Dear Muntaha Azhar,

Being retired I cannot give literature suggestions or references, so I make the following preliminary remarks.

* Slow/ fast temperature ramping are supposed to be equivalent to low/high temperature gradients during cooling.

* Your question regards metals or solid solution metal alloys; so crystallinity is only marginally influenced by cooling conditions: crystallinity seems given.

* Nucleation is presumed to occur heterogeneously: no lack of nucleation sites i.e. the effective amount of nucleation sites seems solely determined by supercooling.

* Low temperature gradients seems to enhance grain growth, while high temperature gradients will limit the grain growth.

I do hope that the above remarks stimulate discussion and research.

Good luck!

Dear Ahzar,

You can check this recent publication on the heating rate effect on crystal nucleation.

All the best

Article Heating rate effects in time-dependent homogeneous nucleatio...

Hi，Ahzar,

Recently, we published one paper on crystal shape evolution with cooling changing for your reference. 

Good  luck!

Article Investigation of the operating conditions to morphology evol...

Dear Muntaha Azhar,

I dare to make some remarks additional to my contribution of Sept 11, 2017.

* In my contribution of Sept 11, 2017 I apparently wrongly supposed metals or solid solution metal alloys.

* In case supercooled liquid glasses are the question's subject, a temperature increase can indeed provoke crystallization, the driving force is then a decrease of the specific volume (see Figure 3.34 in the attached link). 

* That crystallization can probably characterized as homogeneously: the transformation starts in a supercooled solid, no outside nuclei present. After crystallization the chemical composition has not changed.

* The amount of active nuclei in homogeneous nucleation is solely given by the supercooling as compared to the equilibrium liquidus/solidification temperature.

* A high temperature gradient during the crystallization heating treatment seems then to limit the amount of active nuclei and hence to enhance the size of the crystalized grains to be formed by nucleation and growth. For a low temperature gradient the opposite seems then to hold. 

* It should be noted that nucleation and growth are kinetic process featured by appropriate parameters like activation energy.

* Given the content of the contributions by Daniel R Cassar and  by Fang-Kun Zhang and the kinetic character of the processes involved, your specific case (which ?) deserves a separate study.

May these remarks stimulate discussion and research.

Good luck!

http://www.delftacademicpress.nl/m017.php

I would like to add to P. Van Mourik's comment from the perspective of a glass science researcher who has intentionally, and for the most part successfully, avoided crystallization during PhD studies.

The formation of crystals that are of the same composition of the supercooled liquid should not influence liquid composition. In complex systems (I've read mostly about nuclear waste glasses), the composition of the crystals may not match the composition of the glass. In fact, this is also a concern during thermal cycling of solid oxide fuel cells. Crystallization tends to occur at sites of heterogeneity, which may be at interfaces, within a composite (coatings research is full of examples) or in heterogeneous (phase separating?) regions of a glass. Due in part to the influence of thermal history on phase separation and the absence of phase diagrams for complex systems, it seems to me like crystal studies are rather exciting! To study crystallization, a well maintained DSC can easily show the onset of crystallization. Also, you can use a cross polarized microscope to estimate how amorphous a sample is; also, geologists know a lot about what common crystals look like in thin sections. Of course, XRD and a multitude of techniques are also useful. EDIT: Casar covers how to study crystallization.

The key to avoid crystallization of a slow cooled glass is to understand the glass transition temperature and changes in viscosity around this region. In my research, I rapidly cooled a glass from melting to avoid crystallization. Then, I would reheat the sample to between crystallization and glass transition temperatures PRIOR to slowly re-cooling it. There are quantitative methods for understanding non-Arrhenius behavior in the glass transition region (edit: see Casar's response). Also, a good DSC study can help you avoid unintentional crystallization.