Holmes/Houtermans model

The Holmes-Houtermans model makes a number of assumptions which are important to enumerate (Faure, 1986 310) ... 

Similar equations can be written for Pb and Pb using their appropriate radioactive parents and decay constants. If t = 0 is taken to represent the time of the formation of the Earth s crust, then these three equations describe the trajectory of the isotopic composition of terrestrial lead from that time. If T is the time elapsed since the formation of the Earth, (i.e., the age of the Earth), and tm is the time before present at which the lead minerals were formed, then, using the assumptions of the Holmes Houtermans model given above, the isotopic composition of a common lead deposit formed tm years ago is given as follows ... 

Figure 9.2 Holmes-Houtermans model for the evolution of common lead deposits.

Serious problems arose with the Holmes/Houtermans model, and these problems came from anomalous lead as opposed to common lead that gave meaningful model dates. It is probable that the small number of ore deposits containing ordinary lead reflects the fact that the lead in most of these underwent a more complex history than that envisaged in the Holmes/ Houtermans model. To conform with this model, the relevant lead must have had a single-stage history and this can be confirmed if the model dates agree reasonably well with isotopic data obtained for other minerals fi-om the ore and if the isotopic ratios of lead from a particular deposit are constant within experimental error. 

Alternatives to the Holmes/Houtermans model have been proposed. The Russell/Standton/ Farquhar (RSF) and the Russell/Farquhar/Cumming (RFS) models were proposed based on the work of Alpher and Herman (1951). While the Holmes/Houtermans model presented a fan... 

Figure 9.5 Schematic diagrams to illustrate some of the models for the evolution of the lead isotope ratios in lead deposits (a) Holmes-Houtermans, (b) Stacey-Kramers, (c) mixing model.

Fig. 12.3. The one-stage Pb evolution model of Holmes-Houtermans according to Eqs. (12.16) and (12.17). The straight lines are isochrones for different values of t. The curved lines are Pb growth curves for U-Pb systems having present-day n ( U/ Pb) values of 7 (solid square), 8 (open circle), and 9 (solid triangle), respectively. Present-day...

In 1946, Arthur Holmes and Fredrich Houtermans built on previous work to independently develop a general model for isotopic evolution of lead in the Earth. The Holmes-Houtermans common-lead method enabled determination of the ages of common leads that have had single-stage histories and was used by Clair Patterson in the mid-1950s to determine the age of the Earth. 

The common-lead method looks at the isotopic evolution of lead in systems with U/Pb and Th/Pb ratios similar to or less than the ratios in bulk solar system materials. The original formulation, by Holmes and Houtermans, is a single stage model that accounts for the isotopic composition of any sample of common lead in terms of primordial lead plus radiogenic lead produced in the source up to the time that lead was separated from uranium and thorium. Multistage models that more accurately describe the evolution of natural systems have been developed. The common-lead method is used in cosmochemistry primarily to study the time of differentiation and reservoir evolution in differentiated bodies... 

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