[remotemass (OP)]

Imagine that in a few thousands of years it was possible to build a column of solid diamond that had 111 Km of height.
How good would a diameter of 111 Km be for a cylinder of diamond 111 Km high?

Please say how good would that diameter comparing it for instance to a diameter of 11 Km or a diameter of 1 Km, making it clear, with all calculations you might have done, what would be a quite sensible diameter to use for such, to achieve such altitude.

- remotemass

[paul cotter]

WTF?

[Bored chemist]

This is a science site.

[Petrochemicals]

It's possible to build a column of water 111km high, it just tends to deform quite quickly.

[alancalverd]

Assuming the OP is talking about a space tower, you wouldn't start with a circular cylinder. A cone or pyramid would be far more sensible.

We know the density of diamond (about 3.5 tonnes per m³) and compressive strength (20 GPa) so it is left to the questioner to calculate the minimum diameter of the base of a frustrated cone that will support, say, a 1 m platform at 111 km altitude, assuming the stress at every level is equally distributed at the level immediately below.

   

[paul cotter]

Single crystal or polycrystalline? If single crystal the orientation would have to be considered, if polycrystalline not so. What does this really mean? It means I have too much free time over this season and boredom has set in.

[remotemass (OP)]

By the way, what would be, theoretically, the size of the mentioned column if we used all carbon atoms available on air, around us?

[Bored chemist]

compressive strength (20 GPa)

That's quite a "safety margin".
"Used in so-called diamond anvil experiments to create high-pressure environments, diamonds are able to withstand crushing pressures in excess of 600 gigapascals"
From
https://en.wikipedia.org/wiki/Material_properties_of_diamond#Pressure_resistance

The maths isn't hard.
Pressure  = density times height times the acceleration due to gravity.
3500 Kg/m3 times 111000 metres * about 10
Only about 4 GPa.

So you could, if you really wanted have a 111km diamond "pin" that was rather narrower at the base than the top.

Not sure what you  would have to make the foundations from.
Concrete is about 30 MPa
https://civiconcepts.com/blog/compressive-strength-of-concrete
Fused quartz is about 1GPa.

https://www.qsiquartz.com/mechanical-properties-of-fused-quartz/

[Bored chemist]

By the way, what would be, theoretically, the size of the mentioned column if we used all carbon atoms available on air, around us?

Why don't you work it out for yourself?

[alancalverd]

The diamond anvil presses used in geological crystallography apply tetrahedral force and thus demonstrate phase changes under isotropic compression. Using diamond as a vertical structural skeleton we are interested in the uniaxial force that might induce lateral slip or cleavage, hence the much lower compression limit.

[Petrochemicals]

I think the rotation of the earth would snap it if it where anything like a column.

[evan_au]

a cylinder of diamond 111 Km high?

Are you thinking that people could take an elevator above the Karmen Line, and get their astronaut wings very cheaply?
- Not that a diamond this big would be cheap!

...or maybe a space launch platform for LEO satellites that is above nearly all of the atmosphere, so you don't even need a fairing on the space probe, and you don't need to fight (much) air resistance?

But if you wanted a real Space Elevator, it's center-of-gravity would be at geosynchronous orbit (around 37,000km altitude), with a counterweight extending far beyond that altitude. This would be better as a launch platform for:
- Geosynchronous satellites
- Moon & Mars
- Deep space exploration
- Building a Halo around Earth
- Building a Halo around the Sun

Shape
The OP asked about a cylinder; alancalverd proposed a pyramid, with a 1m² viewing platform on top
- bored chemist proposed an inverted pyramid
- The ideal shape for a space elevator would be something like a bipyramid, with:
        - the thickest part at geosynchronous orbit, where it experiences the most stress
        - Extending down to a thin point on the Earth's surface (which wouldn't need very much concrete, because there is not much stress here)
        - And extending out to another thinner point beyond geosynchronous orbit (perhaps with a metal-rich asteroid on the end as a counterweight...)

[tomasgreenro]

Assuming the OP is talking about a space tower, you wouldn't start with a circular cylinder. A cone or pyramid would be far more sensible.

We know the density of diamond (about 3.5 tonnes per m³) and compressive strength (20 GPa) so it is left to the questioner to calculate the minimum diameter of the base of a frustrated cone that will support, say, a 1 m platform at 111 km altitude, assuming the stress at every level is equally distributed at the level immediately below.

 

wow

[JimmyW9]

If you build a pillar 111 km high, then it may not deform much due to the hardness of diamond.

[Bored chemist]

I think the rotation of the earth would snap it if it where anything like a column.

Reality never was interested in what you think.

[JimmyW9]

I think the rotation of the earth would snap it if it where anything like a column.

But it would rotate simultaneously with the earth.

[Petrochemicals]

I think the rotation of the earth would snap it if it where anything like a column.

But it would rotate simultaneously with the earth.

Elaborate

[remotemass (OP)]

By the way, what would be, theoretically, the size of the mentioned column if we used all carbon atoms available on air, around us?

What size would be a cube of same structure as diamond made of carbon with all the cabon on the air atmosphere nowadays on our planet?

To determine the size of a cube made of carbon with the same structure as a diamond, we need to know the total amount of carbon available in the Earth's atmosphere.

However, it's important to note that most of the carbon on Earth is not in the form of diamonds. In fact, the vast majority of Earth's carbon is in the form of carbon dioxide (CO2) in the atmosphere, dissolved in the oceans, or stored in the Earth's crust as fossil fuels.

To estimate the amount of carbon in the Earth's atmosphere, we can refer to data from the United States Environmental Protection Agency (EPA), which estimates that the total amount of carbon in the Earth's atmosphere is about 3.1 trillion metric tons.

Now, we need to calculate the volume of a diamond cube with the same mass as 3.1 trillion metric tons of carbon. The density of diamond is about 3.5 grams per cubic centimeter, so the mass of a diamond cube can be calculated as:

mass = density x volume

Solving for volume, we get:

volume = mass / density

Plugging in the values, we get:

volume = (3.1 x 10^12 metric tons) / (3.5 g/cm^3 x 1 x 10^6 metric tons/g)

volume = 8.86 x 10^17 cubic centimeters

Taking the cube root of the volume, we get:

size = (8.86 x 10^17)^(1/3) cm

size = 4,735 km

Therefore, a cube made of carbon with the same structure as a diamond and containing all the carbon in the Earth's atmosphere would have a side length of approximately 4,735 kilometers (2,944 miles).




Daniel Alexandre
What would be the diameter of a cylinder like that instead of a cube if it had altitude 100 km (Karman Line) ?
If we assume that the cylinder has a height of 100 km (the Karman Line, which is commonly regarded as the boundary between Earth's atmosphere and outer space), we can calculate the diameter of the cylinder with the same mass as 3.1 trillion metric tons of carbon.

First, we need to calculate the volume of the cylinder. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

To find the radius of the cylinder, we can rearrange the formula as:

r = √(V / πh)

We know the volume of the cylinder is the same as the volume of the diamond cube we calculated earlier, which is approximately 8.86 x 10^17 cubic centimeters. We also know the height of the cylinder is 100 km, or 10^8 centimeters.

Plugging in these values, we get:

r = √(8.86 x 10^17 / π x 10^8)

r = 1.19 x 10^6 cm

So the radius of the cylinder would be approximately 1.19 million centimeters.

To find the diameter of the cylinder, we simply double the radius:

d = 2r

d = 2 x 1.19 x 10^6 cm

d = 2.38 x 10^6 cm

Therefore, the diameter of the cylinder would be approximately 2.38 million centimeters, or 23,800 kilometers (14,800 miles).

[Petrochemicals]

Two images


en-compression-test-specimen.jpg (81.7 kB . 1920x1080 - viewed 1288 times)
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Compression gives you usually a pyramid like structure around the diameter of the  material, but can shear sideways, far more likely with diamonds atomic structure, depending on the orientation.