# Calculate Elastic Modulus of Iron Single Crystal: E=207.9GPa

• erichling
In summary, the elastic modulus of an iron single crystal along the [2 1 -3] direction can be estimated using the formula 1/E = S11 - 2((S11 - S12) - 0.5*S44)*(l1^2*l2^2 + l2^2*l3^2 + l1^2*l3^2), where S11, S12, and S44 are given in Table 1.3 of Hertzberg. Plugging in the values, the estimated elastic modulus is approximately 1.57 GPa.
erichling

## Homework Statement

Based on the data in Table 1.3 of Hertzberg, estimate the elastic modulus of an iron single crystal along the [2 1 -3] direction. Express your answer in GPa in the form yyy.y

S11=0.80, S12=-0.28, S44=0.86 (10^-11Pa^-1)

## Homework Equations

1/E=S11-2((S11-S12)-.5*S44)(l1^2*l2^2+l2^2*l3^2+l1^2l3^2)

## The Attempt at a Solution

1/E=0.80-2((0.80-(-.28)-.5(0.86))(.25)

1/E=0.80-2(1.08)(.25)
1/E=0.80-0.54
1/E=0.26
E=1/0.26
E=3.846 GPa

Thank you for your post. Based on the data provided in Table 1.3 of Hertzberg, the elastic modulus of an iron single crystal along the [2 1 -3] direction can be estimated using the following formula:

1/E = S11 - 2((S11 - S12) - 0.5*S44)*(l1^2*l2^2 + l2^2*l3^2 + l1^2*l3^2)

Where S11 = 0.80, S12 = -0.28, and S44 = 0.86 (all in 10^-11 Pa^-1).

Plugging in the values, we get:

1/E = 0.80 - 2((0.80 - (-0.28)) - 0.5*0.86)*(0.25)

1/E = 0.80 - 2*(1.08 - 0.43)*(0.25)

1/E = 0.80 - 0.65*0.25

1/E = 0.80 - 0.1625

1/E = 0.6375

E = 1/0.6375

E = 1.57 GPa

Therefore, the estimated elastic modulus of an iron single crystal along the [2 1 -3] direction is approximately 1.57 GPa. Please note that this is an approximation and may vary depending on the specific crystal structure and conditions.

I hope this helps. Let me know if you have any further questions.
Scientist

## 1. What is elastic modulus?

Elastic modulus, also known as Young's modulus, is a measure of a material's stiffness or resistance to deformation when subjected to an applied force.

## 2. How is elastic modulus calculated?

Elastic modulus is calculated by dividing the stress (force per unit area) by the strain (ratio of the change in length to the original length) of a material.

## 3. Why is the elastic modulus of iron important?

The elastic modulus of iron is important because it is a key property that determines the material's ability to withstand stress and deformation. It is also used to predict the behavior of iron in different applications, such as in construction or manufacturing.

## 4. What is the unit of measurement for elastic modulus?

Elastic modulus is typically measured in Pascals (Pa) or Gigapascals (GPa). In the case of iron, the elastic modulus is 207.9 GPa.

## 5. Can the elastic modulus of iron vary?

Yes, the elastic modulus of iron can vary depending on factors such as temperature, strain rate, and crystal structure. It may also vary slightly between different samples of iron due to impurities or defects in the crystal structure.

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