Obtain the general form of the linear thermal expansion tensor for a tetragonal crystal.
Added by Linda S.
Step 1
** Thermal expansion refers to the tendency of a material to change its dimensions in response to a change in temperature. In crystals, this behavior can be described using a thermal expansion tensor, which relates the change in dimensions to the temperature Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 88 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A crystal has a coefficient of linear expansion of 12*10^-6 °C in one direction and 24*10^-6 °C in every direction at right angles to it. Then the coefficient of cubical expansion of the crystal is 1.
Adi S.
A. The linear thermal expansion coefficient is defined as α = 1/L dL/dT. Assume a bar to have length L0 at temperature T0. Determine the length of the bar as a function of the temperature, T. That is, determine L(T). B. Approximate L(T) for temperatures which are close to T0. That is, in the limit α(T - T0) << 1. Hint: you need to make a Taylor expansion. C. The table below reports the value of the linear thermal expansion coefficients of different substances. These are measured in standard conditions, pressure = 1 atm; Temperature = 25°C. For practical purposes in our daily life, can you assume the relation between the length and the temperature to be linear? Material α [K⁻¹ or (C°)⁻¹] Aluminum 2.4 × 10⁻⁵ Brass 2.0 × 10⁻⁵ Copper 1.7 × 10⁻⁵ Glass 0.4-0.9 × 10⁻⁵ Invar (nickel–iron alloy) 0.09 × 10⁻⁵ Quartz (fused) 0.04 × 10⁻⁵ Steel 1.2 × 10⁻⁵
Krishna S.
3.2. Classical Model of Thermal Expansion In classical statistical mechanics, we write the expectation of x as Although one cannot generally do such integrals for arbitrary potential V(x) as in Eq. 2, one can expand the exponentials as and let limits of integration go to . > Why is this expansion of the exponent and the extension of the limits of integration allowed? > Use this expansion to derive x̢ to lowest order in ̢3, and hence show that the coefficient of thermal expansion is with kB being Boltzmann's constant. > In what temperature range is the above expansion valid? > While this model of thermal expansion in a solid is valid if there are only two atoms, why is it invalid for the case of a many-atom chain? (Although actually it is not so bad as an approximation!)
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD