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Anomalously large changes in diffracted X-ray intensity from silicon single crystals produced by microwave fields
S o l i d S t a t e Communications, Vol.53,No.2 pp.107-110,
1985.
0038-1098/85 $3.00 + .00
Printed in Great Britain.
Pergamon Press Ltd.
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X - R A Y INTENSITY FROM SILICON SINGLE CRYSTALS PRODUCED BY MICROWAVE FIELDS Krishan Lal National Physical Laboratory, Hillside Road, New Delhi-110 012, India and Peter Thoma Physikalisch-Technische Bundesanstalt, 3300 Braunschweig, Federal Republic of Germany (Received on 19.9.1984 by A.R. Verma)
Results of a high resolution X-ray diffraction study of effects produced by microwave fields of frequency 2.45 GHz in silicon single crystals are reported. Microwaves travelled along a strip line evaporated along a diameter of the specimen crystal disc, which was aligned for diffraction from a desired set of lattice planes. Diffraction curves and high resolution traverse topographs were recorded and curvature measurements were made before, during and after application of the microwave field. An anamalously large increase in diffracted X-ray intensity from a large volume of the specimen was observed on application of the microwave field. The peak intensity in some cases increased by more than ten times. Integrated intensity also showed similar large changes. No significant change in the shape of the diffraction curves was observed upto microwave powers of '~10W. Some regions of the crystals showed a large decrease in intensity. High resolution traverse topographs directly showed the changes in intensity. Also, dot like defects were observed. Most of these changes were reversible. However, some irreversible effects were observed which suggest the possible "ase of this method in microwave field/power measurement as well as dosimetry. The observed effect could be due to influence of the field on the dispersion surface or due to strong interaction of the field with electron cloud of silicon atoms.
1. Introduction Recently, it has been shown that microstructural changes are produced in semiconducting and insulating single crystals when high electric fields are applied to these 1-3. These defects could be directly observed and characterized by using a high resolution X-ray diffraction technique employing a
(Wacker Chemitronix material; resistivity "~ 50 ~ cm (n-type) diameter '~ 23 mm; thickness • 1 mm). The specimen were carefully lapped and etched to remove surface damage. A 2 tam thick, 20 mm long and 1.8 mm wide aluminium strip line was evaporated along a diameter on one side of the specimen. The dimensions of the strip line were worked out according to the usual considerations for microwave integrated circuits 6. The length of the strip was aligned along <112> or <110> directions. The other side of the specimen was coated with a 2 tam thick aluminium f'dm. A microwave generator having a magnetron as a source operating at a frequency of 2.45 GHz was used. The output of the generator was fed into a directional coupler which in turn was connected to the specimen and a Hewlett-Packard power meter. The microwaves traverse the specimen along the strip line. The other surface of the specimen was earthed. The input power, the reflected power and the transmitted power could be measured. The triple crystal X-ray diffractometer used in this investigation was similar to the one used in the earlier experiments 1,3'7,8. The combination of a fine focus X-ray tube (Philips; Mo; 2 KW), large foreshortening, a special collimator and a grooved crystal monochromator of Bonse-Hart type gives a highly collimated and monochromated K a 1 beam. Its width in the horizontal plane is about 0.2 mm and its height in the vertical plane is about 9 ram. Diffraction curves are recorded from different regions of the specimen. High resolution traverse topographs are obtained by moving the crystal and a photographic f'dm rigidly coupled to it,
highly collimated and monochromated Ka 1 X-ray beam 1,4. The frequency of the electric fields was varied from 0 to 10 MHz. The fields induced large shifts in the angular positions of the diffraction maxima. Intensity at the diffraction peaks was observed to change by a few percents. Filaments or channels which carry bulk of the electric current were directly photographed in high resolution traverse topographs. The fields produced reversible as well as irreversible changes and could be observed even at fairly low power densities 1,2. Power density is defined as the electrical power lost in a unit volume of the specimen. We have now performed experiments at microwave frequencies and some very strong effects have been observed 5. An anomalously large change in the intensity of diffracted X-ray beam (peak intensity as well as integrated intensity) has been observed on application of the microwave electric field. In some regions the intensity increase by a factor of more than ten. In this paper, we report results of these experiments. 2. Experimental Details The specimen used are (111) silicon single crystal discs 107
108
across the X-ray beam. A very useful mode of output was found to be curvature measurements. Angular orientation of the diffraction vector g (0) and the intensity at the diffraction maximum (Im) is recorded from different parts of the specimen, by traversing it across the X-ray beam in a stepwise manner. After each movement, the values of 0 and I m are determined. The plots of 0 as a function of the linear position L of the specimen gives the curvature of the lattice planes under investigation. The lm-vs-L curves give useful information about variation of perfection of the specimen and show spectacular changes on the application of the microwave field. The specimen was aligned in the Lane geometry in (+,-,+) conftguration. 220, 220, 113, 113, 022 and 022, reciprocal points were used. In the present paper we shall mainly discuss results obtained with the (220) planes. The strip was aligned along [112] direction. 3. Results The specimen crystals were thoroughly characterized before the application of the microwave field. Diffraction curves and traverse topographs were recorded and curvature measurements were made. Fig.1 shows a typical diffraction curve recorded before the application of the electric field. On application of the microwave field a very large increase in the intensity of the diffraction maximum was observed from some regions of the specimen. Some regions show a decrease in the intensity. This remarkable effect is also clearly seen in the diffracted intensity I m versus linear position L plots as well as in the traverse topographs. Fig.2 shows typical Im-VS-L plots for an experiment performed with about 9W microwave power. Three curves recorded before, during and after the application of the microwave field are shown. The middle of the strip line is at about L = 12 mm. The diffracting planes are parallel to the strip line. A small dip near the middle of the curve with open circles (before field) is observed at this value. This feature is a result of small strain at the strip line - crystal interface. The curve recorded under the microwave field (fdled circles) is remarkably different from the earlier curve. On the right hand side of the strip (linear position/> 12 ram) there is a I0
(j
Si # 3; O C - 20
8
"o>.-
~20 Relp, MoK¢~I OW
_P LIJ
~4 <
o
Vol. 53, No. 2
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X-RAY INTENSITY
2
0
I
I
20 GLANCING
I
40 ANGLE
60 O,
80
90
SEC. OF A R C
Fig.1 - A typical diffraction curve of a (111) silicon crystal recorded before the application of microwave field. Strip line was parallel to (112) and (220) planes were diffracting. The irradiated area lies on the strip line.
22
(tlt) $ i # 3 ; [ Z 0 Relp;MoK=I Strtplh~e // to [41[] + 18
OW ( C M - 2 ) "~ 9W(CM-3} OW ( C M - 4 |
14 Ix U.I I--
o W I.c~ n,. U. U.
6
I
I
l
6
I0
14
LINEAR
POSITION
I 18
mm
Fig.2 -Plots of diffracted intensity vs. linear position of the specimen across the beam. very large increase in the diffracted intensity. The maximum increase is at about 13 mm. The intensity at this position has increased by a factor of "~ 2.7. On the left hand side of the strip the intensity shows a large decrease. The maximum decrease is of the order of 1.7 times. On removing the field that anomalously large increase and decrease in diffracted intensity disappears. The intensity of diffraction from the left and the right halves of the specimen is practically the same. However, there is an irreversible change in the intensity distribution. This is shown by the shaded area in Fig.2. The changes observed under the field appear as soon as the field is switched on and disappear immediately on switching off the field. It was considered important to determine whether these changes in intensity are also observed in the integrated intensity. Diffraction curves recorded, before, during and after the application of the field were compared for this purpose. Two such curves recorded during (full line) and after (dotted line) the application of field are shown in Fig.3. It may be mentioned that a curve recorded before the application of field is shown in Fig.1. A comparison of the three curves shows that there is no significant change in the shape of the diffraction curve on application of the microwave field. Only a very large increase in the integrated intensity is observed. In the present case the integrated intensity increased by a factor of "- 2.8 under the influence "~ 9W microwave power. This is an extremely large change. Even larger changes of more than a factor of ten have been observed from some parts of the specimen when it was aligned for (113) planes and some what higher microwave power was used. High resolution topographs directly show the changes in the diffracted intensity from the different regions of the crystal. Fig.Z~ shows topographs of a small region of the crystal around the strip line recorded before, during and after the application of microwave field. The left hand side in the topographs corresponds to the right hand side in Fig.2. The microwave field besides producing a change in the intensity distribution also significantly changes the background structure. Several dot like features are produced by the field. Detailed results on this aspect will be published separately.
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X-RAY INTENSITY
Vol. 53, No. 2 25
Sl =N= 3
2O
~ 2 0 Retp, MoK 0¢ t
O
>-
--,'-'
9W D C - 2 3
....
OW D C - 2 4
Z i,i Z
|0
m W 0 ar
0.. ',m
5
2 IO
20
30
40
GLANCING ANGLE O,SEC.OF ARC.
Fig.3-Diffraction curves of a (111) silicon crystal during the application of a microwave application of a microwave field (2.45 GHz) of 9W power (full line curve) and after removing the microwave field (dotted line curve). Other details as in Fig. 1.
I a
,i
,b
C 12 mm I
Fig.4 -High resolution traverse topographs of a small region of the specimen whose other results are shown in Figs. 2 and 3. (a) before the application of microwave field; (b) during the application of the field and (c) after the field was switched off. The change in the diffracted intensity are anisotropically distributed and depend upon the directions of the strip line and the diffraction vector. For example, when (113) planes were diffracting a very large increase in diffracted intensity practically all over the explored volume was obser-
109
ved. In this case decrease in intensity is not observed from any region of the specimen. As for (220) planes, both reversible and irreversible changes were observed. The observed increase in the diffracted X-ray intensity is quite anomalous and cannot be understood on the basis of usual considerations. It may be mentioned that application of microwave field results in heating of the specimen. In some experiments, the specimen were held to the holder by a clamp pressing these softly to the holder. In other experiments these were held by clamps which exerted a slight pressure on the sides. The mode of fixing of the sample did not have any influence on the results. Further, the effects appeared instantaneously on application of the microwave field and disappeared immediately on its removal. This suggests that these are not thermal effects. Moreover, in our earlier experiments with dc and low frequency fields even at higher power densities, no increase in the diffracted X-ray intensity was observed. An increase or decrease in the diffracted X-ray intensity can be expected if lattice planes under investigation are curved 9,10 under the influence of electric fields. If the diffraction vector g and the radius of curvature r are parallel to each other an increase in intensity is to be expected 9,10. A decrease will take place if g and r are pointing towards opposite directions. Such a curvature occurs around dislocation loops 11 and at the boundary of epitaxially grown films on single crystals 9. This situation, however, does not appear t o h o l d in t_he present case. Experiments performed with (113) and (113) lattice planes showed an increase in diffracted intensity from the entire volume when microwave field is applied. It appears that the microwave field is interacting strongly with electromagnetic field of the X-rays inside the crystals. This leads to the modification of the dispersion surface which is responsible for these effects. The change in the structure factor through interaction of microwave field with the electron cloud of silicon atoms is not ruled out. Experiments on effect of the frequency of microwave field on these anomalous changes are planned. Also, crystals of other materials will be used as specimen. These results will be reported separately.
Acknowledgements - One of us (Krishan Lal) would like to express his thanks to the Physikalisch-Technische Bundesanstah for providing a Guest Scientist position at the P.T.B., Braunschweig during which period most of this work was carried out. We are grateful to Prof. Dr. V. Kose and Dr. A.P. Mitra for the keen interest in this work. The authors are grateful to Dr. A.R. Verma for valuable discussions. We dedicate this paper to Dr. G. Bitmer on the occasion of his retirement from active service.
References
1 2 3 4
Krishan Lal and Peter Thoma, Solid State Commun. 40, 637 (1981) Krishnan Lal and Peter Thoma, Acta Crysta, A37, C262 (1981) Krishnan Lal and Peter Thoma, Phys. Stat. Sol. (a)80, 491 (1983) Krishan Lal, Indian J. Pure & App1. Phys. 19, 854 (1981)
Krishan Lal and Peter Thoma, Xlllth Intl. Cong. Crystallography, Hamburg, 1984. Abs. Acta. Cryst. (a) 40, 1984. K.C. Garg and Amarjit Singh (Ed.), Microwave Integrated Circuits, Wiley Eastern, Delhi (1974) Krishan Lal in Synthesis, Crystal Growth and Characterization, Krishan Lal (Ed.), North-Holland, Amsterdam, 1982, p.287
110
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X-RAY INTENSITY
Peter Thoma and Krishan Lal in Synthesis, Crystal Growth and Characterization, Krishan Lal (Ed.), North-Holland, Amsterdam, 1982, p.427 G.H. Schwuttke and J.K. Howard, J. Appl. Phys. 39__ a, 1581 (1969)
Vol. 53, No. 2
10
P. Penning and D. Polder, Philips Res. Reports 16_ 419 (1961)
11
Krishan Lal and S. Mader, J. Crystal Growth, 32, 357 (1976)
1985.
0038-1098/85 $3.00 + .00
Printed in Great Britain.
Pergamon Press Ltd.
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X - R A Y INTENSITY FROM SILICON SINGLE CRYSTALS PRODUCED BY MICROWAVE FIELDS Krishan Lal National Physical Laboratory, Hillside Road, New Delhi-110 012, India and Peter Thoma Physikalisch-Technische Bundesanstalt, 3300 Braunschweig, Federal Republic of Germany (Received on 19.9.1984 by A.R. Verma)
Results of a high resolution X-ray diffraction study of effects produced by microwave fields of frequency 2.45 GHz in silicon single crystals are reported. Microwaves travelled along a strip line evaporated along a diameter of the specimen crystal disc, which was aligned for diffraction from a desired set of lattice planes. Diffraction curves and high resolution traverse topographs were recorded and curvature measurements were made before, during and after application of the microwave field. An anamalously large increase in diffracted X-ray intensity from a large volume of the specimen was observed on application of the microwave field. The peak intensity in some cases increased by more than ten times. Integrated intensity also showed similar large changes. No significant change in the shape of the diffraction curves was observed upto microwave powers of '~10W. Some regions of the crystals showed a large decrease in intensity. High resolution traverse topographs directly showed the changes in intensity. Also, dot like defects were observed. Most of these changes were reversible. However, some irreversible effects were observed which suggest the possible "ase of this method in microwave field/power measurement as well as dosimetry. The observed effect could be due to influence of the field on the dispersion surface or due to strong interaction of the field with electron cloud of silicon atoms.
1. Introduction Recently, it has been shown that microstructural changes are produced in semiconducting and insulating single crystals when high electric fields are applied to these 1-3. These defects could be directly observed and characterized by using a high resolution X-ray diffraction technique employing a
(Wacker Chemitronix material; resistivity "~ 50 ~ cm (n-type) diameter '~ 23 mm; thickness • 1 mm). The specimen were carefully lapped and etched to remove surface damage. A 2 tam thick, 20 mm long and 1.8 mm wide aluminium strip line was evaporated along a diameter on one side of the specimen. The dimensions of the strip line were worked out according to the usual considerations for microwave integrated circuits 6. The length of the strip was aligned along <112> or <110> directions. The other side of the specimen was coated with a 2 tam thick aluminium f'dm. A microwave generator having a magnetron as a source operating at a frequency of 2.45 GHz was used. The output of the generator was fed into a directional coupler which in turn was connected to the specimen and a Hewlett-Packard power meter. The microwaves traverse the specimen along the strip line. The other surface of the specimen was earthed. The input power, the reflected power and the transmitted power could be measured. The triple crystal X-ray diffractometer used in this investigation was similar to the one used in the earlier experiments 1,3'7,8. The combination of a fine focus X-ray tube (Philips; Mo; 2 KW), large foreshortening, a special collimator and a grooved crystal monochromator of Bonse-Hart type gives a highly collimated and monochromated K a 1 beam. Its width in the horizontal plane is about 0.2 mm and its height in the vertical plane is about 9 ram. Diffraction curves are recorded from different regions of the specimen. High resolution traverse topographs are obtained by moving the crystal and a photographic f'dm rigidly coupled to it,
highly collimated and monochromated Ka 1 X-ray beam 1,4. The frequency of the electric fields was varied from 0 to 10 MHz. The fields induced large shifts in the angular positions of the diffraction maxima. Intensity at the diffraction peaks was observed to change by a few percents. Filaments or channels which carry bulk of the electric current were directly photographed in high resolution traverse topographs. The fields produced reversible as well as irreversible changes and could be observed even at fairly low power densities 1,2. Power density is defined as the electrical power lost in a unit volume of the specimen. We have now performed experiments at microwave frequencies and some very strong effects have been observed 5. An anomalously large change in the intensity of diffracted X-ray beam (peak intensity as well as integrated intensity) has been observed on application of the microwave electric field. In some regions the intensity increase by a factor of more than ten. In this paper, we report results of these experiments. 2. Experimental Details The specimen used are (111) silicon single crystal discs 107
108
across the X-ray beam. A very useful mode of output was found to be curvature measurements. Angular orientation of the diffraction vector g (0) and the intensity at the diffraction maximum (Im) is recorded from different parts of the specimen, by traversing it across the X-ray beam in a stepwise manner. After each movement, the values of 0 and I m are determined. The plots of 0 as a function of the linear position L of the specimen gives the curvature of the lattice planes under investigation. The lm-vs-L curves give useful information about variation of perfection of the specimen and show spectacular changes on the application of the microwave field. The specimen was aligned in the Lane geometry in (+,-,+) conftguration. 220, 220, 113, 113, 022 and 022, reciprocal points were used. In the present paper we shall mainly discuss results obtained with the (220) planes. The strip was aligned along [112] direction. 3. Results The specimen crystals were thoroughly characterized before the application of the microwave field. Diffraction curves and traverse topographs were recorded and curvature measurements were made. Fig.1 shows a typical diffraction curve recorded before the application of the electric field. On application of the microwave field a very large increase in the intensity of the diffraction maximum was observed from some regions of the specimen. Some regions show a decrease in the intensity. This remarkable effect is also clearly seen in the diffracted intensity I m versus linear position L plots as well as in the traverse topographs. Fig.2 shows typical Im-VS-L plots for an experiment performed with about 9W microwave power. Three curves recorded before, during and after the application of the microwave field are shown. The middle of the strip line is at about L = 12 mm. The diffracting planes are parallel to the strip line. A small dip near the middle of the curve with open circles (before field) is observed at this value. This feature is a result of small strain at the strip line - crystal interface. The curve recorded under the microwave field (fdled circles) is remarkably different from the earlier curve. On the right hand side of the strip (linear position/> 12 ram) there is a I0
(j
Si # 3; O C - 20
8
"o>.-
~20 Relp, MoK¢~I OW
_P LIJ
~4 <
o
Vol. 53, No. 2
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X-RAY INTENSITY
2
0
I
I
20 GLANCING
I
40 ANGLE
60 O,
80
90
SEC. OF A R C
Fig.1 - A typical diffraction curve of a (111) silicon crystal recorded before the application of microwave field. Strip line was parallel to (112) and (220) planes were diffracting. The irradiated area lies on the strip line.
22
(tlt) $ i # 3 ; [ Z 0 Relp;MoK=I Strtplh~e // to [41[] + 18
OW ( C M - 2 ) "~ 9W(CM-3} OW ( C M - 4 |
14 Ix U.I I--
o W I.c~ n,. U. U.
6
I
I
l
6
I0
14
LINEAR
POSITION
I 18
mm
Fig.2 -Plots of diffracted intensity vs. linear position of the specimen across the beam. very large increase in the diffracted intensity. The maximum increase is at about 13 mm. The intensity at this position has increased by a factor of "~ 2.7. On the left hand side of the strip the intensity shows a large decrease. The maximum decrease is of the order of 1.7 times. On removing the field that anomalously large increase and decrease in diffracted intensity disappears. The intensity of diffraction from the left and the right halves of the specimen is practically the same. However, there is an irreversible change in the intensity distribution. This is shown by the shaded area in Fig.2. The changes observed under the field appear as soon as the field is switched on and disappear immediately on switching off the field. It was considered important to determine whether these changes in intensity are also observed in the integrated intensity. Diffraction curves recorded, before, during and after the application of the field were compared for this purpose. Two such curves recorded during (full line) and after (dotted line) the application of field are shown in Fig.3. It may be mentioned that a curve recorded before the application of field is shown in Fig.1. A comparison of the three curves shows that there is no significant change in the shape of the diffraction curve on application of the microwave field. Only a very large increase in the integrated intensity is observed. In the present case the integrated intensity increased by a factor of "- 2.8 under the influence "~ 9W microwave power. This is an extremely large change. Even larger changes of more than a factor of ten have been observed from some parts of the specimen when it was aligned for (113) planes and some what higher microwave power was used. High resolution topographs directly show the changes in the diffracted intensity from the different regions of the crystal. Fig.Z~ shows topographs of a small region of the crystal around the strip line recorded before, during and after the application of microwave field. The left hand side in the topographs corresponds to the right hand side in Fig.2. The microwave field besides producing a change in the intensity distribution also significantly changes the background structure. Several dot like features are produced by the field. Detailed results on this aspect will be published separately.
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X-RAY INTENSITY
Vol. 53, No. 2 25
Sl =N= 3
2O
~ 2 0 Retp, MoK 0¢ t
O
>-
--,'-'
9W D C - 2 3
....
OW D C - 2 4
Z i,i Z
|0
m W 0 ar
0.. ',m
5
2 IO
20
30
40
GLANCING ANGLE O,SEC.OF ARC.
Fig.3-Diffraction curves of a (111) silicon crystal during the application of a microwave application of a microwave field (2.45 GHz) of 9W power (full line curve) and after removing the microwave field (dotted line curve). Other details as in Fig. 1.
I a
,i
,b
C 12 mm I
Fig.4 -High resolution traverse topographs of a small region of the specimen whose other results are shown in Figs. 2 and 3. (a) before the application of microwave field; (b) during the application of the field and (c) after the field was switched off. The change in the diffracted intensity are anisotropically distributed and depend upon the directions of the strip line and the diffraction vector. For example, when (113) planes were diffracting a very large increase in diffracted intensity practically all over the explored volume was obser-
109
ved. In this case decrease in intensity is not observed from any region of the specimen. As for (220) planes, both reversible and irreversible changes were observed. The observed increase in the diffracted X-ray intensity is quite anomalous and cannot be understood on the basis of usual considerations. It may be mentioned that application of microwave field results in heating of the specimen. In some experiments, the specimen were held to the holder by a clamp pressing these softly to the holder. In other experiments these were held by clamps which exerted a slight pressure on the sides. The mode of fixing of the sample did not have any influence on the results. Further, the effects appeared instantaneously on application of the microwave field and disappeared immediately on its removal. This suggests that these are not thermal effects. Moreover, in our earlier experiments with dc and low frequency fields even at higher power densities, no increase in the diffracted X-ray intensity was observed. An increase or decrease in the diffracted X-ray intensity can be expected if lattice planes under investigation are curved 9,10 under the influence of electric fields. If the diffraction vector g and the radius of curvature r are parallel to each other an increase in intensity is to be expected 9,10. A decrease will take place if g and r are pointing towards opposite directions. Such a curvature occurs around dislocation loops 11 and at the boundary of epitaxially grown films on single crystals 9. This situation, however, does not appear t o h o l d in t_he present case. Experiments performed with (113) and (113) lattice planes showed an increase in diffracted intensity from the entire volume when microwave field is applied. It appears that the microwave field is interacting strongly with electromagnetic field of the X-rays inside the crystals. This leads to the modification of the dispersion surface which is responsible for these effects. The change in the structure factor through interaction of microwave field with the electron cloud of silicon atoms is not ruled out. Experiments on effect of the frequency of microwave field on these anomalous changes are planned. Also, crystals of other materials will be used as specimen. These results will be reported separately.
Acknowledgements - One of us (Krishan Lal) would like to express his thanks to the Physikalisch-Technische Bundesanstah for providing a Guest Scientist position at the P.T.B., Braunschweig during which period most of this work was carried out. We are grateful to Prof. Dr. V. Kose and Dr. A.P. Mitra for the keen interest in this work. The authors are grateful to Dr. A.R. Verma for valuable discussions. We dedicate this paper to Dr. G. Bitmer on the occasion of his retirement from active service.
References
1 2 3 4
Krishan Lal and Peter Thoma, Solid State Commun. 40, 637 (1981) Krishnan Lal and Peter Thoma, Acta Crysta, A37, C262 (1981) Krishnan Lal and Peter Thoma, Phys. Stat. Sol. (a)80, 491 (1983) Krishan Lal, Indian J. Pure & App1. Phys. 19, 854 (1981)
Krishan Lal and Peter Thoma, Xlllth Intl. Cong. Crystallography, Hamburg, 1984. Abs. Acta. Cryst. (a) 40, 1984. K.C. Garg and Amarjit Singh (Ed.), Microwave Integrated Circuits, Wiley Eastern, Delhi (1974) Krishan Lal in Synthesis, Crystal Growth and Characterization, Krishan Lal (Ed.), North-Holland, Amsterdam, 1982, p.287
110
ANOMALOUSLY LARGE CHANGES IN DIFFRACTED X-RAY INTENSITY
Peter Thoma and Krishan Lal in Synthesis, Crystal Growth and Characterization, Krishan Lal (Ed.), North-Holland, Amsterdam, 1982, p.427 G.H. Schwuttke and J.K. Howard, J. Appl. Phys. 39__ a, 1581 (1969)
Vol. 53, No. 2
10
P. Penning and D. Polder, Philips Res. Reports 16_ 419 (1961)
11
Krishan Lal and S. Mader, J. Crystal Growth, 32, 357 (1976)