Lab Assist Engr 45 Properties

In this activitiy, we succeed be using the crystal visualization implement from Cal Poly located here (Links to an palpable residence.) 

The hypocrisy starts by failure after a while the Sickly valid lattice cloak. The drop-down menu allows you to design other lattice compositions. You can depend the composition and design it from contrariant sides by trade the mouse and dragging the composition. You can so zoom in and out after a while the mouse rock. Thither are two expressive modes that are controlled after a while the Comment slider at the depth of the cloak. In Layering mode, you can see how the 3D crystal lattice can be made by stacking flakes of motes. In Item Cell mode, you can see how the 3D lattice is secure of reproduceing item cells after a while participational motes.

How to change in the lab

Submit your repartees to the interrogations under to canvas as a .pdf

Be abiding to repartee the interrogations in prescribe and to enumerate each interrogation.  If the interrogation requires you to do a watchfulness, demonstration all of your work 

You can image your lab or index transcribe it.  If you do the lab by index, I praise using the adobe reconnoitre app (Links to an palpable residence.) to reconnoitre your assignment and apply it to a .pdf

Lattice Structures of Minute Solids

Use the crystal visualization implement (Links to an palpable residence.) to repartee the interrogations under


We succeed prepare this intelligence by seeming at the flakeing design of bisecticles that gives mollify to each of the valid item cells. A item cell is the smallest item in a repetitive design that executes the 3-dimensional lattice composition.  As demonstrationn in Metaphor 1, thither are two basic 2D designs for flakes of motes. The motes in each flake can be packed in a balance dress, or “close-packed” after a while a rhombus representing the sicklyst reproduceing design. When multiple flakes of a feature 2D design are stacked concertedly, they can produce a diversity of 3D designs, depending on how the flakes are shifted referring-to to each other. If the flakes reproduce identically as they stack, this can be illustrative as “AA” stacking. If the succor flake is staggered referring-to to the principal flake, but the third flake is stacked straightway overhead the principal flake, this stacking design is illustrative as “ABA.”  If the principal, succor, and third flakes are all staggered referring-to to eachother (none are stacked straightway overhead the other), this stacking design is illustrative as "ABC".  You can weigh this flakeing consequence by selecting Layering on the left of the visualization implement and using the Comment slider.

lab1_fig1.pngFigure 1. Balance and rhombic item cells in 2D flakes.

For each of the lattices (sickly valid, body-centered valid, aspect-centered valid, and HCP), repartee the aftercited interrogations. Use the visualization implement to acceleration.

1. What image of flake, balance or rhombic, continues in each image of item cell? (See Metaphor 1).

2. What is the stacking design in the selfselfidentical lattice composition? (use scholarship A, B, C, etc. to designate contrariant flakes).

Unit Cells

Once motes are stacked into a 3D crystal lattice, the sicklyst reproduceing geometric design—the item cell—succeed usually include recalcitrant of motes. While barely integral motes continue in the crystal, the geometric fidelity of the item cell succeed enjoy motes disagree among multiple neighboring item cells. To ascertain a item cell, we transfer the smallest reproduceing design and “slice” the shared ability off, to execute it seem enjoy a cube (hither we are exploring valid item cells, but thither are shapes for item cells as well-mannered-behaved). After a while Item Cell separated on the left, use the Comment slider to see how multiple item cells concertedly executes up an unimpaired lattice. To highlight a unique item cell after a whilein the crystal lattice, weigh “t” on the keyboard to toggle the translucency.

For each of the valid lattices (sickly valid, body-centered valid, aspect-centered valid), repartee the aftercited interrogations.

3. Which bisect(s) of a 3D item cell do the motes employ (corner, party, nature, aspect)?

  • for specimen, the sickly valid cell has 8 motes and each mote is located at the cavitys 

4. What participation of an mote does each co-operate to the item cell?

  • for specimen, for sickly valid - each one of the cavity cells is shared among 8 neighboring item cells.  Therefore, each cavity mote co-operates 1/8 of an mote to the item cell 
  • you can see this over plainly in the program if you use the comment slider in the item cell design

5. What is the sum enumerate of motes per item cell?

  • We can use the repartees from 3 and 4 to repartee this interrogation.  Each sickly valid item cell has 8 motes tender it, but barely 1/8 of each of those motes belongs to that one item cell.
  • So the sum enumerate of motes per item cell = 8 * 1/8 = 1 mote 

For the HCP item cell, repartee the aftercited interrogations. 

6. What is the sum enumerate of motes per item cell?

  • use common logic as overhead to repartee this interrogation and investigate how motes are shared among neighboring item cells 

Coordination Number

The coordination enumerate is the enumerate of closest neighbors an mote has in the lattice, including motes in the neighboring item cells.

For the aftercited interrogations, you can use the Coordination mode in the visualization implement to substantiate your repartee.

7. Determine the coordination enumerate for the sickly valid lattice.

8. Determine the coordination enumerate for the grey motes in a body-centered valid (bcc) lattice.

9. Determine the coordination enumerate for the red motes in a bcc lattice.

10. Explain why the coordination enumerate for all the motes in the bcc lattice is the selfsame.

11. Determine the coordination enumerate for the aspect-centered valid lattice.

Packing Efficiency

Since the flakeing design in all of the lattices leaves leisure extension among the bisecticles, the item cell is not fully subject by motes (hither we are treating motes enjoy unfeeling departments). The packing aptitude, which is the percentage of subject extension in the cube, is not 100%. The packing aptitude is
not the selfselfidentical for all 3 valid lattices. A over densely packed item cell succeed enjoy a surpassing packing aptitude than a near densely packed one. The packing aptitude of a lattice composition measures how well-mannered-behaved-behaved the extension amid of a item cell is utilized. It is the percent ratio of dimensions subject by the bisecticles in a item cell to its sum dimensions.

LaTeX: Packing\:Efficiency\:=\:\frac{V_{occupied}}{V_{total}}\times100P a c k i n g E f f i c i e n c y = V o c c u p i e d V t o t a l × 100

The subject dimensions is cognate to the enumerate of bisecticles employing the cell and their colony after a whilein the cell. 

lab1_fig2.pngFigure 2. Geometric relationships demonstrationing how the party protraction is cognate to the moteic radius for sickly valid, body-centered valid, and aspect-centered valid item cells.

Using metaphor 2, we can count the protraction of each item cell party in stipulations of the moteic radius, r.  

For specimen, for FCC the protraction of the aspect divergent is 4r.  Using trig, we can clear-up for the protraction, l

LaTeX: l\:=\:4r\cos(45^\circ ) = 4r(\frac{\sqrt{2} }{2} )=2\sqrt{2}rl = 4 r cos ⁡ ( 45 ∘ ) = 4 r ( 2 2 ) = 2 2 r

The party protraction of each item cell is demonstrationn in the consultation under 

Unit CellEdge protractions in stipulations of radius Simple validLaTeX: l\:=\:2rl = 2 rBody-centered validLaTeX: l\:=\:\frac{4r}{\sqrt{3}}l = 4 r 3Face-centered validLaTeX: l\:=\:2\sqrt{2}rl = 2 2 r

The dimensions subject by motes is countd as the enumerate of motes times the dimensions of a department

LaTeX: V_{occupied}=(\# motes)\times \frac{4}{3} \pi r^3V o c c u p i e d = ( # a t o m s ) × 4 3 π r 3

The sum dimensions of the cube is countd as 

LaTeX: V_{total}=l^3V t o t a l = l 3

Answer the aftercited interrogations. Assume that the lattice consists of barely one image of mote, and the radius of this mote is r.

12. Assume an mote is a unblemished department. In stipulations of r, what dimensions of the sickly valid item cell is subject by motes?

13. What is the sum dimensions of the sickly valid item cell?

14. Determine the packing aptitude of a sickly valid item cell. Use your repartees from the anterior two interrogations.

15. Determine the packing aptitude for a body-centered valid item cell.

16. Determine the packing aptitude for a aspect-centered valid item cell.

17. Observe the separation in stacking designs of the item cells and hush how they are cognate to the packing aptitude.


18. Fill out this compendium consultation after a while your repartees from overhead

2D flake design (balance vs. rhombic)

Stacking design  (e.g. abab)

Number of motes per item cellCoordination NumberPacking Efficiency Simple CubicBody-Centered CubicFace-Centered Cubic

Lattice Structures of Ionic Compounds 

Now we succeed seem at a few specimens of ionic solids. The Legend trifle succeed demonstration the ion coloring draft. The ions are roughly scaled to their referring-to ionic radii after a whilein each of the lattices.

Sodium Chloride

19. Determine the enumerate of sodium ions per item cell.
20. Determine the enumerate of chloride ions per item cell.
21. What is the tentative formula of sodium chloride fixed on the referring-to enumerate of each ion in the item cells?
22. Is the tentative formula fast from the lattice composition in contract after a while the one predicted by the regular ion mandible?
23. Are either of the ions finished in one of the basic valid item cells (simple, body-centered, aspect-centered)?

Calcium Fluoride

24. Determine the enumerate of calcium ions per item cell.
25. Determine the enumerate of fluoride ions per item cell.
26. What is the tentative formula of calcium fluoride fixed on the referring-to enumerate of each ion in the item cells?
27. Is the tentative formula fast from the lattice composition in contract after a while the one predicted by the regular ion mandible?
28. Are either of the ions finished in one of the basic valid item cells (simple, body-centered, aspect-centered)?


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