Magnesium and Titanium form a crystalline oxide in which Mg appears at the eight corners , oxygen appears at face centres and titanium appears at the centre of cube. The atomic mass of magnesium , titanium and oxygen is 24, 45.9 and 16 amu respectively. A similar compound is formed by calcium with titanium and oxygen .
What type of crystalline structure does `MgTiO_3` have ?

Options

A. Spinel
B. Wurtzite
C. Antifluorite
D. pervoskite

Answer

To determine the type of crystalline structure that MgTiO3 has, we can analyze the arrangement of the ions based on the information given in the question.

### Step-by-Step Solution:

1. **Identify the Positions of the Ions:**
- Magnesium (Mg) is located at the eight corners of the cube.
- Oxygen (O) is located at the face centers of the cube.
- Titanium (Ti) is located at the center of the cube.

2. **Calculate the Contribution of Each Ion:**
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell. Since there are 8 corners:
\[ \text{Contribution of Mg} = 8 \times \frac{1}{8} = 1 \text{ Mg atom} \]
- Each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell. Since there are 6 faces:
\[ \text{Contribution of O} = 6 \times \frac{1}{2} = 3 \text{ O atoms} \]
- The atom at the center contributes fully:
\[ \text{Contribution of Ti} = 1 \text{ Ti atom} \]

3. **Determine the Empirical Formula:**
- Based on the contributions, we have:
- 1 Mg
- 1 Ti
- 3 O
- Therefore, the empirical formula can be represented as \( \text{MgTiO}_3 \).

4. **Identify the Structure Type:**
- The arrangement of ions corresponds to the perovskite structure, which is characterized by the general formula \( ABX_3 \). In this case:
- A = Mg (corner positions)
- B = Ti (center position)
- X = O (face centers)
- The perovskite structure is known for its specific arrangement where the cation occupies the corners and the face centers are occupied by anions.

5. **Conclusion:**
- The crystalline structure of \( \text{MgTiO}_3 \) is a **perovskite structure**.