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Interpretation of diffuse scattering in the high- T c superconductor HgBa 2 CuO 4+ δ

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ABSTRACT

Published diffuse X-ray scattering from the high-Tc superconductor HgBa2CuO4+δ has been reexamined with a view to developing a model that more satisfactorily accounts for the observed patterns. The present work agrees with the previous conclusion that the doping oxygen atoms form long and isolated interstitial chains that run in both tetragonal directions. However, a distinctly different model is proposed for the accompanying displacement patterns of the atoms surrounding these linear defects. In this new model it is proposed that it is the correlated shifts of the Ba atoms along the length of the defect chains that are the primary source of the observed scattering, and that the variations of intensity in the generated diffuse streaks of scattering originate from lateral shifts of both Hg and Ba atoms away from defects. The new model yields diffraction patterns that are in much more convincing agreement with the observations than the original model.

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The simple linear chain SRO model. (a) A small region of the simulation array, showing the randomly positioned chains of interstitial O3 atoms. (b) The hk0 diffraction pattern calculated from the full (512 × 512 cells) model with all atoms on their average site positions. Note h is horizontal and k is vertical. (c) The hk0 pattern after size-effect relaxation with ξ1 = 0.0025. (d) The hk0 pattern after size-effect relaxation with ξ1 = −0.0025. (e) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (c). (f) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (d). It should be noted that the maximum intensity in part (b) is less than half of that in (c) or (d).
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fig3: The simple linear chain SRO model. (a) A small region of the simulation array, showing the randomly positioned chains of interstitial O3 atoms. (b) The hk0 diffraction pattern calculated from the full (512 × 512 cells) model with all atoms on their average site positions. Note h is horizontal and k is vertical. (c) The hk0 pattern after size-effect relaxation with ξ1 = 0.0025. (d) The hk0 pattern after size-effect relaxation with ξ1 = −0.0025. (e) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (c). (f) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (d). It should be noted that the maximum intensity in part (b) is less than half of that in (c) or (d).

Mentions: Computer simulation of a model structure has become a powerful and well accepted technique for aiding the interpretation and analysis of diffuse scattering patterns (Welberry & Butler, 1994 ▸; Welberry, 2004 ▸; Welberry & Weber, 2016 ▸). At one extreme, a very simplified model may be useful in demonstrating particular qualitative effects, while at the other a quantitative and very detailed description of a disordered structure can be obtained. In the present case, a large two-dimensional array (512 × 512) was used to represent a single layer of the structure. Initially this was used to represent a single plane of Hg ions together with the interstial O3 atoms, but subsequently the Ba atoms above and below this layer were included. It was assumed throughout that each such layer was independent of those one unit cell above or below. Fig. 3 ▸(a) shows a small representative region (100 × 100 unit cells) of the simulation array. The randomly positioned chains of interstitial O3 atoms are clearly seen. For the present study, the chain length was chosen for convenience to be 20 unit cells. This is less than that estimated by Izquierdo et al. (2011 ▸), but a shorter length allows better statistics to be obtained in a crystal of limited size. The only material difference this makes to the calculated diffraction patterns presented in the paper is that the diffuse lines are somewhat more diffuse than those in the observed data.


Interpretation of diffuse scattering in the high- T c superconductor HgBa 2 CuO 4+ δ
The simple linear chain SRO model. (a) A small region of the simulation array, showing the randomly positioned chains of interstitial O3 atoms. (b) The hk0 diffraction pattern calculated from the full (512 × 512 cells) model with all atoms on their average site positions. Note h is horizontal and k is vertical. (c) The hk0 pattern after size-effect relaxation with ξ1 = 0.0025. (d) The hk0 pattern after size-effect relaxation with ξ1 = −0.0025. (e) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (c). (f) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (d). It should be noted that the maximum intensity in part (b) is less than half of that in (c) or (d).
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Show All Figures
getmorefigures.php?uid=PMC5391853&req=5

fig3: The simple linear chain SRO model. (a) A small region of the simulation array, showing the randomly positioned chains of interstitial O3 atoms. (b) The hk0 diffraction pattern calculated from the full (512 × 512 cells) model with all atoms on their average site positions. Note h is horizontal and k is vertical. (c) The hk0 pattern after size-effect relaxation with ξ1 = 0.0025. (d) The hk0 pattern after size-effect relaxation with ξ1 = −0.0025. (e) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (c). (f) A plot showing the size-effect distortion (exaggerated ×40) around a defect corresponding to part (d). It should be noted that the maximum intensity in part (b) is less than half of that in (c) or (d).
Mentions: Computer simulation of a model structure has become a powerful and well accepted technique for aiding the interpretation and analysis of diffuse scattering patterns (Welberry & Butler, 1994 ▸; Welberry, 2004 ▸; Welberry & Weber, 2016 ▸). At one extreme, a very simplified model may be useful in demonstrating particular qualitative effects, while at the other a quantitative and very detailed description of a disordered structure can be obtained. In the present case, a large two-dimensional array (512 × 512) was used to represent a single layer of the structure. Initially this was used to represent a single plane of Hg ions together with the interstial O3 atoms, but subsequently the Ba atoms above and below this layer were included. It was assumed throughout that each such layer was independent of those one unit cell above or below. Fig. 3 ▸(a) shows a small representative region (100 × 100 unit cells) of the simulation array. The randomly positioned chains of interstitial O3 atoms are clearly seen. For the present study, the chain length was chosen for convenience to be 20 unit cells. This is less than that estimated by Izquierdo et al. (2011 ▸), but a shorter length allows better statistics to be obtained in a crystal of limited size. The only material difference this makes to the calculated diffraction patterns presented in the paper is that the diffuse lines are somewhat more diffuse than those in the observed data.

View Article: PubMed Central - HTML - PubMed

ABSTRACT

Published diffuse X-ray scattering from the high-Tc superconductor HgBa2CuO4+δ has been reexamined with a view to developing a model that more satisfactorily accounts for the observed patterns. The present work agrees with the previous conclusion that the doping oxygen atoms form long and isolated interstitial chains that run in both tetragonal directions. However, a distinctly different model is proposed for the accompanying displacement patterns of the atoms surrounding these linear defects. In this new model it is proposed that it is the correlated shifts of the Ba atoms along the length of the defect chains that are the primary source of the observed scattering, and that the variations of intensity in the generated diffuse streaks of scattering originate from lateral shifts of both Hg and Ba atoms away from defects. The new model yields diffraction patterns that are in much more convincing agreement with the observations than the original model.

No MeSH data available.


Related in: MedlinePlus