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• Glass


  Amorphous solid formed when a liquid is cooled rapidly enough that the atoms do not have time to rearrange into a crystalline pattern
• Glasses


  • Lack long-range order, have short-range order, and exhibit properties different from crystalline solids
• Glass formation


  1. Liquid is cooled rapidly enough that atoms do not have time to rearrange into a crystalline pattern

  2. Atoms become "frozen" in an amorphous structure
• Homogeneous nucleation


  Nucleation that occurs without the benefit of preexisting heterogeneities
• Heterogeneous nucleation


  Nucleation that occurs at heterogeneities in the melt such as container walls, insoluble inclusions, and free surfaces
• Nucleation rate goes through a maximum as a function of undercooling
• Nucleation almost always occurs heterogeneously rather than homogeneously
• Assumptions in deriving nucleation equations: homogeneous nucleation, steady-state rate, no composition change, no volume change
• Homogeneous nucleation


  Nucleation that occurs in the bulk of the material, not at defects or interfaces
• Heterogeneous nucleation


  Nucleation that occurs at defects, interfaces, pores, grain boundaries, and free surfaces
• Measuring nucleation rates


  Heat treat glass to certain temperature for given time, cool, section, count number of nuclei, calculate nucleation rate assuming steady-state nucleation
• Measured nucleation rates are 20 orders of magnitude larger than predicted by theory
• Standard growth


  Growth model where interface is rough on atomic scale, growth rate determined by surface reaction rate, not diffusion
• Surface nucleation growth


  Growth model where interface is smooth, growth occurs by spreading of monolayer at preferred sites like ledges or steps
• Screw dislocation growth


  Growth model where interface is smooth but imperfect, growth occurs at step sites provided by screw dislocations
• As undercooling increases


  Growth rate goes through a maximum due to competing effects of increasing driving force and decreasing atomic mobility
• Time-temperature-transformation (TTT) diagram defines time required at any temperature for given volume fraction to crystallize
• Critical cooling rate (CCR)


  Minimum cooling rate required to avoid detectable crystallization
• Surface reaction rate


  Reaction rate controlled by the rate of reactions occurring at the surface (as opposed to diffusion-controlled)
• Surface reaction rate


  • Three-dimensional with time
  • If the growth were diffusion-limited, the growth rate would be not linear with time but parabolic
• Nucleation rate is random and continuous
• Calculating fraction crystallized


  1. Given the nucleation and growth rates at any given temperature, the fraction crystallized can be calculated as a function of time from Eq. (9.19)

  2. Repeating the process for other temperatures and joining the loci of points having the same volume fraction transformed yield the familiar TTT diagram
• Critical cooling rate (CCR)


  Estimate of the critical cooling rate given by (T_L - T_n)/t_n
• Glass composition


  Strong (log scale) functionality of the CCR on glass composition
• Criteria for glass formation

  • Low nucleation rate
  • High viscosity at or near the melting point
  • Absence of nucleating heterogeneities
• Ratio AS_l/\eta_m


  The smaller the product, the more likely a melt will form a glass
• If cooled rapidly enough, any liquid will form a glass
• Network formers


  Covalently bonded, silicate-based oxide melts with a continuous three-dimensional network of linked polyhedra
• Network modifiers


  Oxides such as alkali or alkaline earth oxides that modify the properties of a glass
• Alumina can behave as either a glass network or a glass modifier
• Glass transition temperature (T_g)


  Temperature at which a supercooled liquid transforms from a rubbery, soft plastic state to a rigid, brittle, glassy state
• Glass transition temperature (T_g)

  • Depends on cooling rate
  • Not a thermodynamic quantity, but rather a kinetic one
  • Abrupt decrease in thermal expansion coefficient and heat capacity due to "freezing out" of molecular degrees of freedom
• Cooling rates affect the rearrangement of atoms, with slower cooling resulting in a denser glass
• The glass transition temperature (Tg) is a kinetic phenomenon, not a thermodynamic one
• The abrupt decrease in properties like thermal expansion coefficient (a) and heat capacity (cp) at Tg is due to the "freezing out" of molecular degrees of freedom
• The viscosity of a glass at Tg is around 10^15 Pa·s, indicating low atomic mobility
• If a glass-forming liquid is cooled slowly enough, its entropy could become lower than that of the crystal, leading to the Kauzmann paradox
• Tg


  A measure of the rigidity of the glass network
• Adding network modifiers tends to reduce Tg, while adding network formers increases it
• Measuring Tg


  Measure any property that changes slope at Tg, such as by using differential thermal analysis (DTA)