All single crystalline anisotropic?

In summary, the conversation discusses the question of whether single crystals can be isotropic and the role of crystal structure in determining their properties. The participants mention that for certain properties, such as second-rank tensors, single crystals can be isotropic, but for others, like fourth-rank tensors, they are not. The concept of diffusivity in cubic single crystals is also discussed, with one participant suggesting that even though the arrangement of atoms may look different in different directions, the diffusive flux remains the same. The conversation also touches on the symmetry of second-rank tensors in cubic crystals.
  • #1
xxh418
11
0
Hi all:
I have a question about the anisotropy properties of SINGLE CRYSTAL. The definition of the isotropy in WiKi is that the properties of the materials are the identical in ALL directions. If so, none of the single crystal is isotropic even though you can find such XYZ planes that the properties are the same(such as BCC FCC). But if you rotate like 1 degree, the properties in the X and X' directions will be different. Am I right? Or I have make mistakes. I know that the macro-properties of the properties are ofter isotropic just due to the polycrystalline structure.
 
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  • #2
xxh418 said:
Hi all:
I have a question about the anisotropy properties of SINGLE CRYSTAL. The definition of the isotropy in WiKi is that the properties of the materials are the identical in ALL directions. If so, none of the single crystal is isotropic even though you can find such XYZ planes that the properties are the same(such as BCC FCC). But if you rotate like 1 degree, the properties in the X and X' directions will be different. Am I right? Or I have make mistakes. I know that the macro-properties of the properties are ofter isotropic just due to the polycrystalline structure.

What property are you asking about? Second-rank tensors (diffusivity, thermal conductivity) of cubic single crystals are isotropic. Fourth-rank tensors (stiffness, compliance) aren't. See Nye's book for discussion.
 
  • #3
Mapes said:
What property are you asking about? Second-rank tensors (diffusivity, thermal conductivity) of cubic single crystals are isotropic. Fourth-rank tensors (stiffness, compliance) aren't. See Nye's book for discussion.

Mapes, Thanks for your reply. I am talking about the diffusivity. But I can not understand how the diffusivity can be all the same in all directions. For example, for Si crystal, If I pick {110},{1 1 -1}{1 1 2} directions, the arrangement of the atoms in every directions are very different. Thus, I suppose the diffusivisty should be different.
 
  • #4
xxh418 said:
Mapes, Thanks for your reply. I am talking about the diffusivity. But I can not understand how the diffusivity can be all the same in all directions. For example, for Si crystal, If I pick {110},{1 1 -1}{1 1 2} directions, the arrangement of the atoms in every directions are very different. Thus, I suppose the diffusivisty should be different.

The arrangement of atoms looks different in that direction, but the diffusive flux adds up to the same value (for cubic crystals). Try calculating it.
 
  • #5
Mapes:
I still can not get it. I drew the crystal lattice and think it over and over. Just assume we have simple cubic structure. The diffusion tension is [D 0 0; 0 D 0; 0 0 D]. If we rotate an small angle thita. Then the new diffusion coefficient in the new direction would be D multiplied by a function of thia. Then given the same temperature gradients for two directions, the diffusion coefficients are different (one has thita, one not). The flux should be different. I know there must be something wrong of my logic. But I do not know what is the problem.


Regards
Xu
 
  • #6
It's easier to keep the structure stationary and imagine the driving force (the temperature gradient) changing direction. Decompose the gradient vector [itex]\textbf{G}[/itex] into the principal axes of the structure: [itex]\textbf{G}=G\textbf{i}\cos \theta+G\textbf{j}\sin \theta[/itex]. Then the flux is [itex]\textbf{F}=\textbf{D}\textbf{G}=DG\textbf{i}\cos \theta+DG\textbf{j}\sin \theta[/itex]. What is the magnitude of vector [itex]\textbf{F}[/itex]?
 
  • #7
Just a comment. For the point cubic symmetry a second rank tensor is isotropic. However in cubic crystal it is not microscopically isotropic, but will depend on the site symmetry. A good example is the Debay-Waller (DW) factor which is tensor and in general it is a scalene ellipsoid even in cubic crystal. In BaTiO3 cubic perovskite the oxygen DW factor can be different in (110) and (001) directions.
 

FAQ: All single crystalline anisotropic?

1. What is a single crystalline anisotropic material?

A single crystalline anisotropic material is a solid material that has a highly ordered atomic structure, with all of its atoms arranged in a repeating pattern. This type of material exhibits different physical and chemical properties when measured along different crystallographic directions due to its anisotropic nature.

2. How is the anisotropy of a single crystalline material determined?

The anisotropy of a single crystalline material can be determined through various techniques such as X-ray diffraction, electron microscopy, and optical microscopy. These techniques allow for the visualization and analysis of the crystal structure and orientation, which can provide insights into the anisotropic properties of the material.

3. What are some examples of single crystalline anisotropic materials?

Some common examples of single crystalline anisotropic materials include diamonds, quartz, and calcite. These materials have a highly ordered crystal structure and exhibit different physical properties depending on the direction in which they are measured.

4. What are the advantages of using single crystalline anisotropic materials in scientific research?

Single crystalline anisotropic materials have unique properties that make them ideal for use in scientific research. They can be used as model systems to study the relationship between structure and function, and their anisotropic properties can be tailored for specific applications such as optics, electronics, and biomaterials.

5. How are single crystalline anisotropic materials produced?

Single crystalline anisotropic materials can be produced through various methods such as crystal growth, epitaxy, and solid-state reactions. These processes involve carefully controlling the conditions under which the material is formed to ensure a highly ordered crystal structure is achieved.

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