Difference Between Unit Cell and Primitive Cell

钥匙差 - 单位单元与原始单元

Unit cell of a格子is the smallest unit that represents all the constituents in a crystal system and their arrangement. The unit cell is the smallest repetitive unit of a lattice. A primitive cell is the smallest possible unit cell of a lattice. Therefore, the primitive cell is a type of unit cell. The key difference between unit cell and primitive cell is that晶胞具有平行磷的几何形状，而2D原始细胞具有平行图几何形状，3D原始细胞具有平行i的几何形状。

内容

1.Overview and Key Difference
2.什么是单元电池
3.What is a Primitive Cell
4.Side by Side Comparison – Unit Cell vs Primitive Cell in Tabular Form
5。概括

什么是单元电池?

Unit cell is the smallest group of atoms that has the overall symmetry of a crystal, and from which the entire lattice can be built up by repetition in three dimensions. Therefore, unit cells are the repeating units of crystal lattices.

A unit cell is described using lattice parameters and lattice points. Lattice parameters are lengths between edges of nit cell (given by a, b and c symbols) and angles of the unit cell (given by α, β and γ symbols). Lattice points are atoms, molecules or ions from which the lattice is made of.

Unit cell has a geometry known as parallelepiped (a 3D figure formed from 6 parallelograms). This geometry is described by the six lattice parameters (mentioned above). The positions of lattice points are given by fractional coordinates denoted by x_i, y_i和z_i, which are measured from a reference point. According to Auguste Bravais (1850), there are 14 types of lattices, known as Bravais lattices. The unit cells of these Bravais lattices are as follows.

下图中的单位单元格（1-14）的名称如下。（在这里，P是指“原始中心”，C是指“单个阶段中心”，我指的是“以身体为中心”，而F则指“面部为中心”）。

1. 立方p
2. 立方i
3. 立方f
4. 四方p
5. 四方i
6. 正交p
7. Orthorhombic C
8. Orthorhombic I
9. Orthorhombic F
10. Monoclinic P
11. Monoclinic C
12. Triclinic
13. Rhomboedral
14. Hexagonal

什么是原始细胞？

一个原始细胞化学是最小的彼得ible unit cell of a lattice, having lattice points only at each of its eight vertices. Hence, it is the simplest form of unit cells. It is a structural representation of a lattice (a crystal system) that can be used to characterize a lattice. Therefore, the primitive cell is a primitive unit. The primitive cell can be drawn in either two-dimensional or three-dimensional form.

There are two types of primitive cells: two-dimensional primitive cells and three-dimensional primitive cells. The two-dimensional primitive cells are parallelograms. This means, there can be orthogonal angles, equal lengths or both in these two-dimensional primitive cells. Types of primitive cells are as follows.

A three-dimensional primitive cell is known to be parallelepiped (a 3D figure formed from 6 parallelograms). It has orthogonal angles, equal lengths or both. Types of three-dimensional primitive cells are listed below.

1. 平行ip缩（三斜切）
2. Oblique rhombic prism (Monoclinic)
3. Oblique rectangular prism (Monoclinic)
4. 右菱形棱镜（正骨）
5. Rectangular cuboid (Orthorhombic)
6. 方长方体（四方）
7. 三角甲虫（菱形）
8. 立方体（立方）

What is the Difference Between Unit Cell and Primitive Cell?

Unit Cell vs Primitive Cell
单位细胞是最小的原子，具有晶体的整体对称性，可以通过三个维度的重复来从中构建整个晶格。	一个原始细胞化学是最小的彼得ible unit cell of a lattice, having lattice points at each of its eight vertices only.
Geometry
Unit cell has parallelepiped geometry.	2D原始细胞具有平行图几何形状，而3D原始细胞具有平行ip的几何形状。
Shape
Unit cell is a three-dimensional structure.	Primitive cell can be given as a two-dimensional structure or three-dimensional structure.

概括– Unit Cell vs Primitive Cell

A primitive cell is a type of unit cell. A unit cell is the smallest repetitive unit of a crystal system that represents the repeating pattern of a lattice. The key difference between unit cell and primitive cell is that the unit cell has parallelepiped geometry whereas 2D primitive cell has parallelogram geometry and 3D primitive cell has parallelepiped geometry.

Reference:

1.“原始细胞”。Wikipedia，Wikimedia基金会，2018年2月28日，Available here.
2.“晶胞，原始细胞和Wigner-Seitz细胞。”晶胞，原始细胞和Wigner-Seitz细胞|简而言之，物理学，Available here.
3. “Categories of Solids.” Unit Cells, Bodner Research Lab,Available here.

Image Courtesy:

1. Napy1Kenobi的“ Bravais Lattices” - 自己的作品(CC BY-SA 3.0)viaCommons Wikimedia