ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

This article explores mineral properties from a thermodynamic perspective, specifically, specific heats, bulk modulus, and Grüneisen parameters. When heat is introduced into a body, it can be stored in the body as internal energy. If the subsequent temperature rise leads to an expansion of volume under pressure, some of this heat can be converted into mechanical energy through work. The combination of these energies is referred to as enthalpy. Specific heat signifies the rate of temperature elevation resulting from heat in a unit amount of material. The isobaric and isochoric specific heats hold relevance in scenarios with or without thermal expansion, respectively, representing enthalpy and internal energy changes. Their relationship is expressed through easily measurable properties. The isobaric specific heat is greater than the isochoric counterpart, with the latter being more fundamental. The article further defines the adiabatic and isothermal bulk moduli, offering a relationship based on easily measurable properties. The ratios between the isobaric and isochoric specific heat and between the adiabatic and isothermal bulk moduli are identical and equal to one plus the product of thermal expansivity, the thermodynamic Grüneisen parameter, and temperature. The isothermal bulk modulus is more fundamental than the adiabatic. The Grüneisen parameter denotes the rate of pressure increase with respect to the increase in internal energy density. The thermodynamic Grüneisen parameter is identical to the Grüneisen parameter. The article provides experimental values of these parameters for various minerals, including forsterite, fayalite, spinel, grossular, pyrope, periclase, corundum, halite, and sylvite. Finally, the adiabatic temperature gradient is deduced and applied to the Earth as the adiabatic geotherm.

The "Lectures on Mineral Physics" series is derived from the author's lectures for the Master's course at the Bayerisches Geoinstitut, University of Bayreuth. It aims to elucidate the fundamental properties of minerals. The topics covered include thermodynamic properties, elasticity theory, lattice vibrations, equation of state, heat transport, point defects, line defects, planar defects, diffusion, electrical conductivity, and deformation. This series is intentionally designed to be accessible to Master's students in geology, even without an extensive background in physics and mathematics.

In orthopedics and oral surgery, clinical trials are being conducted to examine the reconstruction and regeneration of bone defects caused by injuries and diseases. Bone substitutes, mainly composed of calcium phosphate, are employed as biomaterials to reconstruct and regenerate bone defects that cannot be covered by autogenous bone grafts. However, the bone regeneration abilities of existing bone grafting materials are insufficient. Most candidates for bone grafting materials are elderly patients older than 60 years, so improving the bone regeneration capacity of bone grafting materials is a major clinical problem. We have been investigating the enhancement of bone substitutes via ionic insertion, an original method of controlling calcium phosphate crystals and adding elements. In this review, we describe our studies on the addition of silica, a bone-active factor, to calcium phosphate and the usefulness of silica-loaded calcium phosphate as a bone replacement material based on the ionic insertion method. The bone regeneration ability of silica-loaded calcium phosphate was several times higher than that of the current carbonate apatite bone material. Silica-loaded calcium phosphate is expected to be applicable to clinical cases that were difficult to apply in the past; it will also significantly help improve the quality of life of patients, especially the elderly.

Information collected from geological newsmagazines in 2023 is reviewed. First topic is mineral resources such as mineral commodity summary in USA, identified mineral resources in Australia, and metallogenic significance of rare elements in Zambia. Geothermal energy in the UK using borehole heat exchangers is also referred. Second topic is regional geology, that is, the Wyoming Archean craton, the Costanaza mine for sustainability education, and the Jeju Island Geopark activities. Third topic is overview of granites and geological mapping program for next generation.

In Kajishima, granitoid dykes intrude into Cretaceous gabbroic rocks. The granitoids are divided into deformed and massive granitoids based on field occurrence. Massive granitoid shows equigranular texture and consists mainly of quartz, plagioclase, alkali feldspar, and biotite. Poikilitic alkali feldspar including euhedral to subhedral quartz, plagioclase and biotite is locally observed in the massive granitoid. Petrographic data together with phase relationship in granodiorite system suggest that the poikilitic texture indicates partial melting of quartz- and plagioclase-bearing rocks such as tonalite and granodiorite. The presence of this texture in the Kajishima granitoids suggests re-melting of tonalite/granodiorite at deep arc crust.

Several conflicting pressure-temperature (P-T) conditions of granulite in the Bohemian Massif have been proposed, and we estimated a P-T path of felsic granulite from the Zrcadlová Hut’ of the Blanský les body in the Bohemian Massif. The felsic granulite is mainly composed of garnet, biotite, quartz, plagioclase, and potassium feldspar, with or without pyroxenes. Garnet in two granulite samples occurs as porphyroblasts and preserves prograde zoning. Some of the porphyroblasts contain kyanite as inclusions. These felsic granulites also contain coronitic garnet surrounding spinel + plagioclase symplectites. These symplectites can be considered as pseudomorphs after kyanite. The pyroxene-bearing felsic granulite sample also contains garnet with prograde zoning, although the garnet grains are relatively small (1100˚C, 2.3 GPa based on the combination of garnet-biotite geothermometer and garnet-aluminosilicate-quartz-plagioclase barometer. The pyroxene-bearing felsic granulite contains clinopyroxene + plagioclase symplectite that has formed during a low-pressure stage, and its P-T conditions were estimated to be 750˚C, 0.5–0.8 GPa, by orthopyroxene-clinopyroxene geothermometer and jadeite-quartz-albite barometer. It is likely indicating that the pressure was rapidly reduced from the maximum-pressure stage, and then the relatively rapid cooling occurred. Such rapid decompression and cooling are needed to retain the prograde zoning in garnet. Index minerals of ultrahigh pressure such as coesite are not found. Although ultrahigh pressure conditions were not reached, the estimated pressure is relatively high (>2.0 GPa) compared with previous studies.