粉末衍射谱图分解的模拟退火法

Simulated annealing method for powder diffraction pattern decomposition

将模拟退火法应用于中子和x射线粉末衍射谱图分解研究中 .该方法有两个主要优点 :一是解谱结果不依赖于峰参数初始值的选取 ,可以任意给定峰参数初始值而不影响收敛性 ,因而能克服传统最小二乘拟合法在拟合多峰严重重叠的复杂谱图时遇到的初始解的选取困难 ;二是具有寻找全局最优解的能力 ,可有效解决谱图分解在数学上的多解性问题 ,这对于因多峰重叠而可能存在多个局部最优解的谱图分解很有益处 .详细描述了方法的计算步骤 ,讨论了有关参数设置 ,并通过模拟谱和实际谱例子对模拟退火法与传统最小二乘拟合法进行了比较 ,阐明了前者在处理复杂谱图时的独特优越性 .原则上该方法也可应用到与粉末衍射谱类似能用峰形函数描述的其他实验谱的拟合研究中 .

Simulated annealing algorithm was applied in the decomposition of neutron and x-ray powder diffraction pattern. The method described in this paper has two main advantages: first, the pattern decomposition results do not depend on the starting peak parameters, thus the difficulty in the choice of initial solutions, which occurs in fitting a complex pattern composed of severely overlapped peaks by a conventional least-squares profile fitting method, is overcome; secondly, it has the ability of searching for global other than local optimal solutions, thus can effectively resolve the multi-solution problem mathematically, and this advantage is the most useful when decomposing complex patterns with several local optimal solutions. The computing step is described in detail, the setting of relative parameters is discussed, and the simulated annealing method is compared with a conventional least-squares profile fitting method through both simulated pattern and actual pattern to demonstrate its unique advantage in the decomposition, of, complex pattern. In principle, the method can also be applied in other kinds of spectra which can be described by profile shape function.