Calculating the Density of a BCC Crystal with Ta Substitution

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SUMMARY

The discussion focuses on calculating the density of a body-centered cubic (BCC) crystal structure with 7.5 atomic percent tantalum (Ta) substitution for chromium (Cr). The lattice parameter is provided as 0.29158 nm. Density is determined using the formula mass divided by volume, where mass is calculated based on the number of atoms in the unit cell and their respective atomic masses. The adjustment of atomic mass is necessary due to the substitution of Cr atoms with Ta atoms.

PREREQUISITES
  • Understanding of BCC crystal structures
  • Knowledge of X-ray diffraction techniques
  • Familiarity with atomic mass units (amu) and conversions to grams
  • Basic principles of density calculation
NEXT STEPS
  • Research the calculation of density in crystalline structures
  • Learn about the implications of atomic substitution in alloy systems
  • Study X-ray diffraction analysis for lattice parameter determination
  • Explore the properties of tantalum and chromium in metallurgical applications
USEFUL FOR

Materials scientists, metallurgists, and students studying crystallography or solid-state physics will benefit from this discussion.

2slowtogofast
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how would i start this solution off?

we replace 7.5 atomic % of the chromium atoms in its BCC crystal with tantalum. X ray diffraction shows that the lattice parameter is 0.29158 nm find the density.
 
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Well the crystal is bcc, and one is given the length of the side of the cube.

Density is simply mass divided by volume.


The mass is simply the number of atoms in the cell times the mass per unit atom (think amu, which can be converted into grams.). Also, since 7.5% of the Cr atoms are replaced with Ta atoms, simply adjust the atomic mass by the proportions of each element.
 
thank you I am going to try and work it out now the 7.5% Ta was confusing me but i think i get it now
 

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