I was doing a lesson on solid states. There were given two kinds of solids namely amorphous solids and crystalline solids. Some differences between these two solids were given in my book. One of the difference was that crystalline solids are anisotropic in nature whereas amorphous solids are isotropic in nature.

Following is from my book

Crystalline solids are anisotropic in nature, that is, some of their physical properties like electrical resistance or refractive index show different values when measured along different directions in the same crystals.

Diamond is a crystalline solid. That means it is anisotropic in nature. This means that measuring the refractive index of diamond from different direction will give different values of refractive index. Then why we have fixed value of refractive index of diamond.

Not just about diamonds, many other crystalline solids have fixed refractive index.


3 Answers 3


Your textbook is wrong. Some crystalline solids are optically anisotropic. Many crystalline solids are indeed optically isotropic in nature. In solids like this the light beam experiences the same electron density regardless of the direction the crystal is oriented. Some examples of that are (obviously) diamond, halite and sylvite (sodium and potassium chlorides), garnets, spinels and more. Note that this is a feature derived from the electronic structure and it has nothing to do with the actual shape of the crystal.

Even in the case of anisotropic crystals, some are so weakly anisotropic they may considered isotropic in practice. Zeolites are a perfect example of those.

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    $\begingroup$ I would not call those really isotropic in nature. True, they're isotropic to the light; but once you try to split a crystal... Wait, it's simpler than that: just look at the crystal. Is it spherical? Usually no. Then it's not like all directions are equal. $\endgroup$ Sep 12, 2015 at 12:48
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    $\begingroup$ @IvanNeretin obviously, I was referring to isotropic in the optical sense, a feature determined by the spatial electron density. The actual shape of the crystal is not important. A diamond is isotropic whether it's shaped like a sphere, cube, octahedron or carved into an elephant. $\endgroup$
    – Gimelist
    Sep 12, 2015 at 21:05
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    $\begingroup$ What's obvious for us can be less-than-obvious for someone reading this topic in a year from now, so thank you for putting in the word "optically". As for the features, all of them are determined by the spatial electron density, yet some would reveal certain anisotropy, while the others (including optical) would not. $\endgroup$ Sep 12, 2015 at 21:13

Crystal can be isotropic when it is symmetrical about all the axes i.e. the cubic system. Halite (sodium chloride) and diamond form cubic crystals and therefore their optical properties are isotropic.


One property that remains anisotropic even in cubic crystals is their elastic deformation. As described here, a cubic crystal has three elastic constants, and these can be varied in ways that create different deformation characteristics along different directions.

This is because elastic deformation is a more complex physical phenomenon than other processes such as heat conduction. Thermal conductivity correlates one vector (heat flux) to another (temperature gradient) and thus is a second-order tensor. The only component of a second-order tensor that obeys the symmetry laws associated with heat conduction and also conforms with cubic symmetry is the fully isotropic component, which corresponds to equal conductivity in all directions. But the elastic deformation constant correlates two quantities that are already second-order tensors: stress and strain. So the deformation constant is a fourth-order tensor, which has more components than a second-order one.

When we work out the mathematics of this fourth-order tensor for the cubic case, we find that three independent components are allowed. Only two of these correspond to equal elastic responses in all directions; these may be expressed in terms of Young's Modulus and Poisson's ratio. The third independent component can impart different deformation characteristics, which show up as different Young's Modulus and Poisson's ratio, to (for instance) deformation in the [100] direction versus the [111] direction.

An even higher level of symmetry, then, is required to get a truly isotropic crystal with respect to elastic deformation ... and now we know it exists thanks to the rise of quasicrystals. An icosahedral quasicrystal, which must obey more symmetry relations in its properties than a mere cubic crystal, really does have equal values of constants such as Young's Modulus and Poisson's ratio in all directions.


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