. The actual chromium concentration, as determined by X-ray fluorescence spectrometry, was 0.07 mol%. Traces of iron were also detected. Magnetic resonance measurements were performed at room temperature and 9.50 GHz. The ESR spectrum of the chromium-doped A1203 sample is shown in Fig. 17. The spin Hamiltonian parameters for the Cr3+ ion in substitutional sites in A1203, as determined from single-crystal data, are (4) s=

‘/2

g11= 1.9817 g1 = 1.9819 IDl/h = 5.747 GHz.

1

0 FIG.

I

01

I

02

03

I

04

1

05

T

17. ESR spectrum of a powder sample of A1203 doped with 0.07 mol% Cr.

POWDER

ESR SPECTRA FOR AXIAL

0

1

471

SITES

2

3

NORMALIZED FIELD, H/H, FIG.

18. Determination of the resonance fields for the &‘+:A1203 system.

For the accuracy with which points can be plotted in the graphs, we may use g,, N gL N 1.98, ID(/h N 5.75 GHz. In that case, we have W/D = hvlD = 9.5015.75 = 1.65 and Ho = hvjgfl = 0.343 T. The value W/D = 1.65 defines a horizontal line in the graph of Fig. 5. Three transitions are predicted (Fig. 18): transition B, with H/Ho = 0.57 or H N 0.195 T; transition D, with H/Ho = 1.33 or H N 0.456 T; and transition E, with H/Ho = 1.58 or H N 0.542 T. The values of A,, A,, and A& for the three transitions may be obtained from Figs. 6-8. A comparison between the fields and amplitudes obtained from the graphs and the experimental results is shown in Table 1. Since there is a good agreement between the theoretical and experimental results for all four parameters, one can be quite sure that the substitutional Crj’ ions reTABLE COMPARISON EXPERIMENTAL

1

BETWEEN THEORETICAL AND ESR RESULIX FOR CI-?A~~O,~

Theoretical

HI& 4 A. &I.&

A,

Experimental

B

D

E

B

D

E

0.57 1.oo 0.37 2.70

1.33 0.13 0.39 0.33

1.58 0.06 0.14 0.33

0.57 1.a0 0.35 2.85

1.33 0.11 0.45 0.26

1.57 0.04 0.13 0.31

n The values of A, and A. were normalized by taking = 1.00 for transition B.

472

DE BIAS1 AND MENDONCA

sponsible for the spectrum in single-crystal AlzOJ are also responsible for lines B, D, and E in the powder spectrum (Fig. 17). The other strong lines, labeled X in Fig. 17, could presumably be due to CIj’ in lower (orthorhombic) symmetry sites or to the chromium ion in other valence states. However, they fit well the spectrum of Fe3+ in powder A&O3 samples (5), as can be checked using Figs. 13- 16 and the spin Hamiltonian parameters for the Fe3+:A120s system, obtained from single-crystal measurements (6). This is consistent with the fact that, as stated before, traces of iron were detected in the sample by X-ray fluorescence spectroscopy. If the spin Hamiltonian parameters for the C$+:A1203 system were unknown, the graphs in Figs. 5-8 could be used to estimate the value of D from the powder spectrum. The reasoning would be the following. According to Fig. 6, line B has a large positive peak for a wide range of crystal fields. As shown in Fig. 5, this transition occurs in the range 0.5 < H/H0 < 0.8. The largest positive peak in the spectrum of Fig. 17 is in this range and may be thus tentatively identified as line B. This can be checked by looking for the other transitions indicated in the graph of Fig. 5. The absence of transition C in the experimental spectrum implies that W/D < 2. The fact that the negative peak of line B is smaller than the negative peak of line D suggests (Fig. 7) that W/D > 1.6. This leads to the estimate that 1.6 < W/D < 2.0, or 4.5 GHz < IDl/ h < 6 GHz. The real value, W/D = 1.65 or ID[/h = 5.75 GHz, is within this range. CONCLUSIONS

The example of the system C?:A1203 shows that with the help of the graphs presented in this work (Figs. 1-16) it is possible to identify the lines in a powder spectrum associated with the transitions due to a particular ion in axial symmetry sites, once the relevant spin Hamiltonian parameters are known from single-crystal experiments. If the spin Hamiltonian parameters are unknown, it is still possible to estimate the value of the zero-field splitting parameter D from the powder spectrum. The graphs should thus be useful for the study of paramagnetic ions in polycrystalline materials. REFERENCES 1. 2. 3. 4. 5.

L. T. R. T. F.

L. VAN REWEN, Ph.D. Thesis, Technological University, Eindhoven (1964). 1. BARRY, NPL Report, IMU Ex. 6 (1967). S. DE BIASI AND J. A. M. MENDONCA, Comput. Phys. Commun. 28,69 (1982). T. CHANO, D. FOSTER, AND A. H. KAHN, J. Res. Nat. Bur. Stand. 83, 133 (1978). MEHRAN, K. A. MUELLER, W. J. FITZPATRICK, W. BERLINGER, AND M. S. FLJNG,

Sot. 64, C-129 (1981). 6. H. F. SYMMONS AND G. S. BOGLE, Proc. Phys. Sot. 79,468 (1962).

J. Am. Ceram.