Silicon Carbides

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Nan Liu - One of the best experts on this subject based on the ideXlab platform.

  • correlated strontium and barium isotopic compositions of acid cleaned single mainstream Silicon Carbides from murchison
    The Astrophysical Journal, 2015
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, S Bisterzo, Frank Gyngard, F Kappeler, S Cristallo
    Abstract:

    We present strontium, barium, carbon, and Silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contamination. For the first time, by using correlated 88Sr/86Sr and 138Ba/136Ba ratios in mainstream SiC grains, we are able to resolve the effect of 13C concentration from that of 13C-pocket mass on s-process nucleosynthesis, which points toward the existence of large 13C pockets with low 13C concentrations in asymptotic giant branch stars. The presence of such large 13C pockets with a variety of relatively low 13C concentrations seems to require multiple mixing processes in parent asymptotic giant branch stars of mainstream SiC grains.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in asymptotic giant branch stars
    The Astrophysical Journal, 2014
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in δ( 138 Ba/ 136 Ba) values are found, down to −400‰, which can only be modeled with a flatter 13 C profile within the 13 C pocket than is normally used. The dependence of δ( 138 Ba/ 136 Ba) predictions on the distribution of 13 C within the pocket in asymptotic giant branch (AGB) models allows us to probe the 13 C profile within the 13 C pocket and the pocket mass in AGB stars. In addition, we provide constraints on the 22 Ne(α, n) 25 Mg rate in the stellar temperature regime relevant to AGB stars, based on δ( 134 Ba/ 136 Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative δ( 134 Ba/ 136 Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process (i process), which is activated by the very late thermal pulse during the post-AGB phase and characterized by a neutron density much higher than the s process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two p-process isotopes, 130 Ba and 132 Ba, in single SiC grains. These isotopes are destroyed in the s process in AGB stars. By comparing their abundances with respect to that of 135 Ba, we conclude that there is no measurable decay of 135 Cs (t1/2 = 2.3 Ma) to 135 Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before 135 Cs decayed.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in agb stars
    arXiv: Solar and Stellar Astrophysics, 2014
    Co-Authors: Nan Liu, A M Davis, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham, Nicolas Dauphas, M Pignatari
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in $\delta$($^{138}$Ba/$^{136}$Ba) values are found, down to $-$400 permil, which can only be modeled with a flatter $^{13}$C profile within the $^{13}$C pocket than is normally used. The dependence of $\delta$($^{138}$Ba/$^{136}$Ba) predictions on the distribution of $^{13}$C within the pocket in AGB models allows us to probe the $^{13}$C profile within the $^{13}$C pocket and the pocket mass in asymptotic giant branch (AGB) stars. In addition, we provide constraints on the $^{22}$Ne$(\alpha,n)^{25}$Mg rate in the stellar temperature regime relevant to AGB stars, based on $\delta$($^{134}$Ba/$^{136}$Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative $\delta$($^{134}$Ba/$^{136}$Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process ($i$-process), which is activated by the Very Late Thermal Pulse (VLTP) during the post-AGB phase and characterized by a neutron density much higher than the $s$-process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two $p$-process isotopes, $^{130}$Ba and $^{132}$Ba, in single SiC grains. These isotopes are destroyed in the $s$-process in AGB stars. By comparing their abundances with respect to that of $^{135}$Ba, we conclude that there is no measurable decay of $^{135}$Cs ($t_{1/2}$= 2.3 Ma) to $^{135}$Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before $^{135}$Cs decayed.

A M Davis - One of the best experts on this subject based on the ideXlab platform.

  • correlated strontium and barium isotopic compositions of acid cleaned single mainstream Silicon Carbides from murchison
    The Astrophysical Journal, 2015
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, S Bisterzo, Frank Gyngard, F Kappeler, S Cristallo
    Abstract:

    We present strontium, barium, carbon, and Silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contamination. For the first time, by using correlated 88Sr/86Sr and 138Ba/136Ba ratios in mainstream SiC grains, we are able to resolve the effect of 13C concentration from that of 13C-pocket mass on s-process nucleosynthesis, which points toward the existence of large 13C pockets with low 13C concentrations in asymptotic giant branch stars. The presence of such large 13C pockets with a variety of relatively low 13C concentrations seems to require multiple mixing processes in parent asymptotic giant branch stars of mainstream SiC grains.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in asymptotic giant branch stars
    The Astrophysical Journal, 2014
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in δ( 138 Ba/ 136 Ba) values are found, down to −400‰, which can only be modeled with a flatter 13 C profile within the 13 C pocket than is normally used. The dependence of δ( 138 Ba/ 136 Ba) predictions on the distribution of 13 C within the pocket in asymptotic giant branch (AGB) models allows us to probe the 13 C profile within the 13 C pocket and the pocket mass in AGB stars. In addition, we provide constraints on the 22 Ne(α, n) 25 Mg rate in the stellar temperature regime relevant to AGB stars, based on δ( 134 Ba/ 136 Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative δ( 134 Ba/ 136 Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process (i process), which is activated by the very late thermal pulse during the post-AGB phase and characterized by a neutron density much higher than the s process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two p-process isotopes, 130 Ba and 132 Ba, in single SiC grains. These isotopes are destroyed in the s process in AGB stars. By comparing their abundances with respect to that of 135 Ba, we conclude that there is no measurable decay of 135 Cs (t1/2 = 2.3 Ma) to 135 Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before 135 Cs decayed.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in agb stars
    arXiv: Solar and Stellar Astrophysics, 2014
    Co-Authors: Nan Liu, A M Davis, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham, Nicolas Dauphas, M Pignatari
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in $\delta$($^{138}$Ba/$^{136}$Ba) values are found, down to $-$400 permil, which can only be modeled with a flatter $^{13}$C profile within the $^{13}$C pocket than is normally used. The dependence of $\delta$($^{138}$Ba/$^{136}$Ba) predictions on the distribution of $^{13}$C within the pocket in AGB models allows us to probe the $^{13}$C profile within the $^{13}$C pocket and the pocket mass in asymptotic giant branch (AGB) stars. In addition, we provide constraints on the $^{22}$Ne$(\alpha,n)^{25}$Mg rate in the stellar temperature regime relevant to AGB stars, based on $\delta$($^{134}$Ba/$^{136}$Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative $\delta$($^{134}$Ba/$^{136}$Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process ($i$-process), which is activated by the Very Late Thermal Pulse (VLTP) during the post-AGB phase and characterized by a neutron density much higher than the $s$-process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two $p$-process isotopes, $^{130}$Ba and $^{132}$Ba, in single SiC grains. These isotopes are destroyed in the $s$-process in AGB stars. By comparing their abundances with respect to that of $^{135}$Ba, we conclude that there is no measurable decay of $^{135}$Cs ($t_{1/2}$= 2.3 Ma) to $^{135}$Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before $^{135}$Cs decayed.

  • molybdenum isotopic composition of single Silicon Carbides from supernovae
    30th Lunar and Planetary Science Conference Houston TX (US) 03 15 1999--03 19 1999, 1999
    Co-Authors: S Amari, R N Clayton, A M Davis, R S Lewis, M J Pellin
    Abstract:

    Presolar Silicon carbide grains form in a variety of types of stars, including asymptotic giant branch red giant stars and supernovae. The dominant mechanisms of heavy element nucleosynthesis, the s-process and r-process, are thought to occur in AGB stars and supernovae, respectively. We have previously reported that mainstream SiC grains have strong enrichments in the s-process isotopes of Sr, Zr and Mo. We report here the first measurements of Mo isotopes in X-type SiC grains, which have previously been identified as having formed from supernova ejecta.

Frank Gyngard - One of the best experts on this subject based on the ideXlab platform.

  • correlated strontium and barium isotopic compositions of acid cleaned single mainstream Silicon Carbides from murchison
    The Astrophysical Journal, 2015
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, S Bisterzo, Frank Gyngard, F Kappeler, S Cristallo
    Abstract:

    We present strontium, barium, carbon, and Silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contamination. For the first time, by using correlated 88Sr/86Sr and 138Ba/136Ba ratios in mainstream SiC grains, we are able to resolve the effect of 13C concentration from that of 13C-pocket mass on s-process nucleosynthesis, which points toward the existence of large 13C pockets with low 13C concentrations in asymptotic giant branch stars. The presence of such large 13C pockets with a variety of relatively low 13C concentrations seems to require multiple mixing processes in parent asymptotic giant branch stars of mainstream SiC grains.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in asymptotic giant branch stars
    The Astrophysical Journal, 2014
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in δ( 138 Ba/ 136 Ba) values are found, down to −400‰, which can only be modeled with a flatter 13 C profile within the 13 C pocket than is normally used. The dependence of δ( 138 Ba/ 136 Ba) predictions on the distribution of 13 C within the pocket in asymptotic giant branch (AGB) models allows us to probe the 13 C profile within the 13 C pocket and the pocket mass in AGB stars. In addition, we provide constraints on the 22 Ne(α, n) 25 Mg rate in the stellar temperature regime relevant to AGB stars, based on δ( 134 Ba/ 136 Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative δ( 134 Ba/ 136 Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process (i process), which is activated by the very late thermal pulse during the post-AGB phase and characterized by a neutron density much higher than the s process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two p-process isotopes, 130 Ba and 132 Ba, in single SiC grains. These isotopes are destroyed in the s process in AGB stars. By comparing their abundances with respect to that of 135 Ba, we conclude that there is no measurable decay of 135 Cs (t1/2 = 2.3 Ma) to 135 Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before 135 Cs decayed.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in agb stars
    arXiv: Solar and Stellar Astrophysics, 2014
    Co-Authors: Nan Liu, A M Davis, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham, Nicolas Dauphas, M Pignatari
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in $\delta$($^{138}$Ba/$^{136}$Ba) values are found, down to $-$400 permil, which can only be modeled with a flatter $^{13}$C profile within the $^{13}$C pocket than is normally used. The dependence of $\delta$($^{138}$Ba/$^{136}$Ba) predictions on the distribution of $^{13}$C within the pocket in AGB models allows us to probe the $^{13}$C profile within the $^{13}$C pocket and the pocket mass in asymptotic giant branch (AGB) stars. In addition, we provide constraints on the $^{22}$Ne$(\alpha,n)^{25}$Mg rate in the stellar temperature regime relevant to AGB stars, based on $\delta$($^{134}$Ba/$^{136}$Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative $\delta$($^{134}$Ba/$^{136}$Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process ($i$-process), which is activated by the Very Late Thermal Pulse (VLTP) during the post-AGB phase and characterized by a neutron density much higher than the $s$-process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two $p$-process isotopes, $^{130}$Ba and $^{132}$Ba, in single SiC grains. These isotopes are destroyed in the $s$-process in AGB stars. By comparing their abundances with respect to that of $^{135}$Ba, we conclude that there is no measurable decay of $^{135}$Cs ($t_{1/2}$= 2.3 Ma) to $^{135}$Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before $^{135}$Cs decayed.

Michael R Savina - One of the best experts on this subject based on the ideXlab platform.

  • correlated strontium and barium isotopic compositions of acid cleaned single mainstream Silicon Carbides from murchison
    The Astrophysical Journal, 2015
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, S Bisterzo, Frank Gyngard, F Kappeler, S Cristallo
    Abstract:

    We present strontium, barium, carbon, and Silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contamination. For the first time, by using correlated 88Sr/86Sr and 138Ba/136Ba ratios in mainstream SiC grains, we are able to resolve the effect of 13C concentration from that of 13C-pocket mass on s-process nucleosynthesis, which points toward the existence of large 13C pockets with low 13C concentrations in asymptotic giant branch stars. The presence of such large 13C pockets with a variety of relatively low 13C concentrations seems to require multiple mixing processes in parent asymptotic giant branch stars of mainstream SiC grains.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in asymptotic giant branch stars
    The Astrophysical Journal, 2014
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in δ( 138 Ba/ 136 Ba) values are found, down to −400‰, which can only be modeled with a flatter 13 C profile within the 13 C pocket than is normally used. The dependence of δ( 138 Ba/ 136 Ba) predictions on the distribution of 13 C within the pocket in asymptotic giant branch (AGB) models allows us to probe the 13 C profile within the 13 C pocket and the pocket mass in AGB stars. In addition, we provide constraints on the 22 Ne(α, n) 25 Mg rate in the stellar temperature regime relevant to AGB stars, based on δ( 134 Ba/ 136 Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative δ( 134 Ba/ 136 Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process (i process), which is activated by the very late thermal pulse during the post-AGB phase and characterized by a neutron density much higher than the s process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two p-process isotopes, 130 Ba and 132 Ba, in single SiC grains. These isotopes are destroyed in the s process in AGB stars. By comparing their abundances with respect to that of 135 Ba, we conclude that there is no measurable decay of 135 Cs (t1/2 = 2.3 Ma) to 135 Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before 135 Cs decayed.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in agb stars
    arXiv: Solar and Stellar Astrophysics, 2014
    Co-Authors: Nan Liu, A M Davis, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham, Nicolas Dauphas, M Pignatari
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in $\delta$($^{138}$Ba/$^{136}$Ba) values are found, down to $-$400 permil, which can only be modeled with a flatter $^{13}$C profile within the $^{13}$C pocket than is normally used. The dependence of $\delta$($^{138}$Ba/$^{136}$Ba) predictions on the distribution of $^{13}$C within the pocket in AGB models allows us to probe the $^{13}$C profile within the $^{13}$C pocket and the pocket mass in asymptotic giant branch (AGB) stars. In addition, we provide constraints on the $^{22}$Ne$(\alpha,n)^{25}$Mg rate in the stellar temperature regime relevant to AGB stars, based on $\delta$($^{134}$Ba/$^{136}$Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative $\delta$($^{134}$Ba/$^{136}$Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process ($i$-process), which is activated by the Very Late Thermal Pulse (VLTP) during the post-AGB phase and characterized by a neutron density much higher than the $s$-process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two $p$-process isotopes, $^{130}$Ba and $^{132}$Ba, in single SiC grains. These isotopes are destroyed in the $s$-process in AGB stars. By comparing their abundances with respect to that of $^{135}$Ba, we conclude that there is no measurable decay of $^{135}$Cs ($t_{1/2}$= 2.3 Ma) to $^{135}$Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before $^{135}$Cs decayed.

R Gallino - One of the best experts on this subject based on the ideXlab platform.

  • correlated strontium and barium isotopic compositions of acid cleaned single mainstream Silicon Carbides from murchison
    The Astrophysical Journal, 2015
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, S Bisterzo, Frank Gyngard, F Kappeler, S Cristallo
    Abstract:

    We present strontium, barium, carbon, and Silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contamination. For the first time, by using correlated 88Sr/86Sr and 138Ba/136Ba ratios in mainstream SiC grains, we are able to resolve the effect of 13C concentration from that of 13C-pocket mass on s-process nucleosynthesis, which points toward the existence of large 13C pockets with low 13C concentrations in asymptotic giant branch stars. The presence of such large 13C pockets with a variety of relatively low 13C concentrations seems to require multiple mixing processes in parent asymptotic giant branch stars of mainstream SiC grains.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in asymptotic giant branch stars
    The Astrophysical Journal, 2014
    Co-Authors: A M Davis, Nan Liu, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in δ( 138 Ba/ 136 Ba) values are found, down to −400‰, which can only be modeled with a flatter 13 C profile within the 13 C pocket than is normally used. The dependence of δ( 138 Ba/ 136 Ba) predictions on the distribution of 13 C within the pocket in asymptotic giant branch (AGB) models allows us to probe the 13 C profile within the 13 C pocket and the pocket mass in AGB stars. In addition, we provide constraints on the 22 Ne(α, n) 25 Mg rate in the stellar temperature regime relevant to AGB stars, based on δ( 134 Ba/ 136 Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative δ( 134 Ba/ 136 Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process (i process), which is activated by the very late thermal pulse during the post-AGB phase and characterized by a neutron density much higher than the s process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two p-process isotopes, 130 Ba and 132 Ba, in single SiC grains. These isotopes are destroyed in the s process in AGB stars. By comparing their abundances with respect to that of 135 Ba, we conclude that there is no measurable decay of 135 Cs (t1/2 = 2.3 Ma) to 135 Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before 135 Cs decayed.

  • barium isotopic composition of mainstream Silicon Carbides from murchison constraints for s process nucleosynthesis in agb stars
    arXiv: Solar and Stellar Astrophysics, 2014
    Co-Authors: Nan Liu, A M Davis, Michael R Savina, R Gallino, Frank Gyngard, O Straniero, Michael J Pellin, David Willingham, Nicolas Dauphas, M Pignatari
    Abstract:

    We present barium, carbon, and Silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in $\delta$($^{138}$Ba/$^{136}$Ba) values are found, down to $-$400 permil, which can only be modeled with a flatter $^{13}$C profile within the $^{13}$C pocket than is normally used. The dependence of $\delta$($^{138}$Ba/$^{136}$Ba) predictions on the distribution of $^{13}$C within the pocket in AGB models allows us to probe the $^{13}$C profile within the $^{13}$C pocket and the pocket mass in asymptotic giant branch (AGB) stars. In addition, we provide constraints on the $^{22}$Ne$(\alpha,n)^{25}$Mg rate in the stellar temperature regime relevant to AGB stars, based on $\delta$($^{134}$Ba/$^{136}$Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative $\delta$($^{134}$Ba/$^{136}$Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process ($i$-process), which is activated by the Very Late Thermal Pulse (VLTP) during the post-AGB phase and characterized by a neutron density much higher than the $s$-process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two $p$-process isotopes, $^{130}$Ba and $^{132}$Ba, in single SiC grains. These isotopes are destroyed in the $s$-process in AGB stars. By comparing their abundances with respect to that of $^{135}$Ba, we conclude that there is no measurable decay of $^{135}$Cs ($t_{1/2}$= 2.3 Ma) to $^{135}$Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before $^{135}$Cs decayed.