The unit cell of strontium titanate SrTiO3 is depicted on the left in the figure below showing the crystal structure as confirmed by X-ray diffraction experiments. The lattice constant is a = 3.9 × 10-¹0 m. A typical X-ray powder diffraction spectrum is displayed on the right. The wave length of the X-ray beam (Cu-Ka radiation) is λ = 1.54 × 10-¹0 m. Unit cell of SrTiO3; Sr atoms are shown in blue, Ti in black and the oxygen atoms are in red. Normalized intensity (a.u.) (001) 20 = (011) 30 (111) 40 (200) (210) 50 (211) (220) (300) 60 20 (degrees) 70 (01) (311) >(222) (320) 80 (321) (b) 90 100 X ray powder diffraction data for SrTiO3; the plot shows an overlay for two different SrTiO3 samples. [L. da Silva et al, J. Nanomat., doi:10.1155/2012/890397] a) Identify the Bravais lattice of SrTiO 3and specify the basis for the primitive unit cell shown in the figure. b) Explain how the Miller indices (hkl) describe a family of lattice planes. State a set of possible reciprocal lattice vectors. c) Show that the distance between (hkl) lattice planes in cubic lattices is given by dcubic a (hkl) √h²+k² +1² d) Confirm the assignment of the X-ray peak for the (1,1,1) lattice planes by calculating the angle 20. Strontium titanate is a semiconductor with extraordinary properties making it interesting for diverse applications e.g. for energy storage. The figure below shows the Brillouin zone, a UV absorption spectrum and a computed band structure of this compound.
The unit cell of strontium titanate SrTiO3 is depicted on the left in the figure below showing the crystal structure as confirmed by X-ray diffraction experiments. The lattice constant is a = 3.9 × 10-¹0 m. A typical X-ray powder diffraction spectrum is displayed on the right. The wave length of the X-ray beam (Cu-Ka radiation) is λ = 1.54 × 10-¹0 m. Unit cell of SrTiO3; Sr atoms are shown in blue, Ti in black and the oxygen atoms are in red. Normalized intensity (a.u.) (001) 20 = (011) 30 (111) 40 (200) (210) 50 (211) (220) (300) 60 20 (degrees) 70 (01) (311) >(222) (320) 80 (321) (b) 90 100 X ray powder diffraction data for SrTiO3; the plot shows an overlay for two different SrTiO3 samples. [L. da Silva et al, J. Nanomat., doi:10.1155/2012/890397] a) Identify the Bravais lattice of SrTiO 3and specify the basis for the primitive unit cell shown in the figure. b) Explain how the Miller indices (hkl) describe a family of lattice planes. State a set of possible reciprocal lattice vectors. c) Show that the distance between (hkl) lattice planes in cubic lattices is given by dcubic a (hkl) √h²+k² +1² d) Confirm the assignment of the X-ray peak for the (1,1,1) lattice planes by calculating the angle 20. Strontium titanate is a semiconductor with extraordinary properties making it interesting for diverse applications e.g. for energy storage. The figure below shows the Brillouin zone, a UV absorption spectrum and a computed band structure of this compound.
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![The unit cell of strontium titanate SrTiO3 is depicted on the left in the figure below showing the
crystal structure as confirmed by X-ray diffraction experiments. The lattice constant is
a -
3.9 × 10-¹0 m. A typical X-ray powder diffraction spectrum is displayed on the right. The
wave length of the X-ray beam (Cu-Ka radiation) is λ = 1.54 × 10-¹⁰ m.
Unit cell of SrTiO3; Sr atoms are
shown in blue, Ti in black and the
oxygen atoms are in red.
Normalized intensity (a.u.)
(001)
20
(011)
30
(III)
40
(200)
(210)
50
(211)
(220)
(300)
60
20 (degrees)
70
(310)
(311)
>(222)
(320)
80
90
(17)
100
X ray powder diffraction data for SrTiO3; the plot shows
an overlay for two different SrTiO3 samples.
[L. da Silva et al, J. Nanomat., doi:10.1155/2012/890397]
a) Identify the Bravais lattice of SrTiO 3and specify the basis for the primitive unit cell shown in the
figure.
b) Explain how the Miller indices (hkl) describe a family of lattice planes. State a set of possible
reciprocal lattice vectors.
c) Show that the distance between (hkl) lattice planes in cubic lattices is given by
dcubic = √²+k² +1²
a
(hkl)
d) Confirm the assignment of the X-ray peak for the (1,1,1) lattice planes by calculating the angle
20.
Strontium titanate is a semiconductor with extraordinary properties making it interesting for diverse
applications e.g. for energy storage. The figure below shows the Brillouin zone, a UV absorption
spectrum and a computed band structure of this compound.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b164c93-b180-40d7-aeb8-dca73ab45463%2Ff7a6d730-bf95-475a-bac9-9a02e9378b4b%2Fjnb3n7w_processed.png&w=3840&q=75)
Transcribed Image Text:The unit cell of strontium titanate SrTiO3 is depicted on the left in the figure below showing the
crystal structure as confirmed by X-ray diffraction experiments. The lattice constant is
a -
3.9 × 10-¹0 m. A typical X-ray powder diffraction spectrum is displayed on the right. The
wave length of the X-ray beam (Cu-Ka radiation) is λ = 1.54 × 10-¹⁰ m.
Unit cell of SrTiO3; Sr atoms are
shown in blue, Ti in black and the
oxygen atoms are in red.
Normalized intensity (a.u.)
(001)
20
(011)
30
(III)
40
(200)
(210)
50
(211)
(220)
(300)
60
20 (degrees)
70
(310)
(311)
>(222)
(320)
80
90
(17)
100
X ray powder diffraction data for SrTiO3; the plot shows
an overlay for two different SrTiO3 samples.
[L. da Silva et al, J. Nanomat., doi:10.1155/2012/890397]
a) Identify the Bravais lattice of SrTiO 3and specify the basis for the primitive unit cell shown in the
figure.
b) Explain how the Miller indices (hkl) describe a family of lattice planes. State a set of possible
reciprocal lattice vectors.
c) Show that the distance between (hkl) lattice planes in cubic lattices is given by
dcubic = √²+k² +1²
a
(hkl)
d) Confirm the assignment of the X-ray peak for the (1,1,1) lattice planes by calculating the angle
20.
Strontium titanate is a semiconductor with extraordinary properties making it interesting for diverse
applications e.g. for energy storage. The figure below shows the Brillouin zone, a UV absorption
spectrum and a computed band structure of this compound.
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