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Secondary scattering of low energy electrons by rows of atoms
SURFACE
SCIENCE
SECONDARY
4 (1966) 498-501 0 North-Holland
SCATTERING
Publishing
OF LOW ENERGY
Co., Amsterdam
ELECTRONS
BY ROWS OF ATOMS*
Received 6 April 1966
We have observed a multiple scattering diffraction phenomenon with slow electrons in which a row of atoms plays the role of a set of planes in the kinematical interpretation of Kikuchi lines**. The atom rows produce diffraction cones of semi-apex angle 8 given by nA = d(1 -cosQ,
(1)
where d is the spacing of atoms along a row. In experiments upon a tungsten crystal cut to expose a (112) plane, these cones have been found for [liO] and [ 1311 rows of surface atoms, which are the second and third most dense rows lying in the surface. The crystal was oriented in such a way that we were unable to look for cones from the [l 1 l] rows in the surface in which the atoms lie closest together, but cones were found around all three (1 I 1) directions pointing out of the surface and within the angular range of our crystal manipulator. In experiments stimulated by these observations, J. W. May of this laboratory has found cones from [OOl] lines of atoms lying in the (110) face of a different tungsten crystal. In his experiment also, he was unable to look for cones from the most dense [lTl] surface lines. In the photograph of fig. I is shown a diffraction pattern obtained with a conventional LEED (Varian) back-reflection camera. The concentric set of circles in the figure are the first three orders of diffraction, back-reflected from atoms along the [ ITO] line. The primary beam was incident on the (112) face at a glancing angle of only 7.5” in the azimuth determined by the surface normal and the [Ii01 direction in the surface. At these glancing angles the circles appear strongest, although they have been seen and measured up to incidence angles as large as 45”. Upon rotating the crystal the circles are unchanged in size, moving with it and maintaining their common center at the intersection of the [ liO] direction with the fluorescent screen. For voltages above IOOOV and near grazing incidence, these circles
* Work supported by Advanced Research Projects Agency, Washington, ** Kikuchi lines and bands have been seen with slow electrons’). 498
D. C.
SCATTERING
Fig. 1.
OF LOW
ENERGY
ELECTRONS
499
Back reflection diffraction pattern from a tungsten crystal, 1046V. The prominent
circles are the intersection with the fluorescent screen of cones about the [lTO] surface direction.
are the strongest diffraction features that are seen, although they rapidly weaken at lower voltages and have not been photographed below 125V. Angles subtended by these cones are readily obtained by using a calibration from ordinary diffraction spots. The resulting angles for cones about the [liO] direction are plotted in fig. 2 against the voltages at which they were observed. The solid curves of the figure are calculated from eq. (1) with d=a,/2=4.41.&
VOLTS Fig. 2. Measured angles of cones about the [ITO] surface direction at different electron beam voltages. Open circles represent excess cones and the black circles deficit cones.
500
L. H.
GERMER
AND
C. C. CHANG
First and second order circles representing cones about [ 13 1] and [3ii] surface directions are seen also weakly in fig. 1, located on either side of the [liO] circles. Their centers are in the expected places and their cone angles are given by eq. (1) with d =$a,/1 1 = 5.24A. The circles of fig. 1 are deficit circles. They represent directions in which the multiply scattered background electrons are less numerous than in other directions. The missing electrons are diffracted into the axes of their respective cones. Looking for a beam of electrons coming from the crystal along such a direction seems an obvious continuation of the present experiments. It probably requires that the crystal surface be cut at a small angle with the nominal (112) plane, so that the [liO] direction protrudes from the surface. Circles representing excess cones have been observed with forwardscattered fast electrons, apparently reported first by Emslie2) and later by Shinoharas). Emslie found a small displacement of his excess circles, which he attributed to an inner potential of 26.4V, and suggested that this high value might be due to an exceptionally high value of the potential along the line of atoms giving rise to the cones. An inner potential of about 25 V would displace the theoretical curves of fig. 2 into much better agreement with our experimental points, but we are not sure that the plotted displacement is beyond experimental error. Shinohara found his excess circles to be envelopes of Kikuchi lines and ascribed the displacement to a refractive effect arising from dynamical interactions. We wish to point out here that no Kikuchi lines were ever observed with the circles we see. At least six lines can also be seen in the photograph of fig. 1, some slightly curved and each coming close to tangency with one circle. Each line maintains this relation with its circle as the primary voltage is changed, so that these are not Kikuchi lines. The condition for exact tangency of a Kikuchi line hh 1 of the [ liO] zone with a [liO] circle of which has solutions for h and I integral only It is indicated in fig. 2 that the smallest cone above 520V and an excess cone below
order n is 11(2/r’ + Z2+ 2n2) = 4dn for selected values of 1.. [liO] circle represents a deficit this voltage. At the transition,
a set of deficit-excess-deficit circles can be seen (as indicated at 52OV), with the excess cone predominating at lower voltages and the smaller deficit cone predominating at higher voltages. On a kinematical view we suggest relating the transition to the relative importance of multiple scattering at atoms below the surface layer and at atoms in the surface layer itself. No kinematical interpretation can, however, explain the complex nature of the transition. Moreover, a similar transition also occurs ifthe angle of incidence is changed, keeping the primary beam energy fixed. In this case the normally deficit cones at glancing angles give way to excess cones at larger angles of incidence.
SCATTERING
OF LOW
ENERGY
501
ELECTRONS
Diffraction cones have not yet been looked for in the forward direction, although these may be stronger than the back reflection cones reported here. L. H. GERMER
and C. C. CHANG
Department of Physics, Cornell University, Ithaca, New York, U.S.A.
References 1) E. G. McRae and C. W. Caldwell, Surface Sci. 2 (1964) 509; J. L. Robins, R. L. Gerlach and T. N. Rhodin, Appl. Phys. Letters 8 (1966) No. 1; D. C. Johnson a Id A. U. Mac Rae, J. Appl. Phys. 37 (1966) 1945. 2) A. G. Emslie, Phys. Rev. 45 (1934) 43. 3) K. Shinohara, Phys. Rev. 47 (1935) 730.
SCIENCE
SECONDARY
4 (1966) 498-501 0 North-Holland
SCATTERING
Publishing
OF LOW ENERGY
Co., Amsterdam
ELECTRONS
BY ROWS OF ATOMS*
Received 6 April 1966
We have observed a multiple scattering diffraction phenomenon with slow electrons in which a row of atoms plays the role of a set of planes in the kinematical interpretation of Kikuchi lines**. The atom rows produce diffraction cones of semi-apex angle 8 given by nA = d(1 -cosQ,
(1)
where d is the spacing of atoms along a row. In experiments upon a tungsten crystal cut to expose a (112) plane, these cones have been found for [liO] and [ 1311 rows of surface atoms, which are the second and third most dense rows lying in the surface. The crystal was oriented in such a way that we were unable to look for cones from the [l 1 l] rows in the surface in which the atoms lie closest together, but cones were found around all three (1 I 1) directions pointing out of the surface and within the angular range of our crystal manipulator. In experiments stimulated by these observations, J. W. May of this laboratory has found cones from [OOl] lines of atoms lying in the (110) face of a different tungsten crystal. In his experiment also, he was unable to look for cones from the most dense [lTl] surface lines. In the photograph of fig. I is shown a diffraction pattern obtained with a conventional LEED (Varian) back-reflection camera. The concentric set of circles in the figure are the first three orders of diffraction, back-reflected from atoms along the [ ITO] line. The primary beam was incident on the (112) face at a glancing angle of only 7.5” in the azimuth determined by the surface normal and the [Ii01 direction in the surface. At these glancing angles the circles appear strongest, although they have been seen and measured up to incidence angles as large as 45”. Upon rotating the crystal the circles are unchanged in size, moving with it and maintaining their common center at the intersection of the [ liO] direction with the fluorescent screen. For voltages above IOOOV and near grazing incidence, these circles
* Work supported by Advanced Research Projects Agency, Washington, ** Kikuchi lines and bands have been seen with slow electrons’). 498
D. C.
SCATTERING
Fig. 1.
OF LOW
ENERGY
ELECTRONS
499
Back reflection diffraction pattern from a tungsten crystal, 1046V. The prominent
circles are the intersection with the fluorescent screen of cones about the [lTO] surface direction.
are the strongest diffraction features that are seen, although they rapidly weaken at lower voltages and have not been photographed below 125V. Angles subtended by these cones are readily obtained by using a calibration from ordinary diffraction spots. The resulting angles for cones about the [liO] direction are plotted in fig. 2 against the voltages at which they were observed. The solid curves of the figure are calculated from eq. (1) with d=a,/2=4.41.&
VOLTS Fig. 2. Measured angles of cones about the [ITO] surface direction at different electron beam voltages. Open circles represent excess cones and the black circles deficit cones.
500
L. H.
GERMER
AND
C. C. CHANG
First and second order circles representing cones about [ 13 1] and [3ii] surface directions are seen also weakly in fig. 1, located on either side of the [liO] circles. Their centers are in the expected places and their cone angles are given by eq. (1) with d =$a,/1 1 = 5.24A. The circles of fig. 1 are deficit circles. They represent directions in which the multiply scattered background electrons are less numerous than in other directions. The missing electrons are diffracted into the axes of their respective cones. Looking for a beam of electrons coming from the crystal along such a direction seems an obvious continuation of the present experiments. It probably requires that the crystal surface be cut at a small angle with the nominal (112) plane, so that the [liO] direction protrudes from the surface. Circles representing excess cones have been observed with forwardscattered fast electrons, apparently reported first by Emslie2) and later by Shinoharas). Emslie found a small displacement of his excess circles, which he attributed to an inner potential of 26.4V, and suggested that this high value might be due to an exceptionally high value of the potential along the line of atoms giving rise to the cones. An inner potential of about 25 V would displace the theoretical curves of fig. 2 into much better agreement with our experimental points, but we are not sure that the plotted displacement is beyond experimental error. Shinohara found his excess circles to be envelopes of Kikuchi lines and ascribed the displacement to a refractive effect arising from dynamical interactions. We wish to point out here that no Kikuchi lines were ever observed with the circles we see. At least six lines can also be seen in the photograph of fig. 1, some slightly curved and each coming close to tangency with one circle. Each line maintains this relation with its circle as the primary voltage is changed, so that these are not Kikuchi lines. The condition for exact tangency of a Kikuchi line hh 1 of the [ liO] zone with a [liO] circle of which has solutions for h and I integral only It is indicated in fig. 2 that the smallest cone above 520V and an excess cone below
order n is 11(2/r’ + Z2+ 2n2) = 4dn for selected values of 1.. [liO] circle represents a deficit this voltage. At the transition,
a set of deficit-excess-deficit circles can be seen (as indicated at 52OV), with the excess cone predominating at lower voltages and the smaller deficit cone predominating at higher voltages. On a kinematical view we suggest relating the transition to the relative importance of multiple scattering at atoms below the surface layer and at atoms in the surface layer itself. No kinematical interpretation can, however, explain the complex nature of the transition. Moreover, a similar transition also occurs ifthe angle of incidence is changed, keeping the primary beam energy fixed. In this case the normally deficit cones at glancing angles give way to excess cones at larger angles of incidence.
SCATTERING
OF LOW
ENERGY
501
ELECTRONS
Diffraction cones have not yet been looked for in the forward direction, although these may be stronger than the back reflection cones reported here. L. H. GERMER
and C. C. CHANG
Department of Physics, Cornell University, Ithaca, New York, U.S.A.
References 1) E. G. McRae and C. W. Caldwell, Surface Sci. 2 (1964) 509; J. L. Robins, R. L. Gerlach and T. N. Rhodin, Appl. Phys. Letters 8 (1966) No. 1; D. C. Johnson a Id A. U. Mac Rae, J. Appl. Phys. 37 (1966) 1945. 2) A. G. Emslie, Phys. Rev. 45 (1934) 43. 3) K. Shinohara, Phys. Rev. 47 (1935) 730.