Spatial lattice

Basic introduction

spatient (Space Lattice) is also known as "space grid". It is usually seen as a synonym with the "spatial point". It is an unlimited stereoscopic geometry coupled to geometric points (called nodes) that are regularly arranged in a series of three-dimensional spaces. It is abstract from a specific crystal structure. The regularity arranged in spatial lattice reflects the regularity of atoms, ions or molecules in the spatial distribution in the crystal structure. Arranged on a linear junction into a row, the distance between adjacent points on the row is called a node spacing. Where parallel, its node is necessarily equal. The nodes distributed on a plane are connected to the surface network, and the number of nodes in the unit area of the surface is called the surface network density, and the distance between the adjacent two-way lines is a surface spacing. Anyone parallel net network, its surface network density and the internet internet spacing must be all the same. A spatial lattice can always be divided into a series of parallel hexahedrals that are laminated in parallel with each other in parallel. If the divided parallel hexahedral can reflect both the symmetry of the entire spatial lattice, the right angle relationship as much as possible, the size is the smallest, such parallel hexahedral is called the unit parallel. According to the difference in the symmetry of the unit parallel, the spatial lattice belongs to seven crystals. According to the case where the node is distributed in the six-fourth body, the space lattice can be divided into the original lattice, the bottom heart lattice, body heart lattice and Four possible forms of facial corners. Thus, there are 14 different spatial lattice types in the crystals, commonly referred to as 14 kinds of Bravi space grid , also known as 14 translation gather < / b> or Mobile grid .

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f = r

Six-Party crystal system

Table 1
	Original Plaid (P)	bottom heart lattice (C)	body heart gant (i)	Facial plaid (f)
three oblique Crystal system		i = p	f = p		i = c	Tie's Crystal System
	c = p		tripartite crystal system		i = r		Does not conform to the six-part symmetrical	and space grid conditions do not match	Conditions of spatial lattice do not match	integral with the intrinsic symmetry

Note: Six-party heart plaid is the six-party original gantry.

Comprehensive consideration of the shape and node distribution of parallel hexasgers, and there are 14 kinds of spatial plaids. It was originally derived from Bravi, so it was also called 14 Bravi Space Terries (Table 1).

Since there are seven shapes and 4 nodes distribution methods in parallel, why is the space lattice not 28 but 14? This is because some lattice types are repeated, and some lattice types do not match the symmetrical symmetry of the crystal system, and thus cannot appear in the crystal system.

For example, the three slanting sideware can be redistributed to three oblique original plaids; the four-way heart lattice can be converted to a quadroliter whistle; the monographs of the stem can be converted to a single slope of heart. In the equient crystal system, there is no cubic bottom of the bottom of the bottom, since it does not match the intrinsic symmetry.

Three hurry heart gauges can be redistributed to three oblique original plaid

four-party heart lattice can be transformed into four squares Original plaid

single 斜心心子子为为底子子子子子子子子子子子体子子子子子平平平平

It is well known that the crystal structure is a stack or insertion combination of unit parallel hexahedral in three-dimensional space. Obviously, it is important to determine that the minimum structure of the spatial lattice type is of great significance. In the research lattice structure, this unit parallel, the division requirements of the six-sided body, follow the principles:

1 selected unit selected Parallel hexas should be reflected in the symmetry of the entire node distribution;

2 selected units in parallel hexahedral ribs are most angle;

3 selected unit parallel hexahedral volume Minimum.

Figure 1 is a dot matrix with

symmetrical, and 6 selective methods are labeled in Figure 1. Obviously, the four divisions of 3, 4, 5, and 6 do not match the symmetrical symmetry of

, in the remaining methods 1, 2, all of the selection principles 1, 2, but the volume 1 is the smallest , Satisfy the selection principle 3, so it should be selected as the unit of the unit of

Description unit parallel six-sided body has 6 parameters, ie 3 ribs A, B, C and its angle

, called unit parallel silactic lattice constant.

Each of the crystal system is parallel and additional node plaid

According to the division of the above-mentioned unit parallel, the crystal of 7 crystals is analyzed, and the 7 crystal system is obtained. The lattice constant characteristics of the unit parallel hexahedral, and the basic geometry of the respective crystalline unit parallel is shown in Table 2.

Table 2 Units Parallel Hexas - Body
	(a) Cube	( b) Quadrofitting	(c) Six-party grid
(d) tripartite lattice < / p>	(e) Scatters

Cube:

;

Quad-square lattice:

;

Six-party grid:

;

Plaid:

;

方方子:

;

single slant lattice:

;

Three clids:

;

Obviously, unit parallel hexahedral product constants is completely consistent with crystal geometry given in crystal shape studies, which also illustrates The dot matrix structure inside the crystal determines the profile characteristics of the crystal.

The analysis of additional nodes in parallel with parallel of the above unit can be divided into additional nodes in the distribution method, see Table 3.

Original plaid (p) : Node is distributed over 8 corners of the parallel six-sided body.

bottom heart gant : Node distribution 8 corners of parallel six-sided body and 1 pair of planes, and can be subsequently divided into:

< B> C Heart (C) : Node distributions in units of parallel six-sided sides of the top and flat center of 1 pair of planes.

A Heart Grid (a) : Node is distributed in parallel of the 8 corners of the six-sided body to the flat center of 1 pair of planes.

B Heart Grid (B): Node is distributed in parallel of the 8 corners of the six-sided to the center of 1 opposite (010).

Under normal circumstances, the bottom of the heart is C'sid. When the A heart or B heart is converted into C, it should be converted as it is possible. Only in special cases can be used directly to use A heart or B heart scent without conversion.

body heart lattice (I): Node is distributed over 8 corners and intimate hearts of parallel six-sided sides.

Facial lattice (f): Node is distributed in units of 8 corners of the six-sided body and the center of each face.

bottom heart: B heart gant

Table 3
Original Plaid	bottom heart: C Hearts	bottom herb: A heart gather	body heart gant	Facial grid