Crystal Structure of Metals at Absolute Zero, Waves

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SUMMARY

The discussion centers on the crystal structure of solid elemental metals at temperatures approaching absolute zero, highlighting that many metals exhibit a hexagonal close-packed (HCP) structure at low temperatures. Participants emphasize the need for thermodynamic tables and specific references to obtain accurate lattice constants and thermal expansion data for various metals. The CRC Handbook is identified as a key resource for this information, although it requires purchase. Additionally, the conversation touches on the derivation of the wave equation related to particle separation and sound speed in metals.

PREREQUISITES
  • Understanding of crystal structures, specifically hexagonal close-packed (HCP) and body-centered cubic (BCC) arrangements.
  • Familiarity with thermodynamic tables and thermal expansion concepts.
  • Knowledge of wave equations and their derivations in solid mechanics.
  • Proficiency in using the CRC Handbook for material properties and extrapolation techniques.
NEXT STEPS
  • Research the CRC Handbook for thermodynamic tables of elemental metals.
  • Study the thermal expansion properties of metals to understand low-temperature behavior.
  • Explore the derivation and applications of wave equations in solid-state physics.
  • Investigate the relationship between bulk modulus, density, and sound speed in materials.
USEFUL FOR

Researchers, physicists, and materials scientists interested in the low-temperature properties of metals, as well as engineers working on applications involving wave propagation in solid materials.

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I have been trying to find information on the crystal structure or phase of solid elemental metals at temperatures close to absolute zero, but I can only find information on there ambient structures. Does anyone know of any sources that would have thermodynamic tables for solid metals at low temperatures or information on the crystal structure at low temperatures?

From the little information I have found it would appear a lot of the metals all form a HCP crystal structure at very low temperatures, but like I said I am having a hard time getting any information.

I want to make a finite point mass wave equation.

m*utt(x,t) = k*(u(x+h,t)-2*u(x,t)+u(x-h,t))

if you let h -> 0 then you get the wave equation

but h is the particle separation, and it is small. so with a small value approximation you get

m*utt(x,t) = k*h2*uxx(x,t)

but I need information on crystal structure and the particle separation.
 
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There are two separate issues here.
(1) The low-temperature forms of elements (allotropes) are listed in the CRC handbook. For most metals, the room temperature and low temperature structures are the same.
(2) To obtain the lattice constants near low temperature, you need to dig out individual references for each metal that measure the thermal expansion as a function of temperature. The results are normally provided in the form of tables or polynomials, and you would have to extrapolate to 0 K.
 
Thanks for the help. The CRC Handbook looks like a treasure chest of information, but with anything its not free. I understand how to use the tables and polynomials to extrapolate for temperatures close to zero.

So basically to get the data that represents the secrets of the universe you have to buy it... That is a subject of a different discussion.

I just want to test if the speed of sound that is predicted from the equation holds.

c = (kh2/m)1/2=(B/p)1/2

where:
k = the fictitious spring force between particles
h = particle separation
m = mass of the particle
B = Bulk Modulus
p = density
 

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