A question about strain in graphene

In summary, the conversation discusses the new position of carbon atoms under uniaxial strain and a formula for calculating the position after the strain is applied. The person is having trouble calculating the position and asks for help. They are unsure of how to do matrix addition and multiplication and how to obtain the values for |δ1|, |δ2|, and |δ3|. They also mention a discrepancy between their calculation and the original equation.
  • #1
barana
18
0
Dear forum people
The new position of the carbon atoms under uniaxial strain r in the framework of elastic theory is shown by the following equation:
ri'=(I+ε).ri
in which ri and ri' are the position of the carbon atoms before and after the strain is applied, respectively.
I is the unit matrix and ε is the strain tensor which is attached.
I can't calculate ri' .
For example:

δ1=a(√3/2,-1/2) δ2=a(0,1) δ3=a(-√3/2,-1/2)
|δ1|=1+(3/4)ε11-(√3/2)ε12+(1/4)ε22
|δ2|=1+ε22
|δ3|=1+(3/4)ε11+(√3/2)ε12+(1/4)ε22

Can help me?
How calculate |δ1|,|δ2|,|δ3|?
 

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  • #2
Are you uncertain of how to do a matrix addition and then a matrix x vector?
 
  • #3
jedishrfu said:
Are you uncertain of how to do a matrix addition and then a matrix x vector?
I don't know how obtained |δ1|,|δ2|,|δ3|.
δ1=( √3/2*a(1-ε11)-a/2*ε12 ; √3/2a*ε21-a/2*(1-ε22))
According to δ1, |δ1| not equal with |δ1| above maintained.
 

FAQ: A question about strain in graphene

1. What is strain in graphene?

Strain in graphene refers to the deformation or stretching of the flat hexagonal lattice of carbon atoms in graphene. This can be caused by mechanical stress, thermal expansion, or defects in the graphene structure.

2. How does strain affect the properties of graphene?

Strain can significantly alter the electronic, mechanical, and thermal properties of graphene. It can affect the band structure, carrier mobility, and strength of graphene, making it a key factor in the design and optimization of graphene-based devices.

3. What techniques are used to measure strain in graphene?

Some common techniques used to measure strain in graphene include Raman spectroscopy, atomic force microscopy, and scanning electron microscopy. These methods can provide information on both the magnitude and direction of strain in graphene.

4. Can strain be intentionally introduced in graphene?

Yes, strain can be intentionally introduced in graphene through various methods such as stretching, bending, or applying external pressure. This allows for the manipulation of graphene's properties and can be useful in applications such as strain sensors or tunable electronics.

5. What are the potential applications of strain engineering in graphene?

Strain engineering in graphene has a wide range of potential applications, including flexible electronics, strain sensors, energy storage devices, and nanomechanical systems. It also holds promise for improving the performance of existing graphene-based devices and developing new technologies.

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