**4. X-ray diffraction of CH3NH3PbI3**

CH3NH3PbI3, except for the lattice constants. Lattice parameters of these compounds are strongly depedent on the size of halogen ions, as shown in Figure 2. As summarized in Table 8, ion radii of halogen elements increase with increasing atomic numbers, which affect the

**Atom** *x y z* **B (Å2**

Pb 0 0 0 1.61 Br 0 0.0413 0.5 5.41 N 0.413 0.417 0.5 6.02 C 0.578 0.582 0.5 6.05

**Table 7.** Structural parameters of cubic CH3NH3PbBr3. Space group *Pm3m* (Z=1), *a*=5.933 nm at 298 K. B is isotropic

**Hologen element** F- Cl- Br- I-**Ion radius (Å)** 1.33 1.81 1.96 2.20 **14 group element** Ge2+ Sn2+ Pb2+ **Lattice parameters** 0.73 0.93 1.18

> **Halogen ion of CH3NH3PbX3 Cl Br I**

**)**

lattice constants of CH3NH3PbX3, as observed in Figure 2.

displacement parameter.

82 Solar Cells - New Approaches and Reviews

**Table 8.** Ion radii of halogen and 14 group elements.

**5.6**

**Figure 2.** Lattice constants of CH3NH3PbX3 (X=Cl, Br, or I).

**5.7**

**5.8**

**5.9**

**6.0**

**6.1**

**Lattice constant (Å)**

**6.2**

**6.3**

**6.4**

**6.5**

Microstructure of the perovskite phases can be investigated by X-ray diffraction (XRD). The XRD will indicate that the sample is a single phase or mixed phase. If the sample consists of nanoparticles or nanocrystals, the crystallite size can be estimated from the full width at half maximum (FWHM). From the XRD data, analyses of high-resolution TEM image and electron diffraction would become easier. If the sample is a known material, plane distances (*d*) and indices can be clarified from the diffraction peaks of XRD. When the sample has an unknown structure, the values of the plane distances can be obtained by the XRD, which will effectively stimulate the structure analysis.

Calculated X-ray diffraction patterns on the CH3NH3PbI3 with cubic, tetragonal and ortho‐ rhombic structures is shown in Figure 3, and calculated X-ray diffraction parameters of cubic, tetragonal and orthorhombic CH3NH3PbI3 are listed in Table 9, 10, and 11, respectively. For the cubic phase, site occupancies were set as 1/4 for I and 1/12 for C and N. Structure factors were averaged for each index. Site occupancies were set as 1/4 for C and N for the tetragonal CH3NH3PbI3. Figure 4 is an enlarged calculated X-ray diffraction patterns of CH3NH3PbI3. Reflection positions of 211 and 213 inconsistent with cubic symmetry for tetragonal structure are indicated by asterisks, which would be helpful for the distinction between the cubic and tetragonal phase [1].


**Table 9.** Calculated X-ray diffraction parameters of cubic CH3NH3PbI3. Equivlent indices were combined. Space group *Pm3m* (Z=1), *a*=6.391 Å at 330 K. *F* is structure factor.

**Figure 3.** Calculated X-ray diffraction patterns of CH3NH3PbI3 with cubic, tetragonal and orthorhombic structures.

**Cubic**

**Tetragonal**

**Orthorhombic**

**20 30 40 50 60**

**(degree)**

**Figure 3.** Calculated X-ray diffraction patterns of CH3NH3PbI3 with cubic, tetragonal and orthorhombic structures.

**Intensity (a. u.)**

Solar Cells - New Approaches and Reviews

**Figure 4.** Enlarged calculated X-ray diffraction patterns of CH3NH3PbI3 with cubic, tetragonal and orthorhombic struc‐ tures. \*Reflection positions inconsistent with cubic symmetry for tetragonal structure.


#### Crystal Structures of CH3NH3PbI3 and Related Perovskite Compounds Used for Solar Cells http://dx.doi.org/10.5772/59284 87


86 Solar Cells - New Approaches and Reviews

**Table 10.** Calculated X-ray diffraction parameters of tetragonal CH3NH3PbI3. Space group *I4/mcm* (Z=4), *a*=8.800 Å, c=12.685 Å at 220 K.



Crystal Structures of CH3NH3PbI3 and Related Perovskite Compounds Used for Solar Cells http://dx.doi.org/10.5772/59284 89


88 Solar Cells - New Approaches and Reviews

**Table 11.** Calculated X-ray diffraction parameters of orthorhombic CH3NH3PbI3. Space group *Pnma* (Z=4), *a*=8.8362 Å, *b*=12.5804 Å, *c*=8.5551 Å at 100 K. B is isotropic displacement parameter. All occupancy factors 1.0.

Calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values are shown in Figure 5. When the crystallite sizes decrease, the FWHM values increase, and different peak intensities are observed in Figure 5.

Figure 6 is an enlarged calculated X-ray diffraction patterns of CH3NH3PbI3. With increasing FWHM values, the diffraction peaks of 200 and 110 seem to be combined, which should be very careful for the XRD structure analysis.

**Figure 5.** Calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values.

**Figure 6.** Enlarged calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values.

**20 30 40 50 60**

**FWHM = 0.1**

**FWHM = 0.2**

**FWHM = 0.3**

**FWHM = 0.4**

**(degree)**

**Intensity (a. u.)**

Solar Cells - New Approaches and Reviews

**200**

**Figure 5.** Calculated X-ray diffraction patterns of CH3NH3PbI3 with various FWHM values.
