晶胞参数计算.doc

晶胞参数计算
Delphi程序计算不同晶系晶胞参数
Abstract
Two programs for cell parameter refinement for index of diffraction lines have been worked out using Delphi language on Windows. The programs are based on the Bragg’s equation and the crystal plane distance formulas, by used least square for cell parameter refinement. They are suited to monoclinic, orthogonal, tetragonal, trigonal, hexagonal and cubic crystal system. The programs are very suitable for spread and study because it’s a visual system. If they have the X-ray power diffraction pattern of materials, even if being non-expert on X-ray crystal structure, they can conveniently get the index of diffraction lines and cell parameters.
Key words: Delphi program; Cell parameters; Least square; X-ray
crystal structure.
Delphi程序计算不同晶系晶胞参数
1 前言
利用X射线衍射图精确计算晶体的晶胞参数,近年来愈来愈多地受到矿物、材料、物理、化学等学科的科技工作者的重视。当衍射图的衍射线能标定衍射指数,而且有足够数目时,精确计算晶体晶胞参数主要是采用柯亨()的最小二乘法处理。柯亨的最小二乘法计算公式在推导过程中,对于误差公式的处理不是特别精确,计算晶胞参数的过程就变
的非常复杂与烦琐。为了减轻科技人员科研过程中的负担,提高科研效率,特编写了这套Delphi程序。这套测定常用六种晶胞参数的Delphi程序,对于非专业X射线人员,在得到材料衍射图谱后,就能很方便地计算晶胞参数。
2 六种晶系的正则方程和程序图
在实际计算前我们首先使用最小二乘法原理,结合线形几何的一些知识,推出了六种晶系的正则方程,推导过程不再祥述,结果如下:
0??????901、立方晶系( a=b=c)
nnn
A??i?1
n2i+D’i?1?????ii=i?1isin2?
iA??i?i
i?1+D’i?1?n?i2=??i?1nsin2?
2222??(H?K?L),??10sin22? ?/4a其中:A=
02、正方晶系(??????90 a=b)
nnnn
A??
i?1
n2i+D’i?1???ii+C2???ii?1ni=
i??i?1nisin2? 2sin?iA??i?i
i?1
n+D’??i?1nni+ C
i?????ii?1=i?1n A??i?i
i?1+D’i?1???i+ Ci?1??n2i=i?1??isin2?
其中:A=?2/4a2 ??H2?K2
3、六方晶系(????900 ??1200
a=b) ?n
?
2
n
n
n
A2i
i
sin?
i?1+D’??i
?
i
i?1
+C
??i?
i
?
i?1
=
?i?1
n
A??2
n
n
i?i
?n
?
i
i
i
sin2?
i?1+D’
i?1+ C??i
?i?1
=
??
i?1
n
n
?n
A??2
i?i
i
?
i
i
sin2?
i?1
+D’?i?1
+ C?n
?
i?1
=??
i
i?1
其中A==?2/3a2 ??H2?HK?K2 C=?2/4a2??10sin22?
4、三方晶系六方晶胞(????900 ??1200
a=b?c) n
2
n
n
n
A??
i
?i?
i
i?1+D’??i?
i
i?1
+C
?i?1
=