z = numpy.zeros(4, dtype='float64')
ctr3 = numpy.ones(4, dtype='float64') / 3.
endmembers = []
lineendpairs = []
#iterate over 4 end members and draw a line from there to center of opposing face, e.g. (0,.33,.33,.33)
for i in range(4):
a = copy.copy(z)
a[i] = 1.
b = copy.copy(ctr3)
b[i] = 0.
q.line(a, b, fmt='b-')
q.scatter([b], c='b', s=15)
endmembers += [a]
lineendpairs += [[a, b]]
#convert the end members and pairs of endpts to cartesian
xyz_lineendpairs = [numpy.array(q.toCart(ls)).T for ls in lineendpairs]
xyz_endmembers = numpy.array(q.toCart(endmembers)).T
#choose the composition of a phase and draw the trivial phase field lines
phcomp = numpy.array([.1, .3, .2, .4])
q.scatter([phcomp], c='r', s=20)
for i in range(4):
a = copy.copy(z)
a[i] = 1.
q.line(a, phcomp, fmt='r-')
# iterate over all 4 phase field triangular boundaries (triangle defined by 3 points, the phase p0 and 2 end members p1,p2) and all 4 composition lines. find intersections
p0 = numpy.array(q.toCart([phcomp])).T[0]
xyz_intr_dlist = []
for countends, (p1, p2) in enumerate(itertools.combinations(xyz_endmembers,
2)):
import pylab, numpy from myquaternaryutility import QuaternaryPlot q=QuaternaryPlot(111) #t=numpy.linspace(0,1.,5) #comps=[[a,b,c,d] for a in t for b in t for c in t for d in t if a+b+c+d==1.] #comps=numpy.float32(comps) t=numpy.linspace(0,1.,30) comps=[[a,b,1.-a-b-(2.*a**2+b),2.*a**2+b] for a in t for b in t[:10] if a+b+(2.*a**2+b)<=1.] comps=numpy.float32(comps) x, y, z=q.toCart(comps) q.scatter(comps,c=comps[:,3]) #q.ax.scatter(x, y, z, c=z) q.plotabcprojection(comps, c=(.4, .4, .4)) q.label(ha='center', va='center', fontsize=16) q.set_projection(azim=-17, elev=-6) pylab.show()
import pylab, numpy
from myquaternaryutility import QuaternaryPlot
q = QuaternaryPlot(111)
#t=numpy.linspace(0,1.,5)
#comps=[[a,b,c,d] for a in t for b in t for c in t for d in t if a+b+c+d==1.]
#comps=numpy.float32(comps)
t = numpy.linspace(0, 1., 30)
comps = [[a, b, 1. - a - b - (2. * a**2 + b), 2. * a**2 + b] for a in t
for b in t[:10] if a + b + (2. * a**2 + b) <= 1.]
comps = numpy.float32(comps)
x, y, z = q.toCart(comps)
q.scatter(comps, c=comps[:, 3])
#q.ax.scatter(x, y, z, c=z)
q.plotabcprojection(comps, c=(.4, .4, .4))
q.label(ha='center', va='center', fontsize=16)
q.set_projection(azim=-17, elev=-6)
pylab.show()
z=numpy.zeros(4, dtype='float64')
ctr3=numpy.ones(4, dtype='float64')/3.
endmembers=[]
lineendpairs=[]
#iterate over 4 end members and draw a line from there to center of opposing face, e.g. (0,.33,.33,.33)
for i in range(4):
a=copy.copy(z)
a[i]=1.
b=copy.copy(ctr3)
b[i]=0.
q.line(a, b, fmt='b-')
q.scatter([b], c='b', s=15)
endmembers+=[a]
lineendpairs+=[[a, b]]
#convert the end members and pairs of endpts to cartesian
xyz_lineendpairs=[numpy.array(q.toCart(ls)).T for ls in lineendpairs]
xyz_endmembers=numpy.array(q.toCart(endmembers)).T
#choose the composition of a phase and draw the trivial phase field lines
phcomp=numpy.array([.1, .3, .2, .4])
q.scatter([phcomp], c='r', s=20)
for i in range(4):
a=copy.copy(z)
a[i]=1.
q.line(a, phcomp, fmt='r-')
# iterate over all 4 phase field triangular boundaries (triangle defined by 3 points, the phase p0 and 2 end members p1,p2) and all 4 composition lines. find intersections
p0=numpy.array(q.toCart([phcomp])).T[0]
xyz_intr_dlist=[]
for countends, (p1, p2) in enumerate(itertools.combinations(xyz_endmembers, 2)):
for countlines, (l0, l1) in enumerate(xyz_lineendpairs):
