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Small-angle neutron scattering on hydrogen- and deuterium-doped nanocrystalline palladium
Physica B 276}278 (2000) 880}881
Small-angle neutron scattering on hydrogen- and deuterium-doped nanocrystalline palladium T. Stri%er *, U. Stuhr, H. Wipf , H. Hahn, S. Egelhaaf Institut fu( r Festko( rperphysik, Technische Universita( t Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Materialwissenschaft, Technische Universita( t Darmstadt, Petersenstrasse 23, D-64287 Darmstadt, Germany Institut Laue Langevin, 6, rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France
Abstract The microstructure of a nanocrystalline Pd sample prepared by inert gas condensation was studied by small-angle neutron scattering. To increase information, the contrast of the sample was additionally varied by doping it with H and D (c "3.2 at%, c "3.5 at%). We modeled the measured intensity by a Porod contribution caused by large heterogeni& " ties (pores) and a second contribution caused by a logarithmic normal distribution of spherical grains surrounded by shells of reduced Pd density describing the grain boundaries. This model yields a volume-weighted mean grain radius of 10 nm and a grain boundary thickness of approximately 0.8 nm. The contrast variation due to doping with H and D indicated that H and D were mainly located in grain boundaries. 2000 Elsevier Science B.V. All rights reserved. Keywords: Grain boundaries; Hydrogen; Metals; Small-angle neutron scattering
1. Introduction Nanocrystalline materials are polycrystals with grain sizes of a few nanometres (+2}50 nm) [1]. These small grain sizes imply that a signi"cant fraction of the atoms is located in grain boundaries, which leads to new physical properties. We studied the microstructure of a nanocrystalline Pd-sample by small-angle neutron scattering. To increase structural information the sample contrast was additionally modi"ed by aimed H- and D-doping of the sample.
2. Experimental Our disc-shaped sample was prepared by inert gas condensation [2] (0.32 g, diameter+9.6 mm, thick-
* Corresponding author. Fax: 49-61-51-16-28-33 . E-mail address: thomas.stri%[email protected] (T. Stri%er)
ness+0.5 mm) and measured after doping with either H or D (c "3.2 at%, c "3.5 at%, gas-volumetrically & " determined), and without H- or D-doping. Neutron data were taken at room temperature at the ILL in Grenoble with instrument D22 (Q-range from 10\}0.4 As \). 3. Experimental results and discussion The top diagram of Fig. 1 shows the scattering crosssection dp/dX per Pd atom of the undoped sample (absolute scale by calibration with a H O standard). The bottom diagram in Fig. 1 presents the relative change of the scattering cross-section (dp/dX !dp/dX )/(dp/dX ) B due to H- and D-doping. We modeled the data by assuming contributions to the measured intensity originating from large heterogenities (pores, internal macroscopic density #uctuations and surface roughness) and spherical Pd grains with a log-normal distribution z(R) of radii R. The grains were surrounded by a shell of reduced Pd density and thickness d to account for the grain boundaries. Further, we considered a Q-independent background (B in Eq. (1)). Thus,
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 6 3 1 - 2
T. Stri{er et al. / Physica B 276}278 (2000) 880}881
Fig. 1. dp/dX per Pd-atom of the undoped sample (top dia gram) and relative change of scattering cross-section due to Hand D-doping of the sample (bottom diagram).
the scattering cross-section dp/dX of the sample can be written as
N dR dp "PQ\# z(R) (R) dR#B, (1) dX N dX . where z(R) dR"1. The "rst term on the right-hand side of Eq. (1) is Porod's law [3] describing the contribution from large heterogenities (P is Porod's constant). The second term is the contribution of the grains plus grain boundaries, where N and N is the number of . grains and Pd-atoms, respectively. (dR/dX)(R) is the scattering cross-section of a single spherical grain of radius R surrounded by a shell of reduced density and thickness d [4].
881
The model was simultaneously "tted to the data of the H- and D-doped sample, and to the data of the undoped sample. The solid curves in Fig. 1 are best results of this simultaneous "t to three data sets, performed with identical "tting parameters. The "t yields a volume-weighted mean grain radius 1R 2 of 10 nm and a grain boundary thickness 2d of approximately 0.8 nm. Further, we found that almost all of the H and D is located in grain boundaries. Although the model is not perfect, we consider our "t satisfactory. One reason is that the value of the volumeweighted mean grain radius (1R 2"10 nm) shows good agreement with that determined from Bragg-peak line-broadening from X-ray analysis (1R 2"8 nm). V Further, the H- and D-concentrations (c "3.2 at%, & c "3.3 at%) agree well with the concentrations deter" mined gas-volumetrically. In contrast to former studies, our present "t describes simultaneously three data sets (data of the H-doped, D-doped and undoped sample) with only one set of parameters. This makes a less perfect data description understandable. We also point out that our "t yields a perfect description, as previous studies do, if we consider only a single data set (for instance the data of the undoped sample). Additional "ts performed with the assumption that no H and D are in the grain boundaries yield a completely unsatisfactory description of the data. These "ts showed clearly that the data cannot be described with this assumption. The results of our study will be published in more detail in a forthcoming paper [4].
References [1] H. Gleiter, Progr. Mater. Sci. 33 (1989) 223. [2] C.G. Granqvist, R.A. Buhrmann, J. Appl. Phys. 47 (1976) 2200. [3] G. Porod, Kolloid-Z. 124 (1951) 83. [4] T. Stri%er, U. Stuhr, H. Wipf, H. Hahn, S. Egelhaaf, in preparation.
Small-angle neutron scattering on hydrogen- and deuterium-doped nanocrystalline palladium T. Stri%er *, U. Stuhr, H. Wipf , H. Hahn, S. Egelhaaf Institut fu( r Festko( rperphysik, Technische Universita( t Darmstadt, Hochschulstrasse 6, D-64289 Darmstadt, Germany Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Materialwissenschaft, Technische Universita( t Darmstadt, Petersenstrasse 23, D-64287 Darmstadt, Germany Institut Laue Langevin, 6, rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France
Abstract The microstructure of a nanocrystalline Pd sample prepared by inert gas condensation was studied by small-angle neutron scattering. To increase information, the contrast of the sample was additionally varied by doping it with H and D (c "3.2 at%, c "3.5 at%). We modeled the measured intensity by a Porod contribution caused by large heterogeni& " ties (pores) and a second contribution caused by a logarithmic normal distribution of spherical grains surrounded by shells of reduced Pd density describing the grain boundaries. This model yields a volume-weighted mean grain radius of 10 nm and a grain boundary thickness of approximately 0.8 nm. The contrast variation due to doping with H and D indicated that H and D were mainly located in grain boundaries. 2000 Elsevier Science B.V. All rights reserved. Keywords: Grain boundaries; Hydrogen; Metals; Small-angle neutron scattering
1. Introduction Nanocrystalline materials are polycrystals with grain sizes of a few nanometres (+2}50 nm) [1]. These small grain sizes imply that a signi"cant fraction of the atoms is located in grain boundaries, which leads to new physical properties. We studied the microstructure of a nanocrystalline Pd-sample by small-angle neutron scattering. To increase structural information the sample contrast was additionally modi"ed by aimed H- and D-doping of the sample.
2. Experimental Our disc-shaped sample was prepared by inert gas condensation [2] (0.32 g, diameter+9.6 mm, thick-
* Corresponding author. Fax: 49-61-51-16-28-33 . E-mail address: thomas.stri%[email protected] (T. Stri%er)
ness+0.5 mm) and measured after doping with either H or D (c "3.2 at%, c "3.5 at%, gas-volumetrically & " determined), and without H- or D-doping. Neutron data were taken at room temperature at the ILL in Grenoble with instrument D22 (Q-range from 10\}0.4 As \). 3. Experimental results and discussion The top diagram of Fig. 1 shows the scattering crosssection dp/dX per Pd atom of the undoped sample (absolute scale by calibration with a H O standard). The bottom diagram in Fig. 1 presents the relative change of the scattering cross-section (dp/dX !dp/dX )/(dp/dX ) B due to H- and D-doping. We modeled the data by assuming contributions to the measured intensity originating from large heterogenities (pores, internal macroscopic density #uctuations and surface roughness) and spherical Pd grains with a log-normal distribution z(R) of radii R. The grains were surrounded by a shell of reduced Pd density and thickness d to account for the grain boundaries. Further, we considered a Q-independent background (B in Eq. (1)). Thus,
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 6 3 1 - 2
T. Stri{er et al. / Physica B 276}278 (2000) 880}881
Fig. 1. dp/dX per Pd-atom of the undoped sample (top dia gram) and relative change of scattering cross-section due to Hand D-doping of the sample (bottom diagram).
the scattering cross-section dp/dX of the sample can be written as
N dR dp "PQ\# z(R) (R) dR#B, (1) dX N dX . where z(R) dR"1. The "rst term on the right-hand side of Eq. (1) is Porod's law [3] describing the contribution from large heterogenities (P is Porod's constant). The second term is the contribution of the grains plus grain boundaries, where N and N is the number of . grains and Pd-atoms, respectively. (dR/dX)(R) is the scattering cross-section of a single spherical grain of radius R surrounded by a shell of reduced density and thickness d [4].
881
The model was simultaneously "tted to the data of the H- and D-doped sample, and to the data of the undoped sample. The solid curves in Fig. 1 are best results of this simultaneous "t to three data sets, performed with identical "tting parameters. The "t yields a volume-weighted mean grain radius 1R 2 of 10 nm and a grain boundary thickness 2d of approximately 0.8 nm. Further, we found that almost all of the H and D is located in grain boundaries. Although the model is not perfect, we consider our "t satisfactory. One reason is that the value of the volumeweighted mean grain radius (1R 2"10 nm) shows good agreement with that determined from Bragg-peak line-broadening from X-ray analysis (1R 2"8 nm). V Further, the H- and D-concentrations (c "3.2 at%, & c "3.3 at%) agree well with the concentrations deter" mined gas-volumetrically. In contrast to former studies, our present "t describes simultaneously three data sets (data of the H-doped, D-doped and undoped sample) with only one set of parameters. This makes a less perfect data description understandable. We also point out that our "t yields a perfect description, as previous studies do, if we consider only a single data set (for instance the data of the undoped sample). Additional "ts performed with the assumption that no H and D are in the grain boundaries yield a completely unsatisfactory description of the data. These "ts showed clearly that the data cannot be described with this assumption. The results of our study will be published in more detail in a forthcoming paper [4].
References [1] H. Gleiter, Progr. Mater. Sci. 33 (1989) 223. [2] C.G. Granqvist, R.A. Buhrmann, J. Appl. Phys. 47 (1976) 2200. [3] G. Porod, Kolloid-Z. 124 (1951) 83. [4] T. Stri%er, U. Stuhr, H. Wipf, H. Hahn, S. Egelhaaf, in preparation.