Channeling in Mg and Zr doped gadolinium gallium garnets

Nuclear Instruments and Methods 194 (1982) 175-179 North-Holland Publishing Company

175

C H A N N E L I N G IN Mg A N D Zr D O P E D G A D O L I N I U M GALLIUM GARNETS * Andreas TIMM, Wolfgang Z I M M E R M A N N Fachbereich P,kvsik der Philipps-Univel~iti~t, D-3550 Marburg, Fed. Rep. Germany

and Dieter K O L L E W E lnstitut fiir Strahlenp,kvsik der Universiti~t Stuttgart, D-7000 Stuttgart, Fed. Rep. Germany

Single crystals of pure gadolinium gallium garnets (GGG) and magnesium and zircon doped GGG (GGMZ) have been investigated using particle channeling techniques. Angular dependences of the yield of particles or radiation close to the [100], [110] and [l I l] axes of thick single crystals were measured by means of Rutherford backscattering and particle induced X-ray emission (PIXE). Despite the complex lattice structure of garnets the experimental values of ~1/2 are in accord with the general channeling theory. Also the lattice sites of magnesium and zirconium could be determined.

1. Introduction As shown in many articles [1-3] it is possible to determine the positions of foreign atoms in a host lattice using the channeling technique. Most lattices which have been investigated by channeling have only a few atoms in their unit cell. But even more complex structures with more atoms will show a channeling effect which can be described by the general channeling theory [4]. It is also possible to locate foreign atoms in these structures. We report here on channeling experiments on gadolinium gallium garnets (GGG) and the location of the lattice sites of Mg and Zr in GGG. These garnets have become important in the technology of magneto-optical memories and memories for microcomputers. They are the basis of magnetic bubble memories [5], in which a maximum amount of information can be stored on a minimum area. In these bubble memories an epitaxial film of magnetic garnet is grown on a substrate of non-magnetic garnet [6]. In the film the bubbles (magnetic domains) can be produced by appropriate methods (e.g. magneto-optic Faraday or Kerr effect). The difference between the lattice constants of the substrate a~ and the film af is called the lattice misfit Aa ±----a s - - a t. To prevent the layer from cracking by tension, the misfit has to be less than 0.015 ,k [6]. By doping the substrate garnet [7] the lattice misfit can be reduced. To predict the change in the lattice constant as a result of doping the host lattice, it * Work supported in part by the Deutsche Forschungsgemeinschaft. 0029-554X/82/0000-0000/$02.75 © 1982 North-Holland

is important to know the lattice sites of different dopants [8].

2. Structure of garnets [9,10] Garnets are cubic systems of the spacegroup O~° (Ia3d). They can be described by the general formula: {C3} [A2] (D3)O,2 with: C = cation on dodecahedral (c) site; A = cation on octahedral (a) site; D = cation on tetrahedral (d) site. The different symmetry sites can be occupied by pure elements or compositions of different elements. The unit cell contains 8 formula units, i.e. 160 atoms. In G G G (Gd3Ga5012) gadolinium occupies the (c)-sites, while gallium occupies the (a)- and (d)-sites. The lattice constant a o is 12.3822.~. Figs. I - 3 show the lattice structure formed by atomic chains in [100], [110] and [111] directions. As listed in table 1, gallium on (a)-sites and oxygen always form pure chains in the three axes, while gadolinium (c) and gallium (d) form mixed chains (two chains with different atomic distances) in [I00], mixed and pure chains in [ I 10] and only pure chains in [ 111 ].

3. Experimental We performed our experiments using two different garnet crystals (table 2). The single crystals were grown using the Czochralski technique [12,13]. Three samples IV. APPLICATIONS OF CHANNELING

A. Tmlm et al. / Channeling tn Mg and Zr

176 [],. . . .

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Fig. I. Section through the atomic chains perpendicular to a (100) plane and arrangement of the atoms in the different chains (for the chain symbols see table I). A, C and D denote thc lattice sites of thc cations. O the oxygen. Only a part of the unit cell is shown.

o f 7 m m X 6 m m × 2 m m were cut out from each single crystal, o r i e n t e d [100] 3_ [110], [110] 3_ [100] a n d [111] ± [110] and p o l i s h e d m e c h a n i c a l l y o n (100), (110) a n d ( 111 ), respectively. T h e s a m p l e s were m o u n t e d o n a 2-axis g o n i o m e t e r w h i c h has a r e s o l u t i o n o f angle A,~ = 1 / 5 0 ° a n d A0 = 1 / 1 0 0 % T h e m e a s u r e m e n t s were p e r f o r m e d using a p r o t o n b e a m o f 4 M e V energy with a b e a m spot (on the

o.¢~ 2

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.°/2.

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Fig. 2. Section through the atomic chains perpendicular to a (1 I0) plane. Only a part of the unit cell is shown.

target) o f 0.5 × 0.5 m m 2 a n d < 0.001 ° divergence. R u t h e r f o r d b a c k s c a t t e r i n g (RBS) s p e c t r a were meas u r e d with a surface b a r r i e r d e t e c t o r (scattering angle 165 % T h e particle i n d u c e d X - r a y e m i s s i o n ( P I X E ) f r o m G d , G a a n d Z r were d e t e c t e d b y a Si(Li) d e t e c t o r (at 135°). In o r d e r to o r i e n t a t e the s a m p l e s we m a d e s o m e parallel a n g u l a r scans first using the R B S yield in an

Table 1 Chains in the different axes Axis

Chain (figs. I-3)

Gd Fraction

[]oo]

0 X

[]

-

66.67% 33.33%

Ga

O

Site

Fraction

Site

-

40% 40% 20%

a d

c c

Distance d between atoms/a o

I/2 1/2

d I 0()~

[I lo]

o +

-

33.33% -

X

66.67%

-

40%

.

20% 40%

d

(2/2

(2_/2

c -

c

~/2/2

d 10()¢~

Jill]

0

+

-

100%

c

-

-

I/4 I

40%

a

60%

d

(2/2 d ~/3/4

.)0%

0/2 ,/3/2

A. Timm et al. / Channeling in Mg and Zr

177

the fit parameters we get: I•

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energy window above the G d edge, then the window yield above the oxygen edge, because the expected angle ~ / 2 is narrower for oxygen. After orientation we measured RBS- and X-ray spectra at room temperature, scanning over a range of 4 - 6 ° close to the axis, near the axis in steps of A0 = 0.02 °. To obtain the RBS yields for the different elements we determined the difference between the yield in energy windows above and below the characteristic scattering edges of the different elements to find the yield at "zero" depth. From the X-ray spectra we can only determine the integrated areas of the GdL~, GaK~ and ZrK~ peaks. These values were not extrapolated to zero depth, but they show the same behaviour for qq/2 as the RBS values. To obtain the characteristic RBS channeling parameters ~t/2 and Xmin, the yields of the different elements were plotted as a function of the rotation angle and fitted with the function:

This function has a linear slope in the random region [A + B ( x - D ) ] superimposed with a Gaussian-like function to fit the dip (D = site of the minimum). For

4. Results and discussion

The experimental values of ~1/2 and Xmi, are shown in table 3. For magnesium and zirconium the m i n i m u m parametersD [eq. (I)] coincide with those of Gd, Ga and O (with respect to the angular resolution of the goniometer). The Mg and Zr dips show no structure which might indicate an interstitial or more complex lattice site of the atoms. Therefore we assume the Mgand Zr-atoms to be on lattice sites. They will occupy gallium positions as shown by the chemical composition. Because there are two different Ga sites, the octrahedral G a (a) site and the tetrahedral Ga (d) site, which are in all directions on different chains (see figs. 1-3 and table 1), the magnitude of q~/2 might show which Ga-sites are substituted by the dopants. On the assumption that 100% of the dopants are on one Ga-site we have four different possibilities (see table4: Mg-, Zr-site). Considering this we can calculate the characteristic angle 4q [4] for each chain to get a weighted value q~ for the different elements j :

with qqj = 0,307( Z, ~ / E d , ) ' / z where ~ = average value of Z in the chain i; d i = atomic distance in chain i; n , . / = n u m b e r of atomsj in chain i. These calculated values are shown in table 4. This is a useful method because the vibration amplitudes of the dopants are not known. In fig. 4 the experimental q~/2 of the three axes are shown as a function of the calculated f . For this figure Mg and Zr are supposed to be on G a ( a ) sites. A n average value of the "observable" [14] vibration amplitude ~ of the crystal (for G G G ) can be used as an indicator of the quality of the measurements. Using the Debye temperature 0 v = 5 1 0 K (calculated [15] from

Table 2 Data of the measured garnet crystals [I I]. (A small part of the Gd occupies Ga sites. This is neglected in the calculation of ~) Crystal

Chemical composition

Lattice constant ao/A

GGG GGMZ

Gd3.o4Ga496Oi2 Gda.01Ga3.91Mgo.54Zro.54Ot2

12.3822±5× 10 4 12.4915±6× 10 4

IV. APPLICATIONS OF CHANNELING

A. Timm et al. / Channeling in Mg and Zr

178

Tablc 3 Experimental ~bl/2 and Xmin values for 4 MeV protons (~bl/2 in degrees). [The X-rays were not detected at "zero" depth but at greater depths. Because of dechanneling effects the X-ray values of q-q/2 will be less and the values of Xmin will be greater than the RBS-valucs (at "zero" depth)] Element: Axis Crystal

[100]

[I 10]

[11 I]

GG(i GGMZ GGG GGMZ (}GG GGMZ GGG GGMZ GGG GGMZ GGG (~GMZ

Gd

RBS RBS X-ray X-ray RBS RBS X-ray X-ray RBS RBS X-ray X-ray

Ga

O

Mg

~1/2

Xmin

~1/2

Xmin

1~1/2

Xmin

~ /2

0.43 0.44 0.22 0.22 0.33 0.34 0.23 0.23 0.33 0.33 0.19 0.19

0.032 0.024 0.55 0.59 0.046 0.048 0.65 0.52 0.045 0.066 0.63 0.64

0.36 0.36 0.225 0.22 0.28 0.28 0.215 0.21 0.20 0.21 0.175 0. t75

0.095 0.195 0.49 0.53 0.199 0.234 0.63 0.53 0.107 0.183 0.61 0.64

0.11 0.10

0.238 0.232

0.27 0.24

0.09 0.09

0.13 0.13

0.319 0.311 0.263 0.254 -

Zr

0.32 -

Xmin

~1,/2

Xmin

(l. 10

0.26 0.15

0.14 0.61

0.10

0.22 0.13

0.2 I 0.73

0.15

0.29 0.17

0.11 0.71

Table 4 Characteristic ~ for the different elements calculated for different lattice sites of magnesium and zircon (100~ of Mg or Zr on one lattice site) ( f in degrecs) Axis

Mg-site

Zr-site

Ga

Gd

O

Mg

Zr

[ 1tt0]

a a d d a a d d a a d d

a d a d a d a d a d a d

0.42 0.44 0.42 0.43 0.41 0.32 0.32 0.33 0.33 0.32 0.30 0.28 0.29 0.30 0.31

0.48 0.48 0.49 0.47 0.47 0.38 0.38 0.38 0.37 0.37 0.37 0.37 0.37 0.37 0.37

0.12 0.12 0.12 0.12 0.12 0.10 0.10 0.10 0.10 0.10 0.13 0.13 0.13 0.13 0.13

0.33 0.31 0.47 0.47 0.28 0.26 0.35 0.35 0.35 0.34 0.25 0.25

0.33 0.49 0.36 0.47 0.28 0.34 0.30 0.35 0.35 0.27 0.38 0.25

[111]

¥1/2,exp /Oeg

fig. I

fig. 2

fig. 3

the elastic c o n s t a n t s [16]) for G-GG this v i b r a t i o n a m p l i t u d e will be u(;~;~;= 0.061 ,~. T h e e x p e r i m e n t a l values ( f r o m fig. 4) will be ~ = 0.065 ~, a n d ~ = 0.065 ,~ [Mg a n d Z r o n G a ( a ) sites]. C a l c u l a t i n g the c o r r e l a t i o n coefficient r = b s , / s , (s --mean s q u a r e deviation) of the e x p e r i m e n t a l ~bl/2 v e r s u s qJ for G G G a n d G G M Z , the a s s u m p t i o n that M g a n d Z r o c c u p y i n g G a ( a ) sites leads to the highest value o f r (table 5). This indicates that m a g n e s i u m a n d zircon s u b s t i t u t e gallium o n o c t a h e d r a l ( a ) sites.

Ho

~tOeg '

0!2

'

0!L.

'

Fig. 4. The expcrimental ~bl/2 versus calculated ~ [eq. (4)] calculated for Mg and Zr both on Ga(a) sites.

A. Timm et al. / Channeling m Mg and Zr

Table 5 Correlation coefficients r for the different Mg and Zr sites ( - I <~r~ < I, best correlation for r= 1) Crystal

Mg site

Zr site

r

GGG GGMZ

a a d d

a d a d

0.993 0.989 0.911 0.902 0.841

5. Conclusions We have made particle channeling studies on Mg and Zr doped gadolinium gallium garnets to determine the lattice sites of Mg and Zr. The experimental results of qq/2 are in agreement with the predicted values using the general channeling theory. The results also show that magnesium and zirconium replace gallium on (a) sites, which was assumed by Mateika and Rusche [13]. The authors are indebted to Dr. D. Mateika (Philips, Hamburg) for supplying the Garnet crystals and W. Sch~ifer (SFB 127, Marburg) for polishing the samples. We would like to thank Dr. W. Treutmann (SFB 127, Marburg) for cooperation. We are grateful to J.H. Meier (Fachbereich Physik, Marburg) for his assistance during the measurements.

179

References [I] J.A. Davies, Foreign atom location, in: Channeling, ed., D.V. Morgan (Interscience, New York, 1973). [2] J.U. Andersen, O. Andreasen, J.A. Davies and E. Uggerh~j, Rad. Effects 7 (1971) 25. [3] S.T. Picraux, in: New uses of ion accelerators, ed., J.F. Ziegler (Plenum, New York, 1975). [4] J. Lindhard, Kgl. Dan. Vid. Selsk. Mat. Fys. Medd. 34 (1965) No. 14. [5] A.H. Bobeck and E. Della Torre, Magnetic bubbles (Elsevier, New York, 1975). [6] B. Strocka, P. Holst and W. Tolksdorf, Philips J. Res. 33 (1978) 186. [7] J. Haisma, G. Bartels and W. Tolksdorf, Philips Res. Repts. 29 (1974) 493. [8] S. Geller, Z. Krist. 125 (1967) 1. [9] Landolt-BiSrnstein, New Series, Vol. III/12a (Springer, Berlin-Heidelberg-New York, 1978). [10] R. Wyckoff, Crystal structures, vol. 4 (Interscience, New York, 1968). [I 1] D. Mateika, private communication. [12] D. Mateika, J. Herrnring, R. Rath and Ch. Rusche, J. Cryst. Growth 30 (1975) 31 I. [13] D. Mateika and Ch. Rusche, J. Cryst. Growth 42 (1977) 440. [14] K. Lonsdale, Acta Cryst. 1 (1948) 142. [15] J. de Launey, J. Chem. Phys. 21 (1953) 1975. [16] S. Haussi~hl and D. Mateika, Z. Naturf. 27a (1972) 1522.

IV. APPLICATIONS OF CHANNELING