In several previous posts I warned to avoid comparing volumes when looking at the 3D-graphs. This was because the “buildings” were representing very different values in their three dimensions. Ratios can be determined by looking at such a graph by comparing two dimensions (e.g. width and depth), but the volume – being the product of e.g. revenue, equity and total assets – is meaningless from an accounting point of view. And so are the surfaces, by the way.

Photo by Matthias Böckel on Pixabay

Although it’s an important warning, ** it doesn’t apply to all visualisations** to be made with the help of the 3D-generator! In some cases the three dimensions

**be multiplied and then the volume will have a meaning after all. If we break down a value in three dimensions, making the volume meaningful, we can easily compare values we cannot show in a simple bar-graph.**

*can*

Think about a series like 10, 15, 25, 100, 125, 175, 500, 1200, 10000. It would be boring to show them in a bar-graph (left).

Presenting those values s a volume however, will be much more interesting and now comparisons can be made because height, width and depth will be like (or equal to) the cubic root of the values. *In short:* when it is allowed to multiply height, width and depth, the volume has a meaning. This is another strength of 3D-graphs we didn’t reveal before.

To present a nice example, I took the annual production of some critical metals. A lot of so called “Rare Earth” metals are in this set (neither rare nor earth as the latter used to refer to the Boron-group) and then some others like Cobalt and Lithium. Below a concise overview will be presented.

*Before we go on, I have to disclose that I hold some positions in REE-related companies. **Yet the only purpose of this post is to show the power of 3D-graphs! *

The 3D-graph will present real volumes of materials traded. Although we are talking about critical metals – including the “rare earth elements” (REEs), the trading is usually done with their oxides (Rare Earth Oxides – abbreviated REO – be aware that not all metals in the graph are REEs). Two exceptions are Cobalt which is traded as a pure metal and Lithium, mostly traded as a carbonate (kind of soda).

What will be in the 3D-graph? We will show the annual consumption *volume* of oxide (cubic metres) at the front row (represented by the volume of the blocks) and at the second row the amount of tonnes (*weight)*. The tonnes-row will show larger buildings, because the density of most oxides is between 6.5 and 8.5 g/cm^{3} (or tonnes per m3). Be aware that if the density is 8 g/cm3, this will mean that the length, width and depth of the “building” for the volume will only be half of those values for the weight, since 2 x 2 x 2 = 8! This time I thought it would be fun to make all buildings green (entering four times the same cubic-root value). The only exceptions are the red reference-buildings showing 10000 m^{3} and 10000 tonnes respectively (same size of course, because here the artificial “density” would be 1).

*Some properties of the metals for which the annual consumption is shown in the graph:*

###### – Yttrium: Atomic weight 39. Used in superconductors and exotic light sources.

###### – Lanthanum: Atomic weight 57. Used in specialty glasses and optics, electrodes and hydrogen storage.

###### – Cerium: Atomic weight 58. Makes an excellent oxidizer, used in oil cracking during petroleum refining and is used for yellow coloring in ceramics and glass.

###### – Praseodymium: Atomic weight 59. Used in magnets, lasers and as green color in ceramics and glass.

###### – Neodymium: Atomic weight 60. Used in magnets, lasers and as purple color in ceramics and glass.

###### – Gadolinium: Atomic weight 64. Used in magnets, specialty optics, and computer memory.

###### – Dysprosium: Atomic weight 66. Used in magnets and lasers.

###### – Samarium: Atomic weight 62. Used in magnets, lasers and neutron capture.

###### – Europium: Atomic weight 63. Makes colored phosphors, lasers, and mercury-vapor lamps.

###### – Terbium: Atomic weight 65. Used as green in ceramics and paints, and in lasers and fluorescent lamps.

###### – Tantalum: Atomic weight 181. Used in electornics, alloys and orthopedic implants.

###### – Scandium: Atomic weight 21. Used to strengthen aluminum alloys.

###### – Cobalt: Atomic weight 59. Used in lithium-ion batteries, magnetic, wear-resistant and high-strength alloys, deep blue color: glass, ceramics, inks, paints.

###### – Lithium: Atomic weight 7. Used in lithium-ion batteries, alloys, ceremics, pharmaceuticals.

For those who want to know more about these valuable elements, the links below might be useful. Link 1, Link 2, Link 3, Link 4, Link 5 and Link 6

How did I get the annual consumption for all the metals (or their oxides)? Well, it is not easy to get the numbers and often the values are contradicting – or at least they don’t match. The annual global consumption of REOs seems to be around 158000 tonnes (in 2018 – it’s increasing every year). In an article by Goodenough Wall and Merriman I found a pie-chart showing the distribution (also changing but at a slower rate). That one I used to derived the individual values. Then using the commonly available densities I calculated back to m^{3}. The other values – like for Cobalt and Lithium – were found on the internet. Of course the values will have high error-margins, but again: this post is only meant to illustrate the power of 3D-graphs. As usual, the input-file is available. Finally the result is shown below.

*Double-clicking the screenshot will open the 3D-graph in your browser. **Beware:** the graph haw so many “buildings” that zooming out is necessary to see the whole picture! Clicking the right mouse-button and moving the mouse up and down at the same time, will zoom the graph in and out. ***For maniputalion of this 3D-graph: **Clicking left while moving the mouse will tilt the graph in different directions. Double clicking in the graph translates it and readjusts the centre at the same time. Just try it – If you don’t know how to get the normal position back, refresh the page in your browser.

*Double-clicking the screenshot will open the 3D-graph in your browser.*

*Beware:*

**For maniputalion of this 3D-graph:**Clicking left while moving the mouse will tilt the graph in different directions. Double clicking in the graph translates it and readjusts the centre at the same time. Just try it – If you don’t know how to get the normal position back, refresh the page in your browser.

To see the relative sizes of the buildings a top-view is helpful, but remember that the the volumes have to be compared and not the surfaces!

Don’t forget to download your free copy of AnRep3D at our website. Short tutorials, explaining different parts of AnRep3D are available at our Youtube-channel The white-paper and inspirational graphs can be downloaded at our website Follow @AnRep3D on Twitter, to be informed about new posts.