Sergei B. Brandt

Radiogenic isotopes in geologic processes

Preface 1. Theory and Experience 2. Geochronometric Models 3. Principle Geochronometric Isotope Systems 4. Atmospheric Argon 5. Distribution of Radiogenic Argon within a Mineral 6. Thermal Spectra of Argon Isotopes 7. Radiogenic Argon in a Cooling Dike 8. Radiogenic Isotopes in an Exocontact Zone of a Magmatic Body 9. Diffusion in a Laplace Regime 10. Early Earth 11. Important Phanerozoic Boundaries 12. Late Phanerozoic Magmatic Evolution of Asia 13. Late Phanerozoic Magmatic Evolution of North America and Northeast Africa: Comparisons with Asia 14. Separated Lead Isotopes References Index

Thermal-Field Propagation in an Exocontact Zone of a Magmatic Body and its Impact on Radiogenic Isotope Concentrations in Minerals

Abstract In application of radioactive isotope systems (K–Ar, Rb–Sr etc.) during the last decades, experience was gained not only on their geochronometrical uses, but also on estimations of some important parameters of geological processes, especially temperatures and durations of superimposed thermal events. In this paper, the formation of an exocontact thermal field of a magmatic intrusion is considered as a spreading of a thermal source deltafunction. Appropriate solutions of the heat-transfer equation are deduced and correlated with diffusion parameters of the radiogenic argon, coupling radioactive, thermal and kinetic parameters in an exocontant zone of a magmatic body. These solutions were used for quantitative reinterpretations of data taken from Harts classical paper [The petrology and isotopic mineral age relations of a contact zone in the Front Range, Colorado. J. Geol., 1964, v. 72, pp. 493–525]. Theoretic and measured radiogenic argon and strontium concentrations within exocontact aureoles are found to be in good concordance.

Theory and Experience

We shall not discuss the philosophical contents of the concept “time”. Geochronology deals with functional time, providing a measurement procedure not of the time itself, but of values that are included in a certain law that gives time through other parameters. For instance, the time of passage by an airplane at some distance is calculated by division of the distance of passage into speed. The time of a liquid transfusion from one vessel to another is calculated using the rate of this transfusion and ratios of liquid volumes in the vessels. The Roman water clock is based on this principle. In geochronometry, isotopes of natural radioactive elements (uranium, thorium, rubidium etc.) are used and the time is calculated by the formula:

Diffusion in a Laplace Regime

t=\frac{1}{\lambda }\ln\!\left(\frac{D}{P}+1\right)

Separated Lead Isotopes

where λ – constant of radioactive transformation, P – number of parent particles, left at present, D – number of daughter particles.

Thermal Spectra of Argon Isotopes

The main advantage of the system—two series of radioactive decay: 238U→ 206Pb and 235U→ 207Pb—provides reliable results of dating (Faure 1989; Dickin 1997). The ages are calculated in the U–Pb, Pb–Pb, and mixed coordinates with simultaneous measurements of 206Pb/238U, 207Pb/235U, and 207Pb/206Pb ratios (Ludwig 2000).

Radiogenic Argon in a Cooling Dike

Rocks and minerals might occur in conditions of elevated temperatures favorable for accelerated diffusion processes. This results in accumulation of radiogenic isotopes in rocks and K–Ar isotope system in the Laplace diffusion losses. It is important to define boundary conditions of such an isotope system. As diffusion losses increase, the rate of accumulation of daughter substance approaches zero (∂40Ar/∂t=0) and the Fick equation turns to the Laplace equation. Unlike convective mixing, resulting in complete homogenization of all isotope systems, the Laplace regime may affect some radiogenic isotopes, while the others obey the Law of Radioactivity of Rutherford–Soddy without diffusion losses.

Distribution of Radiogenic Argon Within a Mineral

Recent decades have brought enormous progress in analytical laboratory techniques and publication of many high precision results on radioactive isotope systems. The measured isotope ratios are usually shown in data tables and graphs with standard deviations of 5 or 6 true ciphers. Often, the measured results are considered as an ultimate step for an isotope study. The precise data presume however a satisfactory description of natural geologic processes in terms of precise models and an adequate development of a strict theory based on fundamental differential equations.