Utilization of Eggshell Waste Calcite as a Sorbent for Rare Earth Element Recovery

The green energy transition requires rare earth elements (REE) for the permanent magnets used in electric cars and wind turbines. REE extraction and beneficiation are chemically intensive and highly damaging to the environment. We investigated the use of eggshell waste as a sustainable alternative sorbent for the capture and separation of REE from aqueous solutions. Hen eggshell calcite was placed in multi-REE (La, Nd, Dy) solutions at 25 to 205 °C for up to 3 months. A pervasive diffusion of the REE inside the eggshell calcite was observed along pathways formed by the intracrystalline organic matrix and calcite crystal boundaries. At 90 °C, kozoite (REECO3OH, orthorhombic) spherulites precipitate on the surface of the dissolving calcite. At 165 and 205 °C, an interface-coupled dissolution–precipitation mechanism is observed, resulting in the complete dissolution of the calcite shell and its pseudomorphic replacement by polycrystalline kozoite. At 205 °C, kozoite is slowly replaced by hydroxylbastnäsite (REECO3OH, hexagonal), the stable form of the rare earth hydroxycarbonate polymorphs. Our results demonstrate two potential applications of eggshell waste for the uptake of rare earth elements in solution: at low temperatures, as a mixed organic–inorganic adsorbent and absorbent, given sufficient sorption time; and at higher temperatures, as an efficient sacrificial template for the precipitation of rare earth hydroxycarbonates.

This supporting information contains 24 pages.
The number of eggs for consumption produced in 2021 is represented here by the variable S (S = 1.652x10 12 ).For each laying hen raised that year, we count two eggs having been produced, as only 50 % of chicks are female and therefore an equal number of male chicks must have been born and then immediately killed.Therefore, the number of eggshells associated with the raising of laying hens is twice the number of hens, represented here by the variable H (H = 2 x 7.827x10 9 ).
Finally, we count one eggshell for each of the 75 billion chickens killed for meat in 2022, represented by the variable M (M = 7.520x10 10 ).

SI Text S2 -Pin stubs and pucks preparation
Several representative grains of each experiment were placed with a tweezer on a taped 12 mm wide metallic stub and either 1) carbon coated using a 208carbon carbon coater (Cressington) with 12 nm-thick of pure graphite carbon (TED PELLA, Inc.), for standard SEM-SE and BSE imaging and EDS elemental spectrum analyses and mapping; or 2) gold-coated using a 108auto sputter coater (Cressington; Au(-Pd), 8 nm-thick) for high resolution SEM SE imaging.
Several representative grains of each experiment were placed on a taped flat surface and inside a SeriForm 25 mm mounting cup (Struers) in which a mixture of EpoFix resin and hardener (Struers) was poured.The resin was left to solidify overnight in an oven at 50 °C.The resin pucks were then polished using a LaboPol-30 polishing machine fitted with a LaboForce-100 control panel/specimen mover unit (Struers) and a three-steps procedure using polishing fluids with 9, 6 and 1 μm diamond particles to expose internal surfaces of the grains.The 1 μm-polished pucks were cleaned in an ultrasonic bath of deionized water for three minutes.Isopropanol-based PELCO colloidal graphite (TED PELLA, Inc.) was painted on the side and circumference of the pucks.
The pucks were then carbon-coated as described with the stubs above.Pucks selected for LA-ICP-MS mapping were then cleaned with alcohol and re-polished at 1 μm for one minute and cleaned in an ultrasonic bath for three minutes before ablation.

Existing data
The solubility product constants of kozoite and hydroxylbastnäsite has only been measured for a handful of pure phases where the lanthanide site is occupied by a single rare earth element (SI Table S2).
The majority of analyses have been dedicated to kozoite-(Nd), as Nd3+ can be used as a representative proxy for trivalent actinides in radioactive waste studies. 1 The latest experimental measurement of the solubility product constant of kozoite-(Nd), for the dissolution reaction REE(CO 3 )(OH) cr,orthorhombic ⇌ Ln 3+ aq + OH -aq + CO 3 2-aq , yielded a value of 10 -22.3 ± 0.2 2 ; close to two orders of magnitude lower than the previous thermochemical calculation 3 , illustrating the large uncertainties associated with the measurement or calculation of KSP.The only two other known kozoite K SP are for kozoite-(Sm), at 10 -21.2 ± 0.7 3 , and kozoite-(Eu), at 10 -20.3 ± 1.0 3 (SI Table S2).
For this study, kozoite-(Nd) and hydroxylbastnäsite-(Nd) will be used as representative phases for our synthetic rare earth hydroxycarbonate solid solutions, as 1) Nd chemical and physical properties are intermediate between the properties of La and Dy; and 2) there are no measurements of the solubility product constants of kozoite-(La), kozoite-(Dy), and hydroxylbastnäsite-(Dy) (SI Table S2).
For both kozoite-(Nd) and hydroxylbastnäsite-(Nd), we select the values from the latest study 2 , as they are likely to be the most accurate and also can be compared to each other as they have been derived using the same protocol and assumptions.S2

Derivation of the enthalpy of reaction
The solubility product constants are usually calculated at 25 °C.Moreover, in PHREEQC, the log K SP parameter for each dissolution reaction is required to have been calculated at 25 °C.The solubility product constant at other temperatures than 25 °C is calculated by PHREEQC based on one of two methods; one of them using the enthalpy of reaction at 25 °C and the Van't Hoff equation 12 : With T 1 and T 2 the initial (25 °C) and final temperatures; K T1 and K T2 the solubility product constant of the solid phase at, respectively, temperature T 1,25°C and T 2 ; Δ r H 0 is the standard enthalpy of reaction at 25 °C, and R is the ideal gas constant.Reorganizing the equation to find K T2 , we obtain: The standard enthalpies of reaction, Δ r H 0 for both kozoite-(Nd) and hydroxylbastnäsite-(Nd) are not published, but can be calculated using Hess's Law, by subtracting the sum of the enthalpies of formation of the products, Δ f H 0 , multiplied by their stoichiometric coefficients, from the sum of the enthalpies of formation of the reactants, also multiplied by their own stochiometric coefficients.
In the case of the rare earth hydroxycarbonates, we have: The standard enthalpies of formation of each species are provided in SI Table S3.Using Hess's Law, we calculate for kozoite-(Nd) and hydroxylbastnäsite-(Nd) an enthalpy of reaction of, respectively, 143.9 and 13.8 kJ.mol -1 .

SI Table S3 -Standard enthalpies of formation of the reactant and products in the REE hydroxycarbonate dissolution reaction.
Table S3: Standard enthalpies of formation of the reactant and product in the rare earth hydroxycarbonate dissolution reaction.

Starting solution
The 1 L 50 mM single rare earth bearing solutions were modelled using a one-step dissolution reaction (REACTION command) of 50 mM of REE salt in 1 kg of pure water.The assumed equilibrium with atmospheric air was modelled by equilibrating the solution with CO 2 (EQUILIBRIUM_PHASES command).For gases, the saturation index is defined as the logarithm of their partial pressure, i.e., of their concentration in air.At the time of the experiments, in 2022-2023, the selected representative concentration is 4.172 ppm of CO 2 15 .
The 15 mL of starting solution in the air-tight reactor was modelled using a mixing (MIX command) of 0.005% of each of three 1 kg 50 mM single rare earth solution.Following the mixing, the solution is put into contact with a fixed 0.005 mL volume of air, representing the head space inside the Teflon reactor.This volume remains constant in any subsequent reactions applied to the solution inside the reactor.This 15 mL mixed REE solution is named the "starting solution" in the rest of this study.

Dissolution of hen eggshell calcite
In PHREEQC, the dissolution of a crystalline phase can be modelled either from a purely thermodynamic point of view, using the REACTION keyword; or else it can be modelled from a kinetic point of view, using a kinetic model and the KINETICS keyword.
For thermodynamic modelling only, the input data for the modelling of a dissolution reaction are the name and quantity (in mol) of a dissolving phase, and the number of dissolution steps.The thermodynamic information for calcite is already comprised within the llnl.datdatabase under the name "calcite", which is the one to be used for this model.As > 95% of the hen eggshell is made of calcite, with the rest being water and the organic matrix 16 , we make the simplification that the entirety of the 0.05 g of dissolving eggshell clasts is made of calcite.With a calcite molar mass of 100.0869 g.mol -1 , the dissolution can be modelled with a dissolution of 5.0x10 -4 mol of calcite.
For kinetics modelling, We use the llnl.datdatabase built-in calcite dissolution kinetics model 17,18 .The model requires the definition of an initial quantity of calcite, n 0,cal (M0 in the PHREEQC Basic code block); the initial specific surface area of calcite, SSA (PARM(1) in PHREEQC), given in cm 2 .mol - ; and an exponent, i (PARM(2) in PHREEQC), to model the dependence of the rate of reaction on grain size.The model is valid for the temperature range 5 to 60 °C 17 .
To calculate the specific surface area, we will assume that the dissolving eggshell calcite is represented by a flattened square rectangular cuboid (SI Figure S1).Given the known experimental mass of 0.05 g, and a thickness of 0.03 cm, representative of the 0.02-0.04cm range of hen eggshell thicknesses of eggshell 19 ; we can set the dimension of the square faces to 0.85 x 0.85 cm, which then yields a cuboid density , representative of the density of eggshell calcite in the range of 2.24-2.39 20(SI Figure S1).As presented in the previous section, the initial mass of mineral to dissolve can be represented by 4.995704x10 -4 mol of calcite.For the specific surface area, we assume that the dissolution occurs solely on the two square surfaces, and not on the narrow sides, as observed in the experiments.Therefore, the total surface area is equal to twice 0.85 2 , or 1.445 cm -2 , which when divided by the quantity of calcite, yields a specific surface area of 2,892 cm 2 .mol - (Table S4).As we assume that the dissolution occurs on the two opposite square surfaces only, as the dissolution proceeds, the surface area remains the same, and the dissolution rate is not affected by the decreasing quantity of calcite remaining.Therefore, we set the coefficient i to a very small value, e.g., 0.0001, so that the surface area of calcite remains constant at ca. 1.28 cm -2 (Table S4):             -chart_title "Quantity of dissolved calcite vs SI and pH @25degC" -headings SI(Cal)@25degC SI(Koz-Nd)@25degC SI(Hbas-Nd)@25degC pH@25degC -axis_scale x_axis 0 500 50 10 -axis_titles "[Ca], umol" "Saturation index" "pH"  -chart_title "Quantity of dissolved calcite vs SI and pH @25degC" -headings SI(Cal)@50degC SI(Koz-Nd)@50degC SI(Hbas-Nd)@50degC pH@50degC -axis_scale x_axis 0 500 50 10 -axis_titles "[Ca], umol" "Saturation index" "pH" -initial_solutions true -connect_simulations false -start 10 PLOT_XY TOT("Ca")*0.015*1000000,SI("Calcite") , color = Orange, symbol = None, symbol_size = 8, y-axis = 1, line_width = For all experiments, the concentrations of all three REE is visually equal, with no indication of any significant partitioning between them.The kozoite crystals were not ablated by the laser as the ICP-MS was tuned for trace element concentration of REE and the ablation of minerals with 30+ % of REE could damage the electron multiplier detector of the mass spectrometer.

=
Figure S1.A simplified representation of the hen eggshell calcite for the PHREEQC dissolution

Table S1 :
SEM EDS quantitative analysis of the secondary elemental standard, a monazite from

Table S4 :
PHREEQC kinetic model input data for the modelling of the speed of calcite dissolution.n = Amount of substance, SSA = Specific surface area, i = Coefficient for grain size-dependent dissolution rate.