The trigonal system belongs to the intermediate crystal family.featuresSymmetrical elementIt is a triple axis of symmetry.HexahedralRhombohedronUnit cell.
crystalAccording to the ideal crystal shape or comprehensive macrophysical propertyThe features presented in can be divided into seven categories: cubic, hexagonal, tripartite, tetragonal, orthogonal, monoclinic and triclinic, that is, sevenCrystal system, belonging to 3 differentCrystal family。Advanced crystal family only includes oneCubic system；The intermediate crystal family includes hexagonal, tetragonal and tripartite crystal systems;The low-grade crystal family includes three crystal systems: orthorhombic, monoclinic and triclinic.
Chinese name
Trigonal system
Foreign name
trigonal system
Level
Belongs to intermediate crystal family
Features
The characteristic symmetry element is a triple symmetry axis
Solid materials are divided into crystals andAmorphous。From a macro perspective, naturallycoagulationThe crystals formed without external interference have their own uniqueSymmetryThe shape of, for example, salt is a cube;iceHexagonalprismBody;alumpresentOctahedronEtc.
When a crystal absorbs heat from the outside, its interiormolecule、atomThe average kinetic energy increases and the temperature starts to rise, but it does not damage theSpatial lattice, still keep regular arrangement.When the heat absorption continues to reach a certain temperature - melting point, the violent movement of its molecules and atoms can destroy its regular arrangement,Spatial latticeThey also began to disintegrate, and the crystals began to become liquid.During the transformation of crystal from solid to liquid, the absorbed heat is used to destroy the spatial lattice of crystal partially, so the temperature of solid-liquid mixture does not rise.When the crystal is completely melted, the temperature starts to rise again as it absorbs heat from the outside.However, due to the irregular arrangement of molecules and atoms, amorphous crystals do not need to destroy their spatial lattice after absorbing heat, but only to increase the average kinetic energy. Therefore, when absorbing heat from the outside, they will change from hard to soft, and finally become liquid.Glass、rosin、asphaltandrubberIs commonAmorphous。Macroscopically, whether it can produceX-ray diffractionPhenomenon is the main method to determine whether a substance is a crystal in experiment.[1]
Crystal system
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According to its ideal shape in the crystal or comprehensive macrophysical propertyFeatures presented inSymmetrical elementIt can be divided into cubic, hexagonal, tripartite, tetragonal, orthogonalmonoclinic , triclinic, etc. are 7 crystal systems, belonging to 3 differentCrystal family。There is only one advanced crystal familyCubic system；There are three crystal systems in the intermediate crystal family: hexagonal, tetragonal and tripartite;There are orthorhombic, monoclinic and triclinic crystal systems in the low-grade crystal family.Characteristic symmetry elements can also be confirmed to correspond to each crystal systemUnit cellThe shape of orCell parameterCharacteristics of correlation.The cell type of each crystal system is generally represented by cell parameters a, b, c and α, β, γ.Where a, b and c are the lengths of the three sides of the cell, which are customarily called axis lengths, and α, β and γ are calledAxis angle, they are the included angles of b and c, a and c, a and b, respectively.asHigher axisDirection Quadruple Axis orCounter shaftThe existence of determines the crystal genusTetragonal systemFor the unit cell with square column shape, the unit cell parameters must have a=b ≠ c and α=β=γ=90 ° correlation.
Definition of tripartite system
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Trigonal system
It can show unique high order in crystal shape or macroscopic physical propertiesTriple axleorTriple counter shaftThe crystals of characteristic symmetric elements belong to the trigonal system.
pattern
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A Kind of Justification of Trilateral SystemlatticeThere are two selection modes for units: one is diamondhexahedronTrihedral lattice R ofLattice parameterIt is characterized by a=b=c, α=β=γ<120 ° ≠ 90 °;The other is to take the volume asPrime lattice RTriple tripartiteH grid, hereCrystallographyCommonly used in the worldshaftingThe transformation method isTripartite H gridIt has the characteristics of a=b ≠ c, α=β=90 °, γ=120 °.
Structure determination method
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Powder photography is a basic method for X-ray crystal structure analysis.The lattice formula and cell parameters of cubic, hexagonal, tetragonal and tripartite crystal systems can be determined by this method.Due to the high symmetry of the first three crystal systems, the angle is a constant among the cell parameters to be measured, and only one or two length parameters need to be measured. Therefore, there are methods to directly determine its point array formula andCell parameter。However, the symmetry of the triangular (rhombic) crystal system is relatively low, which is reflected in the fact that not only a length parameter but also an angle parameter should be determined for the cell parameters, so there is no direct theoretical analysis method for its powder diagram.It needs to be measured as a hexagonal system first, and then converted into the parameters of a triangular R lattice.[2]
Pure mode axis of cubic system
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Because the crystal is elastic, when some mechanical disturbance occurs in a part of the crystal, this disturbance will spread in the crystal to form elastic waves.The propagation of elastic waves in crystals has some properties closely related to the symmetry and anisotropy of crystals.In the problem of elastic wave propagation, the direction of energy velocity and phase velocity is consistent, which is the pure mode axis.
Slowness Surface and Energy Velocity
For elastic wave of crystal, the direction of phase velocity and wave vector must be consistent, but the direction of energy propagation velocity and wave vector are not necessarily consistent, as shown in the figure.When the two are consistent, the wave vector direction is the pure mode axis of the crystal.Since the normal direction of any point on the slowness surface represents the direction of energy propagation speed, the vector path direction is the wave vector direction.Therefore, according to whether the normal direction of any point on the slowness surface is parallel to the vector diameter direction of the point, we can judge whether the wave vector direction is pure mode axis.Generally, one wave vector direction in the slowness surface corresponds to three phase velocities, so it is necessary to judge the relationship between three energy velocity directions and wave vector.Only when the three energy velocity directions are parallel to the wave vector direction can this wave vector direction be called the pure mode axis.
Liu Limei et al. used the slowness curve of the specific crystal plane of the cubic crystal system to study the pure mode axis of the cubic crystal system by analyzing the relationship between the energy velocity of the elastic wave reflected by the slowness curve and the direction of the phase velocity (wave vector). This method can reduce the trouble caused by tedious calculations.The results show that this method is feasible to judge whether the specific wave vector direction of crystal is pure mode axis.Similarly, this method is also applicable to other crystal systems in the seven major crystal systems.[3]
