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Commit 8f6fb1c0 authored by Kostas Vilkelis's avatar Kostas Vilkelis :flamingo:
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fixed plot in lecture 10

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...@@ -100,162 +100,108 @@ which is clearly 1. ...@@ -100,162 +100,108 @@ which is clearly 1.
### Example of a two-dimensional reciprocal lattice ### Example of a two-dimensional reciprocal lattice
```python ```python
# Define the lattice vectors # Define primitive lattice vectors
a1 = np.array([1,0]) a1 = np.array([1,0])
a2 = np.array([0.5,sqrt(3)/2]) a2 = np.array([0.5,sqrt(3)/2])
a1_alt = -a1-a2 # Compute reciprocal lattice vectors
a2_alt = a1_alt + a1 b1,b2 = np.linalg.inv(np.array([a1,a2]).T) @ np.eye(2)*2*pi
a2_c = np.array([0,sqrt(3)])
# Produces the lattice to be fed into plotly fig = make_subplots(rows=1, cols=2,shared_yaxes=True,subplot_titles=('Real Space', 'Reciprocal Space'))
def lattice_generation(a1,a2,N=6):
# Generates the lattice given the lattice vectors
def lattice_generation(a1,a2,N):
grid = np.arange(-N//2,N//2,1) grid = np.arange(-N//2,N//2,1)
xGrid, yGrid = np.meshgrid(grid,grid) xGrid, yGrid = np.meshgrid(grid,grid)
return np.reshape(np.kron(xGrid.flatten(),a1),(-1,2))+np.reshape(np.kron(yGrid.flatten(),a2),(-1,2)) return np.reshape(np.kron(xGrid.flatten(),a1),(-1,2))+np.reshape(np.kron(yGrid.flatten(),a2),(-1,2))
def subplot(a1,a2,col):
# Produces the dotted lines of the unit cell N = 6
def dash_contour(a1,a2, vec_zero = np.array([0,0]), color='Red'): lat_points = lattice_generation(a1,a2,N)
dotLine_a1 = np.transpose(np.array([a1,a1+a2])+vec_zero) line_a1 = np.transpose([[0,0],a1])
dotLine_a2 = np.transpose(np.array([a2,a1+a2])+vec_zero) line_a2 = np.transpose([[0,0],a2])
dotLine_a1 = np.transpose([a1,a1+a2])
dotLine_a2 = np.transpose([a2,a1+a2])
def dash_trace(vec,color):
trace = go.Scatter(
x=vec[0],
y=vec[1],
mode = 'lines',
line_width = 2,
line_color = color,
line_dash='dot',
visible=False
)
return trace
return dash_trace(dotLine_a1,color),dash_trace(dotLine_a2,color) fig.add_trace(
go.Scatter(visible=False, x=line_a1[0],y=line_a1[1],mode='lines',line_color='red'
# Makes the lattice vector arrow ), row = 1, col = col
def make_arrow(vec,text,color = 'Red',vec_zero = [0,0],text_shift = [-0.2,-0.1]):
annot = [dict(
x=vec[0]+vec_zero[0],
y=vec[1]+vec_zero[1],
ax=vec_zero[0],
ay=vec_zero[1],
xref='x',
yref='y',
axref='x',
ayref = 'y',
showarrow=True,
arrowhead=2,
arrowsize=1,
arrowwidth=3,
arrowcolor = color
),
dict(
x=(vec[0]+vec_zero[0])/2+text_shift[0],
y=(vec[1]+vec_zero[1])/2+text_shift[1],
xref='x',
ayref = 'y',
text = text,
font = dict(
color = color,
size = 20
),
showarrow=False,
)
]
return annot
# Create the pattern
pattern_points = lattice_generation(a1,a2)
pattern = go.Scatter(x=pattern_points.T[0],y=pattern_points.T[1],mode='markers',marker=dict(
color='Black',
size = 20,
symbol = 'star-open-dot')
) )
fig.add_trace(
# Lattice Choice A go.Scatter(visible=False, x=line_a2[0],y=line_a2[1],mode='lines',line_color='red'
latticeA = go.Scatter(visible = False,x=pattern_points.T[0],y=pattern_points.T[1],mode='markers',marker=dict( ), row = 1, col = col
color='Red',
size = 10,
)
) )
fig.add_trace(
# Lattice Choice B go.Scatter(visible=False, x=dotLine_a1[0],y=dotLine_a1[1],mode='lines',line_color='red',line_dash='dot'
latB_points = lattice_generation(a1,a2) ), row = 1, col = col
latticeB = go.Scatter(visible = False, x=latB_points.T[0]+0.5,y=latB_points.T[1],mode='markers',marker=dict(
color='Blue',
size = 10,
)
) )
fig.add_trace(
# Annotate the lattice vectors go.Scatter(visible=False, x=dotLine_a2[0],y=dotLine_a2[1],mode='lines',line_color='red',line_dash='dot'
# Button 2 ), row = 1, col = col
bt2_annot = make_arrow(a1,'$a_1$') + make_arrow(a2,'$a_2$') + make_arrow(a1_alt,'$a`_1$',color='Black',text_shift=[-0.55,-0.1]) + make_arrow(a2_alt,'$a`_2$',color='Black')
#Button 3
bt3_annot = make_arrow(a1,'$a_1$', vec_zero = [-0.5,0], color = 'Blue') + make_arrow(a2,'$a_2$',vec_zero = [-0.5,0], color = 'Blue')
#Button 4
bt4_annot = make_arrow(a2_c,'$a_2$') + make_arrow(a1,'$a_1$')
# (0) Button 1, (0, 1-5) Button 2, (0, 6-8) Button 3, (0,1,9,10)
data = [pattern,latticeA,*dash_contour(a1,a2),*dash_contour(a1_alt,a2_alt,color='Black'),
latticeB, *dash_contour(a1,a2,vec_zero=[-0.5,0],color='Blue'),
*dash_contour(a1, a2_c)]
updatemenus=list([
dict(
type="buttons",
direction="down",
active=0,
buttons=list([
dict(label="Pattern",
method="update",
args=[{"visible": [True, False, False, False, False, False, False, False, False, False, False]},
{"title": "Pattern",
"annotations": []}]),
dict(label="Lattice A",
method="update",
args=[{"visible": [True, True, True, True, True, True, False, False, False, False, False]},
{"title": "Lattice A with a Primitive Unit Cell",
"annotations": bt2_annot}]),
dict(label="Lattice B",
method="update",
args=[{"visible": [True, False, False, False, False, False, True, True, True, False, False]},
{"title": "Lattice B with a Primitive Unit Cell",
"annotations": bt3_annot}]),
dict(label="C.U.Cell",
method="update",
args=[{"visible": [True, True, False, False, False, False, False, False, False, True, True]},
{"title": "Conventional Unit Cell",
"annotations": bt4_annot}])
]),
) )
]
)
fig.add_trace(
go.Scatter(visible=False, x=lat_points.T[0],y=lat_points.T[1],mode='markers',marker=dict(
color='Black',
size = 20
)
), row = 1, col = col
)
plot_range = 2 # Generate subplots to be used by the slider
axis = dict( N_values = 10
for i in np.linspace(2.5,3.5,N_values):
subplot(a1*i,a2*i,1)
subplot(b1/i,b2/i,2)
# Define the default subplot
active = 4
for i in range(10):
fig.data[active*10+i].visible = True
steps = []
for i in range(N_values):
step = dict(
label = 'Lattice Constant',
method="restyle",
args=["visible", [False] * len(fig.data)],
)
for j in range(10):
step["args"][1][i*10+j] = True # Toggle i'th trace to "visible"
steps.append(step)
sliders = [dict(
tickcolor = 'White',
font_color = 'White',
currentvalue_font_color = 'Black',
active = active,
name = 'Lattice Constant',
steps = steps
)]
plot_range = 5
fig.update_layout(
sliders=sliders,
showlegend = False,
plot_bgcolor = 'rgb(254, 254, 254)',
width = 1000,
height = 500,
xaxis = dict(
range=[-plot_range,plot_range], range=[-plot_range,plot_range],
visible = False, visible = False,
showgrid = False, showgrid = False,
fixedrange = True fixedrange = True
),
yaxis = dict(
range = [-plot_range,plot_range],
visible = False,
showgrid = False,
fixedrange = True
) )
layout = dict(
showlegend = False,
updatemenus=updatemenus,
plot_bgcolor = 'rgb(254, 254, 254)',
width = 600,
height = 600,
xaxis = axis,
yaxis = axis
) )
fig.update_yaxes(range=[-plot_range, plot_range], row=1, col=2)
fig.update_xaxes(range=[-plot_range, plot_range], row=1, col=2,visible=False)
fig.show()
fig=dict(data=data, layout=layout)
py.iplot(fig, filename='lattice_basics')
``` ```
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