HL)L-TR-1 788

zc' RARE EARTH IONoHM$T LATTICE, 1NTERACTIONSI3~La v~I~iIn YA~Oj

February '1877 Wiw,,

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God fteadinass Commwond~I1~ ~HARRY DIAMOND~ LAbOftATORIES

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H~i-TRl7B8 3 GVT ACCESSION NO. 3 Ae I ' S CATALOG NLJMNER

4 T! L E(@ýn d. labiw4_ýT PERIOD C.OYERtED

'Rare- Earth Ton-Host Lattice Interactions,13. Lanth a nid es in YAl0W 3 '. 7Technical, oportt -

*--- ER

r-AS OR ORANT NUM111ti'a

Clyde A.'o6nNick/Karayianis DA-TlTl6l1.O2AH46.

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IS. SUPPLEMENTARY NOTES L I )HDL Project: 308637DRCMS Code; 611102.ll.Hi46112. APR 1 qr

IS. KEY WoRDS (Comfinue on revere side It nec~esary and Ideantify by block nuffber)Yttrium aluminate AOptical absoxption and fluorescence spectra9 Crystal field parametersRare earth spectraLanthanide spectra

*30. ANTRAcr (ceribwje m revere. stf It nameewa, sind Idertil(F by block num~bet)

Phenomenoloyical even-fold crystal field parameters, Bkm'#are 9,btained for triply ionized Nd, Tb, Dy, 11o, Err and Tm inYA103~ by diagonalizing a C,',(C.1h1_ crystal field Hamiltonian ina free-ion wave-function basis. These parameters a~e reducedto gjive the part of the crystal fiej~d components, Akm" du~e solelyto the crystal lattice, and new D km)are then calculated for all ,-the lanthanides by using previously derived I)", where f~~~ik

DO i JQn I I[Dl Dops or i NOV 69 It ONSOL11TE rAM I IUNCT 1ASSTF-TET

SECURITY CLAVISIPICATIORt OP THIS PAGE (When 1)ie -nl-rsiI)

-1002

UNCLASSIFIED ,SECURITY CLASSIFICATION OP THIS PAOR(Whon ml0g Intvtlff

'The latter Nm ate used to calculate the energy leves of thelower J-multiplets for the lanthanide series in YAlO'•.

ArCURITY 6LASIMPICAtION OF THiIS P40t(When Date. h~rlfrd)

- ~ f~~*i

CON THN'TS

.1. T NITRODUCTI ()N .T . . . . . . . . . . . . . . . . . . . . . . . .

2. (AI,C~tl ATIUN5 . . . . . . . . . . . . . . . . . . . . .. . .

3. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . .. I

LITERATUIJRE CITED . . . . . . . . . . . . . . . . . . . . . . . 38

DTSTRIBUTTON . . . . . . . . . . . . . . . . . . . . . . . . . .

TA13I.,ES

I Phenomenological Crystal Field Parameters, Bkm, forTriply Ionized Lanthaiiides in YAIO 3 ............ 7

II Values for ()k .rk>( -. k) i. k ... . 8

IIl Crystal Field Paramoters, lik, for Triply IonizedLanthanides in YAU 3. . . . . .. .. .. .. . . . . . . . . .. . . . . . . . . ..

IV Crystal Field Paramt-er3,, l•l, and Energy Levelsfor Pr"+ in YAl.O... ....... . . .................... ....

V Energy LeVeLs and Phenoinunuoluqical Crystal Field

Parameters for Nd 3+ in YAI()\.0 ......... ............... 14

VI Crystal Field Param',t,.,rs, ikm, and Enargy Levelsfor Nd"' in YAP).-. ............ ...................... 15

VII crystal kiin•d I'~r.ter:.; 3ki, and Energy LevelsVI )for Pil l in YALu)... . ...... ..................... 16

Vill Crystal Fiold Paramht,.r:;, Bkm, and Energy Levelsfor Slmý+ in YALO... . .......... ..................... .. 18

IX Crystal Pirld 1'nirameters, Bkm, and Energy Levelsfor Eu + in YAlOI ().............. ..................... 20

X Crystal I.-'Ild Parameters, Bkm, and Energy Leve.sfor Gd3+ in YAIC)3 . . . .. .. .. .. .. . . . . . . . . . . .. . . . . . . . . . 22

XT Energy Ievel:i and Phenomenological Bkm for rh 3 +.i.. YA... .. ......... ......................... 23

XII Crystal Field Parameters, Bkfi, and Energy Levelsfor Tb I+ in YAlO0 . ................. ..................... 24

"XIII Energy Levels arid Phenomenological Crystal FieldParameters for Dy" ill YAlO3 .. . . . .. .. .. .. .. . . . . . . .. . . . . . . . 26

3

wc 0

TABLE'S (:CNT'))

xIv ( ry~itll I Iik. lcid r13z t kin, c~nd Enr~cry I ,(vuLsfu D " n YAI() . . . . . . . . 27

.\V IErI(,rqy ' o(' " aeL( nd [III iIrlonoioJf l . o(I&(I.i.(Jdil. Cv:y(ihtd P1cIQ.dfoi~iiLe ~ t r. Ho" iii YAJ.U, . . * . . . . . 2

XVI Crystai.L ['jcd Pairamoturs, Bkmp and Encurcy Lovolsfor )103+ in YAlO), . . . . . . . . . :

xvr l,-.xvrtE Enercl' u~vciL ndd I'llclotrincnoloiq1 ia ICry(ItdJ. FicidParaimeters for Er~in YAIO- . ~ . * 30- 31

XIX Crystal Viec]i Ptramut~urs, B3 and E'norgy Lovuelsfor Er'+ in YAIOj..........................................32

XX Energy 1,evols andd Phenomeouoocj i~ua Crysta.1 FieldParamnut~rurs for Trml+ Ini YA103 ................................

XXI crys tal. Pield Paramuotrs , rBkm' and Eneirgy Loveisfuk: 'tm i+ in YAlE)j ~.... . .. . ... .. .. .. . ..

XXI I Ampti UI tuUS , Cryn tal Vield Components-, AkM inCI - of Sphoricol Decompo)usit-inn of

YA1.Oj Latticu Suw .... .. 3

XXIII1 AmpI1. 1It uces, Crystal Ibidlc Componont-9, Akm inCMn A, of Sphurical Ducampos;itiur, ofYAlE)' Latt.ice Skims for~ Evun Vaiiuclsi f k .. ............... 37

4

1. INTRODUCTION

The optical spectra of a number of triply ionized lanthanides in

yttrium orthoaluminaie (YAI0) have been reported.)-' Because of the

excellont laser properties of this material,' we have examined these

reported spectra in order to obtain a unified theory of the crystal field

interactions at the laser ion site in YAlO:-. In !.4q report,

phenomenological crystal field parameters, Bk., for triply jonized Ad,

Tb, uy, Ho, Er, and Tm were obtained by diagonalizing a C (C lh) crystalz s l

field Hamiltonian in a free-ion wave-function basis. The paraNiaters were

reduced to give the part of the crystal field components, Akm, due solely

to the crystal lattice, and new Bkm were then calculated for all the

lanthanides by using previoucly derived 7 p' where BkM f A km, These

Bkm were then used to calculate the energy levels of the lower

J-multiplets for the lanthanide series in YAlO 3 .

2. CALCULATIONS

The point group symmetry 8 at the yttrium site in YA1O:3 is Cs (Clh),

which includes a reflection plane in addition to the identity operation.

IM. Bass and M. 7. Weber, Laser Focus, 7 (1971), 34-36.2 M. j. Weber and T. E. Varitimos, J. Appl. Phys., 42 (1971),

4996-5005.3 Kh. S. Bagdasarov, A. A. Kaminskci, and G. 1. Rogov, Sov. Phys.

Doklady, 14 (1969), 346-348.4j. L. Berg, High Resolution Low Temperature Spectra of Tb 3 ý in YAle 3 ,

Master's Thesis, Air Force Institute of Technology, Wright-Patterson AirForce Base, OH (June 1973).

5 V. A. Antanov, P. A. Arsenev, K. E. Bienert, and A. V. Pobemkin,Phys. Status Sol.di A, 19 (1973), 289-299.

6 V. 1,. Ponla and A. 7A. Santiaqou, Jr., J. Chei. Ph!s., 5.- (9.'72),4717-4723.

0D. 1-. Wortman, C. A. Morrison, and N. Karaiianis, Rare EarthIon-Host Lattice Interactions 11. Lanthanides in Y3 A1 5 01 2 , Harry DiamondLaboratories TR-1773 (August 1976).

8R. Diehl and G. Brandt, Materia Research Bulletin, 10 (1975), R5-90.

If the z-axis is taken perpendicular to the reflection plane, the crystal

field Hamniltonian is of the form

H = r B C ,k -2, 4, 61 m - 0, ±2......k,()

where the B km for mn # 0 may be complex. With no loss in generality, we

chose real B;,;, and imaginary Bi4,ý 0.

The crystal field Hamiltonian was diagonalized in the low-lying

J-multiplets of free-ion wave functions,, and the B were varied tokmn

obtain best fits between theoretical and excperimental energy levels

reported for Nd,~''3 Tb, 10Dy, 5 Ho,5 Er5,6 and Tm.5 The resultant

best-fit parameters aro given in table 1, where the next to last four

columns give the number of 3-inultiplets diagonalized, the number of

levels in these multiplets, the number of experimental energies used, and

finally the rms deviation between these energies and their corresponding

theoretical energies. The znuitiplets included for each ion were

Cl te I em,'F~/,and 1?qfor Nd, (2) the a trm and D0 for Tb,

(3) 11H andp ,r for oyj (4) *,and

-1 for Ito; (5) the 'r tern,, 1frTh/,), and 11SI12 fnr Xr) and (6) the 1H

term, 3r,1. and 1G4 for Tm. The lack of sufficient data in~ some cases

plus ambiguities owing to overlapping multiplets governed the choice of

2M. J. Weber and T. E. Varitimos, J. Appi. Phys., 42 (1971),4996-5005.

3Kh. S. Bagdasarov, A. A. Kaminakil, and G. I. Rogov, Soy. Phys.Dokiady, 14 (1969), 346-3411.

4j. L. Berg, High Resolution Low Temperature Spectra ol Tb3+ in YA1O3,Master's Thesis, Air Force Institute of Technology, Wright-Patterson AirForce Base, OH (June 1973).

5V. A. Antanov, P. A. Arsenev, K. N. Eionert, and A. V. Potummkin,Phys. Status Solidi A, 1 *9 (1973), .189-299.

6 V. i,_ Donla~n a nd A. A. SantLilcto r, J.Cjjwtfl. 'hys . , 57 (11072) ,

9W. T. Carnall, P. R. Fields, and K. Rajnakp J. Chem. Phys.,~f..(1968U), 4412-4455.

I0

,-j,

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o• ,.I en , ,',

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multiplots and experimental energies that were used in the fitting

procedure. Table I, line 6, gives the set of initial Bkm for Er that

were chosen to begin the fitting procedure. For starting parameters,

previously reported parameters for Er:yttrium aluminum garnet

(YAG) were used. Since the YAG crystal field is real, imaginary B1,

was arbitrarily set at 200 cm-.

Subsequent choices for starting parameters for the other ions were

chosen by scaling the Ho parameters, which were obtained by averaging the

best-fit Dy and Er phenomenological Bkm, according to the pk in table TI.

Thene ()k, given by

TABLE I. VALVES FOR Pk - .TI, (i -k)IN Ak TO CONVERT LATTICE SUMS

CRYSTAL FIELD COMPONENTS, Akin,TO CRYSTAL FIELD PARAMETERS, Bkm,AS kiii , PkAkrn

I, 1

IC' Ij,(, C (II, i• l I I ,,

11, o, l /I o] ll,1// I I

Cl, , ,III,' Cl .5'$ I , Ih l0m. 1 6(H 1 ) 5 /4 ' 11 1,0614 I{

ill 1 ,. IiI , o

10C, A. Morrison# D. E, Wortman, and N. Xarayianis, J. Phys. C: Solid51t:ite, Jp/ys., 9 (1976), L191.

l~~c. A. Morrison, D. •. Woreman, aria . aaini,,.hU.CSod

U't hs,9 17) ll

.' *w t r ~ ~ ~ * ~~ * ~ ~ -,. *

P krk> a1 . ) (2)

are rare-earth-ion dependent and relate the Bkm to the lattice sum field

Akm 'y

Bkm p kAk (3)

"where it is assumed that the Akm are host dependent only. The are

smoothed values of Freeman and Watson, the 0 are linearly interpolated

calculations of Erdos and Kang,12 and the T are quadratically fit

wave-function expansion parameters found in studies of lanthanides in

CaWO 4 . 13 The Bkm for the lanthanide series obtained by using these ik

values of table 11 in equation (3) and the Bkm for Dy and Er of table I

are given in table I1I.

Energy levels calculated hyr using the Bkm of tables . and IXI for

the lowest-lying rix to eight multiplets of the lanthanides in YA101 are

given in tables IV to XXI.

To make intensity calculations, some estimates of the odd-fold

(odd-k) Akm are necessary. Th. : can be obtained by appropriate lattice

sums.l11 In this work, we hayv performed the lattice sums for YAlO3 using

the x-ray data of Diehl and Tir.andt8 for oxygen charges q0 w -1 and -2p

the results are given in table XXII. The one-fold field, A1 m, was not

8R. Diehl and (s. Brandt, Materia Research Bulletin, 10 (1975), 85-90.'IA. J. Freeman and R. E. Watson, Phys. Rev., 127 (1962), 2058-2075.1 2p. Erdos and J. H. Kang, Phys. Rev. B, 6 (1972), 3393-3408.

,1 13R. I l,rmvwitA, C. A. Morrison, and- V, IP'. Wortn.,irn, Ra•li' lart:htIon-flost Ct'ryjsta L Itilractions 3. Throo-Paramelter ''htori' of CrystalFields, Harry Diamond Laboratorien TR-1673 (June 1975).

1'N. Karatlianls and C. A. Morrison, Rare Earth ton-Host Lattice*, Interactions 1. Point Charge Lattice Sum In Scheelites, Harry Diamond

Laboratories TR-1648 (October 1973).

J•9

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included because of its slow convergence. By appropriate rotations of

the coordinate system chosen for the calculation of the Akm of

table XXII, different sets of Ak. can be generated. Thus by appropriate

rotation, the sets of Akm for qo = -1 and -1.5 given in table XXIII were

calculated. Since the Akm are linear functions of q0, a value of q0 can

be chosen by using equation (3) and the Pk of table II to obtain a best

fit of calculated B km to phenomenological Bkm* The results of this

calculation give q0 M -1.52, and the corresponding Akm are reported1kmelsewhere.

3. SUMMARY

Reported energy levels for Nd, Tb, Dy, Ho, Er, and Tm were used to

obtain phenomenoloqical Bkm that yielded least-rms deviations between

these levels and levels calcuiated by using the Hamiltonian given in

equation (1) and unpublished theoretical methods and computer programs.

These parameters were then scalcd to get even-k Bkm for the entire

lanthanldc series in YAI0i. It is expected that these Bkm will at least

serve as starting parameters f-r the analysis of yet unreported ions in

YA10 3. No intensities were ý'-ilculated because the symmetry of the

Y1+ site was low and becaus;,* no reasonable higher symmetry approximation

could be made as was doneV for the lanthanides in YAG.

7 0. R. WortNaln, C. A. Morrison, and N. Karayianis, Rare Earth Ton-I1oLt La tt i cu Interactions 11. Lanthanides in Y 3 A1 5 0 1 2 , Harry DiamondLaboratories TR-1773 (August 1976).

15N. Karayianis, D. E. Wortman, and C. A. Morrison, Solid State Comm.,18 (1976).

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TABLE XXII, AMPLITUDES, CRYSTAL FIELD COMPONENTS,Akm IN cn"1 ,-k, OF SPHERICAL DECOM-POSITION OF YAIO 3 LATTICE SUMSa

4.,,

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i.36

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TABLE XXIII. AMPLITUDES, CRYSTAL FIELD COMPONENTS,Akm IN c..| -k, OF SPHERICAL DECOM-POSITION OF YAIO LATTICE SUMS FOREVEN VALUES OF ka

I I

W o., *3 61i.

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I • i/•, 0 6 2 . W,

t , I 6?.I 0 146,,0 ?

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37), ,

-I, *''a• /.~ I • '~ ' f f I h * . ,IV .' I, " /,• ;,t .\l '" ,. I Ia '

337

LITERATURE CITED

(1) M. Bass and M. J. Weber, Lamer Focus, 7 (1971), 34-36.

(2) M. J. Weber and T. E.,Varitmos, J. Appl. Phys., 42 (1971),4996-5005.

(3) Kh. S. Bagdasarov, A. A. Kaminskii, nnd G. I. Rogov, Sov.Phys. Doklady, 14 (1969), 346-348.

(4) J. L. Berg, High Resolution Low Temperature Spectra of Tb + inYAI0,, Master's Thesis, Air Force Institute of Technology,"Wright-Patterson Air Force Base, OH (June 1973).

(5) V. A. Antanov, P. A. Armenev, K. E. Bienert, andA. V. Potemkin, Phys. Status Solidi A, 19 (1973), 289-299.

(6) V. L. Donlan anre A. A. Santiago, Jr., J, Cham. Phys., 57(1972), 4717-4723.

(7) D. E. Wortman, C. A. Morrison, and N. Karayianis, RareEarth lon-Host Lattice Interactions 11. LanthLanidws inYA1, 0,., Harry Diamond Laboratories TR-1773 (August 1976).

,3) R. Diehl and 0. Brandt, Materia Research Bulletin, 10 (1975),85-90.

(9) W. T. Carnall, P. R. Fields, and K. RaJnak, J. Chem. Phys., 49(1968) , 4412-4455.

(10) C. A. Morrison, D. E. Wortman, and N. Karayianis, J. Phys.Ci Solid State Phys., 9 (1976), L1g9.

(11) A. J. Freeman and R. E. Watson, Phys. Rev., 127 (1962),2058-2075.

(12) P. Erdoa and J. H. Kang, Phys. Rev. B, 6 (1972), 3393-3408.

(13) R. P. Leavitt, C. A. Morrison, and D. I!. Wortman, RareEarth Ion-Host Cryntal Interautionm 3. Threo-ParamoturTheory of Crystal Fields, Harry Diamond Laboratories TR-1673(June 1975).

(14) N. Karayianis and C. A. Morrison, Rare Earth Ion-Host LatticeInteractions 1. Point Charge Lattice Sum in Scheelites, HarryDiamond Laboratories TR-1648 (October 1973).

(15) N. Karayianis, D. E. Wortman, and C. A. Morrison, Solid StateComm., 18 (1976).

1'k U.' P' ~ - * *~ * .

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