pwscf中建立晶体模型
因为pwscf没有像ms中的visualizer一样的可视化的建立晶体的模块，很多时候很不方便。
这里就来学习如何利用MS的visualizer进行晶体结构的输入。
下面是Input_PW中关于pwscf中的晶体系统的信息。
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ibrav is the structure index:
ibrav structure celldm(2)-celldm(6)
0 "free", see above not used
1 cubic P (sc) not used
2 cubic F (fcc) not used
3 cubic I (bcc) not used
4 Hexagonal and Trigonal P celldm(3)=c/a
5 Trigonal R celldm(4)=cos(alpha)
6 Tetragonal P (st) celldm(3)=c/a
7 Tetragonal I (bct) celldm(3)=c/a
8 Orthorhombic P celldm(2)=b/a,celldm(3)=c/a
9 Orthorhombic base-centered(bco) celldm(2)=b/a,celldm(3)=c/a
10 Orthorhombic face-centered celldm(2)=b/a,celldm(3)=c/a
11 Orthorhombic body-centered celldm(2)=b/a,celldm(3)=c/a
12 Monoclinic P celldm(2)=b/a,celldm(3)=c/a,
celldm(4)=cos(ab)
13 Monoclinic base-centered celldm(2)=b/a,celldm(3)=c/a,
celldm(4)=cos(ab)
14 Triclinic celldm(2)= b/a,
celldm(3)= c/a,
celldm(4)= cos(bc),
celldm(5)= cos(ac),
celldm(6)= cos(ab)
For P lattices: the special axis (c) is the z-axis, one basal-plane
vector (a) is along x, the other basal-plane vector (b) is at angle
gamma for monoclinic, at 120 degrees for trigonal and hexagonal
lattices, at 90 degrees for cubic, tetragonal, orthorhombic lattices
sc simple cubic
====================
a1 = a(1,0,0), a2 = a(0,1,0), a3 = a(0,0,1)
fcc face centered cubic
====================
a1 = (a/2)(-1,0,1), a2 = (a/2)(0,1,1), a3 = (a/2)(-1,1,0).
bcc body entered cubic
====================
a1 = (a/2)(1,1,1), a2 = (a/2)(-1,1,1), a3 = (a/2)(-1,-1,1).
simple hexagonal and trigonal(p)
====================
a1 = a(1,0,0), a2 = a(-1/2,sqrt(3)/2,0), a3 = a(0,0,c/a).
trigonal(r)
===================
for these groups, the z-axis is chosen as the 3-fold axis, but the
crystallographic vectors form a three-fold star around the z-axis,
and the primitive cell is a simple rhombohedron. The crystallographic
vectors are:
a1 = a(tx,-ty,tz), a2 = a(0,2ty,tz), a3 = a(-tx,-ty,tz).
where c=cos(alpha) is the cosine of the angle alpha between any pair
of crystallographic vectors, tc, ty, tz are defined as
tx=sqrt((1-c)/2), ty=sqrt((1-c)/6), tz=sqrt((1+2c)/3)
simple tetragonal (p)
====================
a1 = a(1,0,0), a2 = a(0,1,0), a3 = a(0,0,c/a)
body centered tetragonal (i)
================================
a1 = (a/2)(1,-1,c/a), a2 = (a/2)(1,1,c/a), a3 = (a/2)(-1,-1,c/a).
simple orthorhombic (p)
=============================
a1 = (a,0,0), a2 = (0,b,0), a3 = (0,0,c)
bco base centered orthorhombic
=============================
a1 = (a/2,b/2,0), a2 = (-a/2,b/2,0), a3 = (0,0,c)
face centered orthorhombic
=============================
a1 = (a/2,0,c/2), a2 = (a/2,b/2,0), a3 = (0,b/2,c/2)
body centered orthorhombic
=============================
a1 = (a/2,b/2,c/2), a2 = (-a/2,b/2,c/2), a3 = (-a/2,-b/2,c/2)
monoclinic (p)
=============================
a1 = (a,0,0), a2= (b*sin(gamma), b*cos(gamma), 0), a3 = (0, 0, c)
where gamma is the angle between axis a and b
base centered monoclinic
=============================
a1 = ( a/2, 0, -c/2),
a2 = (b*cos(gamma), b*sin(gamma), 0),
a3 = ( a/2, 0, c/2),
where gamma is the angle between axis a and b
triclinic
=============================
a1 = (a, 0, 0),
a2 = (b*cos(gamma), b*sin(gamma), 0)
a3 = (c*cos(beta), c*(cos(alpha)-cos(beta)cos(gamma))/sin(gamma),
c*sqrt( 1 + 2*cos(alpha)cos(beta)cos(gamma)
- cos(alpha)^2-cos(beta)^2-cos(gamma)^2 )/sin(gamma) )
where alpha is the angle between axis b and c
beta is the angle between axis a and c
gamm is the angle between axis a and b
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下面以Si为例子
在MS中建立Si的元胞，show symmetry, 我们得到这样一些信息：primitive of face centered-cubic，转换到单胞
a=b=c=5.4307A,转换为原子单位，为：10.25a.u.。三个角为60度,元胞中有2个si原子
坐标分别为：
0 0 0
0.25 0.25 0.25
那么在pwscf中，输入&system部分
ibrav= 2, celldm(1) =10.25, nat= 2, ntyp= 1,
输入&electrons
ATOMIC_POSITIONS
Si 0.00 0.00 0.00
Si 0.25 0.25 0.25
========================================================================
下面以Al为例子，
在MS中建立Al的元胞，show symmetry， 得到：primitive of face centered-cubic，转换到单胞，a=b=c=4.0495A，为7.64a.u.,三个角为60度.元胞中只有1个Al原子
坐标为：
0 0 0
&system
ibrav= 2, celldm(1) =7.64, nat= 1, ntyp= 1,
&electrons
ATOMIC_POSITIONS
Al 0.00 0.00 0.00
=========================================================================
下面以FeSi2为例子，
在MS中建立FeSi2元胞，show symmetry，得到：Tetragonal ，其中元胞内有Si原子，所以为Tetragonal I，ibrav=7，
a=b=2.684A，c=5.128A。celldm(1)=5.06,celldm(3)=1.9.
Fe 0 0 0
Si 0.5 0.5 0.27
=========================================================================
下面讨论如何建立Al的单原子线
Al晶体中，Al-Al的键长大约为2.385A，即为1.264a.u.，为了避免线与线直接的相互作用，把celldm(1)=12a.u.,那么celldm(3)=0.375
Al 0 0 0
======================================================
