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On the morphology of small particles under weak beam conditions
Journal of Crystal Growth 78 (1986) 563—566 North-Holland, Amsterdam
563
LETTER TO THE EDITORS ON THE MORPHOLOGY OF SMALL PARTICLES UNDER WEAK BEAM CONDITIONS R. PEREZ and M. AVALOS-BORJA Inst ituro de Fisica, UNAM, Apdo. Postal 2681, Ensenada, BCN, 22800 Mexico Received 18 September 1985; manuscript received in final form 1 August 1986
It has been commonly assumed in the literature that the absence of thickness fringes in the central regions of weak beam images from small particles can be associated with more or less extended plateaus indicating truncation in the top part of the particle. However, it is shown in this communication that the absence of fringes can be produced by the operating diffraction conditions. Therefore, in order to build more realistic models of the morphology of small particles, an investigation of the image contrast characteristics under different diffraction conditions have to be performed.
Transmission electron microscopy under weak beam diffraction conditions (WB) has been widely used in the determination of the morphology of small particles [1—4].Based on this approach, it has been possible to find the morphology for most of the small particles that usually appear on evaporated specimens. For example, the ones that exhibit a square or rectangular profile in bright field, can be interpreted [2—4]as single or double pyramids, based on the geometry of fringes (fig. 1 in this paper or figs. 1 and 2 in ref. [3]). Besides
this general characteristic, some of the particles show an absence of fringes in the central region (like the one in fig. 2) which is usually interpreted (based on one micrograph) as coming from an extended plateau in the particle. We want to mdicate that this conclusion is not necessarily true and can be misleading in many cases. The reason for this is that the image contrast is very sensitive to the diffraction conditions, as we will illustrate below, and more than one picture will be usually needed to identify correctly the topography of the
_ I ____ particle.
Fig. 1. Weak beam image of a rectangular-profiled particle. Note that extinction contours can be seen up to the central region of the particle, suggesting a pyramidal or bipyramidal particle,
Fig. 2 WB image of a square-profiles particle. The absence of fringes in the center of the particle “suggest” a truncated octahedral shape.
0022-0248/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
564
R. Perez, M. A valos-Borja
/
Morphology of small particles under WB conditions
We performed theoretical calculations based on the multibeam dynamical theory. The calculations z
take into account absorption by using the imaginary part of the lattice potential as given by Radi [5], and the Fourier coefficients of the potential were Debye—Waller corrected. The accelerating voltage was 100 kV. The number of beams used was 12, unless another number is specified. Fig. 3b
a
—
15
In
30
45
CRYSTAL THICKNESS Cnn’)
z
a
15
30 45 CRYSTAL THICKNESS Cnm)
60
75
I
~±=Iuic:=i’ _____________________________________ 020
•
•
Fig. 3. (a) Theoretical intensity calculations for the (002) 1. Twelve systematic reflections WBDF, with Sg 0.178 nm were considered in the calculation. (b) Computed “micrograph” for these conditions.
Fig. 4. (a) Theoretical intensity calculations for the (002) WBDF, with .s~~O.l78nm’. (b) Computed “micrograph” for these conditions. (c) Spots considered in the calculations are indicated by crossed spots.
•
C
002 K
•
•
•
•
K
60
75
R. Perez, M. Avalos-Borja / Morphology of smallparticles under WB conditions
a
I 15
ç’..
~—.._..
~_
30 45 CRYSTAL THICKNESS (Nm)
60
•
565
shows a simulated image for a complete (not truncated) cuboctahedral particle in which only sistematic reflections are included (from 0 0 —8 to 0 0 14). The image is obtained with the 002 reflection and the Bragg deviation parameter is 0.178 nm~. Fig. 4b shows a similar case, but a different set of beams is included; in this case we considered the beams that are close to the intersection of the Ewald sphere and the zero-order Laue zone, as indicated in fig. 4c. Imaging beam and Bragg deviation remain the same. Finally, fig Sb shows another image, for a different set of beams, as indicated in fig. 5c, but for the same imaging beam and Bragg deviation. In principle, one might think that by increasing fringe resolution, that is, for larger Bragg deviations, we should be able to resolve properly the topography. However, when doing so, the overall intensity is decreased considerably for the thicker portions of the particle as indicated in fig. 6 [41
10_I
I
I
III 8 6
74—beam DT\
‘.
‘U.
b
\‘N \“~
fl C
~—~----—--———~
20
~2-b~rn
i6~ 1
Fig. 5. (a) Theoretical intensity calculations for the (002) WBDF, with S5 = 0.178 nm’. (b) Computed “micrograph” for these conditions. (c) Spots considered in the calculations are indicated by crossed spots.
4~
2
3
I I 45678910
—
ANGLE bEG I Fig. 6. Intensity calculations as a function of Bragg deviation (expressed in degrees), for the 2-beam kinematical and 74-beam dynamical theories.
R.
566
-
Perez, M. Avalos-Borja
ci
-~
~
/
Morphology of small particles under WB conditions
50 n m
d
~
Fig. 8. WBDF image of a particle clearly showing a flat top.
_______________________
-~~•1
________
_____ ~_
t~~L’~
_________________
_____
I.
—‘-
-
Fig. 7. Variation of fringe spacings and intensities as a function of tilting angle; series taken at 10 difference between any twc consecutive micrographs.
and shown in the experimental sequence in fig. 7. So the solution is not found by moving towards higher Bragg deviation, but by finding the proper combination of beam penetration and fringe resolution. In other words, from the theoretical analysis (figs. 3 to 5) it seems that the systematic diffraction conditions are the best for this purpose. However, when dealing with particles this small, it is nearly impossible to orient them mdividually in routine work. Therefore, the most practical approach will be to take several micrographs from the same particle in different diffraction conditions, hoping that in some cases we will
have positive evidence of truncation or non-truncation. An example is shown in fig. 8, where the flat top of the particle is clearly visible. In conclusion, image interpretation in transmission electron microscopy is not as straightforward as we would sometimes desire, and talking about particles with the shape of “rafts” [6], or truncated pyramids requires a more elaborate analysis. The authors would like to thank Mr. Francisco
.
Ruiz for technical help with the micrographs and Mat. Arturo Gamietea and Mr. Raul Michel for technical help with computer intricacies.
References [1] M.J. Yacamán and T. Ocana, Phys. Status Saudi (a) 42 (1977) 571. [2] K. Heinemann, M. Avalos-Borja H. Poppa and M.J. , . . Yacaman, in: Electron Microscopy and Analysis 1979, Inst. Phys. Conf. Ser 52, Ed. T. Mulvey (Inst. Phys, London—Bristol, 1980) p. 387. [3] H. Hofmeister, H. Haefke and M. Krohn, J. Crystal Growth 58 (1982) 507. [4] M. Avalos-Boija, PhD Thesis, Stanford University (1983). [5] G. Radi, Acta Cryst. A26 (1970) 41. [6] E.B. Prestridge, G.H. Via and J.H. Sinfelt, J. Catalysis 50 (1977) 115.
563
LETTER TO THE EDITORS ON THE MORPHOLOGY OF SMALL PARTICLES UNDER WEAK BEAM CONDITIONS R. PEREZ and M. AVALOS-BORJA Inst ituro de Fisica, UNAM, Apdo. Postal 2681, Ensenada, BCN, 22800 Mexico Received 18 September 1985; manuscript received in final form 1 August 1986
It has been commonly assumed in the literature that the absence of thickness fringes in the central regions of weak beam images from small particles can be associated with more or less extended plateaus indicating truncation in the top part of the particle. However, it is shown in this communication that the absence of fringes can be produced by the operating diffraction conditions. Therefore, in order to build more realistic models of the morphology of small particles, an investigation of the image contrast characteristics under different diffraction conditions have to be performed.
Transmission electron microscopy under weak beam diffraction conditions (WB) has been widely used in the determination of the morphology of small particles [1—4].Based on this approach, it has been possible to find the morphology for most of the small particles that usually appear on evaporated specimens. For example, the ones that exhibit a square or rectangular profile in bright field, can be interpreted [2—4]as single or double pyramids, based on the geometry of fringes (fig. 1 in this paper or figs. 1 and 2 in ref. [3]). Besides
this general characteristic, some of the particles show an absence of fringes in the central region (like the one in fig. 2) which is usually interpreted (based on one micrograph) as coming from an extended plateau in the particle. We want to mdicate that this conclusion is not necessarily true and can be misleading in many cases. The reason for this is that the image contrast is very sensitive to the diffraction conditions, as we will illustrate below, and more than one picture will be usually needed to identify correctly the topography of the
_ I ____ particle.
Fig. 1. Weak beam image of a rectangular-profiled particle. Note that extinction contours can be seen up to the central region of the particle, suggesting a pyramidal or bipyramidal particle,
Fig. 2 WB image of a square-profiles particle. The absence of fringes in the center of the particle “suggest” a truncated octahedral shape.
0022-0248/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
564
R. Perez, M. A valos-Borja
/
Morphology of small particles under WB conditions
We performed theoretical calculations based on the multibeam dynamical theory. The calculations z
take into account absorption by using the imaginary part of the lattice potential as given by Radi [5], and the Fourier coefficients of the potential were Debye—Waller corrected. The accelerating voltage was 100 kV. The number of beams used was 12, unless another number is specified. Fig. 3b
a
—
15
In
30
45
CRYSTAL THICKNESS Cnn’)
z
a
15
30 45 CRYSTAL THICKNESS Cnm)
60
75
I
~±=Iuic:=i’ _____________________________________ 020
•
•
Fig. 3. (a) Theoretical intensity calculations for the (002) 1. Twelve systematic reflections WBDF, with Sg 0.178 nm were considered in the calculation. (b) Computed “micrograph” for these conditions.
Fig. 4. (a) Theoretical intensity calculations for the (002) WBDF, with .s~~O.l78nm’. (b) Computed “micrograph” for these conditions. (c) Spots considered in the calculations are indicated by crossed spots.
•
C
002 K
•
•
•
•
K
60
75
R. Perez, M. Avalos-Borja / Morphology of smallparticles under WB conditions
a
I 15
ç’..
~—.._..
~_
30 45 CRYSTAL THICKNESS (Nm)
60
•
565
shows a simulated image for a complete (not truncated) cuboctahedral particle in which only sistematic reflections are included (from 0 0 —8 to 0 0 14). The image is obtained with the 002 reflection and the Bragg deviation parameter is 0.178 nm~. Fig. 4b shows a similar case, but a different set of beams is included; in this case we considered the beams that are close to the intersection of the Ewald sphere and the zero-order Laue zone, as indicated in fig. 4c. Imaging beam and Bragg deviation remain the same. Finally, fig Sb shows another image, for a different set of beams, as indicated in fig. 5c, but for the same imaging beam and Bragg deviation. In principle, one might think that by increasing fringe resolution, that is, for larger Bragg deviations, we should be able to resolve properly the topography. However, when doing so, the overall intensity is decreased considerably for the thicker portions of the particle as indicated in fig. 6 [41
10_I
I
I
III 8 6
74—beam DT\
‘.
‘U.
b
\‘N \“~
fl C
~—~----—--———~
20
~2-b~rn
i6~ 1
Fig. 5. (a) Theoretical intensity calculations for the (002) WBDF, with S5 = 0.178 nm’. (b) Computed “micrograph” for these conditions. (c) Spots considered in the calculations are indicated by crossed spots.
4~
2
3
I I 45678910
—
ANGLE bEG I Fig. 6. Intensity calculations as a function of Bragg deviation (expressed in degrees), for the 2-beam kinematical and 74-beam dynamical theories.
R.
566
-
Perez, M. Avalos-Borja
ci
-~
~
/
Morphology of small particles under WB conditions
50 n m
d
~
Fig. 8. WBDF image of a particle clearly showing a flat top.
_______________________
-~~•1
________
_____ ~_
t~~L’~
_________________
_____
I.
—‘-
-
Fig. 7. Variation of fringe spacings and intensities as a function of tilting angle; series taken at 10 difference between any twc consecutive micrographs.
and shown in the experimental sequence in fig. 7. So the solution is not found by moving towards higher Bragg deviation, but by finding the proper combination of beam penetration and fringe resolution. In other words, from the theoretical analysis (figs. 3 to 5) it seems that the systematic diffraction conditions are the best for this purpose. However, when dealing with particles this small, it is nearly impossible to orient them mdividually in routine work. Therefore, the most practical approach will be to take several micrographs from the same particle in different diffraction conditions, hoping that in some cases we will
have positive evidence of truncation or non-truncation. An example is shown in fig. 8, where the flat top of the particle is clearly visible. In conclusion, image interpretation in transmission electron microscopy is not as straightforward as we would sometimes desire, and talking about particles with the shape of “rafts” [6], or truncated pyramids requires a more elaborate analysis. The authors would like to thank Mr. Francisco
.
Ruiz for technical help with the micrographs and Mat. Arturo Gamietea and Mr. Raul Michel for technical help with computer intricacies.
References [1] M.J. Yacamán and T. Ocana, Phys. Status Saudi (a) 42 (1977) 571. [2] K. Heinemann, M. Avalos-Borja H. Poppa and M.J. , . . Yacaman, in: Electron Microscopy and Analysis 1979, Inst. Phys. Conf. Ser 52, Ed. T. Mulvey (Inst. Phys, London—Bristol, 1980) p. 387. [3] H. Hofmeister, H. Haefke and M. Krohn, J. Crystal Growth 58 (1982) 507. [4] M. Avalos-Boija, PhD Thesis, Stanford University (1983). [5] G. Radi, Acta Cryst. A26 (1970) 41. [6] E.B. Prestridge, G.H. Via and J.H. Sinfelt, J. Catalysis 50 (1977) 115.