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Lambert W function
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=== Crystal growth === In the crystal growth, the negative principal of the Lambert W-function can be used to calculate the distribution coefficient, <math display="inline">k</math>, and solute concentration in the melt, <math display="inline">C_L</math>,<ref>{{cite journal |last1=Asadian |first1=M |last2=Saeedi |first2=H |last3=Yadegari |first3=M |last4=Shojaee |first4=M |title=Determinations of equilibrium segregation, effective segregation and diffusion coefficients for Nd+3 doped in molten YAG |journal=Journal of Crystal Growth |date=June 2014 |volume=396 |issue=15 |pages=61β65|doi=10.1016/j.jcrysgro.2014.03.028 |bibcode=2014JCrGr.396...61A }} https://doi.org/10.1016/j.jcrysgro.2014.03.028</ref><ref>{{cite journal |last1=Asadian |first1=M |last2=Zabihi |first2=F |last3=Saeedi |first3=H |title=Segregation and constitutional supercooling in Nd:YAG Czochralski crystal growth |journal=Journal of Crystal Growth |date=March 2024 |volume=630 |issue= |pages=127605 |doi=10.1016/j.jcrysgro.2024.127605 |bibcode=2024JCrGr.63027605A |s2cid=267414096 }} https://doi.org/10.1016/j.jcrysgro.2024.127605</ref> from the [[Scheil equation]]: <!-- k=W(Z)/ln(1-fs) CL=(C0/(1-fs))exp(W(Z)) Z=(Cs/C0)(1-fs)ln(1-fs) --> : <math>\begin{align} & k = \frac{W_0(Z)}{\ln(1-fs)} \\ & C_L=\frac{C_0}{(1-fs)} e^{W_0(Z)}\\ & Z = \frac{C_S}{C_0} (1-fs) \ln(1-fs) \end{align} </math>
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