def calcValidTauRange(mu, tth, psi):
th = tth / 2
etaMin = calcEtaMin(tth, psi)
tauMin = calcTauPsiEta(mu, tth, psi, etaMin)
# Psi mode
tauMax = (bc.sind(th) ** 2 - bc.sind(psi) ** 2 + bc.cosd(th) ** 2 * bc.sind(psi) ** 2) / \
(2 * mu * bc.sind(th) * bc.cosd(psi))
return etaMin, tauMax
def calcTauRange(mu, tth, psi, etaMin):
th = tth / 2
tauMin = calcTauPsiEta(mu, tth, psi, etaMin)
if abs(psi) > th:
tauMin = None # NaN heißt nichts?
else:
# Omega mode
tauMin = (bc.sind(th) ** 2 - bc.sind(psi) ** 2 + bc.cosd(th) ** 2 * bc.sind(psi) ** 2) / \
(2 * mu * bc.sind(th) * bc.cosd(psi))
# Psi mode
tauMax = (bc.sind(th) ** 2 - bc.sind(psi) ** 2 + bc.cosd(th) ** 2 * bc.sind(psi) ** 2) / \
(2 * mu * bc.sind(th) * bc.cosd(psi))
return tauMin, tauMax
def calcEtaMin(tth, psi):
th = tth / 2
# if psi <= th:
# etaMin = 0
# else:
# etaMin = asind((sind(psi)**2 - sind(th)**2)**0.5 / (bc.cosd(th) * sind(psi)))
if psi == 0:
return 0
else:
return bc.asind((max(0,
bc.sind(psi)**2 - bc.sind(th)**2))**0.5 /
(bc.cosd(th) * bc.sind(psi)))
def calcEtaTau(mu, tau, tth, psi):
th = tth / 2
return bc.asind(2 * mu * tau * bc.sind(th) * bc.cosd(psi) - bc.sind(th) ** 2 + bc.sind(psi) ** 2) ** 0.5 / \
(bc.cosd(th) * bc.sind(psi))
def latticeSpacings(spacings, angles, h, k, l):
# check if single values are arrays or not
if bf.length(spacings) == 1:
if len(bf.size(spacings)) > 0:
spacing = spacings[0]
else:
spacing = spacings
if bf.length(angles) == 1:
if len(bf.size(angles)) > 0:
angle = angles[0]
else:
angle = angles
# determine lattice spacings
if bf.length(spacings) == 1 and bf.length(angles) == 1 and angle == 90:
# cubic
dVals = conv.aVals2latticeDists(spacing, h, k, l)
elif bf.length(spacings) == 1 and bf.length(angles) == 1 and angle != 90:
# rhomboedric
dVals = (spacing**2 *
(1 - 3 * bc.cosd(angle)**2 + 2 * bc.cosd(angle)**3) /
((h**2 + k**2 + l**2) * bc.sind(angle)**2 + 2 *
(h * k + k * l + h * l) *
(bc.cosd(angle)**2 - bc.cosd(angle))))**0.5
elif bf.length(spacings) == 2 and bf.length(angles) == 1 and angle == 90:
# tetragonal
#dVals = spacings[0] / (h ** 2 + k ** 2 + l ** 2 * (spacings[0] ** 2 / spacings[1] ** 2)) ** 0.5
dVals = 1 / (
(h**2 + k**2) / spacings[0]**2 + l**2 / spacings[1]**2)**0.5
elif bf.length(spacings) == 2 and bf.length(
angles) == 2 and angles[0] == 90 and angles[1] == 120:
# hexagonal
dVals = spacings[0] / (4 / 3 * (h**2 + h * k + k**2) +
l**2 * spacings[0]**2 / spacings[1]**2)**0.5
elif bf.length(spacings) == 3 and bf.length(angles) == 1 and angle == 90:
# orthorhombic
dVals = 1 / ((h / spacings[0])**2 + (k / spacings[1])**2 +
(l / spacings[2])**2)**0.5
elif bf.length(spacings) == 3 and bf.length(
angles) == 2 and angles[0] == 90: # and angles[1] != 90
# monoklin
dVals = 1 / (h**2 / (spacings[0]**2 * bc.sind(angles[1])**2) +
k**2 / spacings[1]**2 + l**2 /
(spacings[2]**2 * bc.sind(angles[1])**2) -
2 * h * l * bc.cosd(angles[1]) /
(spacings[0] * spacings[2] * bc.sind(angles[1])**2))**0.5
elif bf.length(spacings) == 3 and bf.length(angles) == 3:
# triklin
v = spacings[0] * spacings[1] * spacings[2] * (
1 - bc.cosd(angles[0])**2 - bc.cosd(angles[1])**2 -
bc.cosd(angles[2])**2 + 2 * bc.cosd(angles[0]) *
bc.cosd(angles[1]) * bc.cosd(angles[2]))**0.5
s11 = spacings[1]**2 * spacings[2]**2 * bc.sind(angles[0])**2
s22 = spacings[0]**2 * spacings[2]**2 * bc.sind(angles[1])**2
s33 = spacings[0]**2 * spacings[1]**2 * bc.sind(angles[2])**2
s12 = spacings[0] * spacings[1] * spacings[2]**2 * (
bc.cosd(angles[0]) * bc.cosd(angles[1]) - bc.cosd(angles[2]))
s23 = spacings[0]**2 * spacings[1] * spacings[2] * (
bc.cosd(angles[1]) * bc.cosd(angles[2]) - bc.cosd(angles[0]))
s13 = spacings[0] * spacings[1]**2 * spacings[2] * (
bc.cosd(angles[2]) * bc.cosd(angles[0]) - bc.cosd(angles[1]))
dVals = (v**2 /
(s11 * h**2 + s22 * k**2 + s33 * l**2 + 2 * s12 * h * k +
2 * s23 * k * l + 2 * s13 * h * l))**0.5
return dVals
def calcTauPsiEta(mu, tth, psi, eta):
th = tth / 2
return (bc.sind(th) ** 2 - bc.sind(psi) ** 2 + bc.cosd(th) ** 2 * bc.sind(psi) ** 2 * bc.sind(eta) ** 2) / \
(2 * mu * bc.sind(th) * bc.cosd(psi))