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Thank you for the clarification, it makes fine sense to me. The
original problem I am having is that I'm trying to input the titania
antase structure. It is fairly complicated, but I found a source,
<a class="moz-txt-link-freetext" href="http://cst-www.nrl.navy.mil/lattice/struk/c5.html">http://cst-www.nrl.navy.mil/lattice/struk/c5.html</a>, that spells it out
clearly. It says it's a body-centered tetragonal and lists six basis
vectors, presumably to describe the peroidicity of the space group that
it is in. So I figured that ibrav = 7 for bct, nat = 6, and use the
basis vectors to enter the atomic coordinates. Yet when I view my
structure with XCrysDen, it looks nothing like anatase. I then started
looking at the examples and how they are input and starting thinking
that my choice for nat was wrong (based on all the discussion about
Si). I did see that the internet source and PWscf do not use the same
vectors to describe the bct lattice, I thought that they were
equivalent and resulted in the same volume of the unit cell, though I
will double check. Sorry about all this, but I wouldn't have asked if
I hadn't spend so much time trying to enter this structure already.<br>
<br>
Thanks for your help,<br>
Luke<br>
.<br>
<a class="moz-txt-link-abbreviated" href="mailto:baroni@sissa.it">baroni@sissa.it</a> wrote:
<blockquote cite="mid4402C34F-C6E2-4D3D-A203-05EB51232708@sissa.it" type="cite">OK. Let me try to shed some light on this unexpectedly
obscure point.
<div><br>
<div>
<div>On May 11, 2006, at 6:41 AM, Huiqun Zhou wrote:</div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<div style="margin: 0px;">Hmm ..., because there are 4 lattice
points, that are (0,0,0) and 3 end points of the</div>
<div style="margin: 0px;">basis vectors as stated, in a diamond
structure, and there are two primitive elements</div>
<div style="margin: 0px;">which are located at (0,0,0) and
(1/4,1/4,1/4) for this structure, so there should be</div>
<div style="margin: 0px;">4 x 2 = 8 atoms in a conventional unit
cell of diamond structure.</div>
</blockquote>
<div><br class="khtml-block-placeholder">
</div>
I am sorry, Huiqun, but I am afraid that this argument is wrong and
confusing. What do you mean by "4 lattice points"? Of course, every
triplet of vectors originating at (0,0,0) has one common point (the
origin), and 3 end points. AND SO WHAT?</div>
<div><br class="khtml-block-placeholder">
</div>
<div>
<blockquote type="cite">
<div style="margin: 0px;">But because of periodicity, theoretically
you can choose either only the primitive</div>
<div style="margin: 0px;">elements (2 atoms) in an unit cell with
appropriatelly selected large number of k points</div>
<div style="margin: 0px;">for calculation, or the whole member (8
atoms) in an unit cell with less k points for</div>
<div style="margin: 0px;">calculation. I may be wrong, please
correct me.</div>
</blockquote>
<div><br class="khtml-block-placeholder">
</div>
Although it is certainly true that, for a same system, doing a
calculation with a larger conventional unit cell would require a
smaller number of k points, I feel that it is confusing to try to
explain a property of the real-space lattice with something that has
only to do with the way calculations are technically done (the number
of k points).</div>
<div><br class="khtml-block-placeholder">
</div>
<div>Let me try to clarify the matter as much as I can.</div>
<div><br class="khtml-block-placeholder">
</div>
<div>1) The Bravais lattice of the diamond structure is face-centered
cubic (FCC). A basis for this Bravais lattice is, e.g., (1/2,1/2,0),
(1/2,0,1/2), (0,1/2,1/2).</div>
<div><br class="khtml-block-placeholder">
</div>
<div>2) Each elementary cell of this FCC lattice contains two
equivalent atoms, located at (000)+R(l,m,n) and (1/4,1/4,1/4)+R(l,m,n),
where R(l,m,n) = l*(1/2,1/2,0) + m*(1/2,0,1/2) + n*(0,1/2,1/2) is a
generic point of the Bravais lattice (l,m,n being integer numbers).</div>
<div><br class="khtml-block-placeholder">
</div>
<div>3) The above basis for the Bravais lattice defines a unit cell
of *minimum volume*. Of ourse, one is free to choose as a basis any
triplet of integer linear (and linearly independent) combinations of
the minimum basis. For instance, one could choose: (1,0,0) =
(1/2,1/2,0)+(1/2,0,1/2)-(0,1/2,1/2), (0,1,0)= [guess what?], and
(0,0,1)=[guess what?]. These three vectors form a basis for the simple
cubic (SC) Bravais lattice. Calculate the volume of the original FCC
unit cell (defined at point 1 above) and compare it with the volume of
the SC unit cell considered here (hint: the volume of a parallelepiped
is the absolute value of the determinant of the 3x3 matrix whose
columns are the coordinates of the three vectors which form the edges
of the parallelepiped). You will find that the the volume of the SC
cell is 4 times larger than the volume of the FCC cell. This means that
if you choose to describe the diamond lattice as SC instead of FCC
(which you are free to do), the unit cell will contain 4x2 instead of 2
atoms. You see where the factor 4 comes from? Nothing to do with the
"number of lattice points" (whatever these lattice points may be).</div>
<div><br class="khtml-block-placeholder">
</div>
<div>4) Now, the volume of the Brillouin zone (BZ) is (2\pi)^3
divided by the volume of the unit cell. Hence, the volume of the SC BZ
is 1/4 the volume of the FCC BZ. That's why, in order to sample a SC BZ
with the same accuracy of an FCC cell you will need 1/4 as many k
points. But this is another story which has little to do with the main
point of this thread.</div>
<div><br class="khtml-block-placeholder">
</div>
<div>Hope this clarifies a little bit the muddy waters</div>
<div><br class="khtml-block-placeholder">
</div>
<div>Stefano Baroni</div>
<div><br>
<blockquote type="cite">
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">Huiqun Zhou</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">----- Original Message ----- From: "Eyvaz
Isaev" <<a href="mailto:eyvaz_isaev@yahoo.com">eyvaz_isaev@yahoo.com</a>></div>
<div style="margin: 0px;">To: <<a href="mailto:pw_forum@pwscf.org">pw_forum@pwscf.org</a>></div>
<div style="margin: 0px;">Sent: Thursday, May 11, 2006 2:51 AM</div>
<div style="margin: 0px;">Subject: Re: [Pw_forum] Confused on nat
definition</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<blockquote type="cite">
<div style="margin: 0px;">Hi,</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<blockquote type="cite">
<div style="margin: 0px;">This may seem silly, but I'm confused
as to what</div>
<div style="margin: 0px;">exactly the number of</div>
<div style="margin: 0px;">atoms in a unit cell is (nat).<span class="Apple-converted-space"> </span>For example, the</div>
<div style="margin: 0px;">Silicon example says</div>
<div style="margin: 0px;">that nat is only two, yet a diamond
structure such</div>
<div style="margin: 0px;">as this should have</div>
<div style="margin: 0px;">much more than two atoms per unit
cell.</div>
</blockquote>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">Let us consider the diamond case. If
you choose as</div>
<div style="margin: 0px;">basis vectors next 3 vectors (which are
the standard</div>
<div style="margin: 0px;">choice)</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">1/2, 1/2, 0</div>
<div style="margin: 0px;">1/2, 0<span class="Apple-converted-space"> </span>, 1/2</div>
<div style="margin: 0px;">0<span class="Apple-converted-space"> </span>,
1/2, 1/2</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">you have only 2 atoms in the unit cell</div>
<div style="margin: 0px;">(parallelepiped) spanned by these
vectors:</div>
<div style="margin: 0px;">0, <span class="Apple-converted-space">
</span>0, 0</div>
<div style="margin: 0px;">1/4, 1/4, 1/4</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">If you decide to choose as basis
vectors next 3 ones</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">1 0 0</div>
<div style="margin: 0px;">0 1 0</div>
<div style="margin: 0px;">0 0 1</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">you have 8 atoms in the unit cell which
is now a cub.</div>
<div style="margin: 0px;">If your choice is the latter<span class="Apple-converted-space"> </span>for CaF2 structure you</div>
<div style="margin: 0px;">will have 12 atoms, but using the
former - only 3.</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">So, number of atoms (nat) in a unit
cell depends on</div>
<div style="margin: 0px;">your unit cell choice defined by 3
basis vectors.</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<blockquote type="cite">
<div style="margin: 0px;">Is the definition of nat the<span class="Apple-converted-space"> </span>number of basis</div>
<div style="margin: 0px;">vectors?</div>
</blockquote>
<div style="margin: 0px;">To me it is not so clear, but see above.</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<div style="margin: 0px;">Bests,</div>
<div style="margin: 0px;">Eyvaz.</div>
<div style="margin: 0px; min-height: 14px;"><br>
</div>
<blockquote type="cite">
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<div style="margin: 0px;"><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;">---</span></span></span></font></div>
<div style="margin: 0px;"><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;">Stefano Baroni -
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</div>
<div style="margin: 0px;"><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;">Please, if possible,
don't</span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"> </span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;">send me MS Word or PowerPoint attachments</span></span></span></font></div>
<div style="margin: 0px;"><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;">Why? See:</span></span></span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"><span class="Apple-style-span" style="font-size: 12px;"> </span></span></span></font><a href="http://www.gnu.org/philosophy/no-word-attachments.html"><font class="Apple-style-span" color="#0023e9" size="3"><span class="Apple-style-span" style="font-size: 12px; color: rgb(0, 35, 233);"><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px;"><span class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px;">http://www.gnu.org/philosophy/no-word-attachments.html</span></span></span></font></a></div>
<div><br class="khtml-block-placeholder">
</div>
<br class="Apple-interchange-newline">
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<br>
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=
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