Precision measurements of thermoacoustics in a single pore

Abstract: Continuing experiments designed to look at therrnoacoustic effects in a single pore will be described. A volume-modulation technique is employed to measure the complex compressibility of a gas in the pore directly. When a temperature gradient is imposed on the pore, the complex compressibility is sensitive to thermoacoustic effects which can be measured to high precision. These effects depend on both thermal and viscous properties of the gas. Measurements for a wide range of gradients are presented and compared to predictions of the theory. Generally good qualitative agreement is found. The technique can easily be extended to study novel stack geometries such as those with varying cross section or with tailored temperature gradients

Magnetostriction and elasticity of body centered cubic Fe100−xBex alloys

Magnetostriction measurements from 77 K to room temperature on oriented (100) and (110) disk samples of Fe93.9Be6.1 and Fe88.7Be11.3 reveal substantial increases in λ100compared to iron. For the 11.3% alloy, λ100=110 ppm, a sixfold increase above that of α-Fe. For the 6.1% alloy, λ100=81 ppm, ∼40% and ∼170% greater than λ100 of comparable Fe–Ga and Fe–Al alloys, respectively, for H=15 kOe. Large differences exist between the values of λ100 and λ111 (λ100\u3e0, λ111\u3c0) and their temperature dependencies. Elastic constants, c11, c12, and c44, from 4 to 300 K were obtained on the same Fe–Be alloys. From these measurements, the magnetoelastic energy coefficients b1 and b2 were calculated. While the magnitudes of the magnetostrictions λ100 and λ111 are widely different, the magnitudes of b1 and b2 are within a factor of 2. The Fe–Be alloys are highly anisotropic magnetostrictively, elastically, and magnetoelastically. For Fe88.7Be11.3 at room temperature λ100/λ111, 2c44/(c11−c12), and b1/b2 are −6.6, 3.55, and −1.86, respectively

Magnetostrictive and elastic properties of Fe100−xMox (2

In this paper we investigate the magnetostrictive [(3/2)λ100 and (3/2)λ111] and elastic (c′and c44) behavior of single crystalline alloys Fe100−xMox for 21 and −b2) are computed from the measurements. Similar to other Fe–X (X = Al, Ga, and Ge) alloys, the tetragonal magnetostriction (3/2)λ100 increases monotonically from ∼ 70×10−6 at ∼ 2.5 at. % Mo to a maximum of either ∼ 100×10−6 at ∼ 8 at. % Mo for the slow cooled crystals or ∼ 125×10−6 at ∼ 11 at. % Mo for quenched crystals. A sharp decrease after the peak is observed for the slow cooled crystals due to the formation of a second phase. The rhombohedral magnetostriction (3/2)λ111 of the Fe–Mo alloys is found to be insensitive to the Mo content. This behavior is distinctly different from other Fe–X (X = Al, Ga, and Ge) alloys where a slight decrease in magnitude and a sign reversal upon chemical ordering was observed for (3/2)λ111. Both shear elastic constants (c′ and c44) for Fe–Mo are remarkably insensitive to the Mo content, which is also distinct from the other Fe-based alloys used in the comparison. The two magnetoelastic coupling constants −b1 = 3λ100c′ (with values from 7.15 to 9.77 MJ/m3) and −b2 = 3λ111c44 (with values from −4.96 to −5.81 MJ/m3) were calculated and compared with those of other Fe–X (X = Al, Ga, and Ge) alloys

Magnetoelastic coupling in Fe100−xGex single crystals with 4

In this paper we examine the elastic (c′ and c44) and magnetostrictive (λ100 and λ111) behaviors of Fe100−xGex for 4\u3cx\u3c18, quantities used further to find the fundamental magnetoelastic coupling constants b1 and b2 at room temperature. The x dependence ofb1 and b2 for Fe100−xGex is contrasted to those of Fe100−xGax and Fe100−xAlx. While the rhombohedral shear elastic constant c44 is almost insensitive to the type and amount of solute, the tetragonal shear constant c′ shows a pronounced and rapid softening with increasing x for all three alloys but with different decreasing slopes. Similarly, while the rhombohedral magnetostriction λ111 behavior is analogous for all three alloy systems, showing a sign change from negative to positive at the onset of chemical order, the tetragonal magnetostriction λ100 behavior differs. For the Ga and Al alloys, λ100 maintains positive values over the entire x range, both curves showing large peak values, whereasλ100 of Fe100−xGex exhibits a moderate positive peak followed by a negative dip, both of comparable magnitude. Finally the tetragonal coupling constant −b1 of Fe–Ge shows a marked, sharp decrease as chemical order occurs at x ∼ 12 at. % Ge. The decline continues until the ordered D03 phase is fully established at x ∼ 18 at. % Ge. The peak value of |b1| for Fe–Ge is approximately half of those for Fe–Ga and Fe–Al. This smaller value of |b1|, obtained for the higher electron concentration Ge alloy, is consistent with predictions based on band structure calculations. The rhombohedral coupling constant−b2 shows a consistent sign change at the occurrence of chemical ordering in both Fe–Ga and Fe–Ge

The effect of partial substitution of Ge for Ga on the elastic and magnetoelastic properties of Fe–Ga alloys

Both components of the tetragonal magnetoelastic constant b1: the saturation magnetostriction, λγ,2 = (3/2)λ100, and the magnetic-field saturated shear elasticity, c′ = (c11−c12)/2, were investigated over a wide temperature range for the magnetostrictiveFe1−x−yGaxGey alloys, (x+y ≅ 0.125, 0.185, and 0.245; x/y ≅ 1 and 3). The magnetostriction was measured from 77 to 425 K using standard strain gage techniques. Both shear elastic constants (c′ and c44) were measured from 5 to 300 K using resonant ultrasound spectroscopy. Six alloy compositions were prepared to cover three important regions: (I) the disordered solute α-Fe region, (II) a richer solute region containing both disordered and ordered phases, and (III) a rich solute region containing ordered multiphases. Our observations reveal that, when the data is presented versus the total electron/atom (e/a) ratio, the above regions for both the ternary and binary alloys are in almost perfect alignment. Following this analysis, we find that the magnetoelastic coupling, b1, peaks for both the binary and the ternary alloys at e/a ∼ 1.35. The values of c′ as well as of λγ,2 in region I of the ternary alloys, when plotted versus e/a, fall appropriately between the binary limits

Magnetic field dependence of galfenol elastic properties

Elastic shear moduli measurements on Fe100−xGax (x = 12–33) single crystals (via resonant ultrasound spectroscopy) with and without a magnetic field and within 4–300 K are reported. The pronounced softening of the tetragonal shear modulus c′ is concluded to be, based on magnetoelastic coupling, the cause of the second peak in the tetragonal magnetostriction constant λ100 near x = 28. Exceedingly high ΔE effects ( ∼ 25%), combined with the extreme softness in c′ (c′\u3c10 GPa), suggest structural changes take place, yet, gradual in nature, as the moduli show a smooth dependence on Ga concentration, temperature, and magnetic field. Shear anisotropy (c44/c′) as high as 14.7 was observed for Fe71.2Ga28.8

Magnetostriction, elasticity, and D03 phase stability in Fe–Ga and Fe–Ga–Ge alloys

The contrast between the saturation tetragonal magnetostriction, λγ,2 = (3/2)λ100, of Fe1−xGax and Fe1−yGey, at compositions where both alloys exhibit D03 cubic symmetry (second peak region), was investigated. This region corresponds to x = 28 at. % Ga and y = 18 at. % Ge or, in terms of e/a = 2 x + 3 y + 1, to an e/a value of ∼1.55 for each of the alloys. Single crystal, slow-cooled, ternary Fe1−x−y GaxGey alloys with e/a ∼1.55 and gradually increasing y/x were investigated experimentally (magnetostriction, elasticity, powder XRD) and theoretically (density functional calculations). It was found that a small amount of Ge (y = 1.3) replacing Ga in the Fe–Ga alloy has a profound effect on the measured λγ,2. As y increases, the drop in λγ,2 is considerable, reaching negative values at y/x = 0.47. The two shear elastic constants c′ = (c11− c12)/2 and c44 measured for four compositions with 0.06 ≤ y/x ≤ 0.45 at 7 K range from 16 to 21 GPa and from 133 to 138 GPa, respectively. Large temperature dependence was observed for c′ but not for c44, a trend seen in other high-solute Fe alloys. The XRD analysis shows that the metastable D03 structure, observed previously in slow-cooled Fe–Ga at e/a = 1.55, is replaced with two phases, fcc L12 and hexagonal D019, at just 1.6 at. % Ge. The two are the stablephases of the assessed Fe–Ga phase diagram at x ∼ 28. Notably, at y = 7.8, only the D03phase (the equilibrium phase of Fe–Ge at e/a = 1.54) was found in the ternary alloy. The theory also shows that the D03 instability is removed for compositions with y ≥ 3.9, when D03 becomes the structure’s ground-state phase. Thus, the high, positive λγ,2 value for Fe–Ga at x = 28 could be the result of the high sensitivity of its metastable D03 structure