On the geothermal gradient and heat production in the inner core

Abstract: In this thesis I have investigated the upper bounds on the possible presence of radiogenic heat sources in the inner core of the Earth, using both steady state and transient models, built during this work. Necessary theory for this and model descriptions are collected into appendices at the end of this work. In addition, the published literature is reviewed for various formation scenarios, modelling of the inner core, theoretical and experimental values of relevant thermodynamic parameters. A general expression for the upper thermodynamical bounds on the initial heat source abundance at onset of inner core soldification is derived, which in the range of the published values of the thermodynamical parameter space yields upper bounds of 0.20 ± 0.15 wt% initial abundance of 40K, the most favoured radiogenic candidate in the inner core. Alternatively the expression can be used to set an upper limit to the age of the inner core given that we know the present abundance of heatsources and thermal parameters. E.g. assuming a heat transfer coefficient of k = 80 W m−1 K−1, a melting temperature of iron of 5500 K at the inner core boundary, and a value of the thermodynamical Grüneisen parameter of  γth,ICB = 1.5, it is found that if the core is older than 0.9 Gyr the inner core 40K abundance has to be lower than 0.142 wt% (the constraint set by cosmochemical arguments) and if the inner core is older than 2.52 Gyr the upper bound is less than 0.058 wt% (upper limit as set by high pressure experiments). Several geotherms for the inner core in subspaces of the parameter space are also presented. A comparison between the steady state and transient models is also performed, with the result that steady state models generally underestimates the temperatures and are not suitable for the inner core geotherm, mainly due to the transient nature of inner core formation and evolution. Finally the nickel-silicide/georeactor inner core model, as proposed by Herndon is investigated. It is found that this would generate a large molten region at the centre of the inner core, which has not been observed today. Hence it is concluded that a georeactor can not be operational at the centre of the Earth today.