Volumetric Thermal Expansion Coefficient Research Articles

Synthesis, negative thermal expansion and optical performances of In0.5Sc1.5Mo3O12 thin films via sol-gel spin coating

Orthorhombic In0.5Sc1.5Mo3O12 thin films have been synthesized using the sol-gel spin coating. Influences of post-annealing temperatures on crystal structure, morphology, negative thermal expansion (NTE) and optical performances of the thin films were studied using XRD, SEM, XPS, high-temperature XRD and UV–Vis–NIR spectrophotometer. XRD and SEM results show that as-prepared thin film is in an amorphous state with a smooth and dense surface. Orthorhombic In0.5Sc1.5Mo3O12 thin films were obtained after post-annealing in 550–750 °C. The higher the annealing temperature in 550–750 °C, the better the crystallinity of orthorhombic In0.5Sc1.5Mo3O12 thin films. In addition, the grain size of the In0.5Sc1.5Mo3O12 thin film also grows as the annealing temperature increases. The resulting orthorhombic In0.5Sc1.5Mo3O12 thin films exhibit anisotropic NTE. Its volumetric coefficient of thermal expansion (CTE) is −3.44 × 10−6 °C−1, while the CTEs in a-, b- and c-axis directions are −4.70 × 10−6 °C−1, 5.37 × 10−6 °C−1, and -4.10 × 10−6 °C−1 in 25–700 °C, respectively. In addition, the transmittance of orthorhombic In0.5Sc1.5Mo3O12 thin films post-annealed at 750 °C is around 87.75 %–95.03 %.

Compressibility, thermal expansion and Raman scattering of synthetic whitlockite Ca9Mg(PO3OH)(PO4)6 at high pressures and high temperatures

Abstract In-situ X-ray diffraction and 16 Raman scattering of synthetic whitlockite, Ca9Mg(PO3OH)(PO4)6, have been systematically measured at high pressures and high temperatures, respectively. The results show that whitlockite is stable up to ~ 15 GPa at ambient temperature and undergoes a temperature-induced dehydrogenation to merrillite above 973 K at ambient pressure. The obtained pressure-volume data were fitted using a third-order Birch-Murnaghan equation of state to yield the isothermal bulk modulus as K0 = 79(4) GPa with pressure derivative K0' = 4.3(6). When K0' was fixed at 4, the refined isothermal bulk modulus was 81(1) GPa. The volumetric thermal expansion coefficient (αV) is equal to 4.05(8) × 10-5 K-1. The axial thermal expansion coefficients (αa and αc) are 1.07(5) × 10-5 K-1 and 1.91(6) × 10-5 K-1. Both compressibility and thermal expansion show an axial anisotropy. The effects of pressure and temperature on the Raman spectra of whitlockite have been quantitatively analyzed. The isothermal and isobaric mode Grüneisen parameters, and the intrinsic anharmonic mode parameters of whitlockite were calculated. Some amounts of OH--bearing whitlockite may be preserved and could be discovered in meteorites if whitlockite undergoes a low temperature process.

The Thermophysical Properties of TcO2

Technetium-99 is a highly radioactive isotope with a long half-life that is common in nuclear waste. It volatizes at a low temperature, which poses a significant challenge to the clean-up and containment processes. Due to difficulties in purifying technetium compounds, their thermophysical properties have not been measured or calculated. Here, first principle methods are used along with the quasi quasi-harmonic harmonic approximation to compute the Debye temperature, volumetric thermal expansion coefficient, bulk modulus, and heat capacity of rutile TcO2 for temperatures ranging from 0 to 1500 K and applied pressures ranging from 0 to 255 GPa. The computed atomic structures agree well with the results from diffraction measurements. The computed thermophysical properties are in the neighborhood of other rutile metal oxides and, in particular, are within approximately 10–13% of rutile ReO2, which is frequently used as a substitute for TcO2 in experimental studies.

Anisotropic thermo-mechanical response of layered hexagonal boron nitride and black phosphorus: application as a simultaneous pressure and temperature sensor.

Hexagonal boron nitride (hBN) and black phosphorus (bP) are crystalline materials that can be seen as ordered stackings of two-dimensional layers, which lead to outstanding anisotropic physical properties. Knowledge of the thermal equations of state of hBN and bP is of great interest in the field of 2D materials for a better understanding of their anisotropic thermo-mechanical properties and exfoliation mechanism towards the preparation of important single-layer materials like hexagonal boron nitride nanosheets and phosphorene. Despite several theoretical and experimental studies, important uncertainties remain in the determination of the thermoelastic parameters of hBN and bP. Here, we report accurate thermal expansion and compressibility measurements along the individual crystallographic axes, using in situ high-temperature and high-pressure high-resolution synchrotron X-ray diffraction. In particular, we have quantitatively determined the subtle variations of the in-plane and volumetric thermal expansion coefficients and compressibility parameters by subjecting these materials to hydrostatic conditions and by collecting a large number of data points in small pressure and temperature increments. In addition, based on the anisotropic behavior of bP, we propose the use of this material as a sensor for the simultaneous determination of pressure and temperature in the range of 0-5 GPa and 298-1700 K, respectively.

Integrating abnormal thermal expansion and ultralow thermal conductivity into (Cd,Ni)2Re2O7 via synergy of local structure distortion and soft acoustic phonons

Abnormal thermal expansion denotes intriguing negative and zero thermal expansion (NTE and ZTE). The integration of abnormal thermal expansion with low thermal conductivity is highly desirable for high-end devices. However, the coexistence of seemingly contradictory features presents a grand challenge for abnormal-thermal-expansion materials. Herein, a unique NTE, for the first time, is reported in Cd2Re2O7 with a volumetric coefficient of thermal expansion, αV of -5.0 × 10−6/K (5 - 210 K). Moreover, a remarkable ZTE is attained in Cd1.95Ni0.05Re2O7 with αV of 1.1 × 10−6/K (5 - 180 K). Concomitantly, the attained ultralow thermal conductivities of 0.38 and 0.56 W/mK at 300 K of the two compositions are also highly competitive, exceeding prevailing abnormal-thermal-expansion materials. Concurrently, Cd2Re2O7-based oxides demonstrate orders of magnitude higher electrical conductivity than representative NTE materials. By a combined investigation of synchrotron X-ray techniques, aberration-corrected scanning transmission electron microscope, and phonon calculations, the synergy of local structure distortion highlighted by ordered Re-Re dimer and soft acoustic phonons is integral to the simultaneous accomplishment of distinctive thermal expansion and thermal conductivity, which is totally distinct from predominant optical-phonon driven NTE. This integration of intriguing thermal properties effectively resolves thermal issues and permits excellent size and temperature stability. This work opens up an unusual strategy to delicately control thermal expansion and thermal conductivity simultaneously.

Exploring the Relationship between the Structural Characteristics and Mechanical Behavior of Multicomponent Fe-Containing Phases: Experimental Studies and First-Principles Calculations.

A comprehensive understanding of the structural characteristics and mechanical behavior of Fe-containing phases is important for high-Fe-level Al-Si alloys. In this paper, the crystal characteristics, thermal stability, thermophysical properties and mechanical behavior of multicomponent α-AlFeMnSi and α-AlFeMnCrSi phases are investigated by experimental studies and first-principles calculations. The results indicate that it is easier for Fe and Cr to substitute the Mn-12j site in α-AlMnSi in thermodynamics; Cr is preferred to Fe for substituting Mn-12j/k sites due to its lower formation enthalpy after single substitutions at Mn atom sites. The α-AlFeMnCrSi phase shows higher thermal stability, modulus and intrinsic hardness and a lower volumetric thermal expansion coefficient at different temperatures due to the strong chemical bonding of Si-Fe and Si-Cr. Moreover, the α-AlFeMnCrSi phase has a higher ideal strength (10.65 GPa) and lower stacking fault energy (1.10 × 103 mJ/m2). The stacking fault energy evolution of the different Fe-containing phases is mainly attributed to the differential charge-density redistribution. The strong chemical bonds of Si-Fe, Si-Mn and Si-Cr are important factors affecting the thermophysical and mechanical behaviors of the α-AlFeMnCrSi phase.

Variation of Bulk Modulus, Its First Pressure Derivative, and Thermal Expansion Coefficient with Applied High Hydrostatic Pressure

Throughout this work, the equations of variation of the isothermal bulk modulus, its first pressure derivative, and the volumetric thermal expansion coefficient as a function of pressure were derived based on the Birch–Murnaghan equation of state (B–M EOS). The bulk modulus and its first derivative at ambient temperature for nine elements were extracted by fitting the published experimental pressure–volume data to B–M EOS, and the results were compared with other published researches, and there was a good agreement. Moreover, those extracted values were used to study the variation of the isothermal bulk modulus, its first pressure derivative, and the isothermal coefficient of thermal expansion as a function of the applied hydrostatic pressure using the equations that were derived from this work.

A first-principles insight into thermodynamic and mechanical properties of Xonotlite and Wollastonite phases of high temperature geothermal well cement

This study investigates the thermodynamic and mechanical properties of two common calcium silicate phases, xonotlite (Ca6Si6O17(OH)2) and wollastonite (CaSiO3), in high temperature geothermal well cement using first-principles methods. Various properties, including thermal expansion coefficients, elastic constants, free energy, and entropy, were evaluated with the use of accurate anharmonic approximations at high temperatures. The study found that wollastonite has higher mechanical strength (97 GPa) compared to xonotlite (66 GPa) and lower thermal expansion, with decreasing values at higher temperatures. Volumetric thermal expansion coefficients were also calculated at different temperatures. These results demonstrate the potential of wollastonite as a suitable material for high-temperature cement dehydration processes.

Uncertainty Quantification of Thermophysical Property Measurement in Space and on Earth: A Study of Liquid Platinum Using Electrostatic Levitation

A study of uncertainty analysis was conducted on four key thermophysical properties of molten Platinum using a non-contacting levitation technique. More specifically, this work demonstrates a detailed reporting of the uncertainties associated with the density, volumetric thermal expansion coefficient, surface tension and viscosity measurements at higher temperatures for a widely used refractory metal, Platinum using electrostatic levitation (ESL). The microgravity experiments were conducted using JAXA’s Electrostatic Levitation Furnace (ELF) facility on the International Space Station and the terrestrial experiments were conducted using NASA’s Marshal Space Flight Center’s ESL facility. The performance of these two facilities were then quantified based on the measurement precision and accuracy using the metrological International Standards Organization’s Guide to the Expression of Uncertainty Measurement (GUM) principles.

High configurational entropy driven increased heat capacity of refractory multicomponent di-silicides

The high melting point of refractory di-silicides e.g., MoSi2, WSi2, and VSi2, together with their strong resistance to creep and high temperature oxidation, have promoted their potential for use in harsh environments. To realize this promise, an enhanced heat capacity and reduced thermal expansion coefficient are critical for using di-silicides in heat shields and jet engines. Using first principles, we reveal that cationic disordered multicomponent di-silicides with tetragonal structure possess multi-fold higher heat capacity (Cp), and a reduced volumetric thermal expansion coefficient, relative to their low-entropy counterparts. An increase in configurational entropy contributes to metallic bonding, delocalized electrons and a high degree of degeneracy of the optical phonons. Additionally, the average atomic mass, gradient of the dispersion curve and acoustic softening contribute to the variations in the phonon group velocities and subsequently impact the thermal properties.

Exploring the negative thermal expansion and magnetocaloric effect in Fe2(Hf,Ti) Laves phase materials

The transition-metal based Laves phase materials represent an extended family of alloys with rich and fascinating physical properties. In this work, we have investigated the negative thermal expansion and magnetocaloric effect in arc-melted and melt-spun Fe2Hf1-xTix (x = 0.15, 0.27, 0.30, 0.33, 0.36, 0.40) alloys. For x = 0.30–0.40, two hexagonal phases with different compositions share the same P63/mmc lattice symmetry, but have slightly different lattice parameters. The saturation magnetization and Curie temperature both follow a decreasing trend with the average unit-cell volume. For Fe2Hf0.6Ti0.4 melt spinning improves the saturation magnetization from 48.7 to 59.6 Am2/kg and the magnetic entropy change from 0.46 to 0.54 J/kgK at a magnetic field change of 2 T. These enhanced values are attributed to an improved homogeneity caused by a suppression of phase segregation during rapid solidification. We have utilized neutron powder diffraction and Mössbauer spectroscopy to illustrate the correlation between the magnetic order and the negative thermal expansion in single-phase Fe2Hf0.85Ti0.15. The magnetic moments of Fe align below 400 K in the a-b plane and a moment change for the Fe atoms is responsible for the large volumetric coefficient of thermal expansion of −25 × 10−6 K−1 over a wide temperature range of 300–400 K.

Thermal behavior of borax, Na2B4O5(OH)4·8H2O

Abstract Globally, borax is one of the most important borate minerals, both industrially and from a technological viewpoint. Despite its importance, there have been only a few reports on the structural changes of borax upon heating. In this study, we have investigated the thermal behavior and structural characteristics of borax using thermal analysis, in situ high-temperature synchrotron X-ray diffraction, in situ variable-temperature single-crystal X-ray diffraction, and quantum chemical calculations. Differential scanning calorimetry (DSC) curve showed a large endothermic peak at 349 K corresponding to the dehydration reaction of borax. X-ray diffraction (XRD) pattern remained almost unchanged up to 353 K. Above 363 K, the XRD peaks gradually became less intense until they disappeared at 403 K. The unit-cell volume continuously increased with increasing temperature and became constant just before its phase transition to tincalconite. The volumetric thermal expansion coefficient between 113 and 323 K was 7.84 × 10–5 K–1. The a and c lattice parameters exhibited a slight increase trend with increasing temperature, whereas the b lattice parameter increased significantly. Therefore, the thermal expansibilities followed the order b/b0 >> c/c0 > a/a0. The increasing b lattice parameter was closely related to the elongation of the O4···H7B hydrogen-bond interaction along the b-axis. Na-O bond lengths were isotropically expanded with increasing temperature, whereas the B-O bond lengths and angles remained unchanged even after the phase transition to tincalconite. Molecular orbital calculations revealed that an electron cloud shared by two borate tetrahedra led to the formation of a large electron cloud distribution over the B4O5(OH)4 cluster. The intramolecular interactions with substantial covalent character made the cluster quite rigid. The existence of borate minerals containing the B4O5(OH)4 clusters in their structure evidenced the presence of moderately acidic or alkaline water, wherein the borate minerals grew via the incorporation of B4O5(OH)4 clusters. Our results indicate that the connection geometry of the fundamental building block consisting of Bφ3 triangles and Bφ4 tetrahedra (φ: O2–, OH–) can potentially be used as a palaeoenvironmental indicator.

Uncertainty analysis and performance evaluation of thermophysical property measurement of liquid Au in microgravity

A new method for quantifying facility performance has been discussed in this study that encompasses uncertainties associated with thermophysical property measurement. Four key thermophysical properties: density, volumetric thermal expansion coefficient, surface tension, and viscosity of liquid Au have been measured in microgravity environment using two different levitation facilities. Levitation experiments were conducted using the Electrostatic Levitation Furnace (ELF) onboard the ISS in Argon and air, and the TEMPUS Electromagnetic Levitation (EML) facility on a Novespace Zero-G aircraft parabolic flight in Argon. The traditional Maximum Amplitude method was augmented through the use of Frequency Crossover method to identify the natural frequency for oscillations induced on a molten sample during Faraday forcing in ESL. The EML tests were conducted using a pulse excitation method where two techniques, one imaging and one non-imaging, were used to study surface oscillations. The results from both facilities are in excellent agreement with the published literature values. A detailed study of the accuracy and precision of the measured values has also been presented in this work to evaluate facility performance.

Temperature-dependent elastic constants of thorium dioxide probed using time-domain Brillouin scattering

We report the adiabatic elastic constants of single-crystal thorium dioxide over a temperature range of 77–350 K. Time-domain Brillouin scattering, an all-optical, non-contact picosecond ultrasonic technique, is used to generate and detect coherent acoustic phonons that propagate in the bulk perpendicular to the surface of the crystal. These coherent acoustic lattice vibrations have been monitored in two hydrothermally grown single-crystal thorium dioxide samples along the (100) and (311) crystallographic directions. The three independent elastic constants of the cubic crystal (C11, C12, and C44) are determined from the measured bulk acoustic velocities. The longitudinal wave along the (100) orientation provided a direct measurement of C11. Measurement of C44 and C12 was achieved by enhancing the intensity of quasi-shear mode in a (311) oriented crystal by adjusting the polarization angle relative to the crystal axes. We find the magnitude of softening of the three elastic constants to be ∼2.5% over the measured temperature range. Good agreement is found between the measured elastic constants with previously reported values at room temperature, and between the measured temperature-dependent bulk modulus with calculated values. We find that semi-empirical models capturing lattice anharmonicity adequately reproduce the observed trend. We also determine the acoustic Grüneisen anharmonicity parameter from the experimentally derived temperature-dependent bulk modulus and previously reported temperature-dependent values of volumetric thermal expansion coefficient and heat capacity. This work presents measurements of the temperature-dependent elasticity in single-crystal thorium dioxide at cryogenic temperature and provides a basis for testing ab initio theoretical models and evaluating the impact of anharmonicity on thermophysical properties.

Computational Assessment of an Amine-Based Solvent Library for High-Salinity Brine Desalination

Human population growth has increased the demand for freshwater. Simultaneously, improvements to high-salinity brine desalination technology are needed to treat wastewater from expanding industrial activities. Temperature-swing solvent extraction (TSSE), initially proposed in the 1960s for low-salinity brine desalination, has recently been found to be effective for processing high-salinity brines. Although there have been several individual investigations performed to test the TSSE performance of various amine-based solvents, the desired molecular properties of the best solvent candidates remain unknown. Using molecular simulation data and an unsupervised learning method, the molecular characteristics of 60 different amine-based solvents are analyzed and grouped into clusters based on their thermodynamic properties, such as density, heat of vaporization, volumetric thermal expansion coefficient, solvent–solvent binding free energy, solvation free energy, and number of hydrogen-bonds. Solvents with features most similar to one of the best current TSSE solvents (diisopropylamine) were analyzed further by simulating brine–water interfacial systems. Among the 59 amine-based solvents compared to diisopropylamine, we find that secondary amines with a six-carbon branched or linear structure display the most promising TSSE performance and should be experimentally investigated in the future.

Magnetoelastic transition and negative thermal expansion of Fe2Hf0.83Ta0.17 ribbons

In this work, the magnetocaloric effect and negative thermal expansion in melt-spun Fe2Hf0.83Ta0.17 Laves phase alloys were studied. Compared to arc-melted alloys, which undergo a first-order magnetoelastic transition from the ferromagnetic to the antiferromagnetic phase, melt-spun alloys exhibit a second-order transition. For Fe2Hf0.83Ta0.17 ribbons, we observed a large volumetric coefficient of negative thermal expansion of −19 × 10−6 K−1 over a wide temperature range of 197 – 297 K and a moderate adiabatic temperature change of 0.7 K at 290 K for a magnetic field change of 1.5 T. The magnetic field dependence of the transition temperature (dTt/dµ0H = 4.4 K/T) for the melt-spun alloy is about half that of the arc-melted alloy (8.6 K/T). The origin of second-order phase transition of the melt-spun alloy is attributed to the partially suppressed frustration effect, which is due to the atomic disorder introduced by the rapid solidification.

Experimental and numerical investigation of melting and solidification enhancement using Fibonacci-inspired fins in a latent thermal energy storage unit

The major challenge with phase change materials (PCMs) is their low thermal conductivity, eventuating long melting (charging) and solidification (discharging) times in latent thermal energy storage (LTES) units. Using extended surfaces (fins) is a popular method to resulve this issue, with recent developments in novel designs such as tree-like and fractal fins. The complex fin configurations improve the conduction while decreasing the natural convection effects by introducing additional shear stress to the melted PCM. The current work proposes a new fin design based on the Fibonacci sequence in a vertical LTES unit to improve the charging/discharging characteristic. The finned geometry is manufactured out of a solid block of aluminum using the wire-cutting technique. Based on the volume expansion method, an experimental setup is designed to observe the charging/discharging behavior. The PCM under study is RT42 and its density, volumetric thermal expansion coefficient and solid-state thermal conductivity are measured in house. Water is the chosen heat transfer fluid (HTF) set to a constant mass flow rate of about 99 kg/h and 96 kg/h for the melting and solidification processes, respectively. The water charging temperature is 61.5 °C while the water discharge temperature is 21.5 °C. A numerical model based on the enthalpy-porosity method is implemented to investigate the physics behind melting/solidification. A careful investigation of the mushy zone constant is performed based on comparing the experimental and numerical results for melting and solidification. The average liquid PCM velocity on the melt front is studied to evaluate the natural convection behavior. The effects of secondary flows and mixing on the melting process in the new geometry are studied by investigating the liquid PCM flow behavior during the charging. The proposed fin performed 20% better in total melting time than longitudinal fins by introducing more dispersed natural convection dominated regions. The reduction of 45% in solidification time is also established for the novel fin.

Effect of aliovalent substitution on the crystal distortion and negative thermal expansion properties of Zr2SP2O12

We evaluated the thermal expansion of newly synthesized Zr2-xMxSyP2O12-δ, with zirconium (IV) ion (Zr4+) partially substituted by five aliovalent ions (aluminum (III) ion (Al3+), iron (III) ion (Fe3+), yttrium (III) ion (Y3+), niobium (V) ion (Nb5+), and gadolinium (III) (Gd3+)) ion. High-temperature X-ray diffraction patterns showed that Zr2-xMxSyP2O12-δ had the same negative thermal expansion as Zr2SP2O12 and that the volumetric coefficient of thermal expansion (αv) could be controlled by ion substitution. The lowest αv value obtained for Zr1.7Y0.3SP2O12-δ at 373–453 K was approximately −117 ppm/K. Rietveld's analysis showed that aliovalent substitution could make the crystal structure of Zr2SP2O12 at 303–373 K distorted and the lattice volume larger. In addition, multiregression analysis demonstrated that ZrO6 octahedral volume and certain bond angles in the crystal structure were related to the lattice volume.

Thermal Behavior of Saturated Sand at Different Relative Densities

Abstract With the proposal of a dual carbon goal in China, shallow geothermal energy as a kind of clean energy has been gradually promoted and applied. At the same time, more and more geotechnical workers have gradually paid attention to the influence of temperature on the mechanical characteristics of rock and soil mass. Existing experimental research has shown that the thermodynamic behavior for cohesive soil such as clay and silt is relatively mature but is relatively less mature for noncohesive soil, especially for sand. Based on the hollow cylinder triaxial specimen, a series of temperature-controlled triaxial tests have been carried out on saturated Fujian sand under different initial relative density and temperature conditions to capture the change of axial and volumetric strains for saturated sand specimen with increasing temperature. In addition, a bulk volumetric coefficient of thermal expansion of the sand specimen has been put forward, and the relationship between this coefficient and initial relative density also has been established. Then, the thermal deformation mechanism of saturated sand specimen has been revealed. After that, based on the test data during undrained shearing, the stress–strain relationship, deviatoric stress, and pore water pressure at peak state for loose and medium-dense saturated sand specimens have been explored, which can be used to provide some theoretical guidance for shallow geothermal energy and other temperature-related engineering applications.

Synchrotron X-ray diffraction of pyrolusite (MnO2) and rutile (TiO2) during heating to ∼1000 °C

To compare thermal expansion behaviors in isomorphic structures with different redox behaviors, we separately heated pyrolusite (Mn4+O2) and rutile (Ti4+O2) powders from 25 to ∼1000 °C at a rate of 0.05 °C/s at ambient pressure and analyzed them using synchrotron X-ray diffraction and Rietveld refinement. The pyrolusite exhibited two reduction-induced phase decompositions. Between 531 and 583 °C, pyrolusite decomposed to bixbyite (Mn3+2O3), and between 972 and 998 °C, bixbyite decomposed to hausmannite (Mn2+Mn3+2O4). The rutile experienced no phase decompositions or transitions over this same temperature interval.The refined bond lengths and angles for pyrolusite showed that the Mn4+ coordination octahedron became more distorted near the phase decomposition to bixbyite due to the approach of two coordinating oxygen atoms. The 3d electrons of each Mn4+ ion in pyrolusite make π bonds with the 2p electrons of the surrounding O2− ions, whereas the Ti4+ of rutile has no 3d electrons. Thus, π bonding between octahedral Mn4+ and the surrounding O2− anions increases the strength of the Mn–O bonds of pyrolusite relative to the Ti–O bonds of rutile. However, we observed a small decrease in O–O distances in pyrolusite before the decomposition, suggesting that at high temperature, increased π bonding between adjacent O anions precedes the release of O2 and the reduction of Mn4+ to Mn3+. Analogous behavior was observed for bixbyite before its reductive phase decomposition to hausmannite. In contrast, no anomalous changes in the O–O distances occurred for rutile.Our X-ray diffraction analyses provided accurate thermal expansion coefficients for these materials over a broader temperature range than reported in previous studies. The Mn–O bond lengths in pyrolusite were shorter and stronger than the Ti–O bonds of rutile; for example, at 60 °C, <Mn–O> bond distances in pyrolusite refined to 1.8854(6) Å whereas the <Ti–O> bond lengths of rutile were 1.9575(4) Å. Accordingly, the axial and volumetric thermal expansion coefficients refined for rutile were greater than those for pyrolusite. The axial coefficients of thermal expansion (CTE) for pyrolusite were 96% (a-axis) and 69% (c-axis) of the corresponding values for rutile, and the volumetric CTE for pyrolusite was 85% of that for rutile.