4.3 Analytical Method
4.4.4 Divalent cation diffusion
The diffusion of strontium is very slow and therefore the profiles are very short. The LA- ICP-MS data for the “natural” melt diffusion experiments was confirmed by nanoSIMS (Appendix 3; Figure 121(pg. 263)) and the results are within error (Figure 60).
Strontium is assumed to partition onto the M site of plagioclase, and requires no charge balancing.
112
Equation 61 substituion of strontium in anorthite
CaAl Si O + SrO = SrAl Si O + CaO
Although anorthite has more calcium site available for diffusive exchange than albite, anorthite has a slower rate of diffusion for strontium than albite.
Cherniak and Watson (1994) found that the diffusion rate of strontium can differ by 0.7 log units between the (001) and (010) orientations. In this study, the largest deviation in Log Dsr is experiment AGV58, with a standard deviation of 0.5 log units (from 13 analysis). As the melt well is circular, it should be expected that the diffusion rate will change around the circumference of the melt pool, however the standard deviation of the diffusion coefficients is very low for most experiments. As the deviation is small, it suggests that the orientation of the crystal has very little effect on the diffusion of strontium.
The partition coefficient for strontium, is up to an order of magnitude higher than expected. As the diffusion direction is “out” (i.e. higher concentrations in the plagioclase than at the interface), this could indicate that we have not analysed the full profile. Comparing BF60 and BF68, there is no significant difference between the diffusion rate of Sr into plagioclase of composition An60 and An68. Although there is a significant variation in the strontium diffusion rate between experiments BIR66 and AGV66, which is measured by both nanoSIMS and LA-ICP-MS, this difference is not observed in the simple system experiments (Figure 62B,C). As such, AGV66 is considered an outlier. Comparing this study with previous studies on the diffusion in labradorite, this AGV66 experiment is clearly anomalous (Figure 66). The interface between the plagioclase and melt is one of the best of all the experiments.
Determining the Arrhenius relationship between the data presented in this study (with AGV66 omitted) we obtain an activation energy of aE = 427 kJ /mol and a pre- exponential factor of log D0 = -1.97 m2 / s however you must keep in mind that this study is only 2 temperature points at extremely high temperatures compared to natural samples. The closest composition of labradorite (An67) was studied by Cherniak and Watson, (1994). These two experimental series cover different temperature ranges so can be combined to give a more accurate relationship between temperature and An67 (Figure 66). Cherniak and Watson (1994) concluded that Sr diffuses in An67 at a pre-exponential factor
113 of log D0 = -7.03 ± 0.37 with an activation energy of aE = 268 ± 8 kJ / mol. With the inclusion of the hotter temperatures studied here this shifts to slower rates of log D0 = - 7.76 and an activation energy of aE = 254 kJ / mol.
Figure 66: The Arrhenius relationship between the partitioning of strontium in labradorite (An61-An68)
and temperature. squares; An67 Cherniak and Watson (1994), triangles; An63 Giletti and Casserly
(1994), grey circles; This study An66-An68. Sample AGV66 (open circle) is considered an outlier.
This can be compared to Giletti and Casserly (1994) who studied a range of plagioclase compositions (Figure 66). Giletti and Casserly (1994) find a pre-exponential factor of Log D0 = -5.8 and an activation energy of aE = 298 kJ / mol.
Barium Diffusion
Ba was measurable in all labradorite experiments even though the profiles are extremely short (Appendix 3; Figure 121(pg. 263)). Ba diffusion is not effected by melt composition.
There is an Arrhenius relationship between the diffusion of Ba in labradorite (~An67) and temperature.
The diffusion of barium in labradorite (An67) was investigated by Cherniak (2002) and the results are in good agreement with those discovered here, with the exception of the simple system diffusion experiment. Cherniak (2002) found that diffusion of barium along the (001) axis had a diffusion rate of log D0 = -6.6 ± 0.84 and an activation energy of 323 ± 20 kJ / mol while the (010) has log D0 = -5.98 ± 0.99 with an activation energy of aE = 341 ± 23 kJ / mol.
114
Combining the data presented here and the data from both orientations of labradorite given in Cherniak (2002) the relationship is changed to aE = 376 and a pre-exponential factor of log D0 = -4.29
Figure 67: Arrhenius relationship of Ba in labradorite plagioclase (An66-An68 in blue, An23 in orange)
Open symbols represent published data from Cherniak (2002). Diffusivity is logD (m/s2)
Magnesium Diffusion
Figure 68: diffusion of Mg as mapped by EPMA in 4 samples. Diffusion directions are: BF60, diffusion in. BF68, diffusion in and out. AGV58, diffusion in and out. AGV66 diffusion out.
115 Magnesium was of high enough concentrations in the plagioclase that the diffusive change could be visually mapped. Both diffusion into the plagioclase from the melt (Figure 68, BF60) and diffusion from the plagioclase out into the melt (Figure 68, AGV66) are visible in these experiments.
In samples BF60 and BIR66, Mg diffuses into the crystals with diffusivities of -16.1±0.5 and -16.4±0.3 respectively. Sample AGV66 diffuses out of the plagioclase at a faster rate, with a diffusivity of -15.2±0.2 (Appendix 3; Table 57, pg.264).
Samples BF68 and AGV58 have two complimentary diffusion profiles visible. The Mg diffuses both “in” (slower) and “out” (faster) of the plagioclase. This diffusion behaviour is witnessed in all the measured Mg isotopes; Mg24, Mg25 and Mg26. This behaviour is not exhibited by either Fe or Mn, which also can be divalent cations, but are larger cations at 0.92 and 0.96 Å respectively compared to Mg2+ at 0.89 Å in VIII fold co-ordination.
Figure 69: Diffusion of Mg between plagioclase and “natural” melts at 1190°C measured with LA-ICP- MS A) An66 with andesitic AGV melt B) An66 with basaltic BIR melt C) An58 with andesitic AGV melt D) An68 with basaltic BF melt. Both C and D display both diffusion “in” and “out” of two competing diffusion mechanisms.
116
Miller et al. (2006) investigated the partitioning of the divalent cations into anorthite and found that Mg can exist both on the large cation site as; MgAl2Si2O8 and on the tetrahedral site as; CaMgSi3O8.
The simplified substitution of Mg into anorthite is given by the following exchanges: Mg on the T site:
Equation 62 substitution of Mg on the tetrahedral site of anorthite
CaAl Si O + MgO + SiO = CaMgSi O + Al O
Mg on the M site:
Equation 63 substitution of Mg into the large cation site in anorthite
CaAl Si O + MgO = MgAl Si O + CaO
The actual substitution will be complicated by the albitic component. The Mg on the T site exchange will be favoured by systems with high silica activity as the Mg exchange is tied with a Si. The Mg on the M site, is not dependent on silica activity so should not be affected by melt changes. It is likely that these to mechanisms generally overprint each other. It is generally assumed that elements that substitute onto the large cation site diffuse faster than those in the tetrahedral site. In the previous chapter it was concluded that Mg is most likely to partition onto the tetrahedral site in plagioclase as the partitioning is effected strongly by the silica activity of the melt.
The effective partition coefficient of these diffusion “out” profiles are calculated by projecting the diffusion profile to the interface. The effective partition coefficient is 80% of the actual partition coefficient; which suggests this fast diffusion is the more dominant mechanism for partitioning. As the tetrahedral coordinated Mg is known to be the dominant form in plagioclase, this suggests the fast diffusion is tetrahedral Mg.
Faak et al. (2013) found that the experiments buffered for silica are 0.75-1 order of magnitude faster than unbuffered experiments (Figure 70). It was observed that high silica activities allows for a higher proportion of silica vacancies in the form □Si4O8 which likely contributes to the diffusion rate.
They conclude with giving a descriptor of the diffusion rate in plagioclase that depends on the activity of silica in the form:
117
𝐷 = 1.25 ∗ 10 ∗ exp −320,924
𝑅𝑇 ∗ (𝛼𝑆𝑖𝑂 )
.
Which gives the log D0 = -3.90 and an activation energy of 320 kJ / mol.
The additional SiO2 would also allow an increase in the diffusion of the tetrahedral site Mg.
The diffusivities of Mg in the buffered “simple system” experiments are variable, with one experiment showing gradually faster diffusion toward one end of the crystal. This brings up a possible uncertainty of these diffusion profiles.
If the plagioclase crystal is not cut directly perpendicular to the diffusive interface, the diffusion profiles can be artificially lengthened. The profiles cannot be shortened by this method. Therefore, where there is a large standard deviation in the diffusivities, the shorter profiles represent more robust data than the longer profiles.
These buffered diffusion experiments are not useful in determining the diffusion mechanisms in Mg.
Figure 70: Diffusion of Mg in labradorite in both published work by Faak et al. (2013); open symbols, and this study; filled symbols
Beryllium diffusion
Beryllium was doped into only samples AGV66, AGV58 and BIR66. These experiments allow for the comparison of melt composition. As the plagioclase compositions are very similar and the experiments with beryllium are carried out at only 1 temperature, no other variables can be compared confidently.
118
The Be profiles are very short; <5μm for AGV experiments and <10μm for the BIR66 experiment (Appendix 3; Figure 121(pg. 263)). These samples were measured by both nanoSIMS and LA-ICP-MS and results are within error.
The partition coefficients are within an order of magnitude of the predicted partitioning values, with the nanoSIMS partition coefficients more precise than those calculated by LA-ICP-MS.
Beryllium exists as a divalent cation and is very small; 0.27 Å in IV-coordination. Rather than the large cation site “M”, the beryllium is diffusing on the tetrahedral site replacing Al3+. This would require a charge balancing in the form:
Equation 64 beryllium substitution for aluminium onto the tetrahedral site of anorthite
𝐶𝑎𝐴𝑙 𝑆𝑖 𝑂 + 𝐵𝑒𝑂 + 𝑆𝑖𝑂 = 𝐶𝑎𝐵𝑒𝑆𝑖 𝑂 + 𝐴𝑙 𝑂
Al3+ + Al3+ Be2+ + Si4+
Incorporating beryllium on the tetrahedral site for aluminium causes the beryllium partitioning to increase as the aluminium activity of the melt decreases and/or the activity of silica in the melt increases.
Figure 71: Diffusion rate of Be and Ga at 1190°C A) in An66 as a function of melt alumina content B)
from the same melt composition as a function of anorthite content.
The diffusivity of beryllium is within error when comparing the two AGV experiments with different plagioclase compositions (Figure 63B). Conversely, when comparing similar plagioclase compositions and different melt compositions; there is an order of magnitude difference (Figure 62B). The samples with the andesitic melt have diffusivities
119 of -19.0 ± 0.5, while the basaltic melt diffuses faster (logDBe = -17.5 ± 0.2) (Appendix 3; Table 57, pg.264).
It is difficult to determine the activity of the components in a natural system. It is usually assumed that the increase in molar proportion indicates an increase in activity of that component. The proportion of aluminium and silica both increase when moving from basaltic (BIR) to andesitic (AGV) compositions while the diffusion rate decreases (Figure 71).
Beryllium diffusion was only measured at one temperature and this element has not been investigated as a diffusant in plagioclase previously and as such, no Arrhenius relationship can be calculated.
Manganese and Iron diffusion
Figure 72: Diffusion of Fe as mapped by EPMA
Iron is a minor component in most plagioclase and occurs in these tested plagioclase at 0.40-0.46 wt. % FeO. Fe diffuses out of the plagioclase in all experiments. In the andesitic experiments, the change in concentration is only 300 ppm while in the basaltic experiments the change is in the range of 800 ppm. The change in concentration due to diffusion from the andesitic melt is too small to be resolved with EPMA.
Iron diffusion has been investigated in An66 at different oxygen fugacity by Behrens et al. (1990), however no data table was published. The Fe diffusivities at 1200°C are log D=- 16.58 ± 0.19 at log αO2 = -0.68 and log D = -15.28 ± 0.11 at log αO2 = -10.59. Furthermore they discover a dependence of oxygen fugacity on the diffusion of Fe, of 1.5 log units in a change of 10 log units of αO2 (Behrens et al., 1990; Cherniak, 2010). The Behrens et al. (1990) data point is within error of the data presented in this study.
Mn can exist as 2+, 3+, 4+, 5+, 6+ or 7+. Mn2+ would be the most compatible in plagioclase. Mn2+ is of similar size as Fe2+; 0.96 and 0.92 Å respectively (assuming
120
divalent cation in VIII-fold co-ordination) and therefore these two elements are assumed to behave similarly. Mn is in much lower concentrations in plagioclase than Fe and can be measured precisely with LA-ICP-MS. As Mn diffuses out of the plagioclase in all experiments, though has high concentrations in the melt and buffers it was used as the indicator element for where the interface is placed.
Substitution of divalent cations on the “M” site is given by:
Equation 65 Divalent substituion in anorthite
CaAl Si O + M O = MAl Si O + CaO
This equation shows that the substitution of divalent cations into the anorthite crystal structure is a straight substitution with no effect from the melt component.
There is very little orientation effect found with the diffusion of Mn with a standard deviation of ~0.2 log units for all experiments (Appendix 3; Table 57, pg.264) except for An67-II(TM) which has the largest deviation of 0.5 log units. This is very robust data as between 11-28 profiles were collected for Mn in plagioclase diffusion from melt experiments.
Figure 73: Diffusion as a function of the silica component of the melt, at 1290°C (grey symbols) and 1190°C (open symbols) in An66 (circles) and An95 (triangles) plagioclase. A) Diffusivity of Mn B)
Diffusivities of Fe.
There is an apparent effect of melt composition on the diffusion of Mn in An67 at 1290°C. There is also an apparent effect of melt composition on the diffusion of Fe into An95 at 1290°C. This is not seen in An67. As all other samples have diffusion rates within error of
121 one another; even when comparing An67 and An95, it is likely that these are anomalous results (Figure 74).
Figure 74: a comparison of the diffusivities of Mn and Fe at 1190°C (circles) and 1290°C (squares) and QFM.
Comparing divalent cation diffusivities
These multi-element diffusion experiments have the advantage of directly comparing the diffusivities of elements in each experiment. Strontium and barium both partition onto the large cation site of plagioclase while Be partitions onto the tetrahedral site. Mg is thought to prefer to partition onto the tetrahedral site however may have some input into the M-site.
Comparing the divalent cations in the M-site; Ba and Sr, the diffusivities of these two elements are identical at composition An68. At composition An70 the diffusion of Ba is faster than Sr and as the calcium content of the plagioclase decreases, the diffusivity of Sr increases. In plagioclase with composition An58 Sr diffuses an order of magnitude faster than Ba (Figure 75A).
Beryllium partitions onto the tetrahedral site. Comparing the Sr and Be diffusivities, there are no discernible trends. This suggests different diffusion mechanisms for these two divalent cations (Figure 75d).
There are two observable diffusion mechanisms for Mg in plagioclase. Comparing the diffusivities of Mg and Sr (the latter of which diffuses only on the M-site), the contribution to the M-site diffusion in plagioclase can be assessed. The “slow” diffusion
122
of Mg, is consistently faster than strontium in all experiments (Figure 75C) by roughly an order of magnitude.
Figure 75: A comparison of the diffusivities of the divalent cations in all experiments (1190 and 1290°C). The black line represents identical diffusivities. Circles represent 1190°C and squares are 1290°C. A) comparing the diffusivities of VIII-fold coordinated divalent cations; Ba and Sr. B) comparing the diffusivities of Be and Mg. C) comparing the diffusivities of Mg and Sr. D) comparing the diffusivities of tetrahedral coordinated divalent cations (Be) and VIII-fold coordinated divalent cations (Sr).
As the relationship between the Mg slow diffusion and Sr is consistent, it is assumed this slow diffusion is the M-site diffusion mechanism for Mg. Additionally, the diffusion “in” and “out” of this diffusion mechanisms are comparable. The directionality of the diffusion profiles is dependent only on partition coefficients rather than diffusion mechanism. There is a consistent ratio between the “fast” Mg diffusion and the diffusion of Be. This could suggest a relationship between these two diffusion mechanisms, however with only two data points, conclusions are not robust.
123
Figure 76: The comparison between diffusivities of divalent cations with their respective ionic radius in VIII-fold coordination. An~60 composition in yellow, and An~70 composition in blue. Open symbols are
slow “in” diffusion of Mg. Fe, Mn and Eu diffusivities could be the sum of multiple valence cation diffusion, though the 2+ cations will be the most compatible.