1 00:00:00,975 --> 00:00:02,925 大家好我是 Shelly Kelly 2 00:00:02,925 --> 00:00:06,925 欢迎来到第二节 3 00:00:06,925 --> 00:00:11,450 接下来是拟合铜片的第二壳层 4 00:00:11,450 --> 00:00:12,875 也就是这里 5 00:00:12,875 --> 00:00:16,400 上一节是第一壳层拟合 6 00:00:17,650 --> 00:00:23,375 现在我们要加载新的路径拟合第二壳层 7 00:00:24,075 --> 00:00:26,075 首先 8 00:00:26,075 --> 00:00:31,000 回到 Feff 窗口 9 00:00:31,000 --> 00:00:35,525 观察有哪些散射路径可能出现在第二壳层 10 00:00:36,175 --> 00:00:38,175 可以看到 11 00:00:38,175 --> 00:00:43,750 下一步要考虑是在 3.5 Å 12 00:00:44,075 --> 00:00:51,375 以及图中所示的距离偏移了大约 0.5 Â 13 00:00:51,375 --> 00:00:56,675 我们可以调整 0.5 Å 或更少 14 00:00:57,100 --> 00:01:05,150 可以看到这一个峰在 2.27 Å 15 00:01:05,150 --> 00:01:09,225 但第一条路径的距离是 2.553 Å 16 00:01:09,225 --> 00:01:10,250 所以这里是有偏移的 17 00:01:10,725 --> 00:01:15,175 所以我们需要考虑这条路径 18 00:01:15,579 --> 00:01:18,750 然后搞清楚它跟图里面的峰有什么关系 19 00:01:19,925 --> 00:01:23,225 打开数据窗口 20 00:01:23,575 --> 00:01:25,499 放到左手边 21 00:01:25,499 --> 00:01:28,325 Feff 窗口放右手边 22 00:01:28,325 --> 00:01:31,550 把第二条路径拖进到数据窗口中 23 00:01:32,664 --> 00:01:35,375 直接拖过去 24 00:01:36,075 --> 00:01:38,400 这条距离 3.8 Å 25 00:01:39,325 --> 00:01:42,701 这条在 4.3 Å 26 00:01:42,701 --> 00:01:45,700 这条也在大约 4.3 Å 27 00:01:46,450 --> 00:01:49,700 这些路径我们先考虑着 28 00:01:49,700 --> 00:01:53,925 来看下它们在 R 空间的什么地方 29 00:01:56,100 --> 00:01:59,425 我们可以 30 00:02:01,525 --> 00:02:06,075 回到猜测窗口 31 00:02:06,075 --> 00:02:10,475 不用设置任何参数,暂时姑且为 0 32 00:02:10,850 --> 00:02:12,850 是拟合的开始 33 00:02:13,616 --> 00:02:18,125 到猜测窗口中把变量全设为常量 34 00:02:20,100 --> 00:02:22,100 这样路径就不会参与拟合 35 00:02:22,100 --> 00:02:24,100 只是加和在一起 36 00:02:24,100 --> 00:02:27,050 也要改变拟合的范围 37 00:02:27,165 --> 00:02:34,425 上限从 3 Å 延长到 3.8 Å 38 00:02:34,875 --> 00:02:36,875 点击 Fit 39 00:02:36,875 --> 00:02:38,875 (虽然只是在加和) 40 00:02:38,875 --> 00:02:44,925 可以看到加和的信号跟实验数据所在的位置接近 41 00:02:44,925 --> 00:02:51,575 以及形状也跟第二壳层的信号一致 42 00:02:52,702 --> 00:02:56,025 去到画图窗口 43 00:02:56,025 --> 00:02:58,875 画出每个路径的贡献 44 00:02:59,600 --> 00:03:05,000 也就是展示出这个列表里面所有的数据 45 00:03:05,300 --> 00:03:11,225 你可以点击每个路径中这个蓝色按钮来画图 46 00:03:11,225 --> 00:03:15,100 点了之后,路径就会出现在列表中 47 00:03:15,825 --> 00:03:22,475 或者勾选上 plot after fit 48 00:03:22,475 --> 00:03:27,200 路径就会在拟合之后自动出现 49 00:03:27,775 --> 00:03:32,100 那就把它们都选中并勾选上 50 00:03:32,100 --> 00:03:35,250 这样下次拟合它们就自动出现 51 00:03:36,475 --> 00:03:40,125 这个列表每次拟合后都会重置 52 00:03:40,125 --> 00:03:43,550 你也可以选择不让列表重置 53 00:03:43,550 --> 00:03:45,275 勾选上 Freeze 就行 54 00:03:45,275 --> 00:03:48,875 或者是点击 Clear 清除掉 55 00:03:49,175 --> 00:03:51,300 当展示出所有路径 56 00:03:51,300 --> 00:03:56,150 (为什么图消失了……回来了……) 57 00:03:56,725 --> 00:04:02,543 你可以把数据和路径都在 R 空间中展示 58 00:04:02,543 --> 00:04:06,325 但我更想看实部空间的谱图 59 00:04:06,325 --> 00:04:09,450 所以我暂时会取消勾选 plot window 60 00:04:09,750 --> 00:04:14,975 选择画图窗口中的Real 跳转到实部图像 61 00:04:14,975 --> 00:04:17,925 图的展现形式改为堆叠 62 00:04:17,925 --> 00:04:20,850 到 stack 页面 63 00:04:20,850 --> 00:04:25,675 让每个图向下移动 0.5 64 00:04:25,675 --> 00:04:27,925 点击 R 键 65 00:04:27,925 --> 00:04:33,000 这样每个图相互之间都有点错位 66 00:04:33,000 --> 00:04:38,150 这个偏移值设成 1 可能更好点 67 00:04:39,075 --> 00:04:44,600 可以看到第二壳层的主要贡献来自于第二条路径 68 00:04:44,875 --> 00:04:47,150 也就是紫线 69 00:04:48,025 --> 00:04:51,525 你也可以看到多重散射路径 70 00:04:51,525 --> 00:04:55,850 比如这里的铜三角多重散射路径 71 00:04:55,850 --> 00:04:58,625 其信号也出现在这个区间 72 00:04:58,875 --> 00:05:03,375 棕线代表的多重散射强度很低 73 00:05:03,375 --> 00:05:05,375 我们可以忽略它 74 00:05:06,050 --> 00:05:11,075 这个多重散射路径似乎有所影响 75 00:05:11,075 --> 00:05:15,500 但更多的是在 R 更高的区间 76 00:05:15,825 --> 00:05:18,750 先暂时保留 77 00:05:18,750 --> 00:05:20,750 移除掉贡献忽略不计的 78 00:05:21,600 --> 00:05:25,600 要这么做先回到的数据窗口 79 00:05:25,875 --> 00:05:33,497 告诉 Artemis 不要考虑贡献小的路径 80 00:05:33,975 --> 00:05:35,975 保留其他的路径 81 00:05:37,000 --> 00:05:39,716 以及设置对应的参数 82 00:05:39,716 --> 00:05:45,775 最简单的是回到第一条已经设置好的路径 83 00:05:47,221 --> 00:05:50,869 勾选上剩下的路径 84 00:05:50,869 --> 00:05:55,675 右键点击参数 比如 S02 85 00:05:56,050 --> 00:06:00,050 把这个参数复制到剩下的路径 86 00:06:00,375 --> 00:06:04,625 这样剩下的路径 S02 都有 amp 了 87 00:06:05,975 --> 00:06:09,000 同理可用于 ΔE 88 00:06:09,000 --> 00:06:12,000 扩展到所有路径中去 89 00:06:12,375 --> 00:06:14,375 还有 ΔR 90 00:06:14,375 --> 00:06:19,675 但是不同的路径不应该有一样的 ΔR 91 00:06:19,675 --> 00:06:22,825 但铜结构为立方晶体 92 00:06:22,825 --> 00:06:26,775 我们可以考虑晶格的膨胀/收缩 93 00:06:27,300 --> 00:06:31,275 以数学方式表达 alpha 94 00:06:31,275 --> 00:06:34,525 代表着膨胀收缩系数 95 00:06:34,525 --> 00:06:36,025 乘以参考距离 96 00:06:36,025 --> 00:06:39,575 reff 是个特殊参数 97 00:06:39,575 --> 00:06:45,400 这可以直接告诉 Artemis 使用路径中的距离 98 00:06:45,400 --> 00:06:48,075 也就是 2.553 Å 99 00:06:48,075 --> 00:06:51,800 把 alpha 加到猜测窗口中 100 00:06:52,150 --> 00:06:54,150 σ2 101 00:06:54,975 --> 00:06:58,850 我们可以让不同路径有不同的 σ2 102 00:06:58,850 --> 00:07:01,300 或者使用 Debye-Einstein 模型 103 00:07:01,550 --> 00:07:04,725 这里使用 Debye 模型 104 00:07:04,725 --> 00:07:06,725 这里输入 debye 105 00:07:06,725 --> 00:07:10,300 温度是 10 K 106 00:07:10,800 --> 00:07:13,950 thetad 是变量 107 00:07:13,950 --> 00:07:18,175 把这个设置复制到剩下的路径中去 108 00:07:18,525 --> 00:07:20,525 现在来看下 109 00:07:22,300 --> 00:07:27,900 我还没复制 alpha * reff 110 00:07:27,900 --> 00:07:30,700 得先把这个做了来 111 00:07:31,600 --> 00:07:38,350 确认每个路径都设置合理 112 00:07:38,350 --> 00:07:40,926 回到猜测窗口 113 00:07:41,750 --> 00:07:47,175 因为在路径中已经定义了 temp (10 K) 114 00:07:47,175 --> 00:07:49,175 这个就移除掉 115 00:07:49,175 --> 00:07:51,875 alpha 初始猜测为 0 116 00:07:51,875 --> 00:07:55,650 Debye 温度初始猜测 500 K 117 00:07:55,650 --> 00:07:56,650 合理 118 00:07:56,650 --> 00:07:59,275 我们不再需要 σ2 119 00:07:59,600 --> 00:08:02,800 也不需要 delrcu 变量 120 00:08:02,800 --> 00:08:04,800 移除掉 121 00:08:05,725 --> 00:08:09,925 好那现在设置新的变量 122 00:08:10,950 --> 00:08:12,425 先定为常量 123 00:08:12,425 --> 00:08:15,925 点击 Fit 观察图像 124 00:08:16,250 --> 00:08:19,075 看起来不差 125 00:08:19,075 --> 00:08:27,900 拟合和实验数据在两个壳层中差距不大 126 00:08:27,900 --> 00:08:31,850 看下各自对第二壳层的贡献 127 00:08:32,200 --> 00:08:35,700 既然 σ2 不等于 0 128 00:08:35,743 --> 00:08:42,100 这些多重散射的贡献跟之前比起来小了很多 129 00:08:42,100 --> 00:08:47,750 第二壳层整个拟合数据都变弱了 130 00:08:47,750 --> 00:08:49,750 如果去到 log 文件 131 00:08:50,575 --> 00:08:53,875 可以看到现在的 σ2 值 132 00:08:53,875 --> 00:08:59,700 基本上所有的路径都在 0.002 133 00:08:59,700 --> 00:09:01,750 在500 K Debye 温度考量下 134 00:09:01,750 --> 00:09:07,700 比实际测量时的 10 K 要高了不少 135 00:09:07,700 --> 00:09:10,600 所以这些 σ2 都比较小 136 00:09:11,400 --> 00:09:16,400 回到猜测窗口,全部设为变量 137 00:09:17,600 --> 00:09:19,600 改为 guess 138 00:09:20,100 --> 00:09:22,100 点击 Fit 139 00:09:25,300 --> 00:09:30,575 第一二壳层的拟合都很棒 140 00:09:30,825 --> 00:09:38,100 大概从 3.6 Å 之后就没有拟合了 141 00:09:41,100 --> 00:09:44,325 最优解在 Evaluated 一栏 142 00:09:44,325 --> 00:09:49,625 Debye 温度回到了 278 ± 13 K 143 00:09:50,125 --> 00:09:52,125 非常不错 144 00:09:53,075 --> 00:09:56,925 回到 log 文件 145 00:09:56,925 --> 00:10:04,675 第一条路径的 σ2 回到了大约 0.003 146 00:10:05,122 --> 00:10:08,800 第二条路径是 0.004 147 00:10:08,800 --> 00:10:14,750 通常来说距离越远的路径 σ2 值越高 148 00:10:16,675 --> 00:10:18,675 那么 149 00:10:19,050 --> 00:10:23,975 这是个很好的拟合 150 00:10:23,975 --> 00:10:25,975 amp 值吻合 151 00:10:25,975 --> 00:10:31,000 之前只拟合第一壳层的时候是 0.91 152 00:10:31,000 --> 00:10:35,250 包含第二壳层后是 0.92 153 00:10:35,250 --> 00:10:37,250 结果不错 154 00:10:37,250 --> 00:10:39,250 那么使用这些数值 155 00:10:40,005 --> 00:10:47,125 到 k 空间中 156 00:10:48,425 --> 00:10:49,850 也就是这里 157 00:10:49,850 --> 00:10:53,606 如果你不想看到每条路径贡献 158 00:10:53,606 --> 00:10:55,200 你可以取消勾选 159 00:10:55,200 --> 00:11:00,050 只留下这里的实验和拟合数据 160 00:11:01,075 --> 00:11:06,200 这里两个之间还是有差距的 161 00:11:06,200 --> 00:11:12,200 还是因为一些高频信号没有被拟合进去 162 00:11:12,200 --> 00:11:14,564 如果看反傅里叶变换 163 00:11:14,564 --> 00:11:21,925 就能看到我们拟合的结果在拟合范围内很好 164 00:11:22,275 --> 00:11:24,275 让我们来看个东西 165 00:11:24,750 --> 00:11:36,900 增加 Rmax 到包含这些还没有被拟合的信号 166 00:11:36,900 --> 00:11:41,050 把 Rmax 改成 5 167 00:11:41,575 --> 00:11:45,550 这样所有信号都包含进去了 168 00:11:45,550 --> 00:11:47,445 点击 Fit 键 169 00:11:49,301 --> 00:11:51,675 拟合看起来依然不错 170 00:11:51,675 --> 00:11:54,650 但如果看最优值时 171 00:11:55,509 --> 00:12:00,400 可以看到温度的不确定值 172 00:12:00,400 --> 00:12:04,275 从之前的 15 到现在 95 173 00:12:04,525 --> 00:12:08,325 你也许会问为什么会这样? 174 00:12:08,325 --> 00:12:14,775 原因是不确定值的计算是依据改变这个数值 175 00:12:14,775 --> 00:12:21,050 如果拟合结果变差,不确定值会变大 176 00:12:21,500 --> 00:12:26,325 鉴于我们包含了一些没有拟合信号 177 00:12:26,325 --> 00:12:31,425 所以拟合的值就跟 283 K 差距更远 178 00:12:31,425 --> 00:12:33,800 拟合结果更差 179 00:12:34,500 --> 00:12:38,525 也可以去到历史窗口 180 00:12:39,946 --> 00:12:46,675 可以看到 reduced chi-square 现在是 2600 181 00:12:46,675 --> 00:12:49,925 但之前是 50 182 00:12:50,799 --> 00:12:53,825 温度不确定值是 13 183 00:12:54,175 --> 00:13:01,850 一点点的不确定值改变使得 reduced chi-square 翻倍到 100 184 00:13:01,850 --> 00:13:06,200 现在我们算上了不被拟合的信号 185 00:13:06,200 --> 00:13:14,000 这个温度值必须改动很大才能让 reduced chi-square 翻倍 186 00:13:15,170 --> 00:13:19,550 所以选择合适范围很重要 187 00:13:19,850 --> 00:13:23,975 要框选到你刚刚好要拟合的范围 188 00:13:24,625 --> 00:13:29,075 现在把 Rmax 改回到 3.6 189 00:13:29,075 --> 00:13:32,300 因为第二条路径大约在 3.78 Å 190 00:13:32,750 --> 00:13:35,625 不知道这个改动影响有多大 191 00:13:35,625 --> 00:13:41,975 来看下 reduced chi-square 会不会小点 192 00:13:42,475 --> 00:13:44,475 点击 Fit 193 00:13:52,406 --> 00:13:58,925 这个报错是说我们选择的 Rmax 太小了 194 00:13:58,925 --> 00:14:02,550 那我就不让 Artemis 检查这个错误 195 00:14:04,825 --> 00:14:09,375 跳过这个查验 196 00:14:13,600 --> 00:14:16,725 好了 197 00:14:16,725 --> 00:14:20,350 这下数据出来了 198 00:14:20,625 --> 00:14:24,371 现在的 reduced chi-square 是 34 199 00:14:24,371 --> 00:14:26,950 比之前的 50 还要小 200 00:14:26,950 --> 00:14:31,950 不确定值也从 15 到 10 201 00:14:32,825 --> 00:14:37,125 你可以比较不同条件下的拟合 202 00:14:37,125 --> 00:14:39,125 在历史窗口中查找 203 00:14:39,956 --> 00:14:44,625 选择你想要比较的拟合 204 00:14:44,625 --> 00:14:46,625 到 Report 页面 205 00:14:46,625 --> 00:14:51,400 可以显示统计学报告 206 00:14:51,400 --> 00:14:56,850 可以显示不同拟合各自的 reduced chi-square 207 00:14:57,275 --> 00:15:02,825 你也可以依照温度来比较 208 00:15:03,275 --> 00:15:06,925 可以看到不确定值的变动 209 00:15:06,925 --> 00:15:14,200 虽然三组数据中数值接近,但是不确定值浮动很大 210 00:15:14,825 --> 00:15:20,200 你也可以展示其他参数比如 amp 211 00:15:20,600 --> 00:15:27,500 比如 amp 和不确定之间的关系 212 00:15:27,500 --> 00:15:35,300 这是一个拿来比较不同拟合结果的方法 213 00:15:37,426 --> 00:15:41,225 这个练习到这里就差不多了 214 00:15:41,225 --> 00:15:45,750 如何找到重要的路径 215 00:15:45,750 --> 00:15:48,675 如何比较不同拟合 216 00:15:48,675 --> 00:15:52,475 以及不同模型的问答思路 217 00:15:53,775 --> 00:15:56,450 谢谢