What is the difference and relationship between unit cells, primary cells, and primitives?

Take a lattice point as the vertex in the crystal lattice, and take the parallelepiped formed by the period of the three non-coplanar directions as the side length as the repeating unit, and the parallelepiped will be periodically translated in three different directions, which can fill the entire crystal lattice to form a crystal, and this parallelepiped is the original cell. In an intact crystal, the lattice has a certain periodic symmetry in all three directions of space, so that a parallelepiped with a node as the vertex and an edge length equal to the period in these three directions can be taken as the smallest repeating unit to summarize the characteristics of the lattice, and such a repeating unit is called the primordial primitive. A parallelepiped unit that can completely reflect the chemical-structural characteristics of the atoms or ions in the crystal in three-dimensional space is called a crystallographic protocell.

Among them, the one that can maintain the symmetry of the crystal structure and the smallest volume is called "unit cell", but it is also often referred to as unit cell, customary unit cell or Blafi original cell. <>

Crystal structure =Unit cell, unit cell = structure primitive + lattice.

The unit cell is the basic repeating unit of the crystal structure, and the whole crystal is in three-dimensional space according to the unit cell.

Periodically repeatedly, parallel to each other, each vertex is stacked in a way that 8 unit cells are infiltrated together.

In the complete crystal of Lyric, the lattice has a certain periodic symmetry in all three directions of space, so that a parallelepiped with the node as the vertex and the side length equal to the period in these three directions can be taken.

As the smallest repeating unit, to summarize the characteristics of the crystal lattice, such a repeating unit is called the primordial primitive cell or simply the protocell.

The spatial lattice can be divided by arbitrarily selecting 3 non-parallel unit vectors. Due to the different choice unit vectors, the way of division is also different, and there can be an infinite number of forms.

But it basically boils down to two categories: one is the unit that contains a lattice point, which is called the prime unit. Note that when calculating the number of dots, consider that the dots at the vertices of the flat-liquid tarding hexahedron are all common to the 8 adjacent parallelepipeds, and each parallelepiped unit is only partially spread to that point.

The other type is where each unit contains 2 or more lattice points, which is called a complex unit. Sometimes, for a certain purpose, the spatial lattice is divided into complex units.

First, the form is different.

1. Protocell: Take a lattice point as the vertex in the crystal lattice, and take the parallelepiped formed by the period of three non-coplanar directions as the side length as the repeating unit, and the parallelepiped can be filled with the entire crystal lattice to form a crystal by periodic translation in three different directions, and this parallelepiped is the protocell.

2. Unit cell: Its shape and size are the same as the parallelepiped units of the space lattice, and all the characteristics of the entire lattice are retained.

Second, the nodes are different.

1. Protocell: The node is on the apical angle of the protocell.

2. Unit cell: The junction can not only be on the apex angle, but also on the body center or face center.

Third, the repeating units are different.

1. Protocell: Protocell is the smallest repeating unit of volume, which reflects the periodicity of the crystal lattice, and the selection of protocells is not unique, but their volumes are equal.

2. Unit cell: In order to reflect the symmetry of the crystal at the same time, the volume of the repeating unit taken in crystallography is not necessarily the smallest.

Hello: The selection of unit cells is not unique, and unit cells of different sizes and shapes can be selected in the same lattice.

To avoid trouble, the principle of selecting protocells is:

Reflect periodicity, reflect symmetry, minimum volume, these principles are general.

It can't be both, so the selection method is still not unique. Only the smallest volume is required to obtain the protocells.

The selection of the protocell is not unique, but it must contain only one node, which is the smallest unit of the crystal structure, the selection principle.

It is the shortest translation vector that tries to make each side a lattice.

For example, fcc, bcc, their unit cells can be selected as squares, (fcc contains 4 nodes, bcc contains 2 nodes).

Both of their protocells contain a node, fcc is a hexahedron with a cubic fixed point and a face-centered line as an edge, and bcc is the sum of cubic vertices.

A hexahedron with an edge connected by a body-centered line.

The protocell of the crystal is the smallest periodic structural unit that constitutes the crystal, but the protocell is often too small to reflect the symmetry of the crystal lattice. This is the case with body-centered and face-centered cube grids. In order to reflect the symmetry of the lattice, a larger periodic element must be selected.

On the premise of maintaining lattice symmetry, the smallest periodic structural unit that makes up a crystal is called a single cell of a crystal. The edge vector of a single cell is called a single base vector and is usually given a

b and c indicate that for example, the protocells of the body-centered cubic structure and the face-centered cubic structure are a parallelepiped without cubic symmetry, and the slightly larger periodic structural units that can maintain the cubic symmetry should be taken as the body-centered cube and the face-centered cube, respectively; In the two-dimensional case, the protocell of the centered rectangular lattice is rhomboid, and the symmetry of its rectangle is not intuitive, and the periodic structural unit that can reflect the symmetry of the crystal is a rectangle slightly larger than the rhombic protocell, and the rectangular unit is the monocellular of the crystal, and the side length of the monocell is called the lattice constant. Monocates are sometimes referred to as unit cells, customary protocytes (commonly used in crystallography).

A unit cell is the smallest periodic repeating unit in a crystal structure. The structure of the unit cell can be described in two ways, one is the way it repeats periodically, and the other is the content of the repetition.

The method of periodic repetition can be discussed in mathematical lattice, and the content of repetition is the structural primitive, including the type, quantity, connection mode and arrangement position of atoms and molecular ions in the unit cell world.

Therefore, the ulnar chain is often used to represent the crystal structure by crystal = lattice + structural primitive.

The unit cell refers to the spatial structure composed of the smallest repeatable unit in the crystal, that is, the unit cell is the basic unit structure of the crystal. A unit cell can be regarded as a cube obtained by dispersing a translational lattice through volcanic dispersion, which refers to a spatial network of three linear independent vectors, and the unit cell is the basic structural unit of the lattice. Normally, the unit cell in the crystal is dimensionally 1 order higher than the lattice.

The protocell refers to the spatial structure composed of the smallest repeatable unit in the crystal lattice, and the protocell is also the basic unit structure of the crystal. The protocell can be thought of as a unit obtained by discrete translational lattice, and its degrees of freedom are equal to the degrees of freedom of the lattice. Each lattice point is contained within a protocell in which it is located, not within each unit cell of the entire crystal.

Thus, the protocell is the basic building unit of the crystal lattice. In a nutshell, a unit cell is a complement of a lattice with only one unit cell in the lattice point, and each unit cell contains and contains only one unit cell point.

Further extension and expansion, for crystals, the unit cell and its lattice are the determinants of the structural properties in the crystal. The unit cell is the basic unit that describes the crystal structure, while the crystal lattice defines the periodicity of the crystal structure. In practice, the unit cell is usually used to describe the physical properties of the crystal and the position coordinates of the atoms in the crystal, that is, after the unit cell is determined, any physical quantity in the crystal can be found, such as the position and density of the atoms.

In the study of crystal properties and applications, the understanding and application of unit cells and lattices is very important, and can be used in many fields such as materials science, physics, geology, chemistry, etc.

Therefore, the in-depth understanding and application of unit cells and lattices is very important in practical scientific research. Unit cells and lattices are not only the structural basis in crystals, but also the guarantee of physical properties and engineering applications. If you have a deeper understanding, you can also apply it to different structures of crystals, such as two-dimensional crystals, block copolymers, metal-organic frameworks and other materials.

At the same time, in the field of crystallography, the unit cell is also closely related to the symmetry of the crystal without return, which involves the appearance and physical properties of the crystal, so understanding the symmetry of the unit cell and the crystal lattice is of great significance for the characterization of the crystal structure and the <> properties

The protocellular is the smallest repeating unit in a crystal, and its geometry and size are usually determined by the symmetrical elements and spatial groups in the crystal structure, and are sometimes affected by the chemical composition and coordination of the crystal. The unit cell is an abstract concept used to describe the crystal structure, which is a lattice of segmental space composed of several unit cells of the same species. The size, shape, etc., of the unit cell depends on the group of spaces to which the crystal belongs and the position of the atoms.

Further, the protocell refers to the smallest repeating unit, i.e., the smallest component. In general, any crystal structure can be repeatedly extended outward from this smallest repeating unit. Thus, the protocell is a physically smallest unit.

If a protocell contains only one atom, then this protocell is called a Buhui simple protocell. Usually the protocell of a crystal has multiple atoms, which is called a compound protocell.

A unit cell refers to a repeating unit in a crystal. The unit cell of a crystal should have definite unit cell parameters and unit cell structure, with symmetry in three-dimensional space, where each unit cell parameter has a translation vector corresponding to it, and the product of each unit cell parameter and another unit cell parameter is the crystal length. Therefore, the presence of a unit cell can explain the symmetry of the crystal very directly.

In conclusion, the structures of the primary cell and the unit cell are closely linked. The primary cell is the smallest unit in the crystal structure, which is the intrinsic property of the crystal structure, and the unit cell is the external manifestation of the crystal structure, which is a spatial lattice composed of several unit cells of the same balance and reputation, and the physical and chemical properties of the crystal can be analyzed from the perspective of crystal lattice. Therefore, both primary and unit cells are very important concepts.

One is the smallest unit of the geometric structure, and the other is the crystalline structure.

The unit cell is more able to express the physicochemical structure of the crystal.

The unit cell must be able to describe the symmetry of the crystal, but the original cell is not.

The smallest repeating unit enclosed by a parallelepiped determined by a set of base vectors is called the protocell.

The protocell represents the smallest repeating unit of geometry and volume, and does not have a physical connotation, while the primitive has a physical connotation.

The primary cell often cannot reflect the symmetry of the crystal, so it is customary to choose a repeating unit that can reflect the symmetry of the crystal, and this repeating unit is called the unit cell. In order to clearly understand the arrangement of atoms in space, the atom is artificially regarded as a point, and then some imaginary lines are used to connect the centers of the atoms in the crystal to form a space lattice. A crystal is a structure in which a large number of microscopic material units (atoms, ions, molecules, etc.) are arranged in an orderly manner.

The unit cell involves forces and mechanisms, the crystal lattice does not involve forces, and crystals are concrete substances.

A unit cell is the smallest periodic repeating unit in a crystal structure. The structure of the unit cell can be described from two aspects, one is the way of periodic repetition, and the other is the content of repetition.

The method of periodic repetition can be discussed by mathematical lattice, and the content of repetition is the structural primitive, including the type, quantity, connection mode and arrangement position of atoms and molecular ions in the unit cell.

That's why it's often used.

Crystal = lattice + structural primitive.

The crystal structure is shown on the surface.