Bragg Angles + Thermal Expansion

In summary, the lattice parameter 'a' of a heated crystal increases by 0.17%. The change in the Bragg angle theta when the crystal is heated from 0 to 100 degrees Celsius cannot be determined without knowing the wavelength or d-value. The equation 2dsin(theta) = n\lambda can be used to calculate the change, but without the necessary information, it is not possible to obtain a precise answer.
  • #1
exzacklyright
12
0

Homework Statement



A crystal is heated from 0 to 100 degrees celcius, its lattice parameter 'a' increases by 0.17% due to thermal expansion. if we observe an x-ray reflection at a bragg angle theta= 19.3 degrees at 0 degrees celcius, by how much will theta change when the sample is heated to 100 degrees C. (don't need to know wavelength or d to solve)

Homework Equations



2dsin(theta) = n[itex]\lambda[/itex]

The Attempt at a Solution



Tried using 1 for d. and just seeing how much it'd change but it didn't come out right.
 
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  • #2
Should it be d_1*sin(theta_1) = d_2*sin(theta_2) ?
 
  • #3
Spinnor said:
Should it be d_1*sin(theta_1) = d_2*sin(theta_2) ?

well all we're given is density 1 and theta 1. we don't even know density2 or theta2
 

What is a Bragg angle?

A Bragg angle is the angle at which X-rays, neutrons, or other waves are diffracted by a crystal lattice. It is named after the British physicist William Henry Bragg, who first described this phenomenon in 1913.

What is thermal expansion?

Thermal expansion is the phenomenon where a substance increases in size when heated and decreases in size when cooled. This is due to the increase or decrease in the average distance between the particles that make up the substance.

How are Bragg angles and thermal expansion related?

In a crystal lattice, the atoms are arranged in a regular, repeating pattern. When X-rays or other waves are directed at the crystal at a specific angle, they are diffracted by the crystal's lattice structure. This angle is known as the Bragg angle. Thermal expansion can affect the distance between the atoms in the crystal, and therefore can also affect the Bragg angle.

Why is understanding Bragg angles and thermal expansion important?

Understanding Bragg angles and thermal expansion is important in many fields of science and technology. It can help in the development of new materials, as the properties of a material can be affected by its crystal structure and thermal expansion. It is also important in fields such as X-ray crystallography, which is used to determine the atomic and molecular structure of crystals.

How is the Bragg angle affected by temperature changes?

The Bragg angle is affected by temperature changes because thermal expansion can alter the distance between the atoms in a crystal lattice, thus changing the angle at which waves are diffracted. As the temperature increases, the atoms in the crystal vibrate more, causing the lattice to expand and the Bragg angle to decrease. Similarly, as the temperature decreases, the lattice contracts and the Bragg angle increases.

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