Miller-Bravais to xyz conversion

[grandr...@gmail.com]

For a script I'm working on I want to convert a Miller Bravais HCP direction into an x,y,z (ie orthogonal crystal axis) vector

Using b= Miller(1,0,-1,1,cs,'uvw') and doing this manually, I convert it into rhombohedral coordinates using [u-t,v-t,w] and get [2,1,1] (call this R).  This can then be converted into xyz orthogonal coordinates using
A=[1,-1/2,0;0,(sqrt(3)/2),0;0,0,c/a]  followed by A*R  (where c/a is based on the crystallography of that alloy) which outputs [1.5,0.866,1.6236]

Of course the whole method changes when you're dealing with planes.

So I have three questions;
1.  Is there a function that does this automatically?  I can program it myself, no big issue but I'm curious
2.  when I go into variable b, I notice that the values stored there for x,y,z are completely different.  What do these values represent?
3.  to confirm, I can force the system to consider this as an orthogonal vector by calling it as Miller(0.5,-0.866,1.6236,cs,'xyz')

I appreciate any help you can offer,

Regards, Jessica

[Rüdiger Kilian]

Hi Jessica,
I would have thought .xyz would be what you are looking for.
Doing:

cs=crystalSymmetry('321')
hs= Miller(1,1,-2,2,cs,'uvw')
plot(hs,'MarkerSize',25)
hold on
plot(vector3d(hs.xyz),[1,0,0],'MarkerSize',15)
hold off

looks like both are ending up on the same spot. Maybe that helps.
Cheers,
Rüdiger

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From: mtex...@googlegroups.com [mtex...@googlegroups.com] on behalf of grandr...@gmail.com [grandr...@gmail.com]
Sent: Saturday, July 23, 2016 3:59 AM
To: MTEX
Subject: {MTEX} Miller-Bravais to xyz conversion

For a script I'm working on I want to convert a Miller Bravais HCP direction into an x,y,z (ie orthogonal crystal axis) vector

Using b= Miller(1,0,-1,1,cs,'uvw') and doing this manually, I convert it into rhombohedral coordinates using [u-t,v-t,w] and get [0,-1,1] (call this R).  This can then be converted into xyz orthogonal coordinates using
A=[1,-1/2,0;0,(sqrt(3)/2),0;0,0,c/a]  followed by A*R  (where c/a is based on the crystallography of that alloy) which outputs [0.5,-0.866,1.6236]

Of course the whole method changes when you're dealing with planes.

So I have three questions;
1.  Is there a function that does this automatically?  I can program it myself, no big issue but I'm curious
2.  when I go into variable b, I notice that the values stored there for x,y,z are completely different.  What do these values represent?
3.  to confirm, I can force the system to consider this as an orthogonal vector by calling it as

Miller(0.5,-0.866,1.6236,cs,'xyz')

I appreciate any help you can offer,

Regards, Jessica

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[David Mainprice]

Here are some examples of conversions in MTEX4, this can be  hkil or hkl 

%% Conversion between hkl (or hkil) and uvw (or uvtw) and specimen coordinates

% N.B. converted uvw and hkl not always integer values

h = Miller(1,1,1,CS,'Forsterite','hkl')

% change hkl (h) to uvw

uvw = h.uvw

u = Miller(1,1,1,CS,'Forsterite','uvw')

% change uvw (u) to hkl

hkl = u.hkl

%% conversion of hkl and uvw to specimen coordinates

% N.B. converted uvw and hkl not always integer values

% change hkl (h) to vector3d r1

% Miller indices h parallel to specimen direction r1

r1 = vector3d(h)

% change uvw (u) to vector3d r2

% Miller indices u parallel to specimen direction r2

r2 = vector3d(u)

%% conversion of specimen coordinates to hkl and uvw

% N.B. converted uvw and hkl not always integer values

% change vector3d(1,1,1) to hkl

hkl_111 = Miller(vector3d(1,1,1),CS,'Forsterite','hkl')

% change vector3d(1,1,1) to uvw

uvw_111 = Miller(vector3d(1,1,1),CS,'Forsterite','uvw’)

all the best David

Le 23 juil. 2016 à 03:59, grandr...@gmail.com a écrit :

For a script I'm working on I want to convert a Miller Bravais HCP direction into an x,y,z (ie orthogonal crystal axis) vector

Using b= Miller(1,0,-1,1,cs,'uvw') and doing this manually, I convert it into rhombohedral coordinates using [u-t,v-t,w] and get [0,-1,1] (call this R).  This can then be converted into xyz orthogonal coordinates using
A=[1,-1/2,0;0,(sqrt(3)/2),0;0,0,c/a]  followed by A*R  (where c/a is based on the crystallography of that alloy) which outputs [0.5,-0.866,1.6236]

Of course the whole method changes when you're dealing with planes.

So I have three questions;
1.  Is there a function that does this automatically?  I can program it myself, no big issue but I'm curious
2.  when I go into variable b, I notice that the values stored there for x,y,z are completely different.  What do these values represent?
3.  to confirm, I can force the system to consider this as an orthogonal vector by calling it as

Miller(0.5,-0.866,1.6236,cs,'xyz')

I appreciate any help you can offer,

Regards, Jessica

[grandr...@gmail.com]

This was very helpful, I am having a lot of difficulty with orienting things correctly in my code but I will put in a new question since the issue is a bit different.  Thank you for helping me sort this out.

Jessica