*3.1. Granulometry*

Regarding Stage 1 of Figure 1 and using sieves ranging in aperture size from 0.149 to 4.699 mm, the size distribution of the comminuted sample is shown in Figure 2. It can be seen from this figure that nearly 50% of the material passed through the 0.6 mm sieve size. The 80% passing size (d80) of the comminuted mass is about 1.7 mm.

**Figure 2.** Cumulative particle size distribution of the demagnetized and comminuted sample.

#### *3.2. SEM-EDX Analysis*

Image from the Backscatter Electron (BSE) detector on the SEM-EDX demonstrate some dissimilar phases in the demagnetized and comminuted sample (see Stage 1 of Figure 1). "Three Dots" analysis was performed using the EDX. Of the three indicated points shown in Figure 3, each has a distinctive chemistry: point (a) appears to be Ni, which is the outer layer; point (b) is a combination of Pr, Nd and Fe, where Pr is used to substitute Nd (up to 20–25%) to lower production costs; and point (c) shows a mixture of Nd and Fe. It is noted that boron (B) was not detected due to its low intensity, resulting from it being a light element (i.e., element #5 on the periodic table), as well as from the inherent disability of the BSE detector that was used [45].

**Figure 3.** SEM image and EDX composition of the demagnetized and comminuted sample (see text for details). (**a**) Ni; (**b**) Pr, Nd, Fe; (**c**) Nd, Fe.

#### *3.3. XRD Results*

Figures 4 and 5 show the phase compositions of the precipitates (Stage 2 feed to Stage 3 rich, dry precipitate, as per Figure 1) and the final product (Stage 3 REF residue, as per Figure 1), respectively. From Figure 4, it can be said that most of the Fe remains in solution and that the dry precipitate is made up of mainly (NH4)Nd(SO4)2(H2O)3. This compound is an ammonium neodymium sulfate double salt and is noted to be similar to ammonium jarosite [17] with Nd substituting for Fe. Figure 5 also shows the phases of the product made after adding and stirring the dry precipitate in NH4F·HF for 45 min, which is then heated under argon atmosphere to 400 ◦C and allowed to cool. Equation (4) depicts a possible mechanism for REF formation with the REE being Nd assuming ammonium (NH4+) is in excess:

$$2\text{(NH}\_4\text{)Nd(SO}\_4\text{)}\_2\text{(H}\_2\text{O)}\_3 + 3\text{NH}\_4\text{F-HF} + 3\text{NH}\_4^+ \rightarrow 2\text{NdF}\_3 + 4\text{(NH}\_4\text{)}\_2\text{SO}\_4 + 6\text{H}\_2\text{O} + 3\text{H}^+ \tag{4}$$

The product is clearly a REF containing REEs of Nd, Dy and Pr. It can therefore be concluded that REF can be produced by this process and the resulting fluorides can be used later as feedstock for pyrometallurgical metal production [39].

**Figure 5.** Crystal phases in the REF filtrate after 45 min in NH4F·HF and heated to 400 ◦C.

#### *3.4. ICP Results*

Table 1 shows the chemical composition of REEs in the final REF product indicating Dy and Fe are present, apparently in amounts below the XRD detection limit. Together, the total REE amount sums to 63.25%. Based on stoichiometry and assuming the REEs exist as REF (i.e., NdF3, PrF3 and DyF3), the F-content would be 24.94%. This leaves a balance of 10.59%, which is expected to be ammonium sulfate [(NH4)2SO4] and ammonium jarosite [(NH4)Fe3(SO4)2(OH)6], as per Equation (4). Furthermore, based on the stoichiometry of the jarosite, the Fe content would equate to 3.44% of these other components, suggesting there is 7.15% ammonium sulfate. Both ammonium sulfate and ammonium jarosite can be monohydrated [46] which will thermally decompose at low temperature. In this regard, a TGA-DSC study was undertaken on the final REF residue from Stage 3. Because the product was heated to 400 ◦C under argon, a subsequent TGA-DSC scan did not exceed 400 ◦C. It is important to note that this REF residue, as discussed above, is not pure, and therefore contains some ammonium sulfate and ammonium jarosite.

**Table 1.** The chemical composition of the final product.


#### *3.5. TGA-DSC Results*

The TGA-DSC graphs of the REF residue are shown in Figure 6. The plot shows that mass loss occurs in five steps which agrees with the literature [46–49]. In this regard, the first two steps equate simply to crystalline water loss of the ammonium sulfate (Equation (5)) and ammonium jarosite (Equation (7)), respectively:

25–50 ◦C

$$\text{(NH}\_4\text{)}\_2\text{SO}\_4\cdot\text{H}\_2\text{O} \rightarrow \text{(NH}\_4\text{)}\_2\text{SO}\_4 + \text{H}\_2\text{O} \tag{5}$$

75–125 ◦C

$$\text{(NH}\_4\text{)Fe}\_3\text{(SO}\_4\text{)}\_2\text{(OH)}\_6\text{-H}\_2\text{O} \rightarrow \text{(NH}\_4\text{)Fe}\_3\text{(SO}\_4\text{)}\_2\text{(OH)}\_6 + \text{H}\_2\text{O} \tag{6}$$

The third step corresponds to the decomposition of dehydrated ammonium sulfate to ammonium bisulfate:

140–210 ◦C

$$\text{N(NH}\_4\text{)}\_2\text{SO}\_4 \to \text{NH}\_4\text{HSO}\_4 + \text{NH}\_3\tag{7}$$

The fourth step is likely caused by complete thermal decomposition of the ammonium bisulfate: 220–250 ◦C

$$\text{NH}\_4\text{HSO}\_4 \rightarrow \text{1/3NH}\_3 + \text{1/3N}\_2 + \text{SO}\_2 + 2\text{H}\_2\text{O} \tag{8}$$

Finally, the fifth step appears to be the dehydroxylation of the dehydrated ammonium jarosite, thereby accounting for the continued loss in weight as the temperature increased to 380 ◦C:

>260 ◦C

$$(\text{NH}\_4)\text{Fe}\_3(\text{SO}\_4)\_2(\text{OH})\_6 \to (\text{NH}\_4)(\text{FeO})\_3(\text{SO}\_4)\_2 + 3\text{H}\_2\text{O} \tag{9}$$

If the temperature had been increased to 600 ◦C, three additional steps involving the sequential reactions of the dehydroxylated ammonium jarosite would be observed such that all of the Fe ultimately becomes hematite [46–49]:

>385 ◦C

$$2\text{(NH}\_4\text{)(FeO)}\_3\text{(SO}\_4\text{)}\_2 \to 2\text{NH}\_3 + \text{H}\_2\text{O} + 2\text{Fe}\_3\text{O}\_{2.5}\text{(SO}\_4\text{)}\_2\tag{10}$$

>510 ◦C

$$2\text{Fe}\_3\text{O}\_{2.5}\text{(SO}\_4\text{)}\_2 \rightarrow 2\text{Fe}\_2\text{O}\_3 + \text{Fe}\_2\text{(SO}\_4\text{)}\_3 + \text{SO}\_3\tag{11}$$

>540 ◦C

$$\text{Fe}\_2\text{(SO}\_4\text{)}\_3 \rightarrow \text{Fe}\_2\text{O}\_3 + 3\text{SO}\_3 \tag{12}$$

where Fe3O2.5(SO4)2 is essentially equivalent to a solid solution of 2/3 Fe2(SO4)3 and 5/6 Fe2O3.

**Figure 6.** TGA-DSC curve for REF residue from Stage 3.

#### **4. Model Development and Process Optimization Using RSM**

Table 2 shows the Design of Experiments (DOE) along with the condition variables and responses for Stage 3 processing. In all, 17 experiments were performed, each using 2 g of REE-rich dry precipitate from Stage 2. The following ranges of the condition variables were employed: deionized water volume was 10–30 mL; 2–4 g of NH4F·HF was added; the degree of stirring was 15–45 min. Responses were REE recovery and REF purity where recovery refers to the amount of REE from Stage 2 being converted to REF residue and purity refers to the quality of the REF residue based on ICP analysis.



Furthermore, five experiments were completed with all condition variables being at their midpoints. The results were analyzed to develop a statistically significant model for the responses of the REE recovery and REF purity as shown in Equations (13) and (14):

$$R \to \text{RCE coverage } (\%) = \\$0.14 - 3.87 \text{A} + 0.087 \text{B} + 0.84 \text{C} - 2.70 \text{AB} - 0.53 \text{AC} + 2.68 \text{A}^2 + 4.15 \text{C}^2 + 4.04 \text{A}^2 \text{B} + 1.41 \text{A}^2 \text{C} \tag{13}$$

$$\text{REF\\_Purity} \left( \% \right) = 54.75 + 4.20 \text{A} + 1.65 \text{B} - 1.06 \text{C} - 1.59 \text{AB} + 4.37 \text{AC} + 0.18 \text{A}^2 - 1.40 \text{B}^2 - 2.08 \text{C}^2 - 1.17 \text{A}^2 \text{B} + 2.89 \text{A}^2 \text{C} \quad \text{(14)}$$

where A denotes the volume of deionized water used, B denotes the amount of NH4F·HF added, and C denotes the degree of stirring. In both cases, a cubic model represented the data best and the *R*<sup>2</sup> values were 0.94 and 0.93 for recovery and purity, respectively.

Using Equations (13) and (14), 3-D surface plots in Figures 7 and 8 were generated to illustrate the e ffects of the condition variables on the responses. From Figure 7a,b, it can be said that NH4F·HF addition appears to have more prominent e ffect on the process e fficiency. The impact of deionized water addition is more prominent at higher stirring rates and higher NH4F·HF additions. With respect to stirring, it can be observed from Figure 7a that the amount of REF recovery increases with stirring time for both 10 and 30 mL of water used. However, recovery is higher for lower volumes of water than for higher ones, and this same pattern is observed with respect to NH4F·HF addition as illustrated in Figure 7b when using Equation (13).

**Figure 7.** 3D plots of REF recovery with respect to process variables at (**a**) 4 g of NH4F·HF and (**b**) 43 min for degree of stirring.

**Figure 8.** 3D plots of REF purity with respect to process variables at (**a**) 4 g of NH4F·HF and (**b**) 44 min for degree of stirring.

Figure 8a,b were generated from Equation (14) and illustrates the response surfaces for REF purity in relations to the process variables. From these plots, it is observed that the amount of deionized water again did influence purity of REF recovery to a significant extent at all NH4F·HF additions and also at higher stirring degrees. The degree of stirring, as observed in Figure 8a, seems to affect the REF insignificantly at low water additions. However, REF purity increased sharply with stirring time at a high volume of water addition. Figure 8b shows that NH4F·HF addition has less impact on the purity of REF. Sharp increase in the purity of the REF is seen with increase in the volume of water.

It may also be noted that, in Equations (13) and (14), the process variables are all in terms of the coded values and differ in the range +1 to −1, with the mid-point having a value of zero. Thus, for B, the maximum amount of NH4F·HF used (4 g) corresponds to +1 and the lowest (2 g) corresponds to –1, whereas the midpoint of 3 g corresponds to 0. To use these statistically significant equations, the actual variable value needs to be converted to the coded form lying between +1 and −1. Using the above model equations optimization was carried out to find the conditions that maximized both REF recovery and REF purity. The identified conditions and their maximum corresponding responses are as follows:

