电子理论对话-9：这篇文章不错

人们用余瑞璜EET写了很多文章，前面分析了7篇文章，都有错误，有的错误还很严重，而且是错在晶体学部分，还没有开始EET计算就出错了。

下面这篇文章，涉及到两个化合物，Al₃Ti和Al₃Sc，前一个没有错误，后一个漏掉1条键，是一个小错误（漏掉1条比较长的键）。总而言之，这篇文章的作者还是认真的，在晶体学部分没有出错。

文中引用了“晶面电子密度”的概念，如果深挖，这里还有问题。

在一个平面上，电子密度都是一些等值线，如何定义一个平面上的电子密度，仍然是个问题！以后再讨论这个问题。

对话如下：

作者原文下载

讨论如下：

原文信息:

Al₃Ti：a=3.851，c＝8.608，空间群139号；Al₃Sc：a=4.105；空间群221号。

对于Al₃Ti，

空间群表达式＝2Ti(2a-Ti)2Al(2b-Al)4Al(4d-Al)

约化为化合式，1Ti3Al=1Ti(2a-Ti)1Al(2b-Al)2Al(4d-Al)

I_α=I_M×I_S×I_K 中的：

I_M＝1，对于2a-Ti；

I_M＝1，对于2b-Al；

I_M＝2，对于4d-Al；

1,"  ","2a-Ti","---","2b-Al","      d===",2.7231

"2a-Ti",":",-1.9255,-1.9255,-4.304,"          Z=",4

"  SP coordinates=",0,0,0

"2b-Al",":",0,0,-4.304,"                     Z=",4

"  SP coordinates=",.5,.5,0

I_α=1×4×2=8

2,"  ","4d-Al","---","4d-Al","      d===",2.7231

"4d-Al",":",-1.9255,0,-2.152,"          Z=",4

"  SP coordinates=",0,.5,.25

"4d-Al",":",0,-1.9255,-2.152,"          Z=",4

"  SP coordinates=",.5,0,.25

I_α=2×4×1=8

3,"  ","2a-Ti","---","4d-Al","      d===",2.8877

"2a-Ti",":",-1.9255,-1.9255,12.912,"          Z=",8

"  SP coordinates=",0,0,2

"4d-Al",":",0,-1.9255,10.76,"Z=",8=4(2a-Ti)+4(4d-Al)

"  SP coordinates=",.5,0,1.75

以2a-Ti为参考原子：

I_α=1×8×2=16

以4d-Al为参考原子：

I_α=2×4×2=16

4,"  ","2b-Al","---","4d-Al","      d===",2.8877

"2b-Al",":",0,0,-4.304,"              Z=",8=

"  SP coordinates=",.5,.5,0

"4d-Al",":",0,1.9255,-6.456," Z=",8=4(2b-A)+4(4d-Al)

"  SP coordinates=",.5,1,-.25

以2b-Ti为参考原子：

I_α=1×8×2=16

以4d-Al为参考原子：

I_α=2×4×2=16

5,"  ","4d-Al","---","4d-Al","      d===",3.851

"4d-Al",":",-1.9255,-3.851,2.152,"          Z=",4

"  SP coordinates=",0,-.5,.75

"4d-Al",":",1.9255,-3.851,2.152,"          Z=",4

"  SP coordinates=",1,-.5,.75

I_α=2×4×1=8

6,"  ","2b-Al","---","2b-Al","      d===",3.851

"2b-Al",":",1.9255,5.7765,0,"          Z=",4

"  SP coordinates=",1,2,.5

"2b-Al",":",5.7765,5.7765,0,"          Z=",4

"  SP coordinates=",2,2,.5

I_α=1×4×1=4

7,"  ","2a-Ti","---","2a-Ti","      d===",3.851

"2a-Ti",":",-5.7765,-5.7765,-4.304,"          Z=",4

"  SP coordinates=",-1,-1,0

"2a-Ti",":",-5.7765,-1.9255,-4.304,"          Z=",4

"  SP coordinates=",-1,0,0

I_α=1×4×1=4

8,"  ","2b-Al","---","2a-Ti","      d===",4.304

"2b-Al",":",5.7765,-5.7765,8.608,"          Z=",2

"  SP coordinates=",2,-1,1.5

"2a-Ti",":",5.7765,-5.7765,12.912,"          Z=",2

"  SP coordinates=",2,-1,2

I_α=1×2×2=4

9,"  ","4d-Al","---","4d-Al","      d===",4.304

"4d-Al",":",0,-5.7765,6.456,"          Z=",2

"  SP coordinates=",.5,-1,1.25

"4d-Al",":",0,-5.7765,10.76,"          Z=",2

"  SP coordinates=",.5,-1,1.75

I_α=2×2×1=4

对于Al3Sc：

空间群表达式＝1Sc(1a-Sc)3Al(3c-Al)

约化为化合式，1Sc3Al=1Sc(1a-Sc)3Al(3c-Al)

I_α=I_M×I_S×I_K 中的：

I_M＝1，对于1a-Sc；

I_M＝3，对于3c-Al；

1,"  ","1a-Sc","---","3c-Al","      d===",2.9027

"1a-Sc",":",-2.0525,-2.0525,-2.0525,"   Z=",12

"  SP coordinates=",0,0,0

"3c-Al",":",-2.0525,0,0," Z=",12＝4(1a-Sc)＋8(3c-Al)

"  SP coordinates=",0,.5,.5

以1a-Sc为参考原子：

I_α=1×12×2=24

以3c-Al为参考原子：

I_α=3×4×2=24

2,"  ","3c-Al","---","3c-Al","      d===",2.9027

"3c-Al",":",-2.0525,0,0,"   Z=",12＝8(3c-Al)＋4(1a-Sc)

"  SP coordinates=",0,.5,.5

"3c-Al",":",0,-2.0525,0,"Z=",12＝8(3c-Al)＋4(1a-Sc)

"  SP coordinates=",.5,0,.5

I_α=3×8×1=24

3,"  ","1a-Sc","---","1a-Sc","      d===",4.105

"1a-Sc",":",2.0525,2.0525,-2.0525,"          Z=",6

"  SP coordinates=",1,1,0

"1a-Sc",":",6.1575,2.0525,-2.0525,"          Z=",6

"  SP coordinates=",2,1,0

I_α=1×6×1=6

4,"  ","3c-Al","---","3c-Al","      d===",4.105

"3c-Al",":",0,2.0525,0,"          Z=",6

"  SP coordinates=",.5,1,.5

"3c-Al",":",4.105,2.0525,0,"          Z=",6

"  SP coordinates=",1.5,1,.5

I_α=3×6×1=18

5,"  ","1a-Sc","---","3c-Al","      d===",5.0276

"1a-Sc",":",-2.0525,-2.0525,2.0525,"    Z=",24

"  SP coordinates=",0,0,1

"3c-Al",":",2.0525,0,0,"  Z=",24＝8(1a-Sc)＋16(3c-Al)

"  SP coordinates=",1,.5,.5

以1a-Sc为参考原子：

I_α=1×24×2=48

以3c-Al为参考原子：

I_α=3×8×2=48

6,"  ","3c-Al","---","3c-Al","      d===",5.0276

"3c-Al",":",0,0,-2.0525," Z=",24＝16(3c-Al)＋8(1a-Sc)

"  SP coordinates=",.5,.5,0

"3c-Al",":",4.105,2.0525,0,"Z=",24＝16(3c-Al)＋8(1a-Sc)

"  SP coordinates=",1.5,1,.5

I_α=3×16×1=48

 完整数据下载（Al3Ti）

 完整数据下载（Al3Sc）