Argon-argon (or 40Ar/39Ar) dating is a radiometric dating method invented to supersede potassium-argon (K/Ar) dating in accuracy. The older method required two samples for dating while the newer method requires only one. This newer method converts a stable form of potassium (39K) into 39Ar while irradiated with neutrons in a nuclear reactor.
The decay ratio of radioactive 40K to stable 40Ar* ( * means daughter Ar atoms) is used to compute a radiometric date for a geological event, particularly the eruption and cooling of igneous rock and minerals.
The sample is generally crushed and single crystals of a mineral hand-selected for analysis. These are then irradiated to produce 39Ar from 39K. The sample is then degassed in a high-vacuum mass spectrometer via a laser or resistance furnace. Dating relies on the conversion of K to Ar, and accurate measurement of this conversion. The sample is heated in increments (step heating) which releases argon from different reservoirs within the crystal grain. Each step produces argon with a certain 40Ar:39Ar ratio, and only when 80% or more of these steps are within acceptable error is the crystal's age known. Dating via 40Ar/39Ar geochronology is generally accurate to within 1-2% for properly collected and irradiated and treated samples.
Age equation 
The age of a sample is given by the age equation:
where λ is the radioactive decay constant of 40K (approximately 5.5 x 10−10 year−1, corresponding to a half-life of approximately 1.25 billion years), J is the J-factor (parameter associated with the irradiation process), and R is the 40Ar*/39Ar ratio.
Relative dating only 
The 40Ar/39Ar method only measures relative dates. In order for an age to be calculated by the 40Ar/39Ar technique, the J parameter must be determined by irradiating the unknown sample along with a sample of known age for a standard. Because this (primary) standard ultimately cannot be determined by 40Ar/39Ar, it must be first determined by another isotopic dating method. The method most commonly used to date the primary standard is the conventional K/Ar technique.
The primary use for 40Ar/39Ar geochronology is dating metamorphic and igneous minerals. 40Ar/39Ar is unlikely to provide the age of intrusions of granite as the age typically reflects the time when a mineral cooled through its closure temperature. However, in a metamorphic rock that has not exceeded its closure temperature the age likely dates the crystallization of the mineral. Dating of movement on fault systems is also possible with the 40Ar/39Ar method. Different minerals have different closure temperatures; biotite is ~300°C, muscovite is about 400°C and hornblende has a closure temperature of ~550°C. Thus, a granite containing all three minerals will record three different "ages" of emplacement as it cools down through these closure temperatures. Thus, although a crystallization age is not recorded, the information is still useful in constructing the thermal history of the rock.
Dating minerals may provide age information on a rock, but assumptions must be made. Minerals usually only record the last time they cooled down below the closure temperature, and this may not represent all of the events which the rock has undergone, and may not match the age of intrusion. Thus, discretion and interpretation of age dating is essential. 40Ar/39Ar geochronology assumes that a rock retains all of its 40Ar after cooling past the closing temperature and that this was properly sampled during analysis.
This technique allows the errors involved in K-Ar dating to be checked. Argon–argon dating has the advantage of not requiring determinations of potassium. Modern methods of analysis allow individual regions of crystals to be investigated. This method is important as it allows crystals forming and cooling during different events to be identified.
One problem with argon-argon dating has been a slight discrepancy with other methods of dating. Recent work by Kuiper  (see also Kerr) reports that a correction of 0.65% is needed. Thus the Cretaceous–Paleogene extinction (when the dinosaurs died out) - previously dated at 65.0 or 65.5 million years ago - is more accurately dated to 66.0 Ma. Similarly, the Permian-Triassic extinction is now dated at 252.5 Ma, which is effectively coincident with the age determined by other means for Siberian Traps basalt flows.
- New Mexico Bureau of Geology
- P. R. Renne, D. B. Karner, K. R. Ludwig, Absolute Ages Aren't Exactly, Science 282:1840 (4 Dec. 1998)
- K. F. Kuiper, et al., Synchronizing Rock Clocks of Earth History, Science 320:500 (25 Apr. 2008) 
- R. A. Kerr, Two Geological Clocks Finally Keeping the Same Time, Science 320:434 (25 Apr. 2008)
- UC Berkeley press release: "Precise dating of the destruction of Pompeii proves argon-argon method can reliably date rocks as young as 2,000 years"
- The New Mexico Geochronology Research Laboratory 
- Berkeley Geochronology Center 
- Argon Isotope Facility http://www.gla.ac.uk/departments/suerc/nercfacilities/argonisotopefacility/ of the Scottish Universities Environmental Research Council
- Open University Ar/Ar and Noble Gas Laboratory http://www8.open.ac.uk/science/argon-noble-gas-research