Rana track annealing model 2007, based on an Arrhenius approach, is significantly modified, including new assumptions, fitting parameters, and analysis, to yield a new phenomenological model for annealing of fission tracks in apatite. Construction and optimization of the new six parameter model have been described in detail. The model shows a hybrid behavior. In Arrhenius plot, for higher temperatures (laboratory data included), iso-annealing lines are curved while, for low temperatures (geological time scale), iso-annealing lines become parallel straight lines. This is a new feature for any such model and has produced promising results. C-axis projected lengths from laboratory experiments on Durango apatite are employed to find model parameters. KTB borehole fission-track data are added to build the temperature function that modifies the original equation. Partial annealing zone (PAZ), closure temperature (\(T_{\mathrm{C}}\)) and total annealing temperature (\(T_{\mathrm{A}}\)) were calculated and compared to geological benchmarks. The predictions of the present model agreed well with low and high temperature benchmarks. PAZ, \(T_{\mathrm{C}}\) and \(T_{\mathrm{A}}\) predictions were also compared to the Fanning Curvilinear Arrhenius model predictions, resulting in good agreement. The present model is flexible enough to be applied to other fission-track systems, like zircon, muscovite and titanite.

对基于Arrhenius方法的Rana轨道退火模型2007进行了重大修改，包括新的假设，拟合参数和分析，以生成用于磷灰石中裂变轨道退火的新现象学模型。已经详细描述了新的六参数模型的构建和优化。该模型显示了混合行为。在Arrhenius图中，对于较高的温度（包括实验室数据），等温退火线是弯曲的，而对于低温（地质时标），等温退火线变为平行的直线。这是任何此类模型的新功能，并产生了可喜的结果。来自杜兰戈磷灰石的实验室实验的C轴投影长度用于查找模型参数。添加了KTB钻孔裂变径迹数据，以建立可修改原始方程式的温度函数。部分退火区（PAZ），关闭温度（计算\（T _ {\ mathrm {C}} \））和总退火温度（\（T _ {\ mathrm {A}} \））并将其与地质基准进行比较。本模型的预测与低温基准和高温基准非常吻合。也将PAZ，\（T _ {\ mathrm {C}} \）和\（T _ {\ mathrm {A}} \）的预测与Fanning曲线阿伦尼乌斯模型的预测进行了比较，从而得出了很好的一致性。本模型具有足够的灵活性，可以应用于其他裂变径迹系统，例如锆石，白云母和钛矿。