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Classical Cepheids are the most popular distance indicators and tracers ofyoung stellar populations. The key advantage is that they are bright and theycan be easily identified in Local Group and Local Volume galaxies. Theirevolutionary and pulsation properties depend on their chemical abundances. Themain aim of this investigation is to perform a new and accurate abundanceanalysis of two tens of calibrating Galactic Cepheids using high spectralresolution (R$\sim$40,000-115,000) and high S/N spectra ($\sim$400) coveringthe entire pulsation cycle. We focus our attention on possible systematicsaffecting the estimate of atmospheric parameters and elemental abundances alongthe pulsation cycle. We cleaned the line list by using atomic transitionparameters based on laboratory measurements and by removing lines that areeither blended or display abundance variations along the pulsation cycle. Thespectroscopic approach that we developed brings forward small dispersions inthe variation of the atmospheric parameters ($\sigma$($T_{\rm eff}$)$\sim$50 K,$\sigma$($\log{g}$)$\sim$0.2 dex, and $\sigma$($\xi$)$\sim$0.2 km/s) and in theabundance of both iron ($\lesssim$ 0.05 dex) and alpha elements ($\lesssim$0.10dex) over the entire pulsation cycle. We also provide new and accurateeffective temperature templates by splitting the calibrating Cepheids into fourdifferent period bins, ranging from short to long periods. For each period bin,we performed an analytical fit with Fourier series providing $\theta =5040/{T_{\rm eff}}$ as a function of the pulsation phase. The current findingsare a good viaticum to trace the chemical enrichment of the Galactic thin diskby using classical Cepheids and a fundamental stepping stone for furtherinvestigations into the more metal-poor regime typical of Magellanic Cepheids.

A new and homogeneous metallicity scale for Galactic classical Cepheids II. The abundance of iron and alpha elements