Description Usage Arguments Note Author(s) References Examples

"dluskora1" is a useful function to simulate diffusion-limited REE uptake by a growing eclogite garnet. It returns plots of theoretical REE profiles of a given garnet and its growth time according to various parameters which you can set, such as REE diffusion coefficients around the garnet, its temperature path and the garnet's growth process.

1 | ```
dluskora1(fac1, Q, syR, c_ave, D_0, R, T_1, T_2, K_d, Mr, Mt, fg, ft, garsize)
``` |

`fac1` |
This is a "diffusion length" and equal to D_0/A [cm]. A is the garnet growth coefficient (r = A t^(fg)). The meanings of D_0 and fg are shown below. |

`Q` |
Activation energy of REE diffusion around the garnet [J/mol] |

`syR` |
The size of the system concluding only a big garnet [cm] |

`c_ave` |
The initial concentration of REE on the system [ppm] |

`D_0` |
A pre-exponential factor of REE diffusion around the garnet [cm^2/year] |

`R` |
The universal gas constant [m^2 kg s^(-2) K^(-1) mol^(-1)] |

`T_1, T_2` |
This function can simulate a situation where the temperature around the system increased and you can set the initial and final temperature. T_1 is the initial temperature [degree Celsius] and T_2 is the final temperature [degree Celsius]. |

`K_d` |
partition coefficient > 1 (REE concentration of garnet over REE concentration of the matrix) |

`Mr, Mt` |
They are the numbers of spatial(radial) and time meshes respectively. |

`fg` |
This is an exponent of the garnet's growth law. If you set fg as 1, the garnet will grow with the linear growth rate law: r = A t. |

`ft` |
This is an exponent of the temperature-increase law. If you set ft as 1, the temperature will increase with the linier increase rate law: T = B t. |

`garsize` |
The final size of the garnet [cm] |

>K_d and A do not depend on temperature in this function. Temperature increase affects only the REE diffusion coefficient around the garnet.

>Diffusion in the garnet is ignored.

>This program is based on a Crank-Nicholson scheme. If you set too large Mt, the result would not be appropriate.

>This function returns "mass_gain_percent" with the REE profile plot. Please check whether its absolute value is very small(~e-4). Your result is not appropriate when the value is too big.

Ryo Fukushima

Crank (1975) The mathematics of diffusion. Oxford University Press, p414.

Skora et al. (2006) Diffusion-limited REE uptake by eclogite garnets and its consequences for Lu-Hf and Sm-Nd geochronology. Contrib. Mineral Petrol., 152:703-720.

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