REE abundance patterns, tetrad effect, and Jørgensen’s theory have been considered in relation to REE Geochemistry. The present author proposed a theoretical equation for thermochemical data for ligand-exchange reactions between a pair of isomorphous Ln (III) compound series: ΔY_obs=q(aq+b)(q+25)+c+(9/13)n(S) C₁(q+25)+m(L) C₃(q+25), where q denotes the number of 4f electrons with Ln³⁺=(4f)^q, n(S) and m(L) are coefficients for 4f interelectron repulsion energy given by total spin and total orbital angular momentum quantum numbers (S and L) for Ln³⁺, and a, b, c, C₁, and C₃ are constants given by the least-squares regression. We call it Jørgensen–Kawabe equation, which is applicable to series changes of ΔH_r, ΔS_r, and ΔG_r for ligand-exchange reactions noted above. If a polymorphic change occurs in Ln (III) compound series, a suitable correction for ΔY_obs is necessary to satisfy the isomorphous series condition. The series change of ΔG_r for LnO_1.5(cub)+(3/2) F₂(g)=LnF₃(rhm)+(3/4) O₂(g) has been considered by using thermochemical data for LnO_1.5 (Robie et al., 1979) and for LnF₃ (Chervonnyi, 2012),and the tetrad effect of ΔG_r and its temperature change have been examined. From 298 to 1200 K, the series changes of ΔG_r can be regressed successfully by Jørgensen–Kawabe equation, in which convex upward tetrad effects are always observed. But the magnitude of convex tetrad effect begins to diminish at 900 K. Its extrapolation to above 1200 K suggests that the convex tetrad effect may diminish totally at about 1400 K. This is due to the fact that ΔH_r and ΔS_r for the reactions have similar tetrad effects. ΔG_r’s at higher temperatures above 1400 K are expected to show a concave upward tetrad effect controlled by (-TΔS_r) because of ΔG_r=ΔH_r-TΔS_r. In REE minerals of lanthanite and kimuraite, each Ln (III) ion is in a state of isomorphous series. This satisfies the condition of Jørgensen–Kawabe equation, and it is interesting to regress the REE patterns for lanthanite and kimuraite by Jørgensen–Kawabe equation. The following three types of REE patterns have been examined; (a) a pattern of logarithmic REE concentration ratios between a coexistent pair of lanthanite and kimuraite from Japan, (b) a pattern of logarithmic REE concentration ratios between a pair of lanthanite samples from Japan and New Zealand, and (c) logarithmic chondrite-normalized REE patterns for lanthanite and kimuraite. The three REE patterns are all reproduced satisfactorily by Jørgensen–Kawabe equation. The REE pattern of (a) can be understood in the similar way like the series variation of ΔG_r for the reactions between LnF₃(rhm) and LnO_1.5(cub) discussed here, but (b) and (c) cannot correspond to ΔG_r for such single-step reactions, because (b) and (c) are not dealing with the equilibrium pairs. However, the chondritic REE must be the common REE source for terrestrial samples. If reaction steps of geochemical evolution from the chondritic material to the particular natural material are combined, this may correspond to the REE pattern of (c).Since the REE pattern of (b) is the difference of patterns of (c),the REE pattern of (b) may also be compatible with Jørgensen–Kawabe equation.

This paper begins with how the author became interested in biological weathering and ends with proposing a way to use it to challenge the current problem on the atmospheric carbon dioxide. I describe experimental evidence showing that biological weathering is a physiological activity for some plants and indicating that diatoms dissolve silicate minerals to incorporate elements from silicate minerals into their silica frustules, thus, in effect, participate in weathering. Furthermore, it is shown that weathering in the ocean plays pivotal roles in the carbon cycle and that this is the key to understanding the carbon behavior during the glacial cycles. Two amendments have been introduced to the discussion since the publication of the author’s book in 2022: ocean weathering proceeds independently of organic matter oxidation; and the index representing oceanic carbon dioxide absorption should exclude factors related to photosynthetic activity in the surface ocean.

This paper describes the recent research and development status of neutron-induced prompt γ-ray analysis and muonic X-ray analysis as elemental analysis methods using quantum beams. Neutron-induced prompt γ-ray analysis is an elemental analysis method using neutrons, and is often used as a nondestructive quantitative analysis method for boron and hydrogen. The prompt γ-ray analysis system (PGA) installed at JRR-3 is an old device constructed more than 30 years ago, but recently an articulated robot has been installed and an advanced automated analysis system is in operation. On the other hand, the muonic X-ray analysis method is attracting attention as a new analysis method, and can detect light elements such as oxygen nondestructively. Both analytical methods have been used in the analysis of the samples of asteroid Ryugu, and will continue to evolve greatly as analytical methods in the future.