Quantifying the influence of calcium ion concentration on the corrosion of high-purity magnesium, AZ91, WE43 in modified Hanks’ solutions

The corrosion rate in a modified Hanks’ solution (containing no Ca2+ ions) was higher than in Hanks’ solution. The increase was by a factor of ∼12 for HP Mg and AZ91, and a factor of ∼6 for WE43. This quantitatively highlights the critical role of Ca2+ ions for Mg corrosion in synthetic body fluids. The Ca2+ ion containing solutions produced a dense corrosion-product layer of hydroxyapatite, Ca3(PO4)2) · Ca(OH)2, a greater fraction of which stayed on the corroding surface (∼0.2–0.3) compared with the Ca2+ ion free solutions which produced magnesium phosphate, Mg3(PO4)2.

The corrosion mechanisms of Mg have been elucidated by studies aimed at the use of magnesium for automobile and aerospace applications. These same corrosion mechanisms are applicable to Mg biocorrosion [15,18,[25][26][27][28][29][30][31][32][33][34]. In particular, Mg alloys have corrosion rates higher than that of high purity Mg because the second phases cause micro-galvanic corrosion acceleration of the alpha-Mg matrix [31][32][33]. Impurity elements are a particular issue when their concentrations are above their (composition-dependent) impurity limits, which can be ∼1 ppm for a wrought alloy [31]. Shi and Atrens [35] and Cao et al [28] found that not all the corrosion products stayed on the surface of the corroding specimen. Appendix A provides more details.
This understanding of Mg corrosion has provided the foundation for the understanding of Mg biocorrosion. Witte [5] was the first to use laboratory corrosion studies to understand the factors of importance to Mg biocorrosion. He showed that a simple chloride solution does not reproduce biocorrosion. There has been subsequently much research to understand the factors of importance to the biocorrosion of Mg alloys [2,16,25,[36][37][38][39][40][41][42]. Zainal Abidin et al [43][44][45] showed that a match to biocorrosion was reproduced by immersion tests of Mg alloys in Nor's solution (Hanks' solution with pH buffered by the bubbling of CO 2 through the solution). Taltavull et al [46] showed that (i) increasing chloride ion concentration in the synthetic body fluid (SBF) increased the corrosion rate of Mg alloys mainly by facilitating the micro-galvanic acceleration by the second phases in the microstructure, and (ii) the phosphate present in the SBF decreases the corrosion rate by the formation of a more protective surface film of corrosion products. These laboratory studies have been complemented by in vivo studies of the corrosion behaviour of Mg in animal models such as a rat or a Guinea pig, whose biology is similar to that of humans [5,7]. The in vivo studies have identified the corrosion products of Mg biocorrosion. Witte et al [7] showed that the Mg corrosion product layer mainly contained calcium (Ca) and phosphorous (P). Zainal Abidin [45] found that the corrosion layer consisted of Mg, O, P, C and Ca. Marco et al [47] indicated that the corrosion products contained (Mg,Ca)CO 3 , (Mg,Ca)PO 4 and Mg(OH) 2 .
The laboratory studies (i.e. the in vitro studies) have used solutions whose chemical composition is close to that of human body fluids [16,25,38,43,48,49]. Hanks' solution is such a simulated body fluid (SBF), containing approximately the same concentration of each inorganic compound of blood plasma, and uses the same buffer as blood to maintain appropriate pH [45,50].
Thus, the factors that influence Mg biocorrosion have largely been elucidated [16,36,51]. However, Atrens et al [36] and, Johnston et al [16] have highlighted that there is uncertainty concerning (i) the role of the local environment on the corrosion of Mg in vivo, and (ii) the role of the cations during Mg corrosion, particularly the role of Ca 2+ . The presence of Ca 2+ in the SBF tends to retard the corrosion rate of Mg alloys [16,52], however, this analysis has been qualitative. To date quantitative data analysing effect of Ca 2+ on Mg corrosion in SBF has been absent.
The present study aims at quantitatively elucidating the influence of Ca 2+ ions on the corrosion of Mg alloys. The influence of the Ca 2+ ion concentration was studied by immersion testing HP Mg and the two Mg alloys WE43 and AZ91 in solutions which were based on Hanks' solution and had systematically varied Ca concentrations.

Magnesium specimens
The chemical compositions of the HP Mg, AZ91, and WE43 are presented in table 1 as measured by atomic emission spectroscopy (ICP-AES) by Spectrometer Services Pty Ltd, Coberg, Vic. Fishing line specimens were used [35]. HP Mg is expected to show predominately uniform corrosion, whereas AZ91 as a two-phase alloy consisting of the alpha-Mg matrix and the beta-phase, is expected to show localised corrosion of the alpha-Mg matrix because of the micro-galvanic acceleration by the second phase, the beta-phase. AZ91 serves as a reference Mg alloy that has been widely studied; however, the Al content of this alloy may make it unlikely that AZ91 is used in vivo. WE43 is however suitable for use as an implant in the human body [6].
Each Mg alloy specimen was ground with four different grit SiC papers (320, 600, 1200, 4000). The last grinding step used ethanol instead of water to reduce the corrosion of the specimens [50]. The specimens were dried and weighed to determine the weight of each specimen before immersion testing. The specimens were stored in ethanol until used.  [16]. Table 2 also compares the concentrations of the solutions used with the inorganic compounds present in blood plasma. Hanks' solution is similar to blood plasma with respect to these inorganic compounds.

Immersion tests
A schematic of the experimental apparatus is presented in figure 1. Each specimen was immersed in the solution as a fishing line specimen [35] at 5 cm distance from its neighbours. The temperature was maintained by the water bath between 36 and 37°C, as this is the body temperature. The pH-value was controlled using the CO 2 -bicarbonate buffer, by bubbling CO 2 through the solution. Hanks' solution with pH control by CO 2 is known as Nor's solution and mimics blood plasma [45]. With this buffer, the pH was maintained between 7.35 and 7.45. Mild solution flow was produced via a pump to ensure that the temperature and pH were homogeneous throughout the tank.
Following Shi and Atrens [35] and Cao et al [28] (see appendix A for further details), measurements were made to determine if all the corrosion products remained on the surface during the immersion tests. A measure of the apparent specific corrosion-product weight on the specimen surface after the immersion test, W acpw [mg cm −2 ] was evaluated, as described by Shi and Atrens [35], using: where W acp is the specific specimen weight after the immersion test with the corrosion products still on the surface (i.e. the measured mass divided by the surface area of the specimen, A [cm 2 ]), and W b is the specific weight of the specimen before the immersion test. This formulation was used [35] to test the applicability of using W awcp to monitor the corrosion rate of the specimen during the immersion test. The actual specific mass of corrosion products remaining on the specimen surface after the immersion test, W cp , was evaluated using; where W a is the specific specimen mass after the immersion test after removal of all the corrosion products. The expected mass of the corrosion product, W ecpw , was evaluated using where F=3.60 for Mg 3 (PO 4 ) 2 corrosion products, and F=3.96 for Ca 3 (PO 4 ) 2 )·Ca(OH) 2 , as explained in appendix A.

Corrosion rate
Mg corrosion has the following overall reaction [36]: Consequently, 1 mol of Mg corrosion evolves 1 mol of hydrogen gas (H 2 ). Thus, the corrosion rate can be evaluated from the weight loss of Mg metal, or the volume of evolved hydrogen [53]. However, the corrosion rate measured from the evolved hydrogen becomes inaccurate for low corrosion rates [36,53], less than 1 mm.y −1 . Therefore, the corrosion rate was evaluated in this research as the weight loss rate P w (mm y −1 ) determined by Table 2. Concentration of ions in the immersion solutions compared to that of human blood plasma (mmol l −1 ).  means of [16,36]:

Chemical composition
where DW (mg) is the weight loss over the immersion period, t (in days) is the duration of the immersion, and A (cm 2 ) is the surface area of the specimen. Each specimen, after removal from the solution, was dried and the corrosion products were analysed using a scanning electron microscope (SEM) and Energy Dispersive X-ray Spectroscopy (EDX). The specimen was cleaned by immersion in the standard chromic acid solution [28,[33][34][35] to remove the corrosion products, dried and weighed to measure the weight loss. The specimen was returned to the SEM and the surface corrosion morphology was analysed.
Specimens were immersed again for two weeks in the solution with a calcium concentration twice that of ] H ) and in the solution without calcium ions ([Ca 2+ ]=0), in order to produce sufficient corrosion products on their surface. These specimens were dried and corrosion products were scraped from the surface for X-ray powder diffraction (XRD) analysis. Tables 3 and 4 present the measurements relating to the evaluation of corrosion products analysed using equations (1)-(3), in an effort to determine if all the corrosion products remained on the specimen surface during corrosion. If the corrosion products all remained on the specimen surface, the specimen would gain weight, and the quantity W acpw would be positive. However, inspection of tables 3 and 4 indicates that W acpw was negative for most specimens, indicating that not all the corrosion products remained on the specimen surface. This conclusion was further supported by the fact that the quantity W cp (the measured weight of the corrosion Table 3. Data from immersion tests in the solution without calcium ions ([Ca] = 0) during 5 days (t=5 days); ΔW is the specific mass loss rate [mg cm −2d 1 ], W cp is the actual specific mass of corrosion products on the specimen surface after the immersion test evaluated using equation (2), W acpw is the apparent specific mass of corrosion products on the surface as evaluated by Shi and Atrens [48] (see appendix) evaluated using equation (1), and W ecpw is the expected specific mass of the corrosion products based on the assumption that the corrosion products are Mg 3 (PO 4 ) 2 and evaluated using equation (3).

Specimen designation
Time, t day DW mg.
, W cp is the actual specific mass of corrosion products on the specimen surface after the immersion test evaluated using equation (2), W acpw is the apparent specific mass of corrosion products on the surface as evaluated by Shi and Atrens [48] evaluated using equation (1), and W ecpw is the expected specific mass of the corrosion products based on the assumption that the corrosion products are Ca 3 (PO 4 ) 2 )·Ca(OH) 2 and evaluated using equation (3).

Specimen designation
Time, t day DW mg. products remaining on the specimen surface) was in all cases less than the expected mass of the corrosion products, W ecpw , based on the amount of Mg metal lost by corrosion. Figure 2 and table 5 present the weight loss rate, P w , for each Mg alloy in the four solutions with increasing Ca 2+ concentration. The weight loss rate was expected to increase with decreasing calcium ion, Ca 2+ , concentration, because Ca 2+ ions enable the development of hydroxyapatite on the Mg surface [36], which partially protects the Mg specimen from corrosion. In agreement with these expectations, figure 2 and     HP Mg showed large areas with little corrosion and some areas of localised corrosion including lamellar corrosion. There were more areas of localised corrosion in the solution with no Ca 2+ ([Ca 2+ ]=0), and the lamellar corrosion was deeper.

Corrosion morphology
AZ91 showed a microstructure of large second-phase particles (beta-phase) of substantial size, and small particles expected to be AlMn intermetallic particles. In Hanks' solution ([Ca 2+ ]=[ Ca 2+ ] H ), there was largely uniform corrosion throughout the alpha-Mg matrix with some localized attack next to the second phase particles. In the solution with no Ca 2+ ([Ca 2+ ]=0) there was much more corrosion of the alpha-Mg matrix, and substantial corrosion around the second phase particles.
In Hanks' solution ([Ca 2+ ]=[Ca 2+ ] H ), WE43 had substantial areas that had suffered little corrosion, between which there was some corrosion, and there was some grain boundary attack. In the solution with no Ca 2+ ([Ca 2+ ]=0) the corrosion was somewhat deeper, there were few areas with no corrosion, and there was more grain boundary attack. There was also more incidence of localised corrosion attack. Figure 4 presents the XRD analyses of the corrosion products on WE43 in the modified Hanks' solution but with a Ca 2+   Mg 3 (PO 4 ) 2 . The presence of Mg metal peaks in these spectra indicated that the scraping of the corrosion products included some Mg metal, so that the corrosion product layer was quite thin. This analysis is supported by figure 5, which presents SEM images, with EDX elemental maps, of HP Mg specimens immersed in Hanks' solution with ( figure 5(a)) and without Ca 2+ ( figure 5(b)). For the specimen immersed in Hanks' solution (containing Ca 2+ ), the composition of the corrosion products was consistent with hydroxyapatite containing little Mg. The specimen immersed in the modified Hanks' solution (no Ca 2+ , figure 5(b)), there was no Ca 2+ on the surface, consistent with the XRD analysis of Mg 3 (PO 4 ) 2 .

Discussion
Figures 4 and 5 indicated that the corrosion product in the solutions containing no Ca 2+ ions was magnesium phosphate, Mg 3 (PO 4 ) 2 , whereas, the solution containing Ca 2+ ions produced hydroxyapatite, Ca 3 (PO 4 ) 2 )·Ca(OH) 2 , as the corrosion products. Table 3 indicates that there were measurable corrosion products on the specimen surface for all specimens after immersion in the solution without Ca 2+ ([Ca 2+ ]=0), i.e. W cp was positive, and the fraction of corrosion products remaining on the surface, W cp /W ecpw , varied from 0.006 to 0.15. In contrast, table 4 indicates that the fraction of corrosion products remaining on the specimen surface was larger and within a tighter range, 0.  remaining on the specimen surface was 0.006 to 0.15. These findings were consistent with the prior research [52,[54][55][56][57].
In summary, the modified Hanks' solution containing no Ca 2+ ions produced higher corrosion rates than unmodified Hanks' solution. The increase was substantial. This quantitatively highlights the critical role of Ca 2+ ions for the corrosion of Mg alloys in synthetic body fluids. The Ca 2+ ion containing solutions produced a dense corrosion product layer of hydroxyapatite, Ca 3 (PO 4 ) 2 )·Ca(OH) 2 , a greater fraction of which stayed on the corroding surface (∼0.2-0.3) compared with the Ca 2+ ion free solutions which produced magnesium phosphate, Mg 3 (PO 4 ) 2 , for which the fraction remaining on the specimen surface was 0.006 to 0.15. The higher corrosion rates are attributed to the corrosion products, magnesium phosphate, Mg 3 (PO 4 ) 2 in the Ca 2+ ion free solutions being less protective and allowing more localised corrosion for HP Mg and AZ91, whereas the corrosion was more similar for WE43 in both solutions containing and not containing Ca 2+ . Synthetic body fluids which seek to mimic in vivo corrosion should contain a Ca 2+ ion concentration similar to that in vivo.

The modified Hanks' solution containing no Ca 2+ ions produced higher corrosion rates than unmodified
Hanks' solution. The increase was by a factor of ∼12 for both HP Mg and AZ91, and a factor of ∼6 increase for WE43. This quantitatively highlights the critical role of Ca 2+ ions for the corrosion of Mg alloys in synthetic body fluids.
2. The Ca 2+ ion containing solutions produced a dense corrosion product layer of hydroxyapatite, Ca 3 (PO 4 ) 2 )·Ca(OH) 2 , a greater fraction of which stayed on the corroding surface (∼0.2-0.3) compared with the Ca 2+ ion free solutions which produced magnesium phosphate, Mg 3 (PO 4 ) 2 , for which the fraction remaining on the specimen surface was 0.006 to 0.15.
3. The higher corrosion rates are attributed to the corrosion products, magnesium phosphate, Mg 3 (PO 4 ) 2 in the Ca 2+ ion free solutions being less protective and allowing more localised corrosion for HP Mg and AZ91, whereas the corrosion was more similar for WE43 in both solutions containing and not containing Ca 2+ . 4. Synthetic body fluids which seek to mimic in vivo corrosion should contain a Ca 2+ ion concentration similar to that in vivo.

Acknowledgments
This work was supported by the Australian Research Council Discovery Project DP170102557, the Australian Federal Government through an Australian Government Research Training Program Scholarship, and travel support from Ecole Nationale Supérieure des Mines de Saint-Etienne.

Data statement
The data for these findings are contained within this paper and are also available at https://espace.library.uq. edu.au/view/UQ:732817. The data are embargoed until publication of this paper. (The embargo is nominally set to 1-08-2020).

Appendix A. Corrosion products
Shi and Atrens [23] considered the fate of corrosion products on the surface of high purity Mg (HP Mg) specimens during corrosion in 3.5% NaCl saturated with Mg(OH) 2 . No corrosion products were observed beneath the corroding HP Mg specimens, which was consistent with all the corrosion products remaining on the surface of the corroding specimens. However, the evaluated apparent specific mass of corrosion products on the surface of the corroded specimens, W acpw , was less than that the expected specific mass of corrosion products, W ecpw , so that it was concluded that not all the corrosion products remained on the surface during corrosion. During the current research, this conclusion is revisited. Shi and Atrens [23] evaluated the apparent specific mass of corrosion products on the specimen surface after the immersion test, W acpw [mg cm −2 ], using: where W acp is the specific specimen mass after the immersion test with the corrosion products still on the surface (i.e. the measured mass divided by the surface area of the specimen, A [cm 2 ]), and W b is the specific mass of the specimen before the immersion test. This approach was used to explore the possibility of monitoring the corrosion behaviour using the increase of the specific specimen mass during corrosion. However, the actual specific mass of corrosion products on the specimen surface after the immersion test, W cp , is evaluated using; where W a is the specific specimen mass after the immersion test after removal of all the corrosion products. The corrosion rate, ΔW, is evaluated as the mass loss rate [mg cm −2 d −1 ] using: where W b and W b are in measured in units of [mg cm −2 ], and the duration of the immersion test, t, is expressed in units of [day].
The actual specific mass of corrosion products on the specimen surface after the immersion test, W cp , can be evaluated from the apparent specific mass of corrosion products on the specimen surface after the immersion test used by Shi and Atrens [48], W acpw , by rearranging equation (A3) and substituting for W a in equation (A2) to give: The overall Mg corrosion reaction is usually written as [22,23]:  Table A1 provides data [23] from immersion tests for fishing line specimens of HP Mg immersed in 3.5% NaCl saturated with Mg(OH)2 for the stated duration, t, days. The actual specific mass of corrosion products on the specimen surface after the immersion test, W cp , was in each case essentially as the same as the expected specific mass of the corrosion product, W ecpw , based on the assumption that the corrosion products were composed of Mg(OH) 2 . This was consistent with all the corrosion products remaining on the specimen surface.
The specific mass of the corrosion products, normalised by the corrosion rate, namely the quantity W cp /ΔW, increased with immersion duration, with similar values of this ratio for each immersion duration. This is consistent with the amount of corrosion products increasing with the amount of corrosion.
The quantity W cp /W ecpw is the actual specific mass of corrosion products on the specimen surface after the immersion test, W cp , normalised by the expected specific mass of the corrosion product, W ecpw . This quantity was essentially constant for these tests with an average value of 0.9±0.1. The fact that this quantity was essentially constant and essentially equal to 1.0 was consistent with the corrosion products remaining on the specimen surface. Furthermore, the calculated molecular weight of the corrosion products, M cp , consistent with the data is 53±6 g, was consistent with the value of 58.31 g for Mg(OH) 2 . These deductions are consistent with the observations that there were no corrosion products on the bottom of the beaker during the corrosion experiments indicating that all the corrosion products remained on the surface of the specimens.
However, Mg(OH) 2 does absorb water, up to 10 mol of water of hydration per mol of Mg(OH) 2 [56,57], and the secondary ion mass spectroscopy (SIMS) data of Unocic et al [58] are consistent with the relative degree of hydration decreasing from the specimen surface for the corrosion product film (Mg(OH) 2 ) on ultra-high-purity Mg exposed for 24 h to distilled water.
If the corrosion products after drying in the above experiments [23] did retain some water of hydration so that the actual chemical formula was Mg(OH) 2 · xH 2 O, then the molecular weight of the corrosion products would be larger than 58.31 g, and the data in table A1 would indicate that not all the corrosion products remain on the surface of the corroding HP Mg specimens. Table A1. Data [48] from immersion tests for HP Mg immersed in 3.5% NaCl saturated with Mg(OH) 2 for the stated duration, t, days. ΔW, is the specific mass loss rate [mg cm −2 s] evaluated using equation (A3), W cp is the actual specific mass of corrosion products on the specimen surface after the immersion test evaluated using equation (A2), W acpw is the apparent specific mass of corrosion products on the surface as evaluated by Shi and Atrens [48] evaluated using equation (A1), W ecpw is the expected specific mass of the corrosion products based on the assumption that the corrosion products are Mg(OH) 2 and evaluated using equation (A6), and M cp is the molecular weight of the corrosion products evaluated using equation (A7).