The structure change of the ferroelastic phase transition will cause the change of itsphysicochemical property. Thus, the study of proper ferroelastic phase transition is of greatsignificance to understand the properties of crystals and to apply crystals. In this paper, the threedimensional slowness surface of the orthorhombic crystal system is simulated by themathematical simulation software. Then, the soft-mode theory is used to analyse the slownesssurface. The maximum slowness direction is the most vulnerable to the direction of the phasetransition.The general rule of the ferroelastic phase transition of the orthorhombic system crystalhas been obtained. Finally, the structure change of the orthorhombic system crystal phasetransition is discussed by the Curie symmetry principle. The fundamental work is summarized asfollows:The first part is mainly to get the equation of slowness surface of the orthorhombic systemcrystals.Elastic wave propagation equation is Christoffel equation. This equation has untrivialsolution only when the equation as follows is established.Q （v,l_{1},l_{2},l_{3}） ij（l_{1},l_{2},l_{3}） v2ij0The equation can be rewritten into the slowness surface equation. That isF （k_{1},k_{2},k_{3}）0.The slowness surface equation has three solutions, in other words, itincludes three layer surfaces. Slowness refers to the length of the position vector which points tothe slowness surface from the center of the surface. It is also known as the reciprocal of velocity,namely1v.For the orthorhombic system crystal，when elastic waves only spread in XZ plane oralong Y axis, the slowness surface equation can be factored. This paper uses Matlab software to write programs. The characteristic equations of the elastic waves have been solved in everydirection for the orthorhombic system crystals. The slowness value of the orthorhombic systemcrystal has been got in any direction.The second part is mainly to simulate the slowness surface of orthorhombic system crystal.Then, the slowness surface is used to study the ferroelastic phase transition.The stabilitycondition of the orthorhombic system crystal is that the evaluation of determinants of the elasticstiffness matrix is greater than zero. Under the stability condition, some actual crystals and thepossible existence orthorhombic crystals of the orthorhombic system are simulated. Spontaneousstrain is the only order parameter of the proper ferroelastic phase transition. As the phasetransitions happen easiliest in the directions of the maximum slowness surface according to softmode theory, we find that the phase transitions of the orthorhombic system crystals arecorrelative with the elastic stiffness coefficientsc_{44}, c_{55},c_{66}. So it will produce spontaneousstrainS_{4}, S_{5},S_{6}.The third part is mainly to analyse the structure symmetry of the phase transition. Thestructure change of the crystal phase transition has been carried by Curie principle. The properferroelastic phase is related with spontaneous strainsS_{4}, S_{5},S_{6}. The summetry changecorresponding to the spontaneous strain stated above is discussed, respectively. |