Polycrystal

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A polycrystal (also multicrystalline or, more rarely, polycrystalline ) is a crystalline solid that consists of many small single crystals ( crystallites ) that are separated from one another by grain boundaries . The individual crystallites can have very different sizes. In general, crystals with crystallite sizes in the micrometer to centimeter range are referred to as polycrystalline.

Demarcation

Substances with small crystallites are often referred to as microcrystalline or (rarely) as nanocrystalline . A crystal whose building blocks form a uniform and homogeneous crystal lattice throughout is called a single crystal or monocrystal .

Most crystalline solids in nature are polycrystalline. The polycrystalline structure is therefore often not mentioned, but assumed as a normal case. But there are also substances that arise as single crystals: For example, diamonds have an almost perfectly monocrystalline shape.

use

Since metals usually solidify into polycrystals, structural materials such as steel , aluminum and titanium have a polycrystalline structure - with a few exceptions ( turbine blades are sometimes made from single crystals) . For this reason, metallic materials with a random texture have isotropic properties despite the crystal anisotropy. In technology, polycrystals are also used for solar cells (polycrystalline silicon). As a rule, they are cheaper to manufacture than solar cells made from monocrystalline silicon , which is also used to manufacture microchips . However, polycrystalline solar cells are less efficient .

Artificial polycrystalline diamonds are used as cutting tools in wood, plastic and non-ferrous metal processing .

Elastic properties

In the case of the statistical uniform distribution of all spatial orientations of the per se monocrystalline and elastically anisotropic grains , the polycrystalline is given outwardly elastically isotropic solid-body properties such as elasticity , shear and compression modulus . If those modules are now calculated from measured data of the associated single crystals , two borderline cases of statistical averaging have emerged:

  • Assuming a uniform deformation of all grains of the polycrystal, different stresses result due to the orientation dependency of the components of the elasticity tensor (English: stiffness tensor), so that the latter is averaged (mean values ​​according to Voigt (1887)).
  • Assuming a uniform tension of all grains, different deformations will result, so that the elastic coefficients (compliance tensor) are averaged (mean values ​​according to András Reuss (1929)).

The mean values ​​according to Voigt are generally greater than those according to Reuss. Measured values ​​of these modules are typically between the two mean values: the Voigt mean values ​​therefore form the upper limit, the Reuss mean the lower. Therefore Hill proposed in 1952 to use the arithmetic mean of the Voigt and Reuss mean as a theoretical approximation, today often referred to as the Voigt-Reuss-Hill mean. Theoretical limits are narrower than the mean values according to Voigt and Reuss for the solid-state modules according to the calculation method of Hashin and Shtrikman from 1962/63. A calculation program in the FORTRAN language for all the above-mentioned module values ​​for polycrystals was published in printed form in 1987.

Individual evidence

  1. ↑ W. Voigt: Theoretical studies on the elasticity relationships of the crystals. I. Derivation of the basic equations from the assumption of molecules gifted with polarity . In: Abh. Ges. Wiss., Gottingen . tape 34 , no. 1 , 1887, p. 3–52 ( uni-goettingen.de ).
  2. ↑ A. Reuss: Calculation of the yield point of mixed crystals based on the plasticity condition for single crystals . In: Z. angew. Math. Mech . tape 9 , no. 1 , 1929, p. 49-58 , doi : 10.1002 / zamm . 19290090104 .
  3. ^ R. Hill: The Elastic Behavior of a Crystalline Aggregate . In: Proc. Phys. Soc. Lond . A 65, no. 5 , 1952, pp. 349-354 , doi : 10.1088 / 0370-1298 / 65/5/307 .
  4. ↑ Z. Hashin, p Shtrikman: On some variational principles in anisotropic and nonhomogeneous elasticity . In: J. Mech. Phys. Solids . tape 10 (4) , 1962, pp. 335-342 , doi : 10.1016 / 0022-5096 (62) 90004-2 .
  5. ↑ Z. Hashin, p Shtrikman: A variational approach to the theory of the elastic behavior of multiphase materials . In: J. Mech. Phys. Solids . tape 11 , no. 2 , 1963, p. 127-140 , doi : 10.1016 / 0022-5096 (63) 90060-7 .
  6. ↑ J. Peter Watt: POLYXSTAL: a FORTRAN program to calculate average elastic properties of minerals from single-crystal elasticity data . In: Computers and Geosciences . tape 13 , no. 5 , 1987, pp. 441-462 , doi : 10.1016 / 0098-3004 (87) 90050-1 .