Startup

2019-03-20 13:52:00 +01:00
parent 3084fe0510
commit 5db0f78aee
910 changed files with 191152 additions and 322 deletions
--- a/script/__Lib/diffcalc-2.1/doc/tmp/constraints.txt
+++ b/script/__Lib/diffcalc-2.1/doc/tmp/constraints.txt
@@ -0,0 +1,47 @@
+Take a six circle diffractometer with angles:
+
+delta, nu, mu, eta, chi, phi
+
+and virtual angles:
+
+qaz, naz, psi, alpha, beta.
+
+Many combinations of these can be constrained:
+
+
+constrain
+>>> con nu
+>>> con psi
+>>> con mu
+>>> con nu mu a_eq_b
+
+real angles are always constrained to there last set position. If they are too far from here
+an error will result.
+
+>>> pos nu 0 (moves, parameter tracks last set value (actually checks it when hkl moved))
+>>> pos psi 90 (does not move, sets parameter in diffcalc)
+>>> pos mu 0 (moves)
+>>> pos hkl [1 0 0] (moves based on last set nu, psi, mu)
+>>> pos betain --> Exception, not constrained
+
+moving a virtual angle simply sets it to efftec the next hkl move
+
+Here we need onlu con, uncon and pos.
+
+......
+
+However it would be nice to be able to pos betain for example and have it change
+betain while staying on the same reflection. This might be enabled by locking the
+the current hkl position. It would be trick to make this work with the physical angles though.
+
+>>> lock hkl
+>>> pos psi 90 (moves immediately)
+>>> scan psi 0 90 1 (scans, moving immediately)
+>>> pos mu 0 (does not move immediately) (could work by listening to target positions, and triggering move when complete)
+>>> pos c(mu) moves
+>>> pos mu_c moves
+
+Only one thing would be varyable at a time unless they are put in a CoordinatedMotionGroup,
+which would be hard for the real motors)
+
+
--- a/script/__Lib/diffcalc-2.1/doc/tmp/extensions_to_yous_paper.wxm
+++ b/script/__Lib/diffcalc-2.1/doc/tmp/extensions_to_yous_paper.wxm
@@ -0,0 +1,525 @@
+/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
+/* [ Created with wxMaxima version 11.08.0 ] */
+
+/* [wxMaxima: input   start ] */
+Rx:matrix([1,0,0],[0, cos(theta), -sin(theta)],[0, sin(theta), cos(theta)])$
+Ry:matrix([cos(theta), 0, sin(theta)], [0, 1, 0], [-sin(theta), 0, cos(theta)])$
+Rz:matrix([cos(theta), -sin(theta), 0], [sin(theta), cos(theta), 0], [0, 0, 1])$
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+Equation 5:
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+PHI:subst(-phi, theta, Rz);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+CHI:subst(chi, theta, Ry);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+ETA:subst(-eta, theta, Rz);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+MU:subst(mu, theta, Rx);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+Generic V:
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+V:matrix([v11, v12, v13], [v21, v22, v23], [v31, v32, v33]);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: section start ]
+When one sample-orienting angle is given
+   [wxMaxima: section end   ] */
+
+/* [wxMaxima: subsect start ]
+For mu fixed
+   [wxMaxima: subsect end   ] */
+
+/* [wxMaxima: input   start ] */
+eq34:ETA.CHI.PHI;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq34_chi0:subst(0, chi, eq34);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*phi* with chi <> 0
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigsimp((eq34[3,2]=V[3,2])/(eq34[3,1]=V[3,1])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+show that with phi with v31 == 0 and v12 <> 0, no special case is needed when using atan2
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+solve(cos(phi)=0, phi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+atan2(1234,0);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+show that with phi with v32 == 0 and v31 <> 0, no special case is needed when using atan2
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+solve(sin(phi)=0, phi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+atan2(0,1234);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*eta* with chi <> 0 
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigsimp((-eq34[2,3]=V[2,3]) / (eq34[1, 3]=V[1,3])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+eta with v23 == 0 and v13 == 0 (phi||eta degeneracy because chi == 0)
+Then see equation for phi+eta above
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: comment start ]
+*chi*
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigsimp(sqrt((eq34[3,1]=V[3,1])^2+(eq34[3,2]=V[3,2])^2)/(eq34[3,3]=V[3,3]));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*phi + eta* with chi == 0
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigrat((eq34_chi0[1,2]=V[1,2])/(eq1:eq34_chi0[1,1]=V[1,1])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: subsect start ]
+For phi fixed
+   [wxMaxima: subsect end   ] */
+
+/* [wxMaxima: input   start ] */
+eq36:MU.ETA.CHI;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq36_eta90:subst(%pi/2, eta, eq36);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*eta*
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigsimp((eq36[1,2]=V[1,2])/sqrt((eq36[2,2]=V[2,2])^2+(eq36[3,2]=V[3,2])^2));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*mu* with eta <> +-90
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigsimp((eq36[3,2]=V[3,2])/(eq36[2,2]=V[2,2])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*chi* with eta <> +-90
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigsimp((eq36[1,3]=V[1,3])/(eq36[1,1]=V[1,1])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*chi + mu* with eta == +-90
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigrat((eq36_eta90[2,3]=V[2,3])/(eq36_eta90[2,1]=V[2,1])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: subsect start ]
+For eta or chi fixed
+   [wxMaxima: subsect end   ] */
+
+/* [wxMaxima: input   start ] */
+eq38:MU.ETA.CHI.PHI;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*chi* (eq. 39) given eta, and eta <> +-90 (with eta == +-90 chi||mu)
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+(eq38[1,3]=V[1,3])/cos(eta);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: comment start ]
+*eta* given chi, and chi <> 0 (with chi == 0 phi||eta)
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+(eq38[1,3]=V[1,3])/sin(chi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*mu* given that chi and eta have been given or calclulated respecitively
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+top:(eq38[3,3]=V[3,3])*sin(eta)*sin(chi) + (eq38[2,3]=V[2,3])*cos(chi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+bot:-(eq38[3,3]=V[3,3])*cos(chi)+(eq38[2,3]=V[2,3])*sin(eta)*sin(chi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+factor(top);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+factor(bot);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+trigsimp(top/bot);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*phi - mu* when phi || mu because chi == +-90, eta == 0 or eta == 180
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+phi_mu_parallel:subst(0, eta, subst(%pi/2, chi, eq38));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+trigreduce(trigrat((phi_mu_parallel[2,1]=V[2,1])/(phi_mu_parallel[2,2]=V[2,2])));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: section start ]
+Two sample angles given
+   [wxMaxima: section end   ] */
+
+/* [wxMaxima: input   start ] */
+THETA:subst(-theta, theta, Rz);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+PSI:subst(psi, theta, Rx);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+F:subst(xi, theta, Ry);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: section start ]
+psi, mu, eta given
+   [wxMaxima: section end   ] */
+
+/* [wxMaxima: input   start ] */
+eq49:transpose(PHI).transpose(CHI).transpose(ETA).transpose(MU).F;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*chi*
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: comment start ]
+using the linear combination identity
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+comb_idenity:sqrt(A^2+B^2)*sin(x+omega);
+omega:atan(B/A);
+A*sin(x)+B*cos(x)=comb_idenity;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+a:-sin(eta)*cos(mu)$
+b:-sin(mu)$
+V32=a*sin(chi)+b*cos(chi);
+V32=subst(b, B, subst(a, A, comb_idenity));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+asin(%/(sqrt(sin(mu)^2+sin(eta)^2*cos(mu)^2))), triginverses=all;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*xi and phi*
+
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+top:factor(eq49[3,1]*cos(xi)+eq49[3,3]*sin(xi));
+bot:factor(eq49[3,1]*sin(xi)-eq49[3,3]*cos(xi));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+factor(top/bot);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+When mu=-90 and eta = 0, used to for a surface normal vertical mode
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+eq49_vert:subst(-%pi/2, mu, subst(0, eta, eq49));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+(eq49_vert[2,2]=V[2,2]) / (eq49_vert[1,2]=V[1,2]);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: subsect start ]
+mu, phi, qaz (for three circle on i10 and i06, not in paper )
+   [wxMaxima: subsect end   ] */
+
+/* [wxMaxima: input   start ] */
+thisV:transpose(MU).F.THETA;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+Nphi:matrix([n11, n12, n13], [n21, n22, n23], [n31, n32, n33]);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq:ETA.CHI.PHI.Nphi.transpose(PSI);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*chi*
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: comment start ]
+using the linear combination identity
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+comb_idenity:sqrt(A^2+B^2)*sin(x+omega);
+omega:atan(B/A);
+A*sin(x)+B*cos(x)=comb_idenity;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+on V31:
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+a:-1*(n21*sin(phi)+n11*cos(phi))$
+b:n31$
+V31=a*sin(chi)+b*cos(chi);
+V31=subst(b, B, subst(a, A, comb_idenity));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+asin(%/sqrt((-n21*sin(phi)-n11*cos(phi))^2+n31^2)), triginverses=all;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+*xi and phi*
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+top:factor(eq49[3,1]*cos(xi)+eq49[3,3]*sin(xi));
+bot:factor(eq49[3,1]*sin(xi)-eq49[3,3]*cos(xi));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+factor(top/bot);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+solve();
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: section start ]
+Fixed mu, chi, psi (probably with mu=chi=0) (not in paper)
+   [wxMaxima: section end   ] */
+
+/* [wxMaxima: input   start ] */
+Vcalulated:Nphi.transpose(PSI).transpose(THETA);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+thisV:transpose(PHI).transpose(CHI).transpose(ETA).transpose(MU).F;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+v:thisVvert:subst(0, chi, subst(0, mu, thisV));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+acos(thisVvert[3,3]=V[3,3]), triginverses=all;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+top:(v[1,2]=V[1,2])*cos(phi) + (v[2,2]=V[2,2])*sin(phi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+bot:(v[1,2]=V[1,2])*sin(phi) - (v[2,2]=V[2,2])*cos(phi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+factor(top);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+factor(bot);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+trigsimp(top/bot);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: title   start ]
+5.5 subset with eta=chi=0 & phi set
+   [wxMaxima: title   end   ] */
+
+/* [wxMaxima: input   start ] */
+matrix([cos(theta)*sin(qaz)], [-sin(theta)], [cos(theta)*cos(qaz)]);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+h_phi:matrix([h1], [h2], [h3]);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+Z:MU.ETA.CHI.PHI;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq68yterm:-sin(theta) = ((Z.h_phi))[2][1];
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+expands(%);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq68_chi_eta_0:subst(0, chi, subst(0, eta, Z.h_phi));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq68_chi_eta_0_yterm:-sin(theta)=eq68_chi_eta_0[2];
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+subst(0, chi, subst(0, eta, eq68yterm));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+a;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+ratsubst(a, -h3, eq68_chi_eta_0_yterm);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+a:-h3;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+b:-h1*sin(phi) +h2*cos(phi);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+c:-sin(theta);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+ratsubst(cc, c, ratsubst(bb, b, ratsubst(aa, a, eq68_chi_eta_0_yterm)));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+arcsin(c/sqrt(a^2+b^2)) - arctan(b, a);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+eq68_chi_eta_0[1] /eq68_chi_eta_0[2];
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+without chi=eta=0
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+eq68yterm:-sin(theta) = ((Z.h_phi))[2][1];
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+expand(eq68yterm);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+solve for mu unknown
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+c:-sin(theta);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+a:sin(chi)*h2*sin(phi) + sin(chi)*h1*cos(phi) - cos(chi)*h3;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+b: -cos(chi)*sin(eta)*h2*sin(phi) -cos(eta)*h1*sin(phi)  +cos(eta)*h2*cos(phi) -cos(chi)*sin(eta)*h1*cos(phi) - sin(chi)*sin(eta)*h3;
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+expand(subst(a, aa, subst(b, bb, -sin(theta)=aa*sin(mu) + bb*cos(mu))));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+Check a and b expand to produce original (Okay)
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+expand(eq68yterm);
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: comment start ]
+Check against special case above (Okay)
+   [wxMaxima: comment end   ] */
+
+/* [wxMaxima: input   start ] */
+subst(0, chi, subst(0, eta, a));
+/* [wxMaxima: input   end   ] */
+
+/* [wxMaxima: input   start ] */
+subst(0, chi, subst(0, eta, b));
+/* [wxMaxima: input   end   ] */
+
+/* Maxima can't load/batch files which end with a comment! */
+"Created with wxMaxima"$
--- a/script/__Lib/diffcalc-2.1/doc/tmp/i16_non_diffcalc_manual.txt
+++ b/script/__Lib/diffcalc-2.1/doc/tmp/i16_non_diffcalc_manual.txt
@@ -0,0 +1,71 @@
+Creating a UB Matrix
+There are three euler modes:
+
+=bisecting: eta and delta are fixed, phi and chi are not fixed.
+=fixed phi: phi and 2theta are fixed, eta and chi are not fixed.
+=fixed psi: Not used for creating a UB matrix .
+First creat a reflection file to store the reflections data using:
+
+reffile('name')
+
+Set the crystal lattice:
+
+latt([a]) assumes cubic
+latt([a,b]) assumes tetragonal
+latt([a,b,c]) assumes orthorhombic
+latt([a,b,c,gam]) assumes monclinic/hexagonal gam different from 90.
+latt([a,b,c,alp,bet,gam])
+
+Use:
+
+c2th([h k l])
+
+to calculate the 2 theta position for the hkl for example:
+
+c2th([0 0 2])
+
+Then use the following to move the diffractometer to the correct positions:
+
+pos delta c2th([0 0 2]) eta c2th([0 0 2])/2
+
+You can now scan eta, chi, and delta to optomise the peak intensity using the following scans for example:
+
+scancn eta 0.01 40 w 0.2 t 1
+
+scancn chi 0.01 40 w 0.2 t 1
+
+scancn delta 0.01 40 w 0.2 t 1
+
+A few iterations may be required.
+
+Now that you have the first reflection it can be stored using the following command:
+
+saveref('reflable',[h k l])
+
+saveref('Ti1',[0 0 2]) for the above example.
+
+Then create a dummy UB matrix using a dummy non-parallel hkl plane eg:
+
+ubm('Ti1',[2 0 0])
+
+Useing the following command to calculate the direction of the second reflection:
+
+hkl_calc([0 2 2])
+
+If the calculated positions can be safely achieved then type:
+
+pos hkl [0 2 2]
+
+Find the second reflection by scanning phi, once the reflection is found save the second reflection using:
+
+saveref('Ti2',[0 2 2]) for example.
+
+Now create a real UB-Matrix using:
+
+ubm('Ti1','Ti2')
+
+You can now drive in recriprocal space.
+
+To change the lattice parameters according the found Bragg peaks
+
+latt([latt()[0]*2/l()]) (cubic only)