Mean Linear Thermal Expansion Coefficients Research Articles

Research on the thermal expansion of AgGa1−xInxSe2 single crystals

Thermal expansion coefficients of AgGa1−xInxSe2 (x = 0.2, 0.3, 0.4) single crystals have been measured in the range from 323K to 823K. The values of αa are positive and increase with temperature whereas the values of αc are negative and their absolute magnitudes increase with the increasing temperature for different x. With the increase of x, thermal expansion coefficients αa and αc both decrease numerically. The mean linear thermal expansion coefficient αL and the anisotropy of thermal expansion αη have been calculated, and they are also decreasing numerically with the increasing x. The slope of the straight line αhkl versus cos2ϕ decreases as x increases at 473K and 773K, respectively. According to the variation of thermal expansion coefficients, the relationship between the thermal expansion coefficient, bond length, and melting point of AgGa1−xInxSe2 satisfies the equation αL=0.021Tm−B(d−d0)3. In addition, the mechanism of thermal expansion variation has been discussed in terms of crystal structure, bond lengths, and thermal vibration of bonds in AgGa1−xInxSe2 single crystals.

Thermal expansion characteristics of Fe–9Cr–0.12C–0.56Mn–0.24V–1.38W–0.06Ta (wt.%) reduced activation ferritic–martensitic steel

The lattice and bulk thermal expansion behavior of an Indian version of reduced activation ferritic–martensitic (INRAFM) steel has been quantified using high temperature X-ray diffraction and dilatometry. The lattice parameter of tempered α-ferrite phase exhibited a smooth quadratic increase with temperature, while that of γ-austenite remained fairly linear up to 1273K. The results suggest that α-ferrite+Carbides→γ-austenite transformation occurs upon continuous heating in the temperature range, 1146⩽T⩽1173K. Further, this transformation is found to be accompanied by a reduction in average atomic volume. The mean linear thermal expansion coefficients of tempered α-ferrite and γ-austenite phases are estimated to be about 1.48×10−5 and 2.4×10−5K−1 respectively. The magnetic contribution to relative thermal dilatation (Δl/l298)mag is found to be small and negative, as compared to phonon contribution.

Phase transition and thermal expansion studies of alumina thin films prepared by reactive pulsed laser deposition.

Aluminium oxide (Al2O3) thin films were deposited on Si (100) substrates at an optimized oxygen partial pressure of 3 x 10(-3) mbar at room temperature by pulsed laser deposition (PLD). The films were characterized by high temperature X-ray diffraction (HTXRD), field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). The HTXRD pattern showed the cubic y-Al2O3 phase in the temperature range 300-973 K. At temperatures ≥ 1073 K, the δ and θ-phases of Al2O3 were observed. The mean linear thermal expansion coefficient and volume thermal expansion coefficient of γ-Al2O3 was found to be 12.66 x 10(-6) K(-1) and 38.87 x 10(-6) K(-1) in the temperature range 300 K-1073 K. The field emission scanning electron microscopy revealed a smooth and structureless morphology of the films deposited on Si (100). The atomic force microscopy study indicated the increased crystallinity and surface roughness of the films after annealing at high temperature.

Study on Dependability and Repeatability of Measurement Method of Mean Linear Thermal Expansion Coefficients of Glasses

Coefficient of mean linear thermal expansion is an important physical property of glasses. It is the key thermodynamic property to evaluate the thermal stability and matching sealing of glasses. The measurement results of coefficient of mean linear thermal expansion obtained by different dilatometers showed that glass expands slowly with nonlinearity below 50 °C. It suggested that the initial temperature of measurement would be set above 50 °C, as behaves better repeatability and reliability of measurement than 20 °C as standard method set.

Study of Al2O3/ZrO2 (5 nm/20nm) Nanolaminate Composite

ABSTRACT A nanolaminate consisting of alternate layers of aluminium oxide (Al 2 O 3 ) (5 nm) and zirconium oxide (ZrO 2 ) (20 nm) was deposited at an optimized oxygen partial pressure of 3×10 -2 mbar by pulsed laser deposition. The nanolaminate film was analysed using high temperature X-ray diffraction (HTXRD) to study phase transition and thermal expansion behaviour. The surface morphology was investigated using field emission scanning electron microscopy (FE-SEM). High temperature X-ray diffraction indicated the crystallization temperature of tetragonal zirconia in the Al 2 O 3 /ZrO 2 multilayer -film was 873 K. The mean linear thermal expansion coefficient of tetragonal ZrO 2 was 4.7×10 -6 K -1 along a axis, while it was 13.68×10 -6 K -1 along c axis in the temperature range 873-1373 K. The alumina was in amorphous nature. The FESEM studies showed the formation of uniform crystallites of zirconia with dense surface. Key Words : Thin films, Ceramic, Composites, Multilayers, Alumina and zirconia, Thermal expansion

Thermal behavior of afghanite, an ABABACAC member of the cancrinite group

Thermal behavior of afghanite, (Na15K5Ca11)Σ31[Si24Al24O96](SO4)6Cl6, P31c, a = 12.7961(7) Å, c = 21.4094(13) Å, an eight-layer member of the cancrinite group, has been investigated by combined electron microprobe analysis, X-ray single-crystal diffraction, and high-temperature X-ray powder diffraction. Non-ambient X-ray powder diffraction data were collected in the 323-1223 K thermal range on a specimen from Case Collina, Latium, Italy. Structural refinement and site assignment based on the bond-valence analysis, performed on room-temperature single-crystal X-ray diffraction data, provided more accurate site allocation of cations than the available model in the literature. The results show that the cancrinite cages alternating with the liottite cages are more compressed along the c-axis than the remaining ones. As a result the chlorine atom, located at the center of the cages, is driven off-axis to release the steric strain due to the cage compression. Thermal expansion shows a discontinuity at 448 K for both a and c unit-cell parameters, a feature previously reported for other cancrinite-like minerals. Up to 448 K, the c-parameter expands significantly and more than the aparameter. A further discontinuity has been detected at 1073 K for the c-parameter. Mean linear and volume thermal expansion coefficients (×10-6 K-1) in the 323 < T < 448 K thermal range are ᾱa = 12.9(4), ᾱc = 17.9(9), and ᾱV = 43.7(18). Above this discontinuity temperature, the thermal expansion is reverted becoming greater for the a-parameter. Mean linear and volume thermal expansion coefficients in the 448 < T < 1073 K thermal range are ᾱc = 8.22(3), ᾱc = 3.52(4), and ᾱV = 19.68(8). In the 1073 < T < 1223 K thermal range the values are ᾱa = 6.35(9), ᾱc = 5.02(14), and ᾱV = 17.74(9). Afghanite shows a significant microstrain at RT that increases up to ca. 700 K and subsequently decreases as a function of T. Cooling to RT allows a significantly release of ε0 microstrain, which is coupled with a significant expansion of the c-parameter as compared to the starting RT data. The expansion of the c-parameter has been mainly attributed to the full expansion of the cancrinite cages alternating with the liottite cages. Upon reheating at 1173 K, the microstrain increases back to approximately the same value calculated for the first heating process. Repeated heating-RT-cooling cycles led to the partial afghanite structure disruption and the partial conversion, via an intermediate disordered phase, to haüyne. As repeated heating/cooling cycles did not modify the ε0 values both at RT and at HT, it can therefore be concluded that the strain release occurs prevalently during the first heating/cooling cycle.

Thermophysical properties of hafnium titanate

Heat capacity and lattice thermal expansion of hafnium titanate (HfTiO4) have been studied by differential scanning calorimeter (DSC) and high temperature X-ray diffraction technique (HT-XRD) in the temperature range 298–800K and 298–1973K respectively. From the heat capacity data, other thermodynamic functions such as enthalpy, entropy and Gibbs energy functions were computed. Percentage linear thermal expansion and mean linear thermal expansion coefficients were computed from the lattice parameter data. The thermal expansion of HfTiO4 was found to be anisotropic. The lattice parameters at 298K viz., a, b and c axes are 0.5042, 0.5579 and 0.4732nm respectively. The expansivity along the ‘a’ axis was found to be larger than the expansivity along ‘b’ and ‘c’ axes. The lattice was found to contract along b-axis below 1073K. The heat capacity of HfTiO4 at 298K was found to be121.4JK−1mol−1. The percentage linear thermal expansion in the temperature range 298–1973K along a, b and c axes are 2.74, 0.91 and 1.817 respectively.

Thermal Behavior of Celsian Ceramics Synthesized from Coal Fly Ash

ABSTRACTCelsian with a chemical composition of Ba0.75Sr0.25Al2Si2O8, is synthesized by using coal fly ash (byproduct of a Mexican coal-burning power plant, composed mainly by SiO2 and Al2O3) as main raw material. The thermal behavior of the synthesized material is evaluated by differential (DTA) and gravimetric (TGA) thermal analyses as well as by heating microscopy; its coefficient of linear thermal expansion (CTE) is also determined. Heating microscopy shows that cylinders of compacted powdered Celsian start sintering at ∼1140 ºC, which is associated with a considerable contraction occurring up to 1500 ºC. The mean CTE value of the material in the temperature range of 30-1100ºC is slightly affected by the synthesis conditions employed. Synthesis at 1400 or 1300 ºC during 10 h, with a pre-calcination step at 900 ºC/5h in both cases, produce mean CTE values of 5.15 x 10-6 and 5.43 x 10-6 ºC-1, respectively. On the other hand, Celsian synthesized at 1400 ºC/10 h, without the pre-calcination step, has a mean CTE value of 5.25 x 10-6 ºC-1. Lastly, the DTA/TGA analysis of the synthesized material shows that a slight weight gain takes place from room temperature to 1100ºC, which is followed by a slight weight loss up to 1300ºC. This is attributed to oxidation and evaporation of some of the impurities present in the material.

Aluminium‐silicon alloy and its composites reinforces by silicon carbide particles

PurposeThe purpose of this paper is to investigate the effect of SiC addition up to 60 percent SiC on the mechanical properties and thermal expansion of Al‐7vol.% Si/SiC composites.Design/methodology/approachComposite specimens containing 7, 15, 30, 45 and 60 vol.% SiCp are fabricated by pressureless infiltration technique. The obtained metal‐matrix composites (MMCs) then are characterized for density, porosity, microhardness, ductility, and coefficients of thermal expansion (CTE).FindingsThe results show that the composite specimens have very low‐porosity volumes. Moreover, it is found that silicon carbide particles are distributed uniformly in the matrix. Both porosity and mean linear CTE of the composites decreases with silicon carbide volume fraction. However, higher amount of SiCp reinforcement content tends to increase density, microhardness and improve ductility.Originality/valueThe processing employed in this paper would enable realization of electronic packages made out of Al‐Si/SiCp MMCs.

Synthesis, characterization and thermal expansion studies on ThO 2–SmO 1.5 solid solutions

Highly homogeneous Th 1− x Sm x O 2; 0 ≤ x ≤ 0.8 solid solutions were synthesized by a co-precipitation technique and the co-precipitated samples were sintered at 1473 K. Compositions of the solid solutions were characterized by standard wet-chemical analysis. X-ray diffraction measurements were performed on the sintered pellets for structural analysis, lattice parameter calculation and determination of solid solubility of SmO 1.5 in ThO 2 matrix. Bulk and theoretical densities of solid solutions were also determined. A fluorite structure was observed for ThO 2–SmO 1.5 solid solutions with 0–55.2 mol% SmO 1.5. Thermal expansion coefficients were measured using high temperature X-ray diffraction technique. The mean linear thermal expansivity, α ¯ m for ThO 2–SmO 1.5 solid solutions containing 17.9, 41.7 and 52.0 mol% of SmO 1.5 were determined in the temperature range 298–2000 K for the first time. The mean linear thermal expansion coefficients for ThO 2–SmO 1.5 solid solutions are 10.47, 11.16 and 11.45 × 10 −6 K −1, respectively.

Ultra-high thermal expansion glass–ceramics in the system MgO/Al2O3/TiO2/ZrO2/SiO2 by volume crystallization of cristobalite

Glasses in the system MgO/Al 2 O 3 /TiO 2 /ZrO 2 /SiO 2 with and without the addition of As 2 O 3 and Sb 2 O 3 were thermally treated. Up to a temperature of 950 °C, this resulted in the formation of ZrTiO 4 , sapphirine and high quartz solid solution. Annealing at higher temperatures led to the formation of low quartz solid solutions, ZrTiO 4 and sapphirine. This resulted in a continuous increase of density, hardness, fracture toughness and thermal expansivity. In the glass doped with As 2 O 5 and Sb 2 O 5 annealing temperatures >1000 °C resulted in the formation of cristobalite instead of quartz. Then the density, hardness and strength decreased again, while the fracture toughness (up to 2.8 MPa m 1/2 ) and the thermal expansion coefficient increased strongly. In the dilatometric curves, a steep increase in expansion is observed in the temperature range from 100 to 200 °C, which is attributed to the transformation of low cristobalite to high cristobalite. The mean linear thermal expansion coefficient (25–200 °C) is 20 × 10 −6 K −1 and the largest up to now reported in the literature for alkali-free silicate glass–ceramics.

Synthesis, characterization and thermal expansion studies on europium titanate (Eu 2TiO 5)

The lattice thermal expansion characteristics of europium titanate (Eu 2TiO 5) have been studied by measuring the lattice parameter by high temperature X-ray diffraction technique (HT-XRD) in the temperature range 298–1573 K. Percentage linear thermal expansion and mean linear thermal expansion coefficients were computed from the lattice parameter data. The percentage linear thermal expansion in the temperature range 298–1573 K along a, b and c axes are 1.05, 1.15 and 0.95 respectively.

Structural change of oxide-ion-conducting lanthanum silicate on heating from 295 to 1073 K

Structural change of La 9.33(SiO 4) 6O 2 on heating from 295 to 1073 K was investigated by means of high-temperature laboratory X-ray powder diffraction (Cu Kα 1). The apatite-type crystal structures (space group P6 3/ m) were refined by the Rietveld method, with the anisotropic displacement parameters being assigned for all atoms. The validity of the structural models was verified by the three-dimensional electron density distribution, the structural bias of which was reduced as much as possible using the maximum-entropy methods-based pattern fitting method. Each crystal structure was composed of the three types of polyhedra, LaO 9, LaO 7 and SiO 4. With increasing temperature the La 9.33(SiO 4) 6O 2 crystal, together with the isotypic crystal of Nd 9.33(SiO 4) 6O 2, harmoniously and steadily expanded, with the mean linear thermal expansion coefficient of 9.4(1) × 10 − 6 K − 1 . On the other hand, the thermal expansion behaviors of the coordination polyhedra are different, in particular, between LaO 9 and NdO 9. The thermal motions of O2 atoms at high temperatures showed significant difference between the two materials, which would lead to the different thermal motions of the rigid SiO 4 groups. This could correlate with the high oxide-ion conductivity of La 9.33(SiO 4) 6O 2.

Thermal expansion of polyurethane foam at low temperature

The mean linear thermal expansion coefficient of a newly developed polyurethane foam with a blowing agent of HFC245fa was measured from the liquid nitrogen temperature to room temperature by means of a relative comparison method in this paper. An automatic temperature measuring system, a vacuum system and an electrical heating system were adopted in the experiment. The relative comparison method has been analyzed, and according to the Kelvin model, a model describing thermal expansion of the foams was introduced. A very low thermal expansion with a slowly increasing trend versus temperature rising from 77 K to 230 K was shown in the result. In addition, it was indicated that the thermal expansion rate along a direction perpendicular to the pore rise is a bit higher than that along a parallel direction.

Studies on lattice thermal expansion and XPS of ThO 2[sbnd]NdO 1.5 solid solutions

The lattice parameter changes with respect to temperature ( T) have been measured by high temperature X-ray diffraction (HTXRD) technique for ThO 2 NdO 1.5 solid solutions containing 23.8 and 42.5 mol% NdO 1.5 in the temperature range from 298 to 2000 K. The temperature versus lattice parameter data have been made use of in calculating the lattice thermal expansivity. The values of thermal expansion of the solid solutions were found to be increased with increase in neodymium oxide content and temperature. The mean linear thermal expansion coefficients in this temperature range for ThO 2 NdO 1.5 solid solutions are 12.28 × 10 −6 and 12.90 × 10 −6 K −1, respectively. The binding energies of Th 4f 7/2 and Nd 3d 5/2 energy levels of the solid solutions containing 13.1, 23.8, 31.9, 37.2 and 42.5 mol% NdO 1.5 and two-phase mixtures containing 47.6 and 51.8 mol% NdO 1.5 were experimentally determined by X-ray photoelectron spectroscopy (XPS).

Thermal property characterization of a titanium modified austenitic stainless steel (alloy D9)

The temperature dependence of lattice parameter and enthalpy increment of alloy D9, a titanium modified nuclear grade austenitic stainless steel were studied using high temperature X-ray diffraction and inverse drop calorimetry techniques, respectively. A smooth variation of the lattice parameter of the austenite with temperature was found. The instantaneous and mean linear thermal expansion coefficients at 1350 K were estimated to be 2.12 × 10 −5 K −1 and 1.72 × 10 −5 K −1, respectively. The measured enthalpy data were made use of in estimating heat capacity, entropy and Gibbs energy values. The estimated isobaric heat capacity C p at 298 K was found to be 406 J kg −1 K −1. An integrated theoretical analysis of the thermal expansion and enthalpy data was performed to obtain approximate values of bulk modulus as a function of temperature.

A study on ThO 2–LaO 1.5 solid solution: Lattice thermal expansion measurements and XPS studies

The lattice thermal expansion characteristics of ThO 2–LaO 1.5 solid solutions containing 18.5 and 47.6 mol% LaO 1.5 were determined in the temperature range 298–1600 K by high temperature X-ray diffraction. The mean linear thermal expansion coefficients in this temperature range, for ThO 2–LaO 1.5 solid solutions are (11.89 and 14.09) × 10 −6 K −1, respectively. The binding energies of Th 4f 7/2 and La 3d 5/2 energy levels of the solid solutions containing 12.9, 18.5, 27.9, 40.2, 47.6 and 50.3 mol% LaO 1.5 were experimentally determined by X-ray photoelectron spectroscopy. These results suggested the presence of Th 4+ and La 3+ chemical states in the stoichiometric ThO 2–LaO 1.5 solid solutions.

Thermophysical measurements on dysprosium and gadolinium titanates

Dysprosium and gadolinium titanates were prepared by the solid state route and by the wet chemical route. The compounds were characterized using inductively coupled plasma mass spectrometry (ICPMS) and X-ray diffraction (XRD) techniques. Their thermal expansion coefficients were measured using high temperature X-ray diffraction technique. The quasi-isotropic mean linear thermal expansion coefficient α ̄ m of Dy 2TiO 5 and Gd 2TiO 5 at room temperature are 6.55 × 10 −6 and 6.56 × 10 −6 K −1, respectively, and in the temperature range 298–1573 K are 1.006 × 10 −5 and 1.023 × 10 −5 K −1, respectively. Heat capacity measurements were carried out in the temperature range 320–820 K using differential scanning calorimetry. From the polynomial fit the C p,298 of Dy 2TiO 5 and Gd 2TiO 5 have been computed to be 178.26 and 168.61 J K −1 mol −1, respectively.

Thermal expansion studies on Inconel-600 ® by high temperature X-ray diffraction

The lattice thermal expansion characteristics of Inconel-600 ® have been studied by high temperature X-ray diffraction (HT-XRD) technique in the temperature range 298–1200 K. Altogether four experimental runs were conducted on thin foils of about 75–100 μm thickness. The diffraction profiles have been accurately calibrated to offset the shift in 2 θ values introduced by sample buckling at elevated temperatures. The corrected lattice parameter data have been used to estimate the instantaneous and mean linear thermal expansion coefficients as a function of temperature. The thermal expansion values estimated in the present study show a fair degree of agreement with other existing dilatometer based bulk thermal expansion estimates. The lattice parameter for this alloy at 300 K is found to be 0.3549(1) nm. The mean linear thermal expansivity is found to be 11.4 × 10 −6 K −1.

Anisotropic thermal expansion in yttrium silicate

In this study, crystals of Y2SiO5 were examined by high-temperature powder x-ray diffractometry to determine the changes in unit-cell dimensions with temperatures up to 1273 K for the X1 phase (the low-temperature phase, space group P121/c1) and 1473 K for the X2 phase (the high-temperature phase, space group I12/a1). The lattice deformations of both phases induced by thermal expansion were investigated by matrix algebra analysis to determine the directions and magnitudes of the principal distortions (λi, i = 1, 2, and 3). For the X1 phase, λ1 and λ2 invariably showed a positive thermal expansion. On the other hand, λ3 showed a negative thermal expansion below 1173 K; the maximum contraction of 0.10(4)% occurred at 685 K. The λ2 axis invariably coincides with the crystallographic b axis. The directions of λ1 and λ3, defined by the acute angle λ3 ^ c changed between 53(3)° (T = 394 K) and 45(1)° (T = 788 K). For the X2 phase, all of the principal distortions steadily increased with increasing temperature. The angle λ3 ^ c steadily decreased from 71(2)° to 62.1(1)° with increasing temperature. The mean linear thermal expansion coefficients were, when compared at the same temperatures, necessarily higher for the X1 phase than for the X2 phase. The lattice change of X1–RE2SiO5 (RE = Y and Yb–La), which was induced by the substitution of rare-earth (RE) ions, showed a striking resemblance with the lattice deformation of X1-Y2SiO5, which was caused by the thermal expansion. Because the lattice change of the former must be caused by the isotropic expansion of the RE sites, the anisotropic thermal expansion of the latter would be essentially attributable to the isotropic thermal expansion of the YO9 and YO7 polyhedron.