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电子理论对话-9：这篇文章不错
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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：
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)
Iα=IM×IS×IK 中的：
IM＝1，对于2a-Ti；
IM＝1，对于2b-Al；
IM＝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
Iα=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
Iα=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：
Iα=1×8×2=16
以4d-Al为参考原子：
Iα=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：
Iα=1×8×2=16
以4d-Al为参考原子：
Iα=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
Iα=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
Iα=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
Iα=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
Iα=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
Iα=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)
Iα=IM×IS×IK 中的：
IM＝1，对于1a-Sc；
IM＝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：
Iα=1×12×2=24
以3c-Al为参考原子：
Iα=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
Iα=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
Iα=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
Iα=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：
Iα=1×24×2=48
以3c-Al为参考原子：
Iα=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
Iα=3×16×1=48
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