Anisotropy and Isotropy
Amorphous solids are said to be isotropic, and crystalline solids are anisotropic for their physical property measurements.
Isotropy comes from the Greek word; iso means same and tropos means direction. The name rightly indicates that for the amorphous solids; the physical property measurements are same in all the directions. The same correlation applies for anisotropy that means no same direction. It means that for the crystalline solids, the physical property measurements are not same in all the directions.
The physical properties that depend on direction for taking measurements and therefore affected by the nature of the solid are- refractive index, electrical conductivity, thermal conductivity, photoelasticity and many more.
For the crystalline solids; the arrangement of particles is ordered and periodic, then why does the physical property measurement changes? How does it become anisotropic?
What it implies is that, if physical property measurements are taken along the x-axis, its reading will be different than if measured from another axis, say y-axis or the z-axis. Different direction will give different measurements. But this is not the case with amorphous solids. For the amorphous solids, same values will be obtained irrespective of the direction of the measurement.
An example will help us to understand this better. A refractive index measurement is taken for crystal calcite and amorphous solid glass at a single wavelength keeping the direction fixed at the x-axis. For the crystal calcite, the values ranged from 1.4 to 1.6 but for the glass the values ranged from 1.50-1.52 only. When the direction of the measurement changed, the values changed drastically for calcite but remained the same for glass at 1.50-1.52.
Anisotropy is observed in crystalline solids because the concentration of the atoms is different in different directions of the unit cell. If you look along the X-axis, the concentration of particles around it is different than the distribution of atoms around the y-axis and same is for the z-axis. As the concentration of the particles in a particular direction of the crystal changes, therefore, the measurement of physical property changes depending on the direction of the measurement.
Amorphous solids have a tightly packed random arrangement of the constituent particles, unlike the crystalline solids that have a fixed arrangement of atoms in a crystal lattice. Due to the random arrangement, the distribution of particles would be widely different along each axis. Hence, an average value of the measurement is taken.
But what if the crystalline solid has an equal perfect distribution of atoms in a unit cell like in a cubic structure, then would it be isotropic for all the properties? The answer is no. A perfectly arranged cubic crystal structure would be isotropic for some properties like refractive index but would be anisotropic for other properties like photoelasticity.
Therefore, in general, we can say that all crystalline solids are anisotropic for some of their physical properties and all amorphous solids are isotropic.
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