pith. sign in
def

curie_ratio_Co_Fe

definition
show as:
module
IndisputableMonolith.Chemistry.Ferromagnetism
domain
Chemistry
line
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plain-language theorem explainer

The definition computes the ratio of Curie temperatures for cobalt (Z=27) to iron (Z=26) as approximately 1.337. Condensed matter physicists or Recognition Science researchers modeling magnetic ordering in transition metals would cite this ratio in scaling arguments. It is implemented as a direct division of outputs from the curieTemperature function.

Claim. The ratio of the Curie temperature of cobalt to that of iron, written $T_C(27)/T_C(26)$.

background

In the Recognition Science treatment of ferromagnetism the Curie temperature marks the thermal point where fluctuations overcome exchange coupling between aligned d-electron spins. The upstream curieTemperature definition supplies the concrete values 1043 K for iron (Z=26) and 1394 K for cobalt (Z=27). The module derives these properties from the 8-tick coherence structure, Pauli exclusion statistics, and the Stoner criterion U D(E_F) > 1, with T_C scaling directly with exchange energy.

proof idea

The definition is a one-line wrapper that divides the curieTemperature value for atomic number 27 by the value for atomic number 26.

why it matters

This ratio supplies the numerical input to the downstream theorem curie_ratio_bounds that verifies the interval (1.33, 1.34). Within the framework it connects to phi-ladder scaling of exchange energies, although the observed value lies closer to phi^0.6 than the initially conjectured phi^{2/5}. It supports the module's predictions for ferromagnetic elements Fe, Co, and Ni under the 8-tick octave and D=3 spatial structure.

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