Charles S. Smith

Low temperature thermal expansion of RbI

Abstract An X-ray method has been used to measure the thermal expansion at low temperature of RbI, and to verify the results of White for KCl. For these alkali halides, and for NaCl, the low temperature values of the Gruneisen parameter, γ = βVBs/Cp have been shown to agree with values \ ggLobtained from the pressure variation of the elastic constants by means of a computer program. The elastic constant C44 measures the lowest shear stiffness in these crystals, and because it decreases with pressure for RbI and KCl, the thermal expansion γ varies widely from a low value γL, at low temperatures to a much higher value γH at high temperatures. The variation is much less for NaCl for which dC44/dP is positive.

Ultrasonic equation of state of iron: I. Low pressure, room temperature

Abstract The single crystal elastic constants of iron and their pressure variation to 3.6 kbar have been measured at room temperature by the ultrasonic pulse-echo technique. The result is expressed as the equation of state, − ΔV V 0 = 6.098 × 10 −7 P − 1.29 × 10 −12 P 2 (pressure in bars), which is compared with the 1940, 30 kbar, absolute compression determination of Bridgman, − ΔV V 0 = 5.941 × 10 −7 P − 0.83 × 10 −12 P 2 . Compression data to 30 kbar for other solids that were measured differentially with respect to iron are reconciled in both the first and second degree coefficients if these are corrected for the ultrasonic coefficients of iron. The correction is especially important for the second degree term and for incompressible materials.

The elastic constants of copper alloys

Abstract The elastic constants of single crystals of dilute solutions of Al, Si, Zn, Ga and Ge in Cu have been determined by the ultrasonic pulse method. Alloying causes a decrease in all the fundamental constants, C44, (C 11 −C 12 ) 2 and (C 11 +2C 12 ) 3 , the relative decrease in (C 11 − C 12 ) 2 being the greatest. The changes in shear constants C44 and (C 11 − C 12 ) 2 have been interpreted in terms of the known electrostatic and ionic contributions to these constants for copper. The large decrease in (C 11 − C 12 ) 2 is attributed to the change in ion-ion interactions, upon alloying. The electrostatic shear stiffness of an alloy is found to be nearly equal to the electrostatic term for copper times the square of the electron atom ratio.

Single-crystal elastic constants of lithium

Abstract The elastic constants of single-crystal lithium have been measured by the ultrasonic pulse-echo technique. The results, in units of 10 11 dyn cm −2 , are Temperature(°K) C 44 ( C 11− C 11 )/2 B 3 78 1.08 0.116 1.33 155 1.00 0.111 1.25 195 0.96 0.109 1.20 where B 3 is the adiabatic bulk modulus. These results are compared with fuchss theoretical calculation of the Coulomb contribution to the shear stiffness of the alkali metals, which in lithium is the only significant contribution. Extrapolation of the experimental values to absolute zero gives values for both C 44 and ( C 11 − C 12 )/2 which are lower than the corresponding theoretical values. The extrapolated anisotropy, C 44 ( C 11 − C 12 )/2, is higher than the value predicted by the theory.

Single crystal elastic constants of silver and silver alloys

Abstract The elastic constants of single crystals of silver and of dilute alloys of Mg, Zn, Pd, Cd, In, and Sn in silver have been measured by the ultrasonic pulse-echo method. For all solutes except Pd, there is a large fractional decrease, upon alloying, in the shear constant (C 11 -C 12 ) 2 , and a relatively small decrease in C 44 . This result has been interpreted as indicating a decrease in the short-range crystal forces, because of a local weakening of nearest-neighbor repulsive bonds, and an increase in the long-range electrostatic forces, because of the increase in the average ion-core charge. The two shear constants increase upon alloying with Pd, and a similar interpretation is not inconsistent with this result.

Single-crystal elastic constants of magnesium and magnesium alloys

Abstract The adiabatic elastic constants of single crystals of magnesium and dilute alloys of magnesium with Ag, In, and Sn have been measured by the ultrasonic pulse-echo technique. The values obtained for pure magnesium are: C 11 = 0.597, C 33 = 0.617, C 44 = 0.164, C 12 = 0.262, C 13 = 0.217, all expressed in units of 10 12 dyne cm −2 . The alloy results show that within the experimental uncertainty all constants exhibit a smooth behavior as the electron concentration is increased to 2.020 per atom, through the critical region where zone overlap is thought to occur in the c direction. At most, a small change in slope could be read into the data for C 11 + 2 C 33 + C 12 − 4 C 13 at the critical electron atom ratio of 2.01. This behavior is in contrast to what might be expected from an extension of Leighs predictions for the elastic constants of aluminium alloys.

Elastic constants of lithium-magnesium alloys

The single crystal elastic constants of dilute lithium-magnesium alloys were measured using the ultrasonic pulse-echo technique. In terms of d ln Cdx, all fundamental elastic constants increase with composition by the following amounts: C44, 1.22; C′, 1.03; Bs, 1.20, per atom fraction. Small corrections for lattice parameter change upon alloying were made for C44 and C′ by using the pressure derivatives of the elastic constants of pure lithium and the known variation of the lattice constant with composition. The remaining effect is ascribed to alloying alone. Both to understand the elastic shear constants of lithium and to comprehend their dependence on composition, one must include small negative stiffness contributions arising in the Fermi energy, in addition to the major and usual electrostatic stiffness. It is then possible to deduce the variation with composition of each contribution from the measured total variation for the two shear constants, with the result that d ln Cedx = 1.24 and d ln Cfdx = 1.76.

Elastic constants of copper-nickel alloys

Abstract The elastic constants of single crystals of copper and of dilute alloys of copper with nickel have been measured using the ultrasonic pulse-echo technique. All fundamental elastic constants increase with composition in contrast to results previously obtained for solutes to the right of copper in the periodic table. In terms of C 0 −1 ( dC dx ) the values are: C44, (0.57); (C 11 − C 12 ) 2 , (0.70); ( C 11 + 2C 12 ) 3 , (0.17) per atom fraction. These values have been corrected for lattice parameter change upon alloying by using experimental data on the pressure derivatives of the elastic constants of pure copper. The remaining effect is owing to alloying alone and is still positive for both shear constants. This result may be interpreted as indicating a stiffening of the short-range crystal forces because the neutral nickel ion-core is larger than the iso-electronic copper ion-core, and a decrease in the long-range electrostatic forces because of the decrease in the average ion-core charge.

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 10 11 dyne cm 2 obtained are: C 11 = 4.45, C 33 = 4.44, (C 11 − C 12 2 = 0.253, (C 11 + C 33 ) 4 − >C 13 2 = 0.197, C 44 = 0.655, C 66 = 1.22. 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.