Tham khảo tài liệu 'modern physical metallurgy and materials engineering part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The physical properties of materials 171 where VD is Debye s maximum frequency. Figure shows the atomic heat curves of Figure plotted against T 0D in most metals for low temperatures T D 1 a T3 law is obeyed but at high temperatures the free electrons make a contribution to the atomic heat which is proportional to T and this causes a rise of C above the classical value. The specific heat curve and transformations The specific heat of a metal varies smoothly with temperature as shown in Figure provided that no phase change occurs. On the other hand if the metal undergoes a structural transformation the specific heat curve exhibits a discontinuity as shown in Figure . If the phase change occurs at a fixed temperature the metal undergoes what is known as a first-order transformation for example the a to y y to u and u to liquid phase changes in iron shown in Figure . At the transformation temperature the latent heat is absorbed without a rise in temperature so that the specific heat dQ dT at the transformation temperature is infinite. In some cases known as transformations of the second order the phase transition occurs over a range of temperature . the order-disorder transformation in alloys and is associated with a specific heat peak of the form shown in Figure . Obviously the narrower the temperature range T1 Tc the sharper is the specific heat peak and in the limit when the total change occurs at a single temperature . T1 Tc the specific heat becomes infinite and equal to the latent heat of transformation. A second-order transformation also occurs in iron see Figure and in this case is due to a change in ferromagnetic properties with temperature. Free energy of transformation In Section it was shown that any structural changes of a phase could be accounted for in terms of the variation of free energy with temperature. The Figure The variation of atomic heat with temperature. Figure The effect of .
