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大家好我是 Shelly Kelly

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继续我们铂样品的数据处理

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之前的 Athena 文件

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也做了第一壳层拟合 

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定了 S02 值

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加载我们之前处理的文件到 Artemis 中

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打开 Athena 文件

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有一系列数据

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选择任一数据可以看到谱图预览

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加载选中数据

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现在看到的是被加载的数据窗口

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下一步需要 Feff 计算

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找铂的 cif 文件并加载

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这是基于铂金属晶体学数据

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这里是晶格常数和晶胞中的原子坐标

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中心原子为铂

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L3 边

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点击 Run Atoms 得到一系列簇计算

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有铂原子在中心

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ipot = 0 代表了中心原子

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作为吸收原子

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剩下的是散射原子

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比如第一层的 2.77 Å 

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看起来可以，点击 Run Feff

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出现路径列表

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路径只计算到 5 Å 

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所以需要改动输入参数

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让计算范围扩大到 6 Å 以上

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回到 Atom 页面

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改变簇尺寸到 6.5

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最长路径改为 6.5 Å

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再跑一次

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现在列表更长了，选择更多了

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现在来转移我们所需的路径

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可以通过高亮所需的路径

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选这些

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按住 Shift 键不放鼠标左键旋去

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都选上

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直接拖进去

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比较下路径和实验数据之间的差距

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我在面对一些已知晶体结构样品的数据时会这么做

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可以很直观地判断是否是真的

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来看下会怎么样

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也许这不是最好的数据模拟策略

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但可以告诉你这个 Feff 文件是否适合这个实验数据

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现在有了一长串路径

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需要设置参数

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设 S02 为 amp

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ΔE 设为 ezero

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ΔR 设为 alpha * reff

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reff 在这里特指的是 Feff 计算得到的距离

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也就是上面这里显示的距离

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比如这里是 2.77 的距离

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鉴于这是个立方晶格

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可以用 alpha 来描述晶体中的膨胀收缩效应

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很有用

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还要用 Debye 模型在 σ2

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基于 Debye 温度

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测量温度是 300 K

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Debye 温度由拟合给出

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把参数放到猜测窗口中

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鼠标右键点击参数

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设为 guess

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从控制窗口那里打开猜测窗口

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看下参数怎么设置的

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踢掉温度设置

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因为已经在表达式中设置好了

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也不会变

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改成 set 常量

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知道 S02 是 0.81

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ezero 是 0

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alpha 为 0

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点击 Fit 跑一个并不是拟合的拟合

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仅仅是加在一起

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Artemis 报错拟合范围和路径距离不一致

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所以把 Rmax 改成 6

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再来一次

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这是数据和拟合的对比

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R 的范围可以到 10

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这样更方便看

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看起来第一壳层的强度比较接近

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但是更高壳层的强度就没这么高了

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我觉得是因为我没有设置剩下来路径的参数

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第一个路径有 Debye 温度的设置

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但从第二个开始我就没有设置

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我们可以勾选上所有路径

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鼠标右键点击 S02

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复制到所有勾选的路径中去

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其他参数也是

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再跑次拟合

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看下会不会好些

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可以看到

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数据和拟合吻合得很好

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蓝线是实验，红线是拟合

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基本上拟合中的震荡跟实验步调接近

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这确实是铂片

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检查下参数

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ezero 和 alpha 是唯二变量

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改成 guess

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thetad 作为 Debye 温度也应是变量

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点击 Fit

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看下拟合会不会提升

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实际上确实很好

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很棒

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仅用了三个变量就完成了拟合

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缩小下这个窗口（也许不行）

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点击 Use best fit 使用最优解

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最优解变成了初始猜测变量

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再进一步看

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看起来第一壳层的强度有点不太对

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这里的信号又有点太强了

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这有可能是由于只有一个 Debye 温度变量导致的

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去 log 文件中查看 Debye 温度和其他参数关联性

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跟 σ2

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在这里可以看到

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第一壳层的 σ2 是 0.005

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剩下壳层 σ2 逐渐增大

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发现远距离 (> 6 Å) 的路径 σ2 值只有 0.006

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这可能太小了

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Debye 模型这种同等程度参数限制

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似乎看起来对于前两个铂原子比较有用

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或者说那些距离相近的原子

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2.77 - 5 Å

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但到了这里这个拟合限制太多数值太小

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导致理论信号比实验信号要高

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再看下图

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在 R 值高的地方信号过强

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那么应对方案

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改变 Debye 温度

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这样对于不同路径的限制程度会变得不一样

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包括距离较远的路径

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现在来寻找合适的分水岭

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来看下是不是这里

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第三层铂在 4.8 Å

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点击蓝色按键把它加到画图列表中

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看到这条被加进去后

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点击 R 键

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看到 Pt3 的位置

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这里确实是产生过强信号的地方

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把这第三层 Pt 的 Debye 温度改成 thetad3

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取消勾选所有

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所有在第三层的路径也是最远的

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都设成一样 thetad3 的 Debye 温度 

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这使得内层和外层的原子在拟合中的关联性降低

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在改动原子距离上也是

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我觉得这个操作比较有用

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复制 σ2 设定到勾选路径

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第四层的路径也是一样

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第五层也是

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设为一样的 thetad4

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复制到勾选路径

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接下来就是需要猜测第三四层的参数

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回到猜测窗口

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知道 Debye 温度应该在 240 K 左右

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试下

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现在吻合得很好了

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到历史窗口

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看下第四次拟合结果

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Reduced chi-square 大约 2000

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第三次是大约 3700

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仅仅是改动了一些参数设置降低了一倍

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所以我觉得多使用两个参数可以更好地描述这套数据

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虽然 Debye 温度相差不大

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但各自独立

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不确定值大约 6 K

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温度是 230 K

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通过更多的变量来改善拟合结果

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来看下不同空间的谱图

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这是傅里叶变换强度

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打开画图窗口

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看下 k 空间

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拟合得挺好的

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kmax 还可以再大点

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k 二次方权重

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窗函数代表我们用于拟合的数据范围

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这里

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即使有一部分数据没有用于拟合

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仍然比较接近

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看到这里数据一下子开始

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这是因为我们的能量偏移值是正值

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ezero 大约是 +7 eV 

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这已经接近我心中的上限了

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如果超过了这个值

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我会回到 Athena 重新调整 E0

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但现在还好

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你可以看到拟合范围以外的数据吻合得不错

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到反傅里叶变换 q 空间

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看起来很棒

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在 R 空间中现在是 k 二次方权重

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k 一次方

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k 三次方

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看起来可以

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你也许会说这个拟合看起来太臃肿了

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有太多的路径了

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我们只是走运遇到了立方晶胞样品不需要太多参数

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但如果我是拟合纳米粒子呢

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我们需要这么多路径吗

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那么为了检验这个

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我们来测试哪些路径值得加入到拟合中去

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或是不值得

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我个人喜欢这么做

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大致比较路径之间的强度

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我来操作下是怎么一回事

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第一条路径的强度是最强的

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这一条大约是（第一条的） 30%

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是对这条路径重要程度的预计

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可以把这两条路径都画出来

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加进去后用 k 二次方权重展示

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可以看到第一条高度大约在 2

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这是另一条路径的高度

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Pt-Pt4 路径

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这看起来强度很低

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顶点在 2 左右

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1 这里是 50%

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0.5 大约是 20%

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所以这个比 20% 还要低

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但也是估计

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还可以看下其他重要性更低的路径

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比如找到了这个

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只有 5

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把它加到画图列表中

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在 R 空间

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看起来没想象中那么小

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等下，确实很小

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哦这个是我们之前那条

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基本上看不到

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平线一条

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我们可以错开每条路径展示出来

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每个之间差了 0.3

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点击 R

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现在就可以看到了

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我更倾向于到实部图像中看

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可以看到每个路径的贡献

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这条几乎没有强度

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所以有把握把它剔除掉

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我喜欢这种拿掉路径的思路

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而不是添加路径

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因为如果拟合出现错误

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不知道是参数有问题还是路径数量不够

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我这么做就先知道哪些是合理的

241
00:17:45,450 --> 00:17:49,650
然后再一条一条拿掉不需要的

242
00:17:50,850 --> 00:17:53,050
回到数据面板

243
00:17:53,050 --> 00:17:57,900
我们认为这条可以不要了

244
00:17:57,900 --> 00:18:00,925
取消勾选 include path

245
00:18:00,925 --> 00:18:03,725
再看下其他路径

246
00:18:04,179 --> 00:18:06,900
这是另外一个强度 7% 的

247
00:18:08,575 --> 00:18:10,575
看下

248
00:18:11,347 --> 00:18:13,347
放到画图列表

249
00:18:13,347 --> 00:18:18,400
再次证明这条路径也不需要

250
00:18:18,643 --> 00:18:21,825
取消勾选

251
00:18:25,950 --> 00:18:31,450
来看下这条 15% 的路径

252
00:18:32,403 --> 00:18:37,725
是否有足够明显的贡献

253
00:18:38,975 --> 00:18:40,393
确实

254
00:18:40,393 --> 00:18:45,275
这条路径我们不想拿掉

255
00:18:45,275 --> 00:18:47,475
保留

256
00:18:47,810 --> 00:18:49,810
这是 一条 91% 的

257
00:18:49,810 --> 00:18:52,775
这是向前多重散射路径

258
00:18:52,775 --> 00:18:55,775
肯定要保留的

259
00:18:56,150 --> 00:18:58,500
这是 10% 的路径

260
00:18:59,275 --> 00:19:01,275
画个图

261
00:19:01,275 --> 00:19:04,825
看下 R 空间

262
00:19:05,700 --> 00:19:11,350
踢掉

263
00:19:11,800 --> 00:19:15,450
这个是 3% 的

264
00:19:15,450 --> 00:19:17,850
也踢掉

265
00:19:17,850 --> 00:19:18,925
这个是 5%

266
00:19:20,075 --> 00:19:22,075
11% 的

267
00:19:22,075 --> 00:19:24,075
我不太确定

268
00:19:24,075 --> 00:19:26,075
确认下

269
00:19:26,075 --> 00:19:30,225
确实不需要加进来

270
00:19:34,710 --> 00:19:38,750
3% 的，不需要

271
00:19:38,998 --> 00:19:41,350
这个 3% 的也不需要

272
00:19:41,350 --> 00:19:44,700
这个 28% ，保留

273
00:19:44,700 --> 00:19:46,700
这个 4% 

274
00:19:46,975 --> 00:19:48,125
10%

275
00:19:48,125 --> 00:19:49,275
11%

276
00:19:49,275 --> 00:19:55,100
似乎超过 6 Å 的都不需要

277
00:19:55,700 --> 00:19:57,700
看下

278
00:19:58,550 --> 00:20:02,825
额好像还是保留下这条吧

279
00:20:02,825 --> 00:20:07,700
还想扩大下拟合范围

280
00:20:07,700 --> 00:20:11,025
把这里信号框进去

281
00:20:11,025 --> 00:20:14,975
改成 6.3 Å？ 

282
00:20:15,375 --> 00:20:18,755
保留这个

283
00:20:19,379 --> 00:20:21,379
看下这个

284
00:20:22,387 --> 00:20:25,350
嗯还是保留这两个

285
00:20:25,350 --> 00:20:28,150
我们移除了一部分路径

286
00:20:28,425 --> 00:20:31,850
看下前面几条

287
00:20:31,850 --> 00:20:33,475
这个 16%

288
00:20:33,475 --> 00:20:36,350
这个 3% 不太行

289
00:20:36,350 --> 00:20:40,325
清空下画图列表

290
00:20:40,325 --> 00:20:44,450
把需要的数据再加回去

291
00:20:44,450 --> 00:20:46,200
在 R 空间中

292
00:20:46,200 --> 00:20:52,625
这个正好在我保留和移除的临界线上

293
00:20:53,175 --> 00:20:56,575
先移除看下有什么影响

294
00:20:56,575 --> 00:20:58,252
这个 6 %

295
00:20:58,252 --> 00:21:00,252
看下

296
00:21:00,500 --> 00:21:03,200
也许？

297
00:21:03,750 --> 00:21:05,750
先移除掉

298
00:21:06,877 --> 00:21:11,025
这个 60%  （留下）

299
00:21:11,400 --> 00:21:15,450
10% 的看下

300
00:21:17,817 --> 00:21:20,300
嗯不需要

301
00:21:21,225 --> 00:21:25,525
32% 的这个需要 留下

302
00:21:25,525 --> 00:21:27,350
20% 的（留下）

303
00:21:27,350 --> 00:21:29,350
8% 的看下

304
00:21:31,393 --> 00:21:34,250
需要留下

305
00:21:34,250 --> 00:21:37,409
对我们有用

306
00:21:38,369 --> 00:21:41,700
85%, 15% （留下）

307
00:21:42,050 --> 00:21:43,800
基本上过了一遍

308
00:21:43,800 --> 00:21:51,125
我们最终移除了 12条路径

309
00:21:51,125 --> 00:21:52,425
很好

310
00:21:52,425 --> 00:21:54,425
再跑次拟合

311
00:21:54,425 --> 00:21:56,425
看下有没有影响

312
00:21:57,555 --> 00:22:00,825
点击 Rmr

313
00:22:00,825 --> 00:22:02,625
对比下

314
00:22:02,625 --> 00:22:04,625
点击 Fit

315
00:22:07,150 --> 00:22:10,045
看起来基本没变

316
00:22:10,430 --> 00:22:13,550
到历史窗口

317
00:22:13,550 --> 00:22:17,075
之前 reduced chi-square 是 2000 左右

318
00:22:17,075 --> 00:22:22,175
现在这个到了 2800

319
00:22:22,175 --> 00:22:25,450
这差距还挺明显的

320
00:22:25,450 --> 00:22:32,775
感觉我移除的路径太多了

321
00:22:32,775 --> 00:22:39,900
大概就是那些我犹豫要不要移除的路径

322
00:22:41,650 --> 00:22:43,650
再试试

323
00:22:46,225 --> 00:22:50,250
再留意下 reduced chi-square是否接近

324
00:22:50,650 --> 00:22:54,550
有掉到 2600

325
00:22:54,875 --> 00:22:59,475
但没有回到最一开始的数值

326
00:22:59,875 --> 00:23:03,442
我到底还需要哪些路径

327
00:23:13,150 --> 00:23:19,300
把大约 10% 的加回来

328
00:23:19,300 --> 00:23:22,375
这个 10% 也加回来

329
00:23:22,375 --> 00:23:24,375
再试试

330
00:23:25,331 --> 00:23:31,175
看下 reduced chi-square 能不能下到 2000

331
00:23:33,075 --> 00:23:36,325
在历史窗口中查看

332
00:23:37,171 --> 00:23:41,325
2300

333
00:23:41,325 --> 00:23:44,100
那先就这样吧

334
00:23:44,100 --> 00:23:46,100
移除几条路径后

335
00:23:46,350 --> 00:23:50,406
reduced chi-square 值增加了大约 10%

336
00:23:53,425 --> 00:23:56,225
拟合结果很好

337
00:23:56,225 --> 00:24:01,300
最终移除了 7 条路径

338
00:24:04,000 --> 00:24:09,250
这就是如何拟合铂的数据到 6 Å 范围

339
00:24:10,011 --> 00:24:16,225
下一节是讲解如何拟合纳米粒子

340
00:24:16,225 --> 00:24:18,225
谢谢