How Thin Can Gold Be Stretched?
― One gram spreads to the size of an open newspaper, and light shines through it green
Gold leaf is about one ten-thousandth of a millimetre thick. That is hundreds of times thinner than a human hair, and only a few hundred atoms deep. It still holds together as a single sheet without tearing. The reasons are the way metal atoms are bound together and the fact that gold does not rust.
At New Year, flakes of gold leaf float in celebration sake and on sweets. They are so light that a breath can send them flying when you reach with chopsticks.
The gold on temple Buddha statues and folding screens is usually this same gold leaf, laid on in a thin layer. It is not made of solid gold.
So how thin is that leaf? And why does gold spread out without breaking, when stone and glass shatter if you hit them?
Only two reasons let gold get this thin
Metal atoms are held together by electrons that they all share. When hammering shifts the rows of atoms, the bond stays intact.
Most metals react with air when made thin and turn into brittle rust. Gold barely reacts, so it stays gold even when extremely thin.
The first is a property that "every metal" has. The second is what makes gold special. Let's take them in turn.
Why do some things crack when hit, and others stretch?
Hit a grain of table salt with a hammer and it shatters. Salt is built from positively charged particles and negatively charged particles in alternating rows. As on the right side of Figure 1, if a blow slides one row over by a single place, plus faces plus. Like charges push each other apart, so the crystal splits open along that plane.
Metals are different. As on the left side of Figure 1, metal atoms sit in a "sea" of electrons that move freely. The whole sea of electrons is what holds the atoms together. Even after the rows slide, the same atoms and the same sea of electrons are there on the other side. So the bond does not break.
When you hammer gold, this kind of sliding happens at many places across the layers of atoms. As the thickness shrinks, the gold spreads sideways. The volume does not change, so halving the thickness doubles the area.
Why can only gold go down to "one ten-thousandth of a millimetre"?
Aluminium and copper can also be hammered thin. The aluminium foil in your kitchen is about one hundredth of a millimetre thick. But make a metal 100 times thinner than that, and most metals run into trouble.
The surface of a metal meets oxygen in the air and forms a very thin layer of rust. In a thick plate, it hardly matters if the top few nanometres change. But when the film itself is only a few hundred atoms deep, the rust layer makes up a large share of it. Rust does not stretch like metal, so the film turns brittle and crumbles.
Gold barely reacts with air or water. That is why the gold of a Buddha statue stays bright after hundreds of years. Even thinned to a few hundred atoms, it stays metal to the end.
Use the slider in Figure 2 to change the thickness of the leaf. You can see how far one gram of gold spreads at each thickness.
Gold-leaf craftsmen mix a little silver or copper into the gold, sandwich it between sheets of special paper, and beat it again and again. They cut it apart partway and keep beating, and in the end the leaf is said to reach about one ten-thousandth of a millimetre.
Gold looks gold because it reflects red and yellow light well and soaks up some of the blue. A leaf as thin as gold leaf lets part of the light that is not reflected pass through to the other side. The light that gets through is the blue-green part, which gold reflects poorly. In the 19th century, Faraday used this effect as a clue to study in detail how gold interacts with light.
Summary
Metal atoms sit in a sea of electrons, so when they slide under a hammer, the metal spreads instead of cracking. On top of that, gold does not react with air, so it stays gold even when only a few hundred atoms thick. That is how 1 gram of gold becomes a film as wide as an open newspaper.
The thinness of gold leaf is a record set by craft skill
and by atoms that "slide without parting, and never rust."
For why metals shine in the first place, see "Why Do Metals Shine?". For the real cause of the smell on your hands after touching metal, see "Why Do Your Hands Smell Like Iron After Touching an Iron Railing?".
- Get one sheet of edible gold leaf (sold as a baking ingredient) and lift it gently with tweezers or the tip of a bamboo skewer.
- Hold it up toward a bright window or lamp and look at the light through it. It should look blue-green rather than gold.
- For comparison, hold up a piece of aluminium foil the same way. It lets no light through at all, because it is about 100 times thicker.
Gold leaf is very light and blows away with a breath. Keep your mouth closed and do this in a room with no draught. You could also crush a grain of salt with the back of a spoon and compare how it breaks.
For those who want more ― terms, formulas and links to textbooksEach part is labelled by level, from middle school science to university courses
- Middle schoolCovered in middle school science
- High schoolCovered in high school "Basic Chemistry" and "Chemistry"
- High school+Advanced high school material, or textbook sidebars
- UniversityUniversity courses (materials science, solid-state physics) not taught in high school
- ResearchNot yet settled textbook knowledge; researchers are still working on it
Middle schoolTerms: this phenomenon has a name
- Malleability: the property of spreading thin without breaking when hammered or pressed. It is common to metals.
- Ductility: the property of stretching into a thin wire without snapping when pulled. Gold is said to be among the most malleable and ductile of all metals.
- Metallic bonding: a way of binding in which atoms share electrons, and those electrons surround all the atoms and hold them together. This is the "sea of electrons" in Figure 1.
Middle schoolHigh schoolChecking with a formula: how many square metres does 1 gram of gold cover?
Hammering does not change the amount of gold, so the volume stays constant. Volume is "area × thickness", so once the thickness is fixed, the area is fixed too.
| In symbols | A ＝ m ÷ ( ρ × t ) |
| In words | Area spread = mass of gold ÷ (density × leaf thickness) |
| Where it comes from | Conservation of volume. Volume equals "mass ÷ density" and does not change when hammered. Writing it as "area × thickness" and solving for area gives this formula. |
| A | Area spread (square centimetres) |
| m | Mass of gold (grams) |
| ρ | Density of gold (grams per cubic centimetre) |
| t | Leaf thickness (centimetres) |
| Mass of gold | 1 gram |
| Density of gold | 19.3 grams per cubic centimetre |
| Gold leaf thickness (0.1 micrometres) | 0.00001 centimetres |
| Size of one gold atom | about 0.29 nanometres |
| Thickness of aluminium foil | about 0.01 millimetres |
| Volume of 1 gram of gold (cubic centimetres) | 1 ÷ 19.3 ≒ 0.0518 |
| Divide that volume by the thickness to get the area (square centimetres) | 0.0518 ÷ 0.00001 ＝ 5180 |
| Convert to square metres | 5180 ÷ 10000 ＝ 0.518 |
| Divide the 100 nm thickness by the atom size | 100 ÷ 0.29 ≒ 345 |
| How many times thicker is aluminium foil than gold leaf? | 0.01 ÷ 0.0001 ＝ 100 |
One gram of gold spreads to about 0.52 square metres. That is a little more than an open newspaper (about 0.44 square metres). The thickness is about 340 atoms, only about one hundredth of aluminium foil.
High schoolHigh school+Types of crystal, and how they break differently
High schoolIn Basic Chemistry, solids are sorted into ionic crystals, metallic crystals, covalent crystals and molecular crystals. Ionic crystals split along particular planes when force is applied. This kind of splitting is called "cleavage". In metallic crystals, free electrons do the binding, so they show malleability and ductility.
High school+Gold, silver, copper and aluminium have an arrangement called a "face-centred cubic lattice". This arrangement has many combinations of planes and directions along which atoms slip easily, so these metals stretch especially well. That gold does not rust matches its place at the very end of the ionisation tendency (reactivity) series.
UniversityAtoms slide "one row at a time" ― dislocations
If a whole plane of atoms had to slide at once, calculations say it would take a force thousands of times larger than what is actually needed. Real metals deform under small forces because the crystal contains disordered spots called "dislocations", and these move bit by bit. It is like pushing a wrinkle along a carpet to shift it a little at a time. If you keep hammering, the dislocations tangle and the metal hardens (work hardening). That is why craftsmen sometimes pause to heat the metal and let the atoms realign, a step called "annealing".
📖 Derivations and further reading: Dislocation (Wikipedia, Japanese) ／ Malleability and ductility (Wikipedia, Japanese)
ResearchWhat is still not clear
- We cannot fully predict from atoms how a metal hardens. Calculating accurately, from atomic arrangements, how countless dislocations tangle together is still a hard problem.
- Gold thinned to a few atoms behaves like a different substance. Gold grains a few nanometres across are known to act as helpers for chemical reactions (catalysts), which bulk gold does not. The details of why are still under study.
- How thin can it go? Studies of gold films only a few atoms thick have been reported. But the thickness at which the properties switch is said to vary with how the film is made and the conditions.
So this article, too, is an "explanation of what is known so far". Gold leaf is a technique that is centuries old, yet what the atoms inside it are doing is still being studied.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Grade 7 science "Substances around us" (properties of metals), density | Malleability, the area calculation for 1 gram |
| High school | Basic Chemistry "Chemical bonds" (metallic bonds, ionic crystals) | Figure 1: stretching versus breaking |
| High school+ | Chemistry "Crystal lattices", ionisation tendency | Face-centred cubic lattice, why gold does not rust |
| University | Materials science, solid-state physics (dislocation theory, plastic deformation) | Dislocations, work hardening, annealing |
| Research | Nanomaterials, catalysis by gold nanoparticles | Properties of gold a few atoms thick |
| ― | Connection to daily life | Edible gold leaf, gold on Buddha statues and screens, aluminium foil |
- M. Faraday (1857) "Experimental relations of gold (and other metals) to light", Philosophical Transactions of the Royal Society of London 147
- National Astronomical Observatory of Japan (国立天文台), ed., Chronological Scientific Tables (理科年表), Maruzen Publishing (density of gold)
- C. Kittel, Introduction to Solid State Physics (固体物理学入門, Japanese edition), Maruzen Publishing (metallic bonding, dislocations)
- Wikipedia, "Dislocation" (転位, Japanese)
- High school "Basic Chemistry" (化学基礎) textbooks, units on chemical bonds and crystals
※This article is a popular-science explanation for general readers. The numbers given are rough guides to help you understand the mechanism. The thickness and area of gold leaf vary with how it is made and its grade.