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The volume dependence of the Grüneisen parameter and crystal stability
vi
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
than the density of the contiguous solid and dP/dT becomes negative.
6.
Received 13 August 1974
4.
SYSTEM-INDEPENDENT RELEASE ADIABATS FROM SHOCKED STATES Fernando E. Prieto, Instituto de Fisica, Universidad Nacional Autónoma de Mdxico, Mexico 20, D.F. Mexico.
Suitable combinations of three parameters of any “linear” material: the initial density, and the coefficients of the linear relationship between shock and particle velocities, are used to define in reduced form most of the variables involved in shock pressures thermodynamic phenomena. This reduced variables formalism is applied, in conjunction with the mirrorimage approximation, to obtain pressure—volume relationships for the release adiabats from any given shocked state. The resulting equations are systemindependent, that is, they contain only pure numbers and reduced variables. Each adiabat is characterized by the coordinates of the point of crossing with the Hugoniot. Some of the adiabats so obtained for Al, Cu, W, Ti, and Cr are in good agreement, at least down to pressures about one half that of the initial shocked state, with those computed using other procedures. A table of adiabats, valid for all “linear” materials, is also included. Received 28 Januarv 1974 Revised 3 July 1974
5.
EFFECTS OF SHOCK LOADING ON YOUNG’S MODULUS OF COPPER C.P. Chang, U.K. Sinha, G. Rai and C.H. Ma,, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801, U.S.A.
The effects of shock loading on the Young’s Modulus of copper are investigated at shock pressures of 2.4, 11.6 and 85 Kbars respectively. Also studied is the nature of recovery of Young’s Modulus of shock-loaded specimens in boiling water in terms of maximum percentage recovery and the rate of recovery as a function of shock pressure. Received 29 August 1974 Revised 3 December 1974
Vol. 16, No.4
THE VOLUME DEPENDENCE OF THE GRUNEISEN PARAMETER AND CRYSTAL STABILITY V.V. Palciauskas, Department of Geology, University of Illinois, Urbana, Illinois 61801, U.S.A.
Utilizing only the general features of the lattice structure and potential, the explicit volume dependence of the entire frequency spectrum is derived in terms of its zero pressure values. It is shown that even though the frequencies and the mode Grilneisen parameters depend on the various details of the interactions and lattice structure, their variation with volume can be relatively simple functions of the volume. A criterion for mode instability with pressure is established involving only the measured value of 7(kX). The volume dependence of the high temperature Gruneisen parameter is derived utilizing the characteristics of the full frequency spectrum through the first two moments of the mode gammas and the results are applied to the alkali-halides. Received 8 July 1974 Revised 3 December 1974
7.
ENHANCED SOLUBILITY AND ION PAIRING OF Cu AND Au IN HEAVILY DOPED SILICON AT HIGH TEMPERATURES R.L. Meek and T.E. Seidel, Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.
The equilibrium solubilities of Cu and Au in silicon have been calculated for high temperatures3) (900—1100°C)and heavy dopings (10’s— 1021 cm and are compared with experimental results for uniformly bulk doped and diffusion doped material. The elec5ron activity coefficient is explicitly included in the calculation, and the effect of disturbing the vacancy population is discussed. For strongly extrinsic n type material, a large solubility enhancement (about 1 0~times the intrinsic solubility) is calculated, due to ion pairing of the substitutionalmetal acceptor with donors. It is concluded that pairing of interstitial metal donors with substitutional acceptors is not important because of configurational and vibrational entropy effects, so that for strongly extrinsic
ABSTRACTS OF PAPERS TO APPEAR IN J. PHYS. CHEM. SOLIDS
than the density of the contiguous solid and dP/dT becomes negative.
6.
Received 13 August 1974
4.
SYSTEM-INDEPENDENT RELEASE ADIABATS FROM SHOCKED STATES Fernando E. Prieto, Instituto de Fisica, Universidad Nacional Autónoma de Mdxico, Mexico 20, D.F. Mexico.
Suitable combinations of three parameters of any “linear” material: the initial density, and the coefficients of the linear relationship between shock and particle velocities, are used to define in reduced form most of the variables involved in shock pressures thermodynamic phenomena. This reduced variables formalism is applied, in conjunction with the mirrorimage approximation, to obtain pressure—volume relationships for the release adiabats from any given shocked state. The resulting equations are systemindependent, that is, they contain only pure numbers and reduced variables. Each adiabat is characterized by the coordinates of the point of crossing with the Hugoniot. Some of the adiabats so obtained for Al, Cu, W, Ti, and Cr are in good agreement, at least down to pressures about one half that of the initial shocked state, with those computed using other procedures. A table of adiabats, valid for all “linear” materials, is also included. Received 28 Januarv 1974 Revised 3 July 1974
5.
EFFECTS OF SHOCK LOADING ON YOUNG’S MODULUS OF COPPER C.P. Chang, U.K. Sinha, G. Rai and C.H. Ma,, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801, U.S.A.
The effects of shock loading on the Young’s Modulus of copper are investigated at shock pressures of 2.4, 11.6 and 85 Kbars respectively. Also studied is the nature of recovery of Young’s Modulus of shock-loaded specimens in boiling water in terms of maximum percentage recovery and the rate of recovery as a function of shock pressure. Received 29 August 1974 Revised 3 December 1974
Vol. 16, No.4
THE VOLUME DEPENDENCE OF THE GRUNEISEN PARAMETER AND CRYSTAL STABILITY V.V. Palciauskas, Department of Geology, University of Illinois, Urbana, Illinois 61801, U.S.A.
Utilizing only the general features of the lattice structure and potential, the explicit volume dependence of the entire frequency spectrum is derived in terms of its zero pressure values. It is shown that even though the frequencies and the mode Grilneisen parameters depend on the various details of the interactions and lattice structure, their variation with volume can be relatively simple functions of the volume. A criterion for mode instability with pressure is established involving only the measured value of 7(kX). The volume dependence of the high temperature Gruneisen parameter is derived utilizing the characteristics of the full frequency spectrum through the first two moments of the mode gammas and the results are applied to the alkali-halides. Received 8 July 1974 Revised 3 December 1974
7.
ENHANCED SOLUBILITY AND ION PAIRING OF Cu AND Au IN HEAVILY DOPED SILICON AT HIGH TEMPERATURES R.L. Meek and T.E. Seidel, Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A.
The equilibrium solubilities of Cu and Au in silicon have been calculated for high temperatures3) (900—1100°C)and heavy dopings (10’s— 1021 cm and are compared with experimental results for uniformly bulk doped and diffusion doped material. The elec5ron activity coefficient is explicitly included in the calculation, and the effect of disturbing the vacancy population is discussed. For strongly extrinsic n type material, a large solubility enhancement (about 1 0~times the intrinsic solubility) is calculated, due to ion pairing of the substitutionalmetal acceptor with donors. It is concluded that pairing of interstitial metal donors with substitutional acceptors is not important because of configurational and vibrational entropy effects, so that for strongly extrinsic