Calculating density of a perovskite structure, a question, phase diagr

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Homework Help Overview

The discussion revolves around calculating the density of a perovskite structure and interpreting a phase diagram. Participants are exploring the relationships between lattice constants, ion sizes, and mass contributions in the context of crystallography.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the density based on an assumed lattice constant and seeks clarification on the representation of phases in a diagram. Other participants question the assumptions regarding ion sizes and their contributions to mass calculations.

Discussion Status

Participants are actively engaging with each other's attempts and providing feedback. Some guidance has been offered regarding the correct approach to determining the lattice constant and the inclusion of titanium in mass calculations. Multiple interpretations of the problem are being explored.

Contextual Notes

There are references to attachments that contain visual aids for the perovskite structure and phase diagram, which are critical for understanding the problem but are not included in the text. The discussion also indicates a need for clarity on the roles of specific ions in the structure.

Junkwisch
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Homework Statement



See attachment q2 for the perovskite structure




The Attempt at a Solution


For the perovskite structure, I assume that the lattice constant is equal to 2*(R1+R2+R3) and calculate the density based on this. Am I correct? (The attachment q2ans is my attempt on the question)



For the phase diagram attachment, can anyone tell me what α, γ, ε represent?
i tried searching this on the internet, I assume that α is aluminium, ε is magnesium and γ is vapour phase. Is this correct?



Best Regards
Junkwisch
 

Attachments

  • Q2.png
    Q2.png
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  • q2ans.jpg
    q2ans.jpg
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  • phasediagram.png
    phasediagram.png
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Junkwisch said:

Homework Statement



See attachment q2 for the perovskite structure




The Attempt at a Solution


For the perovskite structure, I assume that the lattice constant is equal to 2*(R1+R2+R3) and calculate the density based on this. Am I correct? (The attachment q2ans is my attempt on the question)

No. The titanium ion is small, it does not touch the other ions. See one face of the cube and figure out the side length so as the arrangement with one oxygen ion at the centre and barium ions at the corners can be established. The lattice constant is equal to the side length of the cube.

ehild
 
Last edited:
thank for your reply ehild

the attachment here is what I did by finding 'a' from a single face. I got a new value for volume which will result in higher density :D. Since Ti is so small, do I still need to include it in the mass calculation?


Junks
 
Sorry, I forgot to attach the pic


Junks
 

Attachments

  • q2anscontinue.jpg
    q2anscontinue.jpg
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Junkwisch said:
thank for your reply ehild

the attachment here is what I did by finding 'a' from a single face. I got a new value for volume which will result in higher density :D. Since Ti is so small, do I still need to include it in the mass calculation?Junks

You need to include it in the mass, but remember, only 1/4 th of the sides in the centre of the cube is filled with titanium ions.
The volume is correct now.

ehild
 
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ah, so only 1/4 of the mass of Ti is included, thank you ehild :D
 

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