https://hdl.handle.net/11256/46 2026-05-20T16:18:14Z 2026-05-20T16:18:14Z Simmons, R.O. Balluffi, R.W. https://hdl.handle.net/11256/81 2023-02-08T17:03:04Z 1959-07-31T00:00:00Z

Measurment of Equilibrium Concentrations in Aluminum Simmons, R.O.; Balluffi, R.W. Measurements of change in length and change in lattice parameter were made at identical temperatures on 99.995% aluminum in the temperature range 229 to 656°C. Length changes, ΔL, were measured on an unconstrained horizontal bar sample using a rigid pair of filar micrometer microscopes. X-ray lattice parameter changes, Δa, were observed using a high-angle, back-reflection, rotating-single-crystal technique. The measurements are compared to earlier work. The relative expansions ΔLL and Δaa were equal within about 1:105 from 229 to 415°C. At higher temperatures additional atomic sites were found to be generated: the difference between the two expansions could be represented by 3(ΔLL−Δaa)=exp(2.4)exp(−0.76 ev/kT). At the melting point (660°C) the equilibrium concentration of additional sites is 3(ΔLL−Δaa)=9.4×10−4. This result is independent of the detailed nature of the defects, for example, the lattice relaxation or degree of association. The nature of the defects is considered and it is concluded that they are predominantly lattice vacancies; it is estimated that the divacancy contribution at the melting point may well be less than about 15%, corresponding to a divacancy binding energy ⩽ 0.25 ev. The observed formation energy agrees with the values obtained by quenching techniques and by interpretation of the high-temperature electrical resistivity of identical material by Simmons and Balluffi. The present work is the first direct measurement of formation entropy; the value is near that expected from theoretical considerations. The contribution of the thermally generated defects to other physical properties at high temperatures is considered briefly.

1959-07-31T00:00:00Z Raju, S. Sivasubramanian, K. Mohandas, E. https://hdl.handle.net/11256/80 2023-02-08T17:06:44Z 2001-07-17T00:00:00Z

The Relation Between Bulk Modulus and Relative Enthalpy: a Broad-Based Thermodynamic Analysis and a Case Study on Aluminum Raju, S.; Sivasubramanian, K.; Mohandas, E. By postulating a linear relationship between logarithmic bulk modulus and relative enthalpy, we have developed in this paper a thermodynamic framework that provides a link between thermal properties and bulk modulus under constant pressure. The proposed model could be used in analyzing the consistency of various bulk modulus estimates of aluminum through an integrated treatment of its thermal and elastic properties.

2001-07-17T00:00:00Z Chang, Y.A. Himmel, L. https://hdl.handle.net/11256/78 2023-02-08T17:08:35Z 1966-02-16T00:00:00Z

Temperature Dependence of the Elastic constants of Cu, Ag, and Au above Room Temperature Chang, Y.A.; Himmel, L. The adiabatic elastic constants C44, 1/2(Cll-C12), and 1/2(cll+C12+2c44) have been measured for copper, silver, and gold over the temperature range from 300° to about BOO 0K using the conventional ultrasonic pulse-echo technique. The room-temperature values of the stiffness coefficients are shown to be in acceptable agreement with previously published data for the noble metals. Over the entire range from 300° to 800oK, it is found that, to a remarkably good approximation, the elastic constants for all three metals decrease linearly with temperature. Additional evidence is presented to show that the linear temperature dependence of the elastic constants for silver extends to at least 1000oK, i.e., to within 80% of the absolute melting temperature. The isothermal compressibilities calculated from the elastic constant data are used to evaluate the dilational term in the specific heat, Cdil=Cp-Cv, and it is established that the approximate Nernst-Lindemann relation for estimating Cdil is valid for Cu, Ag, and Au at least up to 800K

1966-02-16T00:00:00Z Simmons, RO Balluffi, RW https://hdl.handle.net/11256/39 2014-07-15T17:43:19Z 2014-07-02T00:00:00Z

Measurement of Equilibrium Concentrations of Vacancies in Copper Simmons, RO; Balluffi, RW The net added fraction of thermally-generated atomic sites, ΔNN, has been measured, during equilibrium heating to near the melting point, in a coarse-grained copper bar of 99.999% purity. The linear thermal expansion, ΔLL, and the x-ray lattice expansion, Δaa, as measured simultaneously, agree within the measurement error of ±1×10−5 throughout the temperature interval between 56 and 850°C. At 1000 and at 1075°C, ΔNN=3(ΔLL−Δaa) is (0.9±0.5)×10−4 and (1.9±0.5)×10−4, respectively. Using expected limits for the binding energies of vacancy clusters, it is concluded that ΔNN consists almost entirely of monovacancies. An assumed value of (1.5±0.5)k for the formation entropy, combined with these concentrations, yields a monovacancy formation energy of (1.17±0.11) eV. The ratio of this formation energy to the activation energy for self-diffusion is therefore about 0.57, near the ratios found for the other noble metals. The results imply a monovacancy migration energy of (0.88±0.13) eV. The present results are compared with the results of a wide variety of other investigations of defects in copper which include: (1) theoretical calculations, (2) quenching and annealing, (3) thermal diffusion, (4) annealing after irradiation, and (5) annealing after cold work. In certain cases apparent disagreement is found. However, it is concluded that in no case is there a sufficiently firm body of experimental data available either to confirm or to contradict the present monovacancy data. The need for further definitive experiments in these areas is emphasized.

2014-07-02T00:00:00Z