Quantitative cooling histories from stranded diffusion profiles
Quantitative cooling histories from stranded diffusion profiles
复制标题
来自滞留扩散剖面的定量冷却历史
DOI：
10.1007/s00410-015-1153-4
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发表时间：
2015
影响因子：
3.5
通讯作者：
D. Cherniak
中科院分区：
文献类型：
--
作者：
E. Watson;D. Cherniak
地质材料中的搁浅元素或同位素扩散剖面有可能揭示主体样品的热历史信息。在高温下建立浓缩步骤的特定情况下，冷却过程中扩散弛豫的程度取决于冷却路径的细节和感兴趣物种的阿伦尼乌斯扩散定律：原则上，如果扩散定律已知，则样品中的测量轮廓可以提供有关冷却路径性质的定量信息。结合数学和数值模拟，我们得出了一个简单的关系式，描述了轮廓松弛程度（通过扩散轮廓的斜率 S0 来衡量）与系统的初始温度 (Ti) 和冷却速率 ($$\dot{T}$$T˙) 以及扩散的活化能 (Ea) 和指前因子 (D0) 的关系： $$\log S_{0} = 2.504 - \frac{1}{2}\log D_{0} - \log T_{\text{i}} + \frac{1}{2}\log E_{\text{a}} + \frac{1}{2}\log \dot{T} + \left( {26.11\frac{{E_{\text{a}} }}{{T_{\text{i}} }}} \right)$$logS0=2.504-12logD0-logTi+12logEa+12logT˙+26.11EaTi初始温度Ti的单位为K，$$\dot{T}$$T˙的单位为°/s，D0的单位为m2/s，Ea的单位为kJ/mol。感兴趣的轮廓的斜率可以在相互扩散轮廓的中点或晶体边缘处估计。在前一种情况下，浓度被标准化为上限 (=100) 和下限 (=0) 初始浓度平台之间的 100 差异。对于晶体边缘处的分布，归一化范围为 0 到 50。上面的方程同样适用于线性和指数冷却路径，因为对于给定的线性冷却路径和以相同初始冷却速率为特征的指数冷却路径，由 S0 表示的松弛程度基本上相同。从抛物线 T-t“圆顶”顶部进行冷却会导致更广泛的轮廓松弛；如果将前导常数 2.504 更改为 2.165，上面的方程也可以很好地描述这一点。如果绞合轮廓的 S0 已在实验室中表征，并且如果扩散剂的阿伦尼乌斯定律已知，则可以针对其中一个冷却路径参数（Ti 或 $$\dot{T}$$T˙）唯一求解上述方程，前提是另一个参数（通常是 Ti）受到相平衡或样品的地质环境的约束。或者，如果样品表现出具有不同 Ea 和 D0 值的两种扩散剂的绞合分布，则可以针对初始温度和冷却速率同时求解上述方程的两个版本。上面的方程可以用于估计 T-t 历史以外的目的：例如，评估观察到的浓度分布是否确实是扩散的结果，还是生长过程中相组成变化的结果。我们的方法不仅提高了交叉检查多个基于实验室的扩散定律的可能性，而且还提高了估计未表征扩散剂的阿伦尼乌斯参数的可能性。
Stranded elemental or isotopic diffusion profiles in geological materials have the potential to reveal information on the thermal history of the host sample. In the specific case of a concentration step that is established at high temperature, the extent of diffusive relaxation during cooling depends on the details of the cooling path and the Arrhenius diffusion law of the species of interest: In principle, a measured profile in a sample can provide quantitative information on the nature of the cooling path if the diffusion law is known. Using a combination of mathematics and numerical simulations, we derive a simple relationship describing the extent of profile relaxation (as gauged by the slope S0 of a diffusion profile) as a function of the initial temperature (Ti) and cooling rate ($$\dot{T}$$T˙) of the system and the activation energy (Ea) and pre-exponential factor (D0) for diffusion: $$\log S_{0} = 2.504 - \frac{1}{2}\log D_{0} - \log T_{\text{i}} + \frac{1}{2}\log E_{\text{a}} + \frac{1}{2}\log \dot{T} + \left( {26.11\frac{{E_{\text{a}} }}{{T_{\text{i}} }}} \right)$$logS0=2.504-12logD0-logTi+12logEa+12logT˙+26.11EaTiThe initial temperature Ti is expressed in K, $$\dot{T}$$T˙ is in °/s, D0 is in m2/s, and Ea is in kJ/mol. The slope of the profile of interest can be estimated either at the midpoint of an interdiffusion profile or at a crystal margin. In the former case, concentrations are normalized to a difference of 100 between the upper (=100) and lower (=0) initial concentration plateaus. For profiles at crystal margins, the normalization range is 0 to 50. The equation above applies equally well to linear and exponential cooling paths because the extent of relaxation indicated by S0 is essentially the same for a given linear cooling path and an exponential one characterized by the same initial cooling rate. Cooling from the top of parabolic T–t “dome” results in more extensive profile relaxation; this is also well described by the above equation if the leading constant 2.504 is changed to 2.165. If S0 of a stranded profile has been characterized in the laboratory, and if the Arrhenius law of the diffusant is known, the above equation can be solved uniquely for one of the cooling path parameters (Ti or $$\dot{T}$$T˙) if the other—which will usually be Ti—is constrained by phase equilibria or the geological context of the sample. Alternatively, if a sample exhibits stranded profiles for two diffusants having different Ea and D0 values, two versions of the above equation can be solved simultaneously for both the initial temperature and the cooling rate. The equation above can be implemented for purposes other than estimating T–t histories: e.g., assessing whether an observed concentration profile is truly the result of diffusion or a consequence of changing phase composition during growth. Our approach also raises the possibility not only of cross-checking multiple laboratory-based diffusion laws but also of estimating Arrhenius parameters for uncharacterized diffusants.