Material Science- x-ray diffraction and metal densities

In summary, the problem involves a metal with a BCC crystal structure and an atomic weight of 92.91. With monochromatic x-radiation of 0.14 nm wavelength, the angle of diffraction for the (211) set of planes is 41.148 °. The task is to compute the density of the metal in g/cm^3 using decimal notation with 2 digits after the decimal point. The relevant equations are a=4R/sqrt(3), p=n*A/V*N, n*lamba=2d(hkl)sin(theta), and d(hkl)=a/sqrt(h^2 +k^2 + l^2). The attempt at a solution involves breaking down the equation into
  • #1
maiad
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Homework Statement



Consider a metal with an BCC crystal structure and atomic weight 92.91. When monochromatic x-radiation having a wavelength of 0.14 nm is used, the angle of diffraction (2*theta) for the (211) set of planes in this metal occurs at 41.148 ° (first-order reflection).


Compute the density of this metal in g/cm^3


The sin function requires input in radians.


Use decimal notation, digits after decimal: 2

Homework Equations



a=4R/sqrt(3)

p=n*A/V*N

n*lamba=2d(hkl)sin(theta)

d(hkl)=a/sqrt(h^2 +k^2 + l^2)


The Attempt at a Solution



i basically broke down the equation into P=(2Asin(theta)) / ((a^2)(sqrt(h^2+k^2+l^2))

but for the vaule of a... i don't have the radius to find the vaule of a soo any hints would be nice :)
 
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  • #2
maiad said:
n*lamba=2d(hkl)sin(theta)

What is known, what is unknown?
 

Related to Material Science- x-ray diffraction and metal densities

1. What is x-ray diffraction and how is it used in material science?

X-ray diffraction is a technique used to study the atomic and molecular structure of materials. It involves directing a beam of x-rays at a material and analyzing how the x-rays are scattered or diffracted. This information can then be used to determine the arrangement of atoms and molecules within the material, providing valuable insight into its properties and behavior.

2. How does x-ray diffraction help in determining the composition of a material?

By analyzing the diffraction pattern produced by a material, scientists can determine the atomic spacing and crystal structure of the material. This information can then be compared to known patterns of different materials to identify the composition of the material being studied.

3. What is the significance of metal densities in material science?

Metal densities play a crucial role in material science as they directly affect the properties and behavior of a metal. Density is a measure of the mass per unit volume of a material, and it can provide information about the strength, stiffness, and other mechanical properties of a metal. It is also important in determining the suitability of a material for different applications.

4. How are metal densities measured in material science?

Metal densities are typically measured using techniques such as Archimedes' principle, where the volume of the metal is determined by measuring the displacement of a liquid when the metal is immersed in it. Another common method is using a density gradient column, where the metal is placed in a column of liquid with varying densities and its position is noted. The density of the metal can then be calculated based on the known densities of the liquid layers.

5. Can x-ray diffraction be used to determine the density of a metal?

While x-ray diffraction is primarily used to analyze the atomic and molecular structure of materials, it can indirectly provide information about the density of a metal. By measuring the spacing between atoms in a crystal lattice, scientists can determine the volume of the unit cell and subsequently calculate the density of the material. However, other techniques such as the ones mentioned in question 4 are more commonly used for direct measurements of metal densities.

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