C. Discussion
4. LNDC and Compression Maximum
Figure 13. “Bond angle LNDC” versus mean coordination number of network former(s) “A” by bridging oxygen “BO”. Error bars are less than the symbol height and width.
instantaneous relaxation mechanisms, which would presumably be observable within the time window of the present MD simulations. Relative to the SPS model and traditional chemical strengthening from Section III, the MD-predicted MSCM for SLS is considerably higher. In the former case, this is attributed to systematic under-estimation of MCSM by the SPS model, as the model did not consider densification as is detailed in Section III. In the latter case, traditional chemical strengthening profiles have a fully- exchanged surface layer that is maintained in a high compressive state for at least minutes, if not hours, during which time relaxation, thermally-activated or otherwise, takes place.
For SMAS, the most comparable laboratory MCSM measurement is that of Svenson, et al.,37 involving a similar aluminosilicate composition to that simulated here, although the glass was hydrostatically compressed at 1 GPa at 600 °C, then cooled under compression to maintain the densified structure. The resulting specimen, when chemically strengthened, showed about 200 MPa greater surface compression than that of the non-compressed glass, as determined by optical ellipsometry. Again, the MD simulation, while showing better agreement for SMAS than for SLS, has higher MCSM than the SPS model and traditional chemical strengthening from Section III.
Table X. Maximum Compressive Stress Magnitude from Various Sources Maximum Compressive Stress Magnitude (MCSM) Observed, or Computed from LNDC (MPa, biaxial) Glass This MD Study Section III
“SPS” Model Literature
Traditional Chemical Strengthening^
SLS 1,671±35
1,125 with range 900 to 1,300
about 1,400† about 550
SMAS 1,413±92
1,100 with range 800 to 1,400
1,240‡ about 850
†SLS-type, electric field-assist chemical strengthening35,36
‡SMAS-type, compaction prior to chemical strengthening37
^ from Section III, stress-birefringence measurements
One additional point for consideration regarding comparisons of chemical strengthening that has been performed at elevated temperature is that of thermal contraction. Tyagi and Varshneya28,29 noted that in-situ measurements of stress- birefringence exhibited about 20% lower compression magnitude at room temperature than at the chemical strengthening temperature. If the literature values in Table X are revised by a comparable percentage, the resulting agreement with MD-predicted MCSM is quite good for both SLS and SMAS.
A major point of interest is why traditional chemical strengthening produces much lower surface compression than that predicted by MD simulation and observed by specialty chemical strengthening techniques. Often, even short traditional chemical strengthening times, for example 15 minutes, do not exhibit notable surface compression increases over that at one or two hours, i.e. traditional chemical strengthening roughly shows a plateau of surface compressive stress versus increasing time for low to moderate chemical strengthening temperatures. This is especially evident for the SAS glass studied in Section III, which maintains a surface compression magnitude near 800 MPa for chemical strengthening temperatures of 400 °C and 450 °C and times out to 16 hours. It seems one or more relaxation mechanisms exist and are active within the time range after initial SAA (the period observed by MD simulation) and prior to surface compression measurement of traditionally chemically strengthened glass. For convenience, these will be referred to as early relaxation modes (ERM). They are posited to occur, but are not directly witnessed. Key features of the ERM are: (1) they are limited in their relaxation capacity (i.e. they do not fully relax the compressive stress state) and (2) they are mostly complete or are considerably slower by the time surface compression measurements are made.
A likely component to the ERM with the aforementioned features is volume viscosity,38 which has been suggested briefly by Varshneya.3 Glasses have a capacity for volume relaxation. Under an isothermal hold within the glass transition range, i.e.
annealing, glass will undergo both instantaneous and delayed volume changes to approach its equilibrium volume at that temperature, commonly known as structural relaxation.38 Often, glasses that are formed by fusion will contract during annealing because the finite cooling rate after fusion limits the volume relaxation. This capacity for
volume contraction during annealing implies the initial network has greater free volume than its annealed counterpart. If these two hypothetical glasses were to each be traditionally chemically strengthened, it may be presumed that the annealed glass will display greater surface compression for two reasons. First, the network with less free volume will have a higher LNDC, as supported by the present MD simulations (Figure 11A, allowing Poisson’s ratio to be representative of the atomic packing density).
Second, the network with less free volume will have less capacity to relax stresses generated by chemical strengthening via consumption of free volume (permanent densification).
A direct example of the influence of heat treatment upon the compressive stress resulting from traditional chemical strengthening is given in the experiments of Allen, et al.39 Sub-Tg heat treatments of sodium aluminosilicate glass, similar to SMAS, prior to chemical strengthening produced surface compression increases of about 10% relative to as-formed glasses after potassium chemical strengthening. Further, the compressive stress increase over as-formed glass was nearly constant with increasing chemical strengthening time from 0.5 to 32 hours, suggesting the stress relaxation time over this period was not substantially altered. That is, the compressive stress improvement involves alteration of the initial compressive stress magnitude and is apparently largely decoupled from the subsequent relaxation occurring with increasing chemical strengthening time (at 0.5 hours and beyond). The compressive stress resulting from sub- Tg heat treatment remains about 300 MPa to 500 MPa less than that predicted by MD simulation and observed by specialty chemical strengthening techniques (Table X). A likely reason is, at least in part, suggested by Allen, et al.39 that the heat treatment,
“allow[s] for only a subset of the relaxation modes to be activated [during chemical strengthening].” The relaxation modes eliminated by heat treatment would be assigned to volume relaxation in light of the present study and only a fraction of these relaxation modes can be consumed during the heat treatment because of its elevated temperature, relative to the chemical strengthening temperature, and limited time.
Further examination of the ERM hypothesis relative to the literature references in Table X, allows the following observations to be drawn. Electric field-assist chemical strengthening35,36 produces a sub-surface compression maximum in which the leading
edge of the compressive stress profile is nearly in a “time-zero” state. Instantaneous relaxation mechanisms will have taken place, but stress relaxation by ERM, and by other later time-dependent processes such as traditional shear flow, have not yet occurred.
Densification of glass prior to chemical strengthening37 activates similar network relaxations that would occur during relaxation of chemical strengthening stress by the ERM, resulting in reduction of free volume and decreased capacity to release stresses by compaction. Thus, the resulting structure when chemically strengthened shows higher compression magnitude. A consequence of the reduced network free volume is that the interdiffusion kinetics are severely hindered.37 This experimental observation indirectly supports the increased atomic packing density.
Note, in addition to volume relaxation, the ERM could potentially contain stress- dependent or strain rate-dependent relaxation under biaxial stress conditions. A high magnitude of compressive stress or rapid straining may promote certain relaxation modes until a lower compression magnitude or strain rate is reached, at which time those relaxation modes would no longer be active.
While the ERM hypothesis may bridge observations of “time-zero” stress between MD simulation and other sources, it is apparently active outside of the 200 ps time window examined presently and/or is dependent upon the system boundary conditions (e.g. ability for application of external stress). This leaves a time span of about 12 orders of magnitude across which one or more ERM processes may reside. As an example, consider the case where two independent relaxation mechanisms are present.
The first relaxation mechanism, “a,” is associated with an ERM and exhibits volume viscosity characteristics, thus it is limited in its relaxation capacity, and the second relaxation mechanism, “b,” is associated with the relaxation generally observed during traditional chemical strengthening and exhibits shear viscosity characteristics. Assuming stretched exponential relaxation with a stretching parameter of 0.5 for both mechanisms and relaxation times τa = 10 seconds and τb = 106 seconds, a representation of the stress relaxation versus time is given in Figure 14. As noted in the figure, the leading-edge compressive stress magnitude measurements obtained by electric field-assisted method may represent a “near-zero” time observation, say effectively from 0.01 to 10 seconds, which may avoid much of the stress relaxation by the ERM. Observations of stress after
traditional chemical strengthening represent a near-fully exchanged surface layer at a time of at least about 1,000 seconds or later. By this time, the ERM mechanism “a” has nearly completely been extinguished and only relaxation by shear flow “b” remains. This example is limited for simplicity. The ERM may contain multiple components, which themselves may be represented by volume viscous and/or shear viscous behavior. These ERM events can potentially be studied via elevated temperature MD simulations of SAA, with much longer observation times, and/or alternative boundary conditions during SAA.
Figure 14. Example of a two-mechanism stress relaxation system, where each mechanism is responsible for half of the total stress. Stretched exponential relaxation with a stretching exponent of 0.5 has been assumed. The relaxation times for each of the mechanism are given in the figure.
Note, Shaisha and Cooper36 suggested the presence of a “fast” relaxation process and/or a temperature-dependent LNDC, albeit in a somewhat different context than that discussed here. Their experiments of potassium stuffing in SLS by electric field-assist chemical strengthening displayed a strong MCSM temperature dependence, ranging from about 1,500 MPa at 200 °C to 700 MPa at 450 °C. Further, by varying the applied potential at 350 °C, the time required for equivalent exchange of ions could be varied,
120 minutes. Assuming their compressive stress measurements were in-fact from the leading edge of the diffusion front, rather than averages across the exchanged zone, one would have to conclude that SAA instantaneous relaxation is temperature-dependent which is in agreement with the free volume arguments presented in the preceding discussion. That is, as the chemical strengthening temperature is increased, the host glass structure will expand and have greater free volume. Silicate networks with greater free volume have less expansion upon chemical stuffing because that expansion is partly consumed by the additional free volume of the network at elevated temperature. The lack of relaxation at 350 °C for the time span of two to 120 minutes, again assuming the compressive stress measurements were made at the leading edge of the diffusion front, is consistent with the leading edge representing a “time-zero” state for the alkali stuffed material.
For commercial glasses a balance of chemical strengthening temperature and time must be achieved. While SLS and 23NS show high LNDC, the high NBO concentrations cause these compositions to be somewhat soft in terms of their viscosity-temperature profiles, relative to SMAS for example, and are thus more susceptible to relaxation by viscous means. Observations within this study highlight the possibility for enhanced surface compression through understanding factors that dictate the initial LNDC and that potentially influence subsequent stress relaxation. This type of understanding will likely be a key to developing future generations of glasses optimized for chemical strengthening and to developing alternative techniques by which chemical strengthening can be imparted, each to optimize surface compression.