Brittleness is the property of a material that causes it to break with little permanent distortion. When a material is brittle, it lacks the ability to deform plastically before failure. Instead, it undergoes brittle fracture, which is characterized by a sudden and catastrophic failure without any significant plastic deformation. This is in contrast to ductility, malleability, and plasticity, which are properties that allow a material to deform without breaking.

Brittle materials have a limited ability to absorb energy before fracture, making them prone to sudden failure when subjected to stress. This is due to the nature of the atomic bonds within the material. In brittle materials, the atomic bonds are strong and the material is unable to accommodate deformation by dislocation movement. As a result, when stress is applied, the material reaches its ultimate strength quickly and fractures with little warning.

There are several factors that contribute to the brittleness of a material:

1. Crystal Structure: Materials with a highly ordered crystal structure, such as ceramics and some metallic alloys, tend to be more brittle. The rigid arrangement of atoms limits the ability of the material to deform plastically.

2. Lack of Ductile Phases: Materials that lack ductile phases, such as certain polymers and brittle ceramics, are inherently brittle. Ductile phases allow for plastic deformation and absorb energy during deformation.

3. High Stiffness: Materials with high stiffness, such as brittle polymers and some metals, are more likely to be brittle. The high stiffness limits the ability of the material to deform and absorb energy.

4. Low Temperature: Brittle fracture is more likely to occur at low temperatures because the energy required for dislocation movement is higher. At low temperatures, materials are less able to deform plastically and are more prone to brittle fracture.

In summary, brittleness is the property of a material that causes it to break with little permanent distortion. It is characterized by a lack of plastic deformation and a sudden, catastrophic failure. Factors such as crystal structure, lack of ductile phases, high stiffness, and low temperature contribute to the brittleness of a material.