Anisotropic Thermal Expansion Behavior Research Articles

Anisotropic thermal expansion of calcium dialuminate (CaAl 4O 7) simulated by molecular dynamics

The anisotropic thermal expansion behavior of CaAl 4O 7 was studied by molecular dynamics (MD) simulation in the temperature range from 298 to 700 K. The monoclinic crystal structure (space group C2/c) has been successfully reproduced by using a simple 2-body potential. The principal distortions ( λ 1, λ 2, λ 3) and the coefficients of linear thermal expansion ( α 1, α 2, α 3) along with the principal axes have been calculated from the temperature dependence of the unit-cell parameters, a, b, c, and β. The distortion λ 3 was much smaller than the other two distortions for all the temperature range, which was partially consistent with the experimental work performed by Fukuda et al. The anisotropic thermal expansion behavior can be explained by the crystallographic geometry, i.e. directional difference in the packing density.

Thermal contraction behavior in Al 2(WO 4) 3 single crystal

The anisotropic thermal expansion behavior of a single crystal of Al 2(WO 4) 3 was obtained for the first time and the anisotropic contraction behavior was identified. The direct clarification of the anisotropic behavior contributes greatly towards designing the thermal expansion characteristics along every axis, realizing unique materials such as a zero expansion material.

Anisotropic thermal expansion of MgSiN2 from 10 to 300 K as measured by neutron diffraction

The lattice parameters of orthorhombic MgSiN2 as a function of the temperature have been determined from time-of-flight neutron powder diffraction. The results indicate that MgSiN2, just like several other adamantine-type crystals, exhibits a relatively small thermal expansion coefficient at low temperatures. This is ascribed to a strongly bonded 3D, relatively open, crystal structure which is characteristic of highly covalent bonded materials. The anisotropic linear thermal expansion behaviour could be qualitatively related to the characteristics of the crystal structure. The least dense packed crystallographic direction showed the smallest anisotropic linear expansion coefficient.

Low thermal expansion materials: a comparison of the structural behaviour of La0.33Ti2(PO4)3, Sr0.5Ti2(PO4)3 and NaTi2(PO4)3

Variable temperature neutron powder diffraction data have been used to examine the structural mechanism of unusual thermal expansion behaviour in La0.33Ti2(PO4)3 (LaTP). These data are compared to those we have recently reported for the related systems NaTi2(PO4)3 (NaTP) and Sr0.5Ti2(PO4)3 (SrTP), which differ in the extent of occupation of the extra-framework MI (La,Sr,Na) cation sites. The root cause of the unusual behaviour is ascribed to the differing expansivities of the occupied and vacant MI sites. This leads to cooperative rotations of TiO6 and PO4 polyhedra, which can be used to quantify and rationalise the overall anisotropic thermal expansion behaviour.

Strong anisotropic thermal expansion in oxides

The strong anisotropic thermal expansion behavior found for cordierite ((Mg2Al4Si5O15), β-eucryptite (LiAlSiO4) and NZP (NaZr2P3O12) is qualitatively rationalized using distance least squares (DLS) modeling. In this approach, the thermal expansion is driven by the ionic bonds of Mg2+, Li+ or Na+. Due to constraints imposed by shared polyhedra edges or faces, thermal expansion of the ionic bonds expands the lattice in only one or two dimensions. Due to the connectivity in these structures, this expansion in some directions causes contraction in the other directions. The thermal expansion of β-eucryptite was determined from powder neutron diffraction data over the temperature range 10–809 K. This revealed that the volume thermal expansion of β-eucryptite becomes substantially more negative below room temperature than it is above room temperature. The structure was refined by the Rietveld method from data collected at 12 different temperatures. DLS modeling studies suggest that Li–O bond expansion plus movement of Li from tetrahedral to octahedral sites can explain the thermal expansion behavior above room temperature. However, such an approach cannot explain the more pronounced low-temperature negative thermal expansion, which is most likely attributable to rocking motions of AlO4 and SiO4 tetrahedra.

Powder neutron diffraction studies of three low thermal expansion phases in the NZP family: K0.5Nb0.5Ti1.5(PO4)3, Ba0.5Ti2(PO4)3 and Ca0.25Sr0.25Zr2(PO4)3

We present the results of variable temperature neutron powder diffraction studies of three low thermal expansion materials belonging to the NZP family; K 0.5 Nb 0.5 Ti 1.5 (PO 4 ) 3 , Ba 0.5 Ti 2 (PO 4 ) 3 and Ca 0.25 Sr 0.25 Zr 2 (PO 4 ) 3 . Each of these structures has half occupancy of the crystallographic site for the large cation (MI = K, Ba or Ca/Sr), but differ in that the vacancies on this site are disordered in the former two (space group \[ R\overline 3 c \] ) but ordered in the latter (space group \[ R\overline 3 \] ). The thermal expansion behaviour is quantified from parameters obtained by Rietveld structure refinement, and is described in terms of rotations and distortions of linked MO 6 (M = Nb, Ti, Zr) and PO 4 polyhedra. The driving force for the anisotropic low thermal expansion behaviour is found to be in the thermal expansivity of the MI–O bonds. This behaviour is intricately linked to the order/disorder behaviour of the MI sites, as shown by a comparison of the three title structures, together with those of NaTi 2 (PO 4 ) 3 in which the MI sites are completely filled, and Sr 0.5 Ti 2 (PO 4 ) 3 , in which the MI sites are half-occupied in an ordered manner.

Anisotropic thermal expansion and effect of pressure on magnetic transition temperatures in chromium chalcogenides Cr 3X 4 with X = Se and Te

The lattice parameters a( T), b( T), c( T), and β( T) as a function of temperature ( T) and the pressure dependence of the magnetic transition temperature T tr for Cr 3X 4 (X  Se and Te) with the NiAs-like crystal structure (space group I2/m) have been measured. For Cr 3X 4 (X  Se and Te), anisotropic thermal expansion behavior of the lattice parameters is observed below T tr. In particular, a( T) and β( T) for Cr 3Se 4 exhibit an abrupt contraction on heating at about 100 K. The sign of the pressure derivative of T tr for Cr 3X 4 (X  Se and Te) is consistent with volumetric expansion behavior. The obtained results are discussed qualitatively from the viewpoint of the band picture.

Effect of Nb2O5 Alloying on Thermal Expansion Anisotropy of 2 mol% Y2O3‐Stabilized Tetragonal ZrO2

Tetragonal ZrO2 (t‐ZrO2) solid solutions were prepared with addit ons of 2 mol% Y2O3 plus up to 0.45 mol% Nb2O5. The thermal expansion coefficients in both the a‐ and c‐axis lattice directions increased with Nb2O5 alloying and the thermal expansion in the c‐axis direction was greater than that in the a‐axis direction over the entire composition range. This anisotropic thermal expansion behavior was related to the 4‐fold coordination of Nb5+ with oxygen ions in t‐ZrO2 solid solutions in the system ZrO2–Y2O3–Nb2O5. The fracture toughness continuously increased with Nb2O5 alloying and suggested that the c/a axial ratio is a more significant factor than the internal stress that arises from the thermal expansion anisotropy, in the determination of the transformability of t‐ZrO2 in this system.

Anisotropic thermal expansion characteristics of lead metaniobate ceramics used in the low-liquid level sensors for fuel tanks of space launch vehicles

Low-liquid level sensors are used to monitor the fuel level in fuel tanks of space launch vehicles. These sensors, which are usually bonded to the bottom surface of the tank, are currently made of lead metaniobate ceramic. Lead metaniobate (PbNb2O6) is used because it has very stable piezoelectric behavior and a relatively low dielectric constant (<500). Very limited thermal expansion data, especially in the operating temperature range of the space launch vehicles, exist in the literature. This paper provides thermal expansion data for PbNb2O6 ceramic in both the radial (in-plane) and the thickness (out-of-plane) directions. These results clearly indicate an anisotropic thermal expansion behavior for this ceramic.

Technique for measuring dynamically the dimensional stability of a flexible magnetic storage disk

The tracking ability of a read/write head on a flexible disk is largely determined by the dynamic and dimensional stabilities of the substrate. Dimensional changes are caused by thermal and hygroscopic expansion/contraction as well as time-dependent shrinkage due to stress relaxation. High-performance tracking system design requires knowledge of the substrate expansion characteristics including mean coefficients, anisotropy and anisotropy frequency spectrum. Efforts to study and control these changes require techniques which provide for their rapid and precise measurement. Methods previously employed have proven either coarse or difficult to apply. This paper describes a novel technique which facilitates the rapid collection of relatively precise data on dimensional changes. The technique, which depends upon a magnetic recording surface being present on the substrate, involves a pair of corresponding skewed core gaps in a single head. Magnetic transitions are prerecorded in closely located tracks; subsequent dimensional changes in the substrate are manifested by timing differences in the signals read by the head. Examples of data from several PET films are presented and clearly illustrate their anisotropic thermal and hygroscopic expansion behavior.

Cracking at grain boundaries in polycrystalline brittle materials

The cracking of grain boundary facets in polycrystalline materials showing anisotropic thermal expansion behaviour is controlled by several microstructural factors in addition to the intrinsic thermal and elastic properties. Of specific interest are the relative orientation of the two grains meeting at the facet, and the size of the facet; these factors thus introduce two statistical aspects to the problem. The criteria for facet fracture are critically reviewed. The statistical factors are then introduced to give quantitative data on crack density vs temperature. The theory is compared briefly with limited experimental measurements of Young's modulus for various rocks as a function of temperature.

Degradation of Rocks, Through Cracking Caused by Differential Thermal Expansion, in Relation to Nuclear Waste Repositories

ABSTRACTHeating to temperatures up to 500°C, gives a reduction in Young's modulus and increase in permeability of granitic rocks and it is likely that a major reason is grain boundary cracking. The cracking of grain boundary facets in polycrystalline multiphase materials showing anisotropic thermal expansion behaviour is controlled by several microstructural factors in addition to the intrinsic thermal and elastic properties. Of specific interest are the relative orientations of the two grains meeting at the facet, and the size of the facet; these factors thus introduce two statistical aspects to the problem and these are introduced to give quantitative data on crack density versus temperature. The theory is compared with experimental measurements of Young's modulus and permeability for various rocks as a function of temperature. There is good qualitative agreement, and the additional (mainly microstructural) data required for a quantitative comparison are defined.

Computer simulation of thermal expansion of non-cubic crystals: forsterite, anhydrite and scheelite

The thermal expansion of non-cubic crystal structures may be simulated by a geometric least-squares refinement of the known structure after predicting the thermal expansions of various coordination polyhedra. This method has been applied to forsterite, Mg2SiO4, anhydrite, CaSO4, and scheelite, CaWO4. The expansions of different M-O bonds (M = Mg or Ca) are predicted by using an empirical relationship between the expansion cofficient, α, and bond-strength, s. The expansions of the polyhedral edges are approximated from the changes in the average M-O bond lengths. The rigid tetrahedral groups (SiO4, SO4 or WO4) were assumed to retain their size and shape during the process of thermal expansion. The structural changes are simulated at 300°C for forsterite and at 200°C for anhydrite and scheelite. Calculated changes in the position parameters for forsterite are generally in the same direction as those observed experimentally. The lattice parameters compare well and calculated values of the expansion coefficients along the three crystallographic axes show the same trend as the observed values namely αa < αc < αb. Thermal expansion behavior of anhydrite has been determined experimentally in the temperature range 20-275°C and the structure has been simulated at 200°C. The observed and calculated values of the expansion coefficients agree well; both show that αa > αc >> αb. The calculations on scheelite successfully reveal the characteristic anisotropic thermal expansion behavior of scheelite-type structures, which is αa < αc.