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lever rule : ウィキペディア英語版
lever rule
The lever rule is a tool used to determine weight percentages of each phase of a binary equilibrium phase diagram. It is used to determine the percent weight of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus.
In an alloy with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the weight percentage of the α phase is
:X_\alpha = \frac
where
* a is the weight percentage of element B in the α phase
* b is the weight percentage of element B in the β phase
* c is the weight percentage of element B in the entire alloy
all at some fixed temperature.
== Derivation ==

Suppose an alloy at an equilibrium temperature ''T'' consists of ''c'' wt% (weight percentage) of element B. Suppose also that at temperature ''T'' the alloy consists of two phases, α and β, for which the α consists of ''a'' wt% B, and β consists of ''b'' wt% B. Let the weight of the α phase in the alloy be W_\alpha so that the weight of the β phase is W_\beta = W_ - W_\alpha, where W_ is the total weight of the alloy.
By definition, then, the total weight of element B in the α phase is W_ = aW_\alpha, while the total weight of element B in the β phase is W_ = b\left(W_-W_\alpha\right). Together these two quantities sum to the total weight of element B in the alloy, which is given by W_B = cW_. Therefore
: cW_ = W_B= W_ + W_ = aW_\alpha + b\left(W_-W_\alpha\right)
By rearranging, one finds that
:\frac
This final quantity is the weight percentage of the α phase in the alloy.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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