Melting point and glass temperature

Definitions and measurement.

Drilling down: melting and the glass transition.

Further reading.

 

Definitions and measurement.  Two temperatures, the melting temperature, and the glass temperature  (units for both: K or C) are fundamental because they relate directly to the strength of the bonds in the solid.  Crystalline solids have a sharp melting point, .  Non-crystalline solids do not; the glass temperature  characterizes the transition from true solid to very viscous liquid.  Measuring melting point sounds easy – just heat till it melts then record the temperature.  That works, but it’s not as precise as you might like because of temperature gradients, and it doesn’t work at all for the glass temperature because this is a gradual change.  Instead    and    (and all other phase transition temperatures) are measured by scanning differential calorimetry, explained in Figure 1.  The test sample and a standard, calibrated material are heated in insulated chambers.  The temperature of each is monitored and the power  to the sample adjusted, using a feed-back loop, so that its temperature is held the same as that of the standard, to which the power is .  When the sample melts or goes through its glass transition, a latent heat is absorbed and that means more power has to be pumped into the sample at the temperature at which it happens.  Plotting  against temperature, as shown in the figure, identifies the transitions.  The same equipment is used to measure latent heat and specific heat. 

Top

Drilling down: melting and the glass transition.  The most striking feature of melting is that the melting temperature is sharp – so sharp that the melting point of ice (0°C) and of sulfur (119°C) are used as temperature standards.  Melting is still not fully understood, but many of its features are explained by suggestion of Lindemann that crystals melt when the amplitude of atomic vibration exceeds about 10% of the atomic spacing.  The higher the modulus, , the harder it is to stretch atomic bonds, so we might expect to find that , and indeed this is the case: for metals and ceramics, for instance,

               

 ( in GPa and  in Kelvin) is a remarkably good approximation – try it, using CES.


         The key concept in understanding the glass transition is that of free volume.  Think for the moment of randomly packed spheres, although the argument holds for molecules of more complex shape.  There is a specific packing density for a random array like that of Figure 3 at which the whole array locks up; it is called the dense-random packing fraction and its value is 0.64 (see Density and atom packing).  Real glasses with spherical atoms have this packing fraction at low temperatures.  On heating through the glass temperature  the structure expands so that the packing fraction is lower and the volume consequently larger. The difference between the actual volume and the lock-up volume is the “free” volume – free in the sense that it gives the atoms freedom to change their configuration. One change of configuration is that of diffusion – mixing – of the atoms; another is change of shape in response to a stress.  It is the glassy equivalent of melting, but the sharp melting point of the crystal is smeared out into a broad transition spanning tens of degrees in a polymer and hundreds in inorganic glasses like soda-glass.  The temperature  is the center of the transition, as shown in Figure 1.

         Polymers such as PP, PE, and PS have both crystalline and glassy forms; for these it is found that  and  are related by  .

Top

Further reading.

Author

Title

Chapter

Ashby et al

Materials: Engineering, Science, Processing and Design

12, 13

Ashby & Jones

Engineering Materials Vol 1 & 2

Vol. 1, Chap. 20

Callister

Materials Science and Engineering: An Introduction

13, 15

Callister & Rethwisch

Fundamentals of Materials Science and Engineering: An Integrated Approach

2, 11, 14

Shackelford

Introduction to Materials Science for Engineers

2

Further reference details

Top