Under conditions where no lead loss or gain from the outside environment has occurred, the age of the zircon can be calculated by assuming
exponential decay of uranium. That is :N_{\mathrm{n}} = N_{\mathrm{o}} e^{-\lambda t} \, where • N_{\mathrm{n}} = \mathrm{U} is the number of uranium atoms measured now. • N_{\mathrm{o}} is the number of uranium atoms originally - equal to the sum of uranium and lead atoms \mathrm{U} + \mathrm{Pb} measured now. • \lambda = \lambda_\mathrm{U} is the decay rate of Uranium. • t is the age of the zircon, which one wants to determine. This gives :\mathrm{U} = \left( \mathrm{U} + \mathrm{Pb} \right) e^{-\lambda_\mathrm{U} t} , which can be written as :{{\mathrm{Pb}}\over{\mathrm{U}}} = e^{\lambda_\mathrm{U} t} - 1. The more commonly used decay chains of Uranium and Lead gives the following equations: {{NumBlk|::|{{^\text{206}\,\!\text{Pb}^*}\over{^\text{238}\,\!\text{U}}}=e^{\lambda_{238}t}-1,|}} {{NumBlk|::|{{^\text{207}\,\!\text{Pb}^*}\over{^\text{235}\,\!\text{U}}}=e^{\lambda_{235}t}-1.|}} (The notation \text{Pb}^*, sometimes used in this context, refers to
radiogenic lead. For unaltered zircon, the
original lead content can be assumed to be zero, and the notation can be ignored.) These are said to yield concordant ages (
t from each equation 1 and 2). It is these concordant ages, plotted over a series of time intervals, that result in the concordant line. Loss (leakage) of lead from the sample will result in a discrepancy in the ages determined by each decay scheme. This effect is referred to as discordance and is demonstrated in Figure 1. If a series of zircon samples has lost different amounts of lead, the samples generate a discordant line. The upper intercept of the concordia and the discordia line will reflect the original age of formation, while the lower intercept will reflect the age of the event that led to open system behavior and therefore the lead loss; although there has been some disagreement regarding the meaning of the lower intercept ages. in Northern California. Ages for the concordia increase in increments of 100 million years. Undamaged zircon retains the lead generated by radioactive decay of uranium and thorium up to very high temperatures (about 900 °C), though accumulated radiation damage within zones of very high uranium can lower this temperature substantially. Zircon is very chemically inert and resistant to mechanical weathering – a mixed blessing for geochronologists, as zones or even whole crystals can survive melting of their parent rock with their original uranium–lead age intact. Thus, zircon crystals with prolonged and complicated histories can contain zones of dramatically different ages (usually with the oldest zone forming the core, and the youngest zone forming the rim of the crystal), and so are said to demonstrate "inherited characteristics". Unraveling such complexities (which can also exist within other minerals, depending on their maximum lead-retention temperature) generally requires in situ micro-beam analysis using, for example, ion microprobe (
SIMS), or laser
ICP-MS. == Lead correction ==