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Direct evidence for a very low atom displacement threshold energy around the 〈110〉 directions in copper
Volume 63A, number 3
PHYSICS LETTERS
14 November 1977
DIRECT EVIDENCE FOR A VERY LOW ATOM DISPLACEMENT THRESHOLD ENERGY AROUND THE (110) DIRECTIONS IN COPPER N. YOSHIDA and K. URBAN Max-Planck-Instjtut für Metcjllforschung, Institut für Physik, Postfach 800665, D7000 Stuttgart 80, W.-Germany Received 27 July 1977
The dependence of the displacement cross section of Cu on electron energy and crystal orientation has very accurately been determined by high-voltage electron microscopy. The minimum displacement threshold energy of (9.5 ± 0.5) eV occurs at an angle of 10°from (110> directions.
The displacement threshold energy Ed is the minimum energy which has to be transferred to a crystal atom in order to obtain permanent atom displacement. Because of the lattice structure the threshold energy has to be considered anisotropic [11. This can best be described by a threshold energy surface which is obtamed by plotting Ed as a function of atom knock.on direction in a spherical coordinate system [2]. The details of the threshold energy surface are of considerable significance since they are related to the nature of the displacement process and the shape of the interatomic potential. Theoretical studies indicated that the lattice structure favours the formation of interstitial atoms by atom replacement collision sequences along closepacked lattice directions, i.e. the (110) directions in face-centred cubic materials. Such a collision sequence can be triggered at an especially low energy if the knock.on direction of the primary struck atom is not parallel to a close-packed direction but at a certain angle from it [3,4]. Thus a ring-shaped “through” rather than a simple minimum is to be expected in the threshold energy surface around the close-packed directions. This concept was used in an analysis [5] of the residual resistivity in copper electron irradiated at low temperature [6]. The data could be fitted assuming a “through” of about 50 angular width close to the (110) directions, in which Ed drops to about 9 eV while for other directions Ed 20 eV. However, resistivity measurements have failed to provide direct evidence for the theoretically predicted shape of the threshold energy surface near (110). The reason for this is that studies of fine details of the threshold en-
ergy surface require the maximum energies transferred to the atoms to be fairly close to the local threshold. This means that for copper electrons of energies less than 300 keV should be used. In the relative thick samples (thickness> 10 pm) necessary for resistivity measurements an electron beam of such an energy is spread considerably by multiple inelastic scattering. Information on the features discussed above can therefore not be obtained this way. As an alternative an extensive study of copper [7] employed electron energies higher than 1 MeV. This did not yield reliable information on the above mentioned “throughs”, since at high energies they contribute very litte to the total displacement cross section. Nevertheless, a best fit of the data was obtained assuming a threshold energy minimum with Ed 20 eV in a ring-shaped range around the (110) directions. Two other methods have recently been demonstrated to be suited for the study of low-energy displacements, namely dislocation pinning [8,9] and high-voltage electron microscopy (HVEM) [10—121. Either method monitors the production of freely mlgrating interstitials and has therefore to be applied at temperatures high enough to allow thermally activated diffusion of these defects. Nevertheless, the data obtamed can be compared to those obtained by resistivity measurements carried out at temperatures where the defects are immobile since the effect of atom vibrations on the threshold energies should be small. Whereas dislocation pinning studies have so far been confined to telatively thick polycrystalline samples and have therefore not directly contributed to the question of the anisotropy of Ed, HVEM provides a 381
Volume 63A, number 3
PHYSICS LETTERS
powerful tool for such investigations, The orientation of the irradiated crystals with respect to the electron beam can be very accurately controlled. In addition, the use of thin samples (thickness ~ 0.5 pm) makes effects of inelastic electron scattering negligible. We present here a novel method which allows us to determine relative displacement cross sections observations of the growth of interstitial dislocation loops by HVEM at high temperatures. Experimental method. Interstitial dislocation loops are created during pre-irradiation with high-energy (e.g. 1 MeV) electrons. Depending on temperature, a range of foil thickness has been found at which these loops grow during irradiation at a rate which is independent of their size and directly proportional to the displacement cross section. In foils of properly chosen thickness relative displacement cross sections may thus be determined as a function of electron energy and irradiation direction using the same ioop population. This method is much more sensitive than previously used HVEM methods and is unaffected by nucleation or thin-foil effects, Experimental results. The orientation dependence of the displacement cross section of copper (99 .999% pure) has been determined at energies between 220 keV and 400 keV by observing at 550 K the growth of Frank loops. The specimen orientation was changed in steps from <110) to (100) (case I) or from (110) to <111) (case II). Since in thin foils diffraction channeling of electrons may have a strong effect on the dis. placement rate [13,14], the exact <100), (110) and
I
100
/7’ /7
50
/7
~ 10
~
;
~
i3.~,ol8
~1ectroncurrent de~lty(e/cm2s) Fig. 1. Loop growth rate at 550 K versus electron current density (400 keV),
382
14 November 1977
__________________________________
A
300keV
1
8
/
/
“ ,,-r~
C
30
20
10
/°\
I’7
________
0 (110)
10
\
20
30
40
4 (degrees) (100) Fig. 2. Loop growth rate versus electron energy and crystal 2. orientation. Electron current density: 9.5 )( 1018 e/s cm Data taken from one and the same loop are denoted by the same symbol. ‘h1~
(111) crystal orientations were avoided and kinematical diffraction conditions applied throughout. A foil thickness of 0.3 pm was chosen, for which fig. 1 demonstrates the linear relation between loop growth rate and electron current density. The displacement rate governing loop growth is proportional to current density and displacement cross section. Fig. 2 shows the loop growth rate at constant electron current density and hence, apart from a constant factor, the displacement cross section as function of irradiation direction and electron energy. These results were found to be independent of the plane a certain loop was lying on and of the direction of the loop diameter chosen for the measurements. The growth rate is strbngly anisotropic and exhibits for all energies a maximum if the irradiation direction makes an angle of about 10°with a <110) direction. With decreasing energy the angular range of irradiation directions yielding loop growth shrinks and contracts towards the orientation of maximum growth rate. A plot of the maximum values versus energy in fig. 3 yields Ed = (9.5 ±0.5) eV. The observation that the cross sections are, within experimental error, identical for cases I and II is in agreement with the view that this threshold value holds in a ring-shaped range of small angular width around the (110) directions. Discussion. Our results provide the first direct experimental evidence for the existence of a ring-shaped low-threshold range of small angular width around the (110) directions in copper. This “through” lies within the orientation range of low threshold found in [7]
Volume 63A, number 3
PHYSICS LETTERS
/
maximum transferred energy (eV) 9 10 11 12 13
10
14 November 1977
tion or dislocation line direction we can exclude the possibility that the observed displacements were occurring on the dislocation loops (which would have tam to the bulk of the crystal [15]. In addition such meant that the measured threshold value does not perdisplacements would presumably have lead to shrinkage rather than growth of the interstitial loops.
C
p References
.._,./
C—.
_________________________
220
[1] J.B. Gibson, A.N. Goland, M. Milgram and G.H. Vineyard, Phys. Rev. 120 (1960) 1229. [21 R. v. Jan and A. Seeger, Phys. Stat. Sol. 3 (1963) 465.
-
260
300
electron ene~gy(keV)
Fig. 3. Peak values of right-hand side of fig. 2 (open symbols) and data obtained from one single ioop (irradiating along direction yielding maximum growth rate) versus energy.
but has the much lower energy postulated in [5]. This is strong support for the view that in face-centered cubic lattices the displacement of atoms occurs preferential. ly via focussing replacement collision sequences along (110) directions. The observed anisotropy down to very low energies rules out for our case the impurity double collision model for low-energy displacements [6] since from this no such orientation dependence would be expected. By the observation that the measured dislocation loop climb rate is independent of ioop orienta-
[3] C. Erginsoy, G.H. Vineyard and A. Englert, Phys. Rev. 133 (1964)A595. [4] G. Duesing and G. Leibfried, Phys. Stat. Sol. 9 (1965) 463. [5] H. Wollenberger and J. Wurm, Phys. Stat. Sol. 9 (1965) 601. [6] W. Bauer and A. Sosin, J. Appi. Phys, 35 (1964) 703. [7] P. Jung et al., Phys. Rev. B8 (1973) 553. [8] G. Roth, H. Wollenberger Ch. Zeckau and K. LOcke, Rad. Eff. 26 (1975) 141. [9] J. Lauzier, C. Mmier and A. Seeger, Phil. Mag., in press. [10] A. Seeger, Mag. 30submitted (1974) 1395. [11] K. R. Urban Drosd, and T. Kosel and J.Phil. Washburn, to J. Nucl. Mat. [12] H. Schmid, Diplomarbeit, Universitàt Stuttgart (1976). [13] L.E. Thomas, Rad. Eff. 5 (1970) 183. [14] K. Urban and N. Yoshida, in: Proc. US-Japan Seminar on HVEM, Honolulu, 1976 (Univ. of Nagoya Press, 1977) p. 121. [15] G. Leibfried, J. Appl. Phys. 31(1960)117.
383
PHYSICS LETTERS
14 November 1977
DIRECT EVIDENCE FOR A VERY LOW ATOM DISPLACEMENT THRESHOLD ENERGY AROUND THE (110) DIRECTIONS IN COPPER N. YOSHIDA and K. URBAN Max-Planck-Instjtut für Metcjllforschung, Institut für Physik, Postfach 800665, D7000 Stuttgart 80, W.-Germany Received 27 July 1977
The dependence of the displacement cross section of Cu on electron energy and crystal orientation has very accurately been determined by high-voltage electron microscopy. The minimum displacement threshold energy of (9.5 ± 0.5) eV occurs at an angle of 10°from (110> directions.
The displacement threshold energy Ed is the minimum energy which has to be transferred to a crystal atom in order to obtain permanent atom displacement. Because of the lattice structure the threshold energy has to be considered anisotropic [11. This can best be described by a threshold energy surface which is obtamed by plotting Ed as a function of atom knock.on direction in a spherical coordinate system [2]. The details of the threshold energy surface are of considerable significance since they are related to the nature of the displacement process and the shape of the interatomic potential. Theoretical studies indicated that the lattice structure favours the formation of interstitial atoms by atom replacement collision sequences along closepacked lattice directions, i.e. the (110) directions in face-centred cubic materials. Such a collision sequence can be triggered at an especially low energy if the knock.on direction of the primary struck atom is not parallel to a close-packed direction but at a certain angle from it [3,4]. Thus a ring-shaped “through” rather than a simple minimum is to be expected in the threshold energy surface around the close-packed directions. This concept was used in an analysis [5] of the residual resistivity in copper electron irradiated at low temperature [6]. The data could be fitted assuming a “through” of about 50 angular width close to the (110) directions, in which Ed drops to about 9 eV while for other directions Ed 20 eV. However, resistivity measurements have failed to provide direct evidence for the theoretically predicted shape of the threshold energy surface near (110). The reason for this is that studies of fine details of the threshold en-
ergy surface require the maximum energies transferred to the atoms to be fairly close to the local threshold. This means that for copper electrons of energies less than 300 keV should be used. In the relative thick samples (thickness> 10 pm) necessary for resistivity measurements an electron beam of such an energy is spread considerably by multiple inelastic scattering. Information on the features discussed above can therefore not be obtained this way. As an alternative an extensive study of copper [7] employed electron energies higher than 1 MeV. This did not yield reliable information on the above mentioned “throughs”, since at high energies they contribute very litte to the total displacement cross section. Nevertheless, a best fit of the data was obtained assuming a threshold energy minimum with Ed 20 eV in a ring-shaped range around the (110) directions. Two other methods have recently been demonstrated to be suited for the study of low-energy displacements, namely dislocation pinning [8,9] and high-voltage electron microscopy (HVEM) [10—121. Either method monitors the production of freely mlgrating interstitials and has therefore to be applied at temperatures high enough to allow thermally activated diffusion of these defects. Nevertheless, the data obtamed can be compared to those obtained by resistivity measurements carried out at temperatures where the defects are immobile since the effect of atom vibrations on the threshold energies should be small. Whereas dislocation pinning studies have so far been confined to telatively thick polycrystalline samples and have therefore not directly contributed to the question of the anisotropy of Ed, HVEM provides a 381
Volume 63A, number 3
PHYSICS LETTERS
powerful tool for such investigations, The orientation of the irradiated crystals with respect to the electron beam can be very accurately controlled. In addition, the use of thin samples (thickness ~ 0.5 pm) makes effects of inelastic electron scattering negligible. We present here a novel method which allows us to determine relative displacement cross sections observations of the growth of interstitial dislocation loops by HVEM at high temperatures. Experimental method. Interstitial dislocation loops are created during pre-irradiation with high-energy (e.g. 1 MeV) electrons. Depending on temperature, a range of foil thickness has been found at which these loops grow during irradiation at a rate which is independent of their size and directly proportional to the displacement cross section. In foils of properly chosen thickness relative displacement cross sections may thus be determined as a function of electron energy and irradiation direction using the same ioop population. This method is much more sensitive than previously used HVEM methods and is unaffected by nucleation or thin-foil effects, Experimental results. The orientation dependence of the displacement cross section of copper (99 .999% pure) has been determined at energies between 220 keV and 400 keV by observing at 550 K the growth of Frank loops. The specimen orientation was changed in steps from <110) to (100) (case I) or from (110) to <111) (case II). Since in thin foils diffraction channeling of electrons may have a strong effect on the dis. placement rate [13,14], the exact <100), (110) and
I
100
/7’ /7
50
/7
~ 10
~
;
~
i3.~,ol8
~1ectroncurrent de~lty(e/cm2s) Fig. 1. Loop growth rate at 550 K versus electron current density (400 keV),
382
14 November 1977
__________________________________
A
300keV
1
8
/
/
“ ,,-r~
C
30
20
10
/°\
I’7
________
0 (110)
10
\
20
30
40
4 (degrees) (100) Fig. 2. Loop growth rate versus electron energy and crystal 2. orientation. Electron current density: 9.5 )( 1018 e/s cm Data taken from one and the same loop are denoted by the same symbol. ‘h1~
(111) crystal orientations were avoided and kinematical diffraction conditions applied throughout. A foil thickness of 0.3 pm was chosen, for which fig. 1 demonstrates the linear relation between loop growth rate and electron current density. The displacement rate governing loop growth is proportional to current density and displacement cross section. Fig. 2 shows the loop growth rate at constant electron current density and hence, apart from a constant factor, the displacement cross section as function of irradiation direction and electron energy. These results were found to be independent of the plane a certain loop was lying on and of the direction of the loop diameter chosen for the measurements. The growth rate is strbngly anisotropic and exhibits for all energies a maximum if the irradiation direction makes an angle of about 10°with a <110) direction. With decreasing energy the angular range of irradiation directions yielding loop growth shrinks and contracts towards the orientation of maximum growth rate. A plot of the maximum values versus energy in fig. 3 yields Ed = (9.5 ±0.5) eV. The observation that the cross sections are, within experimental error, identical for cases I and II is in agreement with the view that this threshold value holds in a ring-shaped range of small angular width around the (110) directions. Discussion. Our results provide the first direct experimental evidence for the existence of a ring-shaped low-threshold range of small angular width around the (110) directions in copper. This “through” lies within the orientation range of low threshold found in [7]
Volume 63A, number 3
PHYSICS LETTERS
/
maximum transferred energy (eV) 9 10 11 12 13
10
14 November 1977
tion or dislocation line direction we can exclude the possibility that the observed displacements were occurring on the dislocation loops (which would have tam to the bulk of the crystal [15]. In addition such meant that the measured threshold value does not perdisplacements would presumably have lead to shrinkage rather than growth of the interstitial loops.
C
p References
.._,./
C—.
_________________________
220
[1] J.B. Gibson, A.N. Goland, M. Milgram and G.H. Vineyard, Phys. Rev. 120 (1960) 1229. [21 R. v. Jan and A. Seeger, Phys. Stat. Sol. 3 (1963) 465.
-
260
300
electron ene~gy(keV)
Fig. 3. Peak values of right-hand side of fig. 2 (open symbols) and data obtained from one single ioop (irradiating along direction yielding maximum growth rate) versus energy.
but has the much lower energy postulated in [5]. This is strong support for the view that in face-centered cubic lattices the displacement of atoms occurs preferential. ly via focussing replacement collision sequences along (110) directions. The observed anisotropy down to very low energies rules out for our case the impurity double collision model for low-energy displacements [6] since from this no such orientation dependence would be expected. By the observation that the measured dislocation loop climb rate is independent of ioop orienta-
[3] C. Erginsoy, G.H. Vineyard and A. Englert, Phys. Rev. 133 (1964)A595. [4] G. Duesing and G. Leibfried, Phys. Stat. Sol. 9 (1965) 463. [5] H. Wollenberger and J. Wurm, Phys. Stat. Sol. 9 (1965) 601. [6] W. Bauer and A. Sosin, J. Appi. Phys, 35 (1964) 703. [7] P. Jung et al., Phys. Rev. B8 (1973) 553. [8] G. Roth, H. Wollenberger Ch. Zeckau and K. LOcke, Rad. Eff. 26 (1975) 141. [9] J. Lauzier, C. Mmier and A. Seeger, Phil. Mag., in press. [10] A. Seeger, Mag. 30submitted (1974) 1395. [11] K. R. Urban Drosd, and T. Kosel and J.Phil. Washburn, to J. Nucl. Mat. [12] H. Schmid, Diplomarbeit, Universitàt Stuttgart (1976). [13] L.E. Thomas, Rad. Eff. 5 (1970) 183. [14] K. Urban and N. Yoshida, in: Proc. US-Japan Seminar on HVEM, Honolulu, 1976 (Univ. of Nagoya Press, 1977) p. 121. [15] G. Leibfried, J. Appl. Phys. 31(1960)117.
383