The fabrication of perfectly spherical silicon-28 ($^{28}$Si) crystals—often referred to as the "Avogadro Project"—is one of the greatest achievements in modern metrology (the science of measurement). This monumental engineering and physics endeavor was a crucial part of the 2019 redefinition of the International System of Units (SI), specifically the kilogram.
Here is a detailed explanation of why this was necessary, the underlying physics, and the incredible process used to create the roundest objects in the world.
1. The Problem: The Artifact Kilogram
From 1889 to 2019, the global standard for mass was the International Prototype of the Kilogram (IPK), affectionately known as Le Grand K. It was a cylinder of platinum-iridium alloy kept in a vault in Paris.
The problem with a physical artifact is that it is subject to the environment. Over a century, despite being kept under nested bell jars, Le Grand K and its official copies absorbed contaminants and lost microscopic amounts of material. The official kilogram's mass was mysteriously drifting by about 50 parts per billion (the weight of an eyelash). Because Le Grand K was the mathematical definition of a kilogram, the artifact technically didn't change mass; the rest of the universe did. Scientists needed to redefine the kilogram using an immutable, fundamental constant of nature, rather than a piece of metal.
2. The Solution: Counting Atoms
If scientists could count the exact number of atoms in a precisely measured object, they could define mass based on the fixed mass of an atom. This approach aimed to determine a highly exact value for the Avogadro constant ($N_A$)—the number of particles in one mole of a substance.
If you know exactly how far apart atoms are in a crystal lattice, and you know the exact total volume of the crystal, you can calculate the exact number of atoms. Multiply the number of atoms by the mass of a single atom, and you have mathematically defined a kilogram.
3. Why Silicon-28?
To do this, scientists needed a material that forms a mathematically perfect, highly predictable crystal lattice without any gaps or flaws. They chose silicon because the semiconductor industry had already spent decades perfecting the growth of silicon crystals for computer chips.
However, natural silicon is a mixture of three isotopes: Silicon-28 (92.2%), Silicon-29 (4.7%), and Silicon-30 (3.1%). Because these isotopes have different atomic masses, a sphere of natural silicon would have an unpredictable total mass. Therefore, scientists had to use Silicon-28, purified to an isotopic purity of 99.999%.
4. The Fabrication Process
Creating the perfectly spherical $^{28}$Si crystal was an international effort that spanned several countries and disciplines.
Step 1: Isotopic Enrichment (Russia) The raw silicon was sent to Russia, where the same centrifuges used to enrich uranium were repurposed to separate silicon isotopes. The silicon was converted into a gas (silicon tetrafluoride) and spun in centrifuges until pure $^{28}$Si was isolated.
Step 2: Crystal Growth (Germany) The purified $^{28}$Si was sent to the Leibniz Institute for Crystal Growth in Germany. Growing a perfect crystal is exceedingly difficult; even a single missing atom (a vacancy) or an extra atom (an interstitial defect) would ruin the math. Using a technique called the "float-zone method," scientists melted the silicon and slowly allowed it to crystallize into a single, massive, perfectly aligned crystal "boule."
Step 3: Machining and Polishing (Australia) The crystal was then sent to the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia, home to master lens makers. The goal was to cut the crystal into a sphere. A sphere was chosen because it has no edges to chip and its volume can be calculated using a single measurement: its diameter.
Using specialized CNC machines and extremely fine polishing techniques (done entirely by hand at the final stages to ensure the heat from machinery didn't warp the shape), the master opticians created what is widely considered the roundest object in the world.
To understand how round it is: The sphere has a diameter of about 93.6 millimeters. Its surface roughness is less than 0.3 nanometers. If you were to blow this sphere up to the size of the Earth, the distance between the highest mountain and the deepest ocean trench would be only 10 to 14 feet (3 to 4 meters).
5. The Metrology (Measuring the Sphere)
Once the spheres were fabricated, they were sent to metrology institutes like PTB in Germany and NMIJ in Japan to be measured. * Measuring the Volume: Scientists used laser interferometers to measure the diameter of the sphere from thousands of different angles, determining its overall volume to an accuracy of fractions of a nanometer. * Measuring the Lattice: Using X-ray crystallography, scientists measured the exact distance between the $^{28}$Si atoms in the crystal lattice.
By dividing the volume of the sphere by the volume of a single "unit cell" of the atomic lattice, they were able to count the exact number of atoms in the sphere: approximately $2.15 \times 10^{25}$ atoms.
6. Redefining the Kilogram
The silicon sphere project allowed scientists to fix the exact numerical value of the Avogadro constant ($N_A$) to $6.02214076 \times 10^{23} \text{ mol}^{-1}$.
Concurrently, other scientists were using a device called a Kibble Balance to measure the Planck constant ($h$), which ties mass to quantum mechanics and electromagnetism. The genius of modern physics is that the Avogadro constant and the Planck constant are mathematically linked. The results from the incredibly precise Silicon-28 spheres perfectly corroborated the results from the Kibble balances.
On May 20, 2019, the scientific community officially retired Le Grand K. The kilogram is no longer defined by a physical object. It is now defined by the fixed numerical value of the Planck constant. Today, if any laboratory in the world needs to create an exact kilogram, they can do so using a Kibble balance or by creating a silicon sphere, relying on the immutable laws of quantum physics rather than a piece of metal in Paris.