Single-crystal elastic constants of indium
Abstract
The elastic constants of tetragonal indium have been measured by the ultrasonic pulse-echo method. Single crystals were cut so that pulses propagated in the approximate directions [100], [110] and [011] respectively. The nine wave velocities allow the six constants to be determined with three internal checks. If indium is regarded as a tetragonally deformed f.c.c. structure, the constants may be referred to axes coincident with the deformed cubic axes, and in this reference frame the values (expressed in units of 1011 dyne cm2 obtained are: The constants and combinations representing stiffness to shear are low, and are anisotropic in contrast to those for aluminum. The microscopic parameters, particularly those pertaining to overlap electrons, which appear in the calculation of Leigh for aluminum can be adjusted to account for these features of indium.
References (11)
- T.R. Long et al.
Acta Met.
(1957) - R.S. Leigh
Phil. Mag.
(1951) - J.R. Reitz et al.
Phys. Rev.
(1956) - E.V. Vernon et al.
- H.B. Huntington
Phys. Rev.
(1947)
Cited by (26)
In-situ mapping of local orientation and strain in a fully operable infrared sensor
2021, Acta MaterialiaCitation Excerpt :The answer may lie in the In bumps that connect the MCT to the ROIC within the epoxy matrix. It is known that In bumps with tetragonal crystal structure are highly anisotropic in their thermomechanical behavior [27–29]. Lebaudy et al. showed that the thermomechanical response of IR detector can yield notable variations due to random crystallographic orientations of the In bumps [30].
Hybridized focal plane array (FPA) HgCdTe (MCT) sensors are the workhorse of high performance infrared detectors covering a broad range of applications from space investigation to gas monitoring. Despite the improvements in the performance of these sensors in the last decades, device failure due to the lattice and thermal expansion mismatches between MCT and the Si readout circuit still affects the overall MCT detector performance. In this work, we use in-situ dark-field X-ray microscopy (DFXM) to map the structural variations of a fully operable MCT sensor at temperatures down to 80 K. We report, for the first time, on the nanoscale structural evolution over a large population of photodiodes at operating temperatures with high spatial and angular resolution. Our results show that lattice distortion and strain in the MCT epilayer increases at lower temperatures. The FWHM values of the rocking curves reach up to 0.02 at 80 K, three times higher than the room temperature value. The thermal cycle results show that the thermal effects are almost completely reversible and the measured strain is in the elastic regime. We discuss the origin of the temperature-generated structural modifications using complementary finite element modelling.
The mechanical behaviour of a CdHgTe-based infrared detector was evaluated after processing at several temperatures to determine the impact of thermomechanical loading on residual stress and reliability. The architecture of the detector was first entirely characterized, relying on SEM, X-ray microtomography and diffraction analysis, in order to get the nature, the morphology and the crystallographic orientation of all the constitutive layers, and in particular the indium solder bumps. The results notably showed the unexpected single crystal aspect of the indium bumps with a repeatable truncated cone geometry. To obtain the thermomechanical response of the structure after processing and in the range of operating temperatures (from 430 K to 100 K), a 3D Finite Element model was then developed. As expected, the numerical results showed a stress gradient evolution in the structure from high to low temperatures, with high loca njvvl stress around 30 MPa in the CdHgTe at 100 K, mainly due to the thermal expansion coefficient mismatch between the different layers. They highlighted the significant influence of the geometry and the single crystal nature of the bumps as well as the behaviour law of the different materials.
The hydrostatic pressure derivatives of the elastic constants of indium and an indium cadmium alloy
1985, Journal of Physics and Chemistry of SolidsThe hydrostatic pressure derivatives of the elastic stiffness constants of indium and indium-3.4 at.% cadmium alloy single crystals have been obtained from pulse echo overlap measurements of the dependence of ultrasonic wave velocities upon pressure. The softest zone centre acoustic phonon mode in indium is a shear mode propagating k along the [101] direction rather than that (k[110], e[11̄0]) which drives the ferroelastic phase transition in the indium-cadmium alloys. The derivative δ((C11 – C12)/2)/δP is positive, accounting for the stability of the fct structure of indium under high pressure. Using the quasiharmonic, anisotropic continuum model the acoustic mode Grüneisen parameters have been calculated and are discussed in terms of mode softening. The high temperature limiting valueγH (= 2.56) of the mean acoustic mode Grüneisen parameter is found to be close to the thermodynamic Grüneisen parameter γth (=2.5).
An examination of the breakdown in creep by viscous glide in solid solution alloys at high stress levels
1982, Acta MetallurgicaExperiments on Al-3.3 at.% Mg and Al-5.6 at.% Mg at a temperature of 623 K show that the stress exponent, n, increases with increasing stress from 3.0 (class A behavior) to 4.6. There is an essentially random distribution of dislocations in the region with n ∼- 3.0, but there is evidence for subgrain formation in the region with n ∼- 4.6. It is demonstrated that the transition to n ∼- 4.6 is not consistent either with normal power-law breakdown or with a transition to a region of viscous glide controlled by pipe diffusion, but the results are in good agreement with a breakaway of the dislocations from their solute atmospheres. Furthermore, the latter concept is consistent with numerous published observations, including the magnitude of the transition stresses, the nature of the creep curves, the shapes of the transients in stress increase experiments, the values of the effective stress exponent for the dislocation velocity, and the substructural features. It is concluded that viscous glide (class A) occurs in solid solution alloys over a limited range of stresses, and there is a transition to dislocation climb (class M) at both lower and higher stress levels. An equation is presented which specifies the range of normalized stresses for class A behavior.
L'étude des alliages Al-3,3at.%Mg et Al-5,6at.%Mg à 623 K montre que l'exposant de la contrainte n augmente avec la contrainte de 3,0 (comportement de classe A) à 4,6. Les dislocations sont essentiellement réparties de manière aléatoire dans la région où n ∼- 3,0, mais on observe la formation de sous-joints dans la région où n ∼- 4,6. Nous démontrons que la transition à n ∼- 4,6 n'est compatible ni avec une déviation par rapport à la loi normale en puissance, ni avec une transition vers une région de glissement visqueux contrôlé par la diffusion le long des dislocations, mais que les résultats sont en bon accord avec un départ des dislocations leurs atmosphères de soluté. De plus, cette guittant explication est cohérente avec de nombreuses observations plubliées antérieurement, en particulier la grandeur des contraintes de transition, la nature des courbes de fluage, la forme des régimes transitoires dans les expériences d'augmentation de la contrainte, les valeurs de l'exposant de la contrainte effective pour la vitesse des dislocations et les caractéristiques de la sous-structure. Nous en concluons que le glissement visqueux (Classe A) se produit dans une solution solide pour un domaine limité de contraintes et qu'il y a transition vers une montée des dislocations (classe M) tant pour les contraintes inférieures que supérieures. Nous présentons une équation qui précise le domaine des contraintes normalisées pour le comportement de classe A.
Untersuchungen al Al-3,3 At,-% Mg und Al-5,6 At.-% Mg bei 623 K zeigen, daβ der Spannungsexponent n mit ansteigender Spannung von 3,0 (Klasse-A-Verhalten) auf 4,6 zunimmt. Bei n ∼- 3,0 liegt eine im wesentlichen zufällige Verteilung von Versetzungen vor; im Bereich mit n ∼- 4,6 liegen Hinweise auf die Bildung von Subkorngrenzen vor. Der Übergang zu n ∼- 4,6 ist weder verträglich mit dem Zusammenbrechen des normalen Potenzgesetz-kriechens noch mit einem Übergang in einen Bereich viskosen, durch Schlauchdiffusion kontrollierten Kriechens. Die Ergebnisse stimmen mit einem Modell überein, bei dem Versetzungen sich von ihren Verunreinigungswolken lösen. Dieses Modell ist auch verträglich mit vielen veröffentlichten Beobachtungen und schlieβt die Höhe der Übergangsspannung, den Verlauf der Kriechkurven, die Transientenform bei Experimenten mit Aufwärtssprüngen in der Spannung, den Wert des effektiven Spannungsexponenten für die Versetzungsgeschwindigkeit und die Eigenschaften der Substruktur ein. Es wird gefolgert, daβ viskose Gleitung (Klasse A) in Mischkristall-Legierungen in einem begrenzten Spannungsbereich und ein Übergang zum Versetzungsklettern (Klasse M) sowohl bei höherer als auch niedriger Spannung auftreten. Es wird eine Gleichung angegeben, die den normalisierten Spannungsbereich des Klasse-A-Verhaltens beschreibt.
Elastic constants of single crystals of the three phases of InPb alloys
1979, Journal of Physics and Chemistry of SolidsIn a study of the elastic behaviour of the InPb alloys, the elastic stiffness tensor components of crystals of each of the three phases (fct, ; fct, ; fcc) have been obtained as a function of temperature from pulse superposition measurements of ultrasonic wave velocities. Comparison of the elastic stiffness constants obtained for a fct () 5 atm.% Pb alloy with those of In itself and those of InTl and InCd alloys, establishes for this phase that alloying with Pb, as with TI and Cd, enhances the softening of the acoustic [110] phonon mode, polarization [10] near the Brillouin zone centre. The elastic properties of a 17 atm.% Pb crystal, which is in the fct () phase, are quite different from those shown by In alloys in the fct ( phase; in particular the response to a shear stress is remarkably isotropie: there is no phonon mode softening in this alloy. Neither is there softening of this mode (which corresponds at the zone centre to the shear stiffness (C11;C12)) in crystals of the fee phase — in complete contrast to the dominating influence of the softening of (C11;C12) in the InTl and InCd fee alloys. In fact for a fcc In-75 atm.% Pb alloy the anistropy ratio for shear is close to unity. The transitions between the three phases of the InPb alloys are markedly first order and acoustic mode softening has a much smaller influence on the elastic behaviour of the fct () and fcc InPb alloys than it has on the fct () InPb, InCd and InTl alloys.
The elastic constants for single-crystal lead and indium from room temperature to the melting point
1977, Journal of Physics and Chemistry of SolidsThe adiabatic elastic stiffness constants of indium and lead were measured from room temperature to their respective melting points using the ultrasonic pulse-echo method. The average temperature derivatives at constant pressure, , for the indium constants are: in units of 1010dyne cm−2deg−1, and are referred to axes coincident with those of the face-centered tetragonal unit cell. The average temperature derivatives at constant pressure for the lead elastic constants are, in the same units, The elastic anisotropies of both lead and indium increase markedly with increasing temperature.
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Now at the National Carbon Research Laboratories, Parma, Ohio.