Question

How many "nearest" and "next nearest" neighbours, respectively, does potassium have in bcc lattice ? (a) 8,8 (b) 8,6 (c) 6,8 (d) 6,6

Short answer

The potassium in a bcc lattice has 8 nearest neighbours and 6 next nearest neighbours, so the answer is (b) 8,6.

Step-by-step solution

Understand the bcc lattice structure

A body-centered cubic (bcc) lattice has one atom at each corner of the cube and one atom at the center of the cube. Each corner atom is shared among eight adjacent cubes, and the central atom is not shared.

Identify the nearest neighbours

The nearest neighbours of the central atom in a bcc lattice are the eight corner atoms of the same cube. They are located at the end of the cube edges that the central atom touches.

Identify the next nearest neighbours

The next nearest neighbours are found by considering the atoms in adjacent cubes that are closest to the central atom after the nearest neighbours. There are six faces to the cube, and each face is shared with an adjacent cube, which has a central atom at a position equivalent to the original cube's central atom. These six atoms in the centers of the adjacent cubes are the next nearest neighbours.

Key concepts

Body-Centered Cubic Lattice

The body-centered cubic (bcc) lattice plays a pivotal role in understanding the arrangement of atoms in some solid materials. Picture a standard cube with an atom at each of its eight corners, and then envision another atom, cozily situated right at the heart of the cube. This central atom is surrounded by the corner atoms. In a bcc structure, the atoms are packed in a specific way that leads to unique properties of the material, such as how it interacts with heat and electricity. Looking at the bcc lattice from an atomic standpoint, each corner atom forms a bridge with other corner atoms of surrounding cubes. This interconnectivity results in each corner atom being a part of eight different cubes.

For instance, in the case of potassium in a bcc lattice, each central atom has nearest neighbours precisely at the cube's corners. The central potassium atom, therefore, has eight nearest neighbours, which forms the basis for understanding various physical properties of the material.

Crystal Lattice Structures

The concept of crystal lattice structures is integral to the field of solid state chemistry and materials science. It represents the regular, repeating arrangement of atoms, molecules, or ions in three-dimensional space. Imagine a grid that extends infinitely in all directions, with each intersection point fixed with a particle. This grid, or lattice, can adopt various shapes and sizes, leading to the different lattice types such as simple cubic, face-centered cubic, and the aforementioned body-centered cubic.

Each of these lattice structures hosts distinct packing efficiencies and coordination numbers, which reflect the number of immediate neighbour atoms. Considering these structures allows scientists and engineers to predict and explain the properties of materials. For example, materials with a bcc lattice typically have lower packing efficiency compared to face-centered cubic structures, but may also exhibit different temperature and strength characteristics that are beneficial for certain applications.

Solid State Chemistry

Solid state chemistry, the cornerstone that links the microscopic structure of materials to their macroscopic properties, delves into the study of solid materials. This broad field encompasses the analysis of structures like the bcc lattice, the interactions between atoms, and the impact these have on a material's physical characteristics.

Through solid state chemistry, we learn not only about crystal structures but also about how alterations in atomic arrangements can result in varied material properties. This can include electrical conductivity, magnetic behaviour, mechanical strength, and much more. In a practical context, grasping the underpinnings of solid state chemistry is essential for the development of new materials and the improvement of existing ones. For a student tackling the concept of nearest and next nearest neighbours in a solid like potassium, this understanding offers insight into the fundamental correlations between atomic structure and overall material behavior.