Introduction
Diamond is a crystalline form of carbon and it has a cubic crystal structure. X-ray diffraction (XRD) is a powerful technique used to study the crystal structure of materials. In XRD, a beam of X-rays is incident on a crystal and the resulting diffraction pattern is recorded. Each peak in the diffraction pattern corresponds to a specific set of crystal planes.

Diamond Cubic Structure
The diamond cubic structure consists of carbon atoms arranged in a face-centered cubic lattice. In this lattice, each carbon atom is bonded to four neighboring carbon atoms, forming a tetrahedral structure. The (311) plane is one of the crystal planes in the diamond cubic structure.

XRD Peaks
When X-rays interact with a crystal, they are diffracted by the crystal lattice. The diffraction occurs when the X-ray wavelength is similar to the interatomic spacing in the crystal. The Bragg's law relates the angle of diffraction (θ) to the spacing between crystal planes (d) and the wavelength of X-rays (λ):

nλ = 2d sin(θ)

where n is an integer representing the order of diffraction. When θ is small (less than 10 degrees), the sin(θ) term is approximately equal to θ in radians.

Analysis
Given that the diffraction peak for the (311) plane occurs at 64 degrees, we can use the Bragg's law to calculate the spacing between the (311) planes. Rearranging the equation, we have:

d = nλ / (2 sin(θ))

Substituting the values, we have:

d = λ / (2 sin(θ)) = λ / (2 sin(64))

To determine the number of XRD peaks below 64 degrees, we need to calculate the diffraction angles for different values of n. The diffraction angles can be calculated using the equation:

θ = sin^(-1)(nλ / (2d))

Calculation
Let's consider the first few values of n (1, 2, 3, ...) and calculate the corresponding diffraction angles.

For n = 1:
θ = sin^(-1)(λ / (2d)) = sin^(-1)(λ / (2(λ / (2 sin(64))))) = sin^(-1)(sin(64)) = 64 degrees

For n = 2:
θ = sin^(-1)(2λ / (2d)) = sin^(-1)(2λ / (2(λ / (2 sin(64))))) = sin^(-1)(2 sin(64)) = 128 degrees

For n = 3:
θ = sin^(-1)(3λ / (2d)) = sin^(-1)(3λ / (2(λ / (2 sin(64))))) = sin^(-1)(3 sin(64)) = 192 degrees

From the calculations, we can see that the diffraction angles for n = 2 and n = 3 are greater than 64 degrees. Therefore, there are no XRD peaks below 64 degrees.

Conclusion
In summary, the X-ray diffraction of diamond cubic gives a peak for the (311) plane at 64 degrees. There are no XRD peaks below this angle because