Phase equilibrium experiments on the simulated high-level waste glass containing platinum group elements

Abstract

Phase equilibrium experiments for the simulated high-level waste (HLW) glass containing palladium, rhodium and ruthenium discharged from a full scale mock up melter have been carried out between 1073 and 1473 K under air and CO₂ atmosphere. The chemical compositions of Pd–Rh–Ru–Te (Pd metal phase) and (Ru, Rh)O₂ (Ru oxide phase) solid solutions and glass matrix were measured by electron probe micro analysis. Palladium content in the Pd metal phase decreased and ruthenium content in the Ru oxide phase increased with increasing temperature and decreasing oxygen fugacity due to progressive reduction of rhodium. The chemical compositions of these crystalline phases are independent of that of borosilicate glass matrix. Partition coefficient of rhodium between Pd metal phase and Ru oxide phase (K_Rh) can be expressed by

$\ln K_{\mathrm{Rh}}=27264/T-18.372+\ln f_{O_2}$

where T and $f_{O_2}$ represent absolute temperature and oxygen fugacity. Based on the comparison of crystal compositions in the HLW glass with experimental results, it can be expected that the HLW glass examined in this study had been equilibrated in the temperature range from 1273 to 1373 K and oxygen fugacity close to that of air just before discharging from the melter.

Keywords:

• fission product
• glass waste form
• high temperature
• platinum group metal

1. Introduction

High-level waste (HLW) arising from reprocessing of spent nuclear fuel is immobilized by vitrification in an alkali borosilicate glass. The HLW is composed of about 30 different elements including fission products, corrosion products and actinoids. Most of these elements are dissolved in the glass matrix. However, fission platinum group metals (PGMs) (palladium, Pd; rhodium, Rh; ruthenium, Ru) are crystallized as Pd–Rh–Te alloy (Pd metal phase) [1–8] and (Ru, Rh)O₂ solid solution (Ru oxide phase) [1,2,5–7] due to their very low solubility in silicate melts (10–1000 ppm) [9–12]. In laboratory-scale experiments, these crystals are not distributed homogeneously throughout glass, but are present on the surface and in the inner part of glass as agglomerates [1].

The PGMs have various effects on vitrification process and physical and chemical durability of HLW glass. Due to radiogenic heat produced by decaying radionuclides, molten HLW glass is slowly cooled from its melting temperature. Then the many types of crystal phases (chrome spinel, cerianite, cristobalite, powellite, Na₂MoO₄, etc.) can be further precipitated [6,7,13–15]. It has been considered that existence of Pd metal and Ru oxide enhances nucleation and crystal growth during cooling process [2,7,16,17]. Furthermore, viscosity and density of HLW glass increase with increase amount of the Ru oxide phase even at low contents (about 1wt%) [3,18]. In Ru-rich HLW glasses, thermal expansion mismatch between Ru oxide and borosilicate glass matrix is responsible for crack initiation [7].

In Japan, liquid-fed joule-heated ceramic melter (LFCM) is used for HLW vitrification, where thermal energy required for melting is generated using metallic electrodes immersed in an electrically conducting molten glass [19–23]. In the vitrification process using LFCM, the PGMs tend to accumulate on the bottom of the melter due to their high density and result in metallic sludges [3,6,20,22,23]. Because these sludges have higher conductivity and viscosity than those of the molten glass [18,24], they cause a loss of heat input and an obstruction of glass discharge from the melter [20,22,23,25]. It is important to understand behavior of the Pd metal phase and the Ru oxide phase in molten HLW glass for stable operation of vitrification process.

The objective of this study is to investigate relationship of chemical composition between coexisting Pd metal phase, Ru oxide phase and borosilicate glass. Using a simulated HLW glass sample discharged from a pilot melter, phase equilibrium experiments were carried out as a function of temperature in air and in CO₂ atmosphere. Partition coefficient of Rh between Pd metal phase and Ru oxide phase was determined from the experimental results. The temperature and oxygen fugacity conditions in the vitrification melter were estimated based on the chemical compositions of Pd metal phase and Ru oxide phase.

2. Experimental method

2.1. Experimental sample

Glass sample used in this study is simulated HLW glass containing PGMs discharged from the LFCM which is a full scale mock-up (KMOC) of an active melter facility in the Rokkasho Reprocessing Plant, located in northern Japan [23,26,27]. This glass (KMOC glass) includes spherical shaped Pd metals with a diameter of 2–10 μm and elongated or needle shaped crystals of Ru oxide with a length of 1–5 μm and a width less than 1 μm. No other metallic or oxide crystals are present. The massive KMOC glass with a mass of about 1 kg was crushed to coarse fragments by a hammer. Glass fragments, each of 50–200 mg mass, were randomly selected and prepared for study. Table 1 shows bulk chemical composition of the KMOC glass analyzed by inductively coupled plasma atomic emission spectroscopy (ICP-AES) [28] (Li₂O, PdO, Rh₂O₃ and RuO₂), mannitol titration method [29] (B₂O₃) and X-ray fluorescence analysis (XRF) (other oxides). The chemical compositions of crystalline phases included in the KMOC glass measured by electron probe micro-analyzer were shown in Table 2. The analytical method will be described later.

Table 1. Chemical composition of the KMOC glass.

Oxides	wt%	Oxides	wt%
SiO2	47.92	MoO3	0.73
B2O3	13.42	TeO2	0.09
Al2O3	5.13	RuO2^a	0.25
Li2O	3.76	Rh2O3^a	0.08
Na2O	9.58	PdO^a	0.37
Cs2O	0.94	Others^b	16.17
CaO	3.07

^aAll Pd, Rh and Ru are assumed as Pd²⁺, Rh³⁺ and Ru⁴⁺, respectively.

^bZnO, MnO, Fe₂O₃, ZrO₂, La₂O₃, Ce₂O₃, Pr₂O₃, Nd₂O₃, Gd₂O₃, etc.

Table 2. Chemical compositions (wt%) of Pd metal phase and Ru oxide phase included in the KMOC glass. Numbers in parenthesis represent standard deviation.

	n	Pd	Rh	Ru	Te
Pd metal phase	64	91.3 (1.8)	5.5 (1.8)	0.2 (0.2)	3.6 (0.4)
	n	RuO2	RhO2
Ru oxide phase	42	88.1 (1.4)	11.9 (1.5)

Note: n: number of analyses.

2.2. Phase equilibrium experiments

Phase equilibrium experiments were carried out using a vertical tube gas mixing furnace and a muffle furnace. Sample temperature was measured with a type R thermocouple located near the sample. Glass samples were held at 1473 and 1373 K for 24 hours, 1273 K for 48 hours and 1073 K for 96 hours, and then quenched by quickly removing it from the furnace. It has reported that temperature distribution and residence time of glass melt in a LFCM in Japan range between 1073 and 1573 K and 8.0–9.5 hours, respectively [20,23]. The heating temperatures in our experiments are within the temperature distribution, whereas the samples were held for longer duration in order to obtain a composition close to chemical equilibrium. We also evaluated effect of oxygen fugacity on the phase equilibrium. Equilibrium oxygen fugacities ($f_{O_2}$) for the reaction MO_x = M+x/2O₂ (M = Pd, Rh and Ru) calculated using FACT thermodynamic database [30] are higher in the order Pd > Rh > Ru (Figure 1). The existence of palladium as a metallic phase and ruthenium as an oxide phase suggests that oxygen fugacity in vitrification melter would be located between Pd/PdO and Ru/RuO₂ buffers. This $f_{O_2}$ range corresponds to concentration of O₂ in air (0.21). The lower bound (Ru/RuO₂ buffer) is close to equilibrium $f_{O_2}$ of CO₂ = CO + 0.5O₂ (Figure 1). Therefore, we tested heating experiments under two redox conditions, in air and in CO₂ atmosphere. In the later experiments, the CO₂ with a purity of 99.9% flowed from the bottom of vertical tube furnace under the flow rate of 500 ml/min.

Figure 1. Temperature and oxygen fugacity of Pd/PdO, Rh/Rh₂O₃ and Ru/RuO₂ equilibria calculated from FACT thermodynamic database [30]. Dashed and dotted lines represent $f_{O_2}$ in air and equilibrium $f_{O_2}$ of CO₂ = CO+0.5O₂, respectively. Experimental temperature and oxygen fugacity are indicated by solid circles.

Sample-holding methods tested in this study were illustrated in Figure 2. In the beginning of this study, two different methods of sample holding were tested. First, platinum wire of 0.3 mm diameter was gently twisted round a glass fragment with a mass of 30–40 mg, and the glass was partly fused to form a bead by suspending it in a furnace controlled at 1473 K for about 30 sec. Then, the resulting glass bead with a diameter of about 3 mm with platinum wire loop was suspended in the hot spot of the vertical furnace. This technique is known as “wire-loop method” and is a common technique in an experimental petrology [31–33]. The wire-loop method has advantages that losses of noble metals and transition metals from molten glass are minimized compared with experiments using platinum container and that oxygen fugacity of a sample can be quantitative controlled by flowing gas. The latter is caused by the small sample size and large surface area of glass bead, whereas they could lead to a serious loss of volatility elements such as B₂O₃ and Na₂O. Therefore, as a second method, we suspended the wire-looped glass bead in a covered alumina crucible. Then another KMOC glass (6–7 g) was placed in the alumina crucible in order to minimize evaporation losses of elements. The crucible was then put in a muffle furnace. It is described as “crucible method” in this paper.

Figure 2. Methods of sample holding tested in this study. (a) Wire-loop method, (b) crucible method, (c) SiO₂ tube method and (d) Al₂O₃ tube method. In all methods, molten samples are held by a surface tension between glass melt and Pt wire or tubes.

We tried wire-loop method and crucible method in preliminary experiments. However, above 1373 K, equilibrium phase relations were not obtained by these methods. This is due to a reaction between platinum wire and Pd and Rh in glass samples as shown in later section. Thus, we carried out experiments that do not use platinum wire as described below. The glass fragments (about 200 mg) were put in the center of silica glass tube or alumina tube (Nikkato, SSA-S) with an inner diameter of 8 mm (silica glass) or 6 mm (alumina), an outer diameter of 10 mm and a length of 10 mm. These tubes were suspended in a horizontal position at a hot spot of vertical furnace. In this technique, it could be expected that the amount of PGMs in a glass sample is kept constant during melting, while glass composition would be changed due to the reaction with tubes. Furthermore, redox reaction would also immediately reach equilibrium because of small sample volume. These methods are described as “SiO₂ tube method” and “Al₂O₃ tube method”. We could obtain satisfactory results by these methods and report them in this paper.

2.3. Analytical method

The electron probe micro-analyses (EPMA) were performed using JEOL JXA-8800 electron microprobe at the Akita University, operated at an accelerating voltage of 15 kV and 20 nA beam current. Eleven oxides in the glass phase (SiO₂, B₂O₃, Al₂O₃, FeO, CaO, Na₂O, ZnO, ZrO₂, La₂O₃, Nd₂O₃ and Ce₂O₃) were measured. Then a simulated HLW glass which does not contain PGMs reported previously (Sample-B in Sugawara et al. [34]) was used for standard material. Beam diameter was 50 μm. The counting times were 10 sec on both peak (except for B₂O₃) and background and 120 sec on peak for B₂O₃. Counts were converted to concentrations using ZAF correction procedure [35]. Five–ten spot analyses were made on each sample and mean compositions were determined.

In contrast to the glass analysis, quantitative measurements of platinum group elements are generally difficult due to proximity of the L lines of Ru, Rh and Pd. The Lα1 of ruthenium (2.558 keV) is independent of any other lines and was used for the Ru analysis. However, the Lα1 lines of palladium (2.838 keV) and rhodium (2.696 keV), which are the most remarkable peaks, overlap Lβ1 lines of rhodium and ruthenium, respectively. This is the same in the other Lα are Lβ lines. Consequently, we used Lγ1 of palladium (3.328 keV) and rhodium (3.143 keV), which are very small peak but independent of other L lines. Tellurium was measured by Lα1 (3.769 keV). Counting times were 10 sec on peak of Ru and Te, 30 sec on peaks of Pd and Rh, and 10 sec on background. Pure metallic Pd, Ru and Te and 40 wt% Rh–Pt alloy were used as standards. Beam diameter of 1 μm was used for analysis in both Pd metal phases and Ru oxide phases.

In the analysis of Ru oxide phase, totals of RuO₂ and RhO₂ contents were always lower than 100 wt% and ranged from 54 to 96 wt%. This is because the Ru oxide has a crystal size smaller than spatial resolution of the EPMA (1 µm). We observed that the measurement total decreases with decreasing an apparent crystal size. In spite of these total losses, RhO₂/(RuO₂ + RhO₂) ratios in the Ru oxide were independent of totals and nearly constants in each of the experimental samples. This suggests that contamination of glass matrix does not affect relative concentration in the Ru oxide in EPMA analysis. This is because of very low solubility of PGMs in a silicate melt [9–12]. Therefore, analytical results of the Ru oxide normalized to 100 wt% are reported in this paper.

3. Experimental results

3.1. Chemical composition of glass phase in the experimental samples

Figure 3 shows SiO₂, Al₂O₃, B₂O₃ and Na₂O contents of glass matrix in experimental samples. It was observed that the glass compositions after phase equilibrium experiments significantly differ from that of starting KMOC glass (Table 1) due to evaporation and contamination. The compositional changes depend on the experimental method. Generally, B₂O₃ and Na₂O contents decrease and SiO₂ increases relatively with increasing temperature. This is caused by evaporation of boron and sodium during melting. The B₂O₃ loss in the crucible method is lower than that in the wire-loop method as expected, whereas the B₂O₃ losses in the Al₂O₃ tube method and SiO₂ tube method are much lower than the crucible method. The Al₂O₃ content in Al₂O₃ tube method and the SiO₂ content in SiO₂ tube method increase with increasing temperature because of dissolution of tube materials. The SiO₂ content in Al₂O₃ tube method and the Al₂O₃ content in SiO₂ tube method are nearly constant and close to those in the starting KMOC glass. This is probably due to compensation of loss of boron and sodium and enrichment of alumina and silica in glass phase.

Figure 3. Plots of chemical compositions of the glass matrix after phase equilibrium experiments against temperature: (a) SiO₂, (b) Al₂O₃, (c) B₂O₃ and (d) Na₂O. Open squares with cross represent concentration in the starting KMOC glass.

3.2. Chemical composition of crystal phases in the experimental samples

Crystals of both Pd metal and Ru oxide were observed in all of the experimental samples. Square shaped CeO₂ phase was also crystallized below 1273 K and the amount was significantly increased at 1073 K. It was observed that some CeO₂ crystals contain a core of Pd metal, indicating that the Pd metal phase act as nucleation agents as suggested by Mitamura et al. [2]. There were no silicate crystals and spinel phase in all samples.

Chemical composition of the Pd metal phase and the Ru oxide phase are given in Tables 3 and 4. Significant differences were observed in composition of metal phase above 1373 K depending on the experimental methods. The chemical composition of Pd metal by SiO₂ tube method is consistent with that by Al₂O₃ tube method at the same temperature and $f_{O_2}$ condition, whereas in crucible method, metal phase shows more Rh-rich and Pd-poor composition at 1373 K and Rh-rich metals were also observed at 1473 K in air. Ru-rich metals were crystallized by wire-loop method at 1373 K in CO₂ atmosphere. In those experiments, it was observed that platinum wire suspending a glass bead includes 0.6 to 6 wt% Pd and Rh at the rim (Table 4). The Pd and Rh contents in Pt wire increased with increasing temperature and decreasing oxygen fugacity. These facts suggest that adsorption of Pd and Rh onto platinum wire causes depletion of Pd metal phase and results in the crystallization of Rh and Ru-rich metal phases. The Pd and Rh were not detected at the core of platinum wire, indicating that the Pt wire have a heterogeneous composition. This implies that it is difficult to obtain equilibrium phase relation by the crucible method and the wire-loop method. Furthermore, tellurium contents of Pd metal phase crystallized by the crucible method and the wire-loop method were significantly lower than those by tube methods (Table 4), indicating that evaporation loss of Te from glass beads occurred. Therefore above 1373 K, we concluded that the only results by the Al₂O₃ tube method and the SiO₂ tube method (Table 3) can be regarded as equilibrium relationship.

Table 3. Chemical compositions of the Pd metal phase and the Ru oxide phase crystalized in the phase equilibrium experiments and calculated partition coefficient of Rh (lnK_Rh). Values normalized to total 100wt%. Numbers in parenthesis represent standard deviation.

	Temperature	Run duration			Metal phase/wt%						Oxide phase^b/wt%
Sample no.	/ K	/ Hours	Atmosphere	Method	n^a	Te	Ru	Rh	Pd	Total	na	RuO2	RhO2	Total	lnKRh
M14-1	1473	24	Air	Al2O3 tube	6	0.71 (0.15)	0.61 (0.09)	20.64 (1.27)	77.03 (2.96)	98.99	10	95.40 (1.74)	4.60 (1.25)	100.00	−1.56
M14-2	1473			SiO2 tube	7	1.20 (0.52)	0.75 (0.29)	20.77 (1.44)	76.43 (1.26)	99.15	10	95.68 (3.51)	4.32 (1.84)	100.00	−1.64
M15-2	1373			Al2O3 tube	8	1.55 (0.41)	0.18 (0.21)	8.03 (0.85)	89.91 (2.03)	99.67	10	87.60 (1.39)	12.40 (1.27)	100.00	0.38
M15-1	1373			SiO2 tube	7	1.16 (0.49)	0.12 (0.05)	10.16 (0.44)	88.45 (1.95)	99.89	10	87.95 (0.79)	12.05 (0.83)	100.00	0.12
M11-7, M11-8	1273	48		Crucible	12	1.60 (0.12)	0.33 (0.30)	3.74 (0.35)	94.57 (1.62)	100.24	15	87.20 (0.88)	12.80 (0.79)	100.00	1.18
M5-1, M5-2	1073	96			11	9.92 (1.16)	0.29 (0.46)	2.03 (0.46)	87.46 (2.24)	99.70	10	86.86 (1.99)	13.14 (1.74)	100.00	1.80
M14-3	1473	24	CO2	Al2O3 tube	6	2.27 (0.63)	3.12 (0.58)	24.40 (3.34)	69.55 (4.10)	99.33	7	98.17 (0.83)	1.83 (0.94)	100.00	−2.65
M14-4	1473			SiO2 tube	8	1.90 (1.29)	5.10 (1.64)	28.52 (6.69)	63.71 (5.82)	99.23	10	98.67 (1.19)	1.33 (1.09)	100.00	−3.12
M15-4	1373			Al2O3 tube	7	5.37 (0.84)	0.51 (0.07)	17.54 (1.03)	75.82 (1.33)	99.24	10	94.57 (1.67)	5.43 (1.45)	100.00	−1.24
M15-3	1373			SiO2 tube	8	6.16 (1.97)	0.91 (0.46)	15.57 (2.90)	78.25 (2.15)	100.89	9	96.94 (2.41)	3.06 (1.48)	100.00	−1.68
M16-2	1273	48		Al2O3 tube	9	12.27 (1.27)	0.22 (0.04)	4.42 (0.53)	85.56 (1.41)	102.47	10	93.66 (2.01)	6.34 (1.90)	100.00	0.31
M16-1	1273	48		SiO2 tube	6	12.60 (1.37)	0.66 (0.28)	4.35 (0.79)	84.07 (1.66)	101.67	8	96.66 (3.26)	3.34 (2.24)	100.00	−0.33
M17-3, M17-4	1073	96		Wire loop	10	7.70 (1.61)	0.06 (0.07)	2.50 (0.92)	90.73 (1.40)	100.99	20	86.57 (1.92)	13.43 (1.33)	100.00	1.62

^aNumbers of analyses.

^bValues normalized to total 100wt%.

Table 4. Chemical compositions of the Pd metal phase and the platinum wire used for sample holding by the crucible method and the wire-loop method above 1373 K. Numbers in parenthesis represent standard deviation.

	Temperature	Run duration					Metal phase/wt%
Sample no.	/ K	/ Hours	Atmosphere	Method	Phase	n	Te	Ru	Rh	Pd	Pt
M11-1, M11-2	1473	24	Air	Crucible	Pd-rich metal	9	0.97(0.28)	0.40(0.37)	16.44(5.91)	82.00(6.56)
					Rh-rich metal	11	0.02(0.04)	2.04(0.50)	88.43(5.63)	9.27(5.63)
					Pt wire (rim)	3		0.80(0.28)	4.03(5.81)	3.15(1.00)	92.02(5.68)
M11-4, M11-5	1373	24	Air	Crucible	Pd-rich metal	13	1.26(0.11)	0.17(0.06)	13.02(0.89)	85.70(1.60)
					Pt wire (rim)	3		0.08(0.08)	0.55(0.07)	6.00(0.57)	93.37(1.17)
M13-5, M13-6	1373	24	CO2	Wire loop	Ru-rich metal	8	0.06(0.09)	74.52(7.22)	15.62(4.21)	10.80(8.46)
					Pt wire (rim)	4		0.20(0.22)	1.78(0.63)	4.98(1.27)	93.04(1.78)

Note: n: numbers of analyses.

Figures 4 and 5 represent chemical compositions of metal phase and oxide phase, respectively. Palladium and tellurium contents in the Pd metal decrease and Rh content increases with increasing temperature and oxygen fugacity. Ruthenium content in the Pd metal is up to 5 wt% at the most reducing condition (1473 K, CO₂ atmosphere). The composition of the Ru oxide in air is constant between 1073 and 1373 K, while RhO₂ decreases at 1473 K. Under CO₂ flow, Ru oxide shows lower RhO₂ contents compared with those in air. The increase of Rh in Pd metal and decrease of Rh in Ru oxide with increasing temperature and decreasing $f_{O_2}$ can be accounted for by reduction of Rh in the sample. It is of interest to note that the compositions of Pd metal and Ru oxide by Al₂O₃ tube method are consistent with those by SiO₂ tube method despite the compositional differences of glass matrix in those two methods (Figure 2). This is probably related to the low solubility of PGMs in silicate melts. Solubility of Pd and Rh in SiO₂–Al₂O₃–CaO–MgO melt at 1723 K is 338 and 35 ppm at 50 wt% SiO₂, respectively, while they are 316 and 22 ppm at 70 wt% SiO₂ [12]. The compositional dependence of PGMs solubility is not significant. Solubility in the alkali-borosilicate melt should be of the same order of magnitude. We conclude that the chemical compositions of Pd metal phase and Ru oxide phase in HLW glass are independent of composition of glass matrix because amounts of Pd, Rh and Ru in the glass matrix are very limited.

Figure 4. Chemical compositions of the Pd metal phase in experimental samples; (a) Pd, (b) Rh, (c) Te. Solid circle and open circle are results in air and in CO₂ atmosphere, respectively. Open square represents composition of Pd metal included in the starting KMOC glass. Error bar is a standard deviation (1σ).

Figure 5. Chemical compositions of the Ru oxide phase in experimental samples; (a) RuO₂ and (b) RhO₂. Values normalized to total 100wt%. Solid circle and open circle are results in air and in CO₂ atmosphere, respectively. Open square represents composition of Ru oxide included in the starting KMOC glass, respectively. Error bar is a standard deviation (1σ).

3.3. Mass fraction of crystalline phases

Mass fractions of crystalline phases were determined by a mass-balance calculation using compositions of both phases (Table 3), bulk contents of Pd, Rh and Ru in the KMOC glass (Table 1) and the Pd, Rh and Ru contents in glass matrix. Then the solubilities of Pd, Rh and Ru in borosilicate melt were assumed as 300, 30 and 30 ppm, respectively [12]. The results are shown in Figure 6. The amounts of Pd metal phase and Ru oxide phase in the starting KMOC glass are calculated to be 0.32 and 0.21 wt%, respectively. In the experimental samples, Pd metal increases and Ru oxide decreases with increasing temperature and decreasing oxygen fugacity due to the reduction of oxygen.

Figure 6. Mass fraction of the Pd metal phase and the Ru oxide phase in the sample of phase equilibrium experiments as a function of temperature. Amount in the KMOC glass is also shown.

4. Discussion

4.1. Estimates of temperature and redox condition from crystal compositions

Operation temperature of LFCM for HLW vitrification ranges from about 1273 to 1573 K at main portion, while it is lowered to about 1073 K in the bottom portion [20,22,23]. Although an actual melt temperature can be measured by thermometer, the measurement position is restricted. Therefore, a numerical simulation has been attempted to estimate temperature distribution and material flow in glass melter [22,34,36,37]. We propose that the chemical compositions of Pd metal and Ru oxide can be used for independent estimates of the temperature and redox condition in vitrification melter.

The Pd metal in the KMOC glass contains 91wt% Pd. This is consistent with metal composition below 1373 K in air and that at 1073 K in CO₂. Similarly, Rh content in the Pd metal (5.5wt%) agrees with that between 1273 and 1373 K and at 1073 K in air and CO₂ condition, respectively (Figure 3). The composition of Ru oxide in the KMOC glass is consistent with results below 1373 K in air (Figure 4). From these comparisons, it can be expected that crystalline phases included in the KMOC glass were equilibrated at the temperature from 1273 to 1373 K and atmospheric oxygen fugacity.

The Te contents of experimental Pd metal in air (1.2–1.6 wt%) are slightly lower than that in the KMOC glass (3.6 wt%). This is considered to be due to the evaporated nature of the tellurium at high temperature.

4.2. Rhodium partitioning between Pd–Rh–Ru–Te and (Ru, Rh)O₂ solid solutions

Comparison between chemical compositions of experimental products and of crystal phases in a HLW glass is useful to estimate physical condition in a vitrification melter. However, the compositional changes given in the Figures 3 and 4 are not always common in an HLW glass since the phase relationship is basically dependent on the proportion of PGMs included in a glass. On the contrary to this, thermodynamic relationship of element partitioning among crystalline phases give insight into more general relationship of chemical composition, temperature and oxygen fugacity.

The rhodium partitioning between Pd–Rh–Ru–Te and (Ru, Rh)O₂ solid solutions can be represented by the reaction: (1) $$\mathrm{Rh}{\mathrm{O}}_2\left(\mathrm{oxide}\right)=\mathrm{Rh}\left(\mathrm{metal}\right)+{\mathrm{O}}_2\left(\mathrm{gas}\right).$$(1)

The chemical potentials (μ^j_i) for each component can be described as follows: (2a) $${\mu }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}=G_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}+RT\ln a_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}},$$(2a) (2b) $${\mu }_{\mathrm{Rh}}^{\mathrm{Metal}}=G_{\mathrm{Rh}}^{\mathrm{Metal}}+RT\ln a_{\mathrm{Rh}}^{\mathrm{Metal}},$$(2b) (2c) $${\mu }_{{\mathrm{O}}_2}^{\mathrm{Gas}}=G_{{\mathrm{O}}_2}^{\mathrm{Gas}}+RT\ln f_{{\mathrm{O}}_2},$$(2c) where a and $f_{{\mathrm{O}}_2}$ are activity and oxygen fugacity, respectively. Inserting Equations. (2(2a) $${\mu }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}=G_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}+RT\ln a_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}},$$(2a) a)–(2(2c) $${\mu }_{{\mathrm{O}}_2}^{\mathrm{Gas}}=G_{{\mathrm{O}}_2}^{\mathrm{Gas}}+RT\ln f_{{\mathrm{O}}_2},$$(2c) c) into ${\mu }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}={\mu }_{\mathrm{Rh}}^{\mathrm{Metal}}+{\mu }_{{\mathrm{O}}_2}^{\mathrm{Gas}}$ yields (3) $$\begin{array}{ccc}\hfill \ln K_{\mathrm{Rh}}& =& \ln \frac{X_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}}{X_{\mathrm{Rh}}^{\mathrm{Metal}}}=\frac{-\Delta G_f^0\left(\mathrm{Rh}{\mathrm{O}}_2\right)}{\mathrm{RT}}\hfill \\ & & +\ln f_{{\mathrm{O}}_2}-\ln \frac{{\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}}{{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}},\hfill \end{array}$$(3) where X^j_i and γ^j_i are mole fraction and activity coefficient of i component in j phase, respectively. ΔG⁰_f(RhO₂) and R represent Gibbs energy of formation of RhO₂ at temperature T and gas constant. $K_{\mathrm{Rh}}=X_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}/\phantom{K_{\mathrm{Rh}}=X_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}{X}_{\mathrm{Rh}}^{\mathrm{Metal}}}{X}_{\mathrm{Rh}}^{\mathrm{Metal}}$ is partition coefficient of rhodium between Pd metal phase and Ru oxide phase. ΔG⁰_f(RhO₂) was measured by electro chemical cell in the temperature range from 850 to 1050 K [38]. Based on these results and estimated value of heat capacity change, ΔC⁰_P= 10 J K⁻¹ mol⁻¹, enthalpy and entropy of formation at 298 K [ΔH⁰_f(298K) and ΔS⁰_f(298K)] were calculated to be −244.94 kJ mol⁻¹ and −191.48 J K⁻¹ mol⁻¹, respectively [38]. Using these values, we calculated the ΔG⁰_f(RhO₂) between 1073 and 1473 K, and obtained the following equation: (4) $$\Delta G_f^0\left(\mathrm{Rh}{\mathrm{O}}_2\right)/\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}=-235315+177.000T,$$(4) where T represents absolute temperature. Figure 7 shows comparison of the lnK_Rh determined by phase equilibrium experiments (Table 3) with the values calculated from the Equations(3) and (4(4) $$\Delta G_f^0\left(\mathrm{Rh}{\mathrm{O}}_2\right)/\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}=-235315+177.000T,$$(4) ) at three different $f_{O_2}$ conditions. Then ${\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}/\phantom{{\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}$ is assumed as unity since thermodynamic mixing properties for the Pd–Rh–Ru–Te and the (Ru, Rh)O₂ solid solutions are not known.

Figure 7. Partition coefficient of Rh (K_Rh) between Pd metal and Ru oxide. Solid circle and open circle are results in air and in CO₂ atmosphere, respectively. Open square represents the K_Rh calculated from crystal compositions in the KMOC glass. Dash lines are the K_Rh calculated from thermodynamic data assuming three difference oxygen fugacities: 0.21(air), 0.021 and equilibrium $f_{O_2}$ of CO₂ dissociation. Errors are comparable to symbol size.

The partition coefficient of Rh determined by the experiments decreases with increasing temperature and decreasing oxygen fugacity. The lnK_Rh in air is slightly higher than the calculated partition coefficient at $f_{O_2}$= 0.21. This indicates the actual value of ${\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}/\phantom{{\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}$ is less than 1. Slope of the lnK_Rh − 1/T plot (Figure 7) primarily depends on ΔG⁰_f(RhO₂) for the equilibrium reaction as expressed by Equation (3)(3) $$\begin{array}{ccc}\hfill \ln K_{\mathrm{Rh}}& =& \ln \frac{X_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}}{X_{\mathrm{Rh}}^{\mathrm{Metal}}}=\frac{-\Delta G_f^0\left(\mathrm{Rh}{\mathrm{O}}_2\right)}{\mathrm{RT}}\hfill \\ & & +\ln f_{{\mathrm{O}}_2}-\ln \frac{{\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}}{{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}},\hfill \end{array}$$(3) . Experimental lnK_Rh in air above 1273 K are close to calculated values, indicating that equilibrium was reached in these experiments. On the contrary to this, there is no difference between measured lnK_Rh in air and in CO₂ at 1073 K, and these values are significantly smaller than that expected from low-temperature extrapolation of the lnK_Rh between 1273 and 1473 K. These facts suggest that the heating duration of 96 hours was too short to attain chemical equilibrium at 1073 K.

The discrepancy of the experimental lnK_Rh from calculated value is more significant for experimental results in CO₂. The lower lnK_Rh in CO₂ compared with that in air certainly suggests reduced oxygen fugacity. However, the difference between calculated and experimental lnK_Rh is probably too large to result in compositional dependence of ${\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}/\phantom{{\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}$ or impurity oxygen in the CO₂ gas. Therefore, we suspect that this discrepancy is caused by slow kinetics of redox reaction. Cochain et al. [39] carried out in-situ high-temperature XANES observations of iron redox ratio in sodium-borosilicate melt, and determined redox diffusivity (D_red) of iron as a function of temperature and composition. They reported that the log D_red ranges from −9.6 to −11.6 between 1070 and 1570 K and decreases more than one order of magnitude as B₂O₃ increases in the range from 0 to 18 wt% at constant temperature. Assuming that the D_red of PGMs is similar to that of iron for 62SiO₂–11B₂O₃–21Na₂O–6FeO (wt%) melt [39], the times required for redox equilibrium in molten glass by tube methods are expected to be 11 hours at 1473 K and 31 hours at 1273 K, which are comparable to heating duration in our experiments. However, if the D_red in multicomponent HLW glass is lower one order of magnitude than the simple sodium-borosilicate melt, the equilibration times become 10 times longer. Then our experimental duration would be too short to allow redox equilibrium. It has been considered that the iron redox reaction in silicate melt is rate limited by diffusion of network-modifier cations along with a counter flux of electrons [40–43]. In RuO₂-glass composites, electronic and ionic transport occurs over a wide temperature range even at very low Ru contents [24]. Thus, the existence of Ru may affects mechanism of redox reaction, and the reaction kinetics in Ru-bearing silicate melts is possibly different from that in PGMs-free iron-bearing melts. Further studies are required to solve these points.

The experimentally determined partition coefficient between 1273 and 1473 K in air ($f_{O_2}$ = 0.21) can be expressed as: (5) $$\ln K_{\mathrm{Rh}}=\frac{27264}{T}-18.372+\ln f_{{\mathrm{O}}_2}.$$(5)

The above equation is nearly independent of the amounts of PGMs as long as that compositional dependence of ${\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}/\phantom{{\gamma }_{\mathrm{Rh}{\mathrm{O}}_2}^{\mathrm{Oxide}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}}{\gamma }_{\mathrm{Rh}}^{\mathrm{Metal}}$ is small. Therefore, it can be generally used for temperature estimate of the molten HLW glass. The lnK_Rh calculated from the crystal compositions in KMOC glass is 0.73(±0.03). Then the equilibrium temperature of the KMOC glass just before discharging is calculated to be 1320K from the Equa-tion (5)(5) $$\ln K_{\mathrm{Rh}}=\frac{27264}{T}-18.372+\ln f_{{\mathrm{O}}_2}.$$(5) at $f_{O_2}$= 0.21 (air). This is consistent with the temperature range estimated from crystal compositions described before (1273–1373 K), and nearly equal to the mean temperature of upper portion (1423 K) and lower portion (1223 K) in the KMOC melter [23].

Another significance of Equation (5)(5) $$\ln K_{\mathrm{Rh}}=\frac{27264}{T}-18.372+\ln f_{{\mathrm{O}}_2}.$$(5) is that the K_Rh is proportional to the oxygen fugacity at constant temperature. Ferric–ferrous ratio (Fe²⁺/ΣFe) of HLW glass has been used to evaluate redox state in vitrification melter [44,45]. The K_Rh can be used as another indicator of redox conditions. For example, if temperature of discharging molten glass is measured by a radiation thermometer, the oxygen fugacity could be roughly estimated by Equation (5)(5) $$\ln K_{\mathrm{Rh}}=\frac{27264}{T}-18.372+\ln f_{{\mathrm{O}}_2}.$$(5) from the discharging temperature and the chemical compositions of Pd metal and Ru oxide. We suggest that the partition coefficient of rhodium is useful to convert the chemical compositions of crystal phases into physical conditions (T, $f_{O_2}$) in the vitrification melter.

5. Summary

Phase equilibrium experiments were carried out using a simulated HLW glass containing Pd, Rh and Ru collected from a full-scale mock up facility. The relationship of chemical compositions of Pd–Rh–Ru–Te (Pd metal) and (Ru, Rh)O₂ (Ru oxide) solid solutions was examined as a function of temperature and oxygen fugacity. The results are summarized as follows.

1. The chemical compositions and the amounts of Pd metal phase and Ru oxide phase are functions of amount of Pd, Rh and Ru in the glass, temperature and oxygen fugacity, whereas they are independent of composition of glass matrix.

2. RuO₂ content in the Ru oxide phase increases and Pd content in the Pd metal phase decreases with increasing temperature and decreasing oxygen fugacity, which are caused by a progressive reduction of rhodium.

3. The partition coefficients of rhodium between Pd metal and Ru oxide (K_Rh) determined in air are slightly higher than those calculated from standard thermodynamic data of formation of RhO₂, because of non-ideal mixing properties in Pd–Rh–Ru–Te and (Ru, Rh,)O₂ solid solutions. The K_Rh can be used to convert chemical compositions of Pd metal and Ru oxide into temperature and oxygen fugacity in a vitrification melter.

4. Based on the comparisons of crystal compositions and K_Rh in the HLW glass with the experimentally determined values, it can be expected that the HLW glass examined in this study (KMOC glass) had been equilibrated in the temperature range from 1273 to 1373 K and oxygen fugacity close to that of air just before discharging from the melter.

Acknowledgements

This work was supported by Grant-in-Aid for Japan Nuclear Fuel Limited by the Ministry of Economy, Trade and Industry, Japan.

Disclosure statement

No potential conflict of interest was reported by the authors.