Thermal vibration amplitude of atoms and fusion behavior of metals

The Lindemann parameters delta, and the root-mean square thermal vibration amplitudes √ of 54 metallic elements both at fusion and at room temperatures are calculated through the combination of the Debye-Waller and the Lindemann equations. The magnitude and ratio of the average Lindemann parameters deltasup(r)fsub(i) with i=1,2 and 3 for the fusion transitions; A2→ liquid, A1→ liquid and A3→ liquid, are respectively deltafisup(r)=0.226, = 0.185 and deltafsub(3)sup(r)=0.131. deltafsub(1)sup(r):deltafsub(2)sup(r):deltafsub(3)sup(r)=1:0821:0.578. The hypotheses of Lindemann, Gilvarry and Shapiro on the fusion phenomena due to lattice vibration of metals are justified. The role of lattice structure of fusion is also demonstrated. (author)