**Answer:**

The illite crystal has a great tendency to split into ultimate platelets. Let's understand this property in detail:

**Illite Crystal:**
Illite is a type of clay mineral that belongs to the mica group. It is composed of layers of aluminum silicate sheets, potassium ions, and water molecules. Illite is commonly found in sedimentary rocks and soils.

**Tendency to Split:**
Illite crystals have a unique property of splitting into thin, flat platelets. This property is attributed to the layered structure of illite. The crystal structure consists of tightly packed layers of aluminum silicate sheets, with potassium ions and water molecules located between these layers.

**Layered Structure:**
The layered structure of illite makes it prone to splitting. The layers are held together by relatively weak van der Waals forces, which are easily overcome by external forces. When these forces are applied, the layers can easily slide past each other, resulting in the splitting of the crystal into thin platelets.

**Ultimate Platelets:**
The splitting of illite crystals occurs at the atomic or molecular level, resulting in the formation of extremely thin platelets. These platelets have a high aspect ratio, with their thickness being much smaller than their length and width.

**Significance:**
The tendency of illite to split into ultimate platelets is significant in various applications. Some of the key applications include:

1. Drilling Fluids: Illite platelets are used in drilling fluids as a rheology modifier. Their large surface area and thinness provide excellent lubrication and reduce friction in the drilling process.

2. Soil Improvement: When illite platelets are added to soils, they can enhance the soil's structural properties. The platelets act as a binder, improving the soil's cohesion and stability.

3. Geotechnical Engineering: Illite platelets are used in geotechnical engineering to stabilize slopes and prevent landslides. The platelets can be mixed with soil to create a reinforced soil mass, increasing its shear strength and stability.

In conclusion, the illite crystal has a great tendency to split into ultimate platelets due to its layered structure and weak interlayer forces. This property has significant applications in various fields, including drilling fluids, soil improvement, and geotechnical engineering.

B