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Frontiers of Chemistry in China

ISSN 1673-3495

ISSN 1673-3614(Online)

CN 11-5726/O6

Front Chem Chin    2011, Vol. 6 Issue (1) : 54-68    https://doi.org/10.1007/s11458-011-0227-8
RESEARCH ARTICLE
Phonon dynamics of glassy copper alloys
Aditya M. VORA()
Humanities and Social Science Department, STBS College of Diploma Engineering, Surat 395006, India
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Abstract

The well recognized model potential is used to investigate the phonon properties for five glassy Copper alloys viz. Cu57Zr43, Cu60W40, Cu33Y67, Cu43Ti57 and Cu66Ti34. The thermodynamic and elastic properties are also computed from the elastic limits of the phonon dispersion curves (PDC). Three theoretical approaches given by Hubbard-Beeby (HB), Takeno-Goda (TG) and Bhatia-Singh (BS) are used in the present study to compute the PDC. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are employed to see the effect of exchange and correlation in the aforesaid properties.

Keywords pseudopotential      pair potential      phonon dispersion curves (PDC)      glassy copper alloys     
Corresponding Author(s): VORA Aditya M.,Email:voraam@yahoo.com   
Issue Date: 05 March 2011
 Cite this article:   
Aditya M. VORA. Phonon dynamics of glassy copper alloys[J]. Front Chem Chin, 2011, 6(1): 54-68.
 URL:  
https://academic.hep.com.cn/fcc/EN/10.1007/s11458-011-0227-8
https://academic.hep.com.cn/fcc/EN/Y2011/V6/I1/54
GlassesZΩO/a.u.rC/a.u.ZdNCrd/a.u.
Cu57Zr433.01158.440.86736.4912.001.87
Cu60W403.00160.480.83277.5010.401.72
Cu33Y672.34126.091.00904.1412.002.42
Cu43Ti572.71114.470.84095.5112.001.71
Cu66Ti342.0290.610.99237.1212.001.53
Tab.1  Input parameters and other constants.
Fig.1  Pair potentials for (a) CuZr, (b) CuW, (c) CuY, (d) CuTi and (e) CuTi metallic glasses.
Fig.2  Screening dependence of the phonon dispersion curves for CuZr metallic glass using HB approach
(a) longitudinal mode; (b) transverse mode
Fig.3  Screening dependence of the phonon dispersion curves for CuW metallic glass using HB approach
(a) longitudinal mode; (b) transverse mode
Fig.4  Screening dependence of the phonon dispersion curves for CuY metallic glass using HB approach
(a) longitudinal mode; (b) transverse mode
Fig.5  Screening dependence of the phonon dispersion curves for CuTi metallic glass using HB approach
(a) longitudinal mode; (b) transverse mode
Fig.6  Screening dependence of the phonon dispersion curves for CuTi metallic glass using HB approach
(a) longitudinal mode; (b) transverse mode
Fig.7  Phonon dispersion curves for (a) CuZr, (b) CuW, (c) CuY, (d) CuTi and (e) CuTi metallic glasses using HB, TG and BS approaches with S-local field correction function.
Fig.8  Screening dependence of the low temperature specific heat for CuZr metallic glasses computed from (a) HB, (b) TG and (c) BS approaches.
Fig.9  Screening dependence of the low temperature specific heat for CuW metallic glasses computed from (a)HB, (b) TG and (c) BS approaches
Fig.10  Screening dependence of the low temperature specific heat for CuY metallic glasses computed from (a)HB, (b) TG and (c) BS approaches
Fig.11  Screening dependence of the low temperature specific heat for CuTi metallic glasses computed from (a) HB, (b) TG and (c) BS approaches
Fig.12  Screening dependence of the low temperature specific heat for CuTi metallic glasses computed from (a)HB, (b)TG and (c)BS approaches
App.SCRvL/(10-5 cm·s-1)vT/(10-5 cm·s-1)BT/(10-11dyne·cm-2)G/(10-11 dyne·cm-2)σY/(10-11 dyne·cm-2)θD/K
HBH1.21010.69860.38250.22950.25000.573877.36
T0.79740.46040.16610.09970.24990.249250.98
IU1.17660.67930.36160.21700.25000.542475.22
F1.17020.67560.35770.21460.25000.536574.81
S0.36740.21210.03530.02120.25000.052923.49
TGH2.02021.05051.22710.51890.31471.3644117.25
T2.21501.38071.11180.89640.18232.1195151.74
IU2.31341.33981.39090.84400.24762.1061148.31
F2.35571.37471.42460.88850.24182.2068152.06
S1.96241.13411.00430.60470.24931.5110125.56
BSH5.72432.449711.64482.82160.38797.8323276.12
T6.25662.966312.88924.13720.355011.2121332.85
IU6.30722.988613.10464.19970.355211.3831335.36
F6.26882.947613.03074.08510.358111.0958330.89
S6.25262.987012.78864.19510.352211.3447335.04
5.812.175.79339.26
3.932.165.49338.16
3.982.175.51333.39
5.792.165.78333.08
1.592.174.48320.23
Others [10]2.222.164.91325.17
Tab.2  Thermodynamic and elastic properties of CuZr glass.
App.SCRvL /(10-5 cm·s-1)vT /(10-5 cm·s-1)BT /(10-11 dyne·cm-2)G/(10-11 dyne·cm-2)σY/(10-11 dyne·cm-2)θD/K
HBH0.87020.50240.36880.22130.25000.553260.08
T0.61280.35380.18290.10970.25000.274342.31
IU0.77400.44690.29180.17510.24990.437753.44
F0.77630.44820.29360.17610.24990.440353.60
S0.92440.53370.41620.24970.25000.624463.83
TGH1.45410.75051.19530.49390.31841.302290.52
T1.61140.98141.15050.84440.20522.0353116.77
IU1.62930.93981.29480.77430.25071.9369112.40
F1.66200.96431.33470.81530.24622.0322115.27
S1.42290.82130.98660.59140.25021.478898.22
BSH4.42111.238215.34441.34410.45743.9179152.12
T4.57391.565415.47672.14840.43376.1601191.75
IU4.61761.597815.70972.23820.43206.4103195.68
F4.59271.560315.64672.13430.43486.1244191.15
S4.56031.573215.33952.16970.43256.2161192.67
Tab.3  Thermodynamic and elastic properties of CuW glass.
App.SCRvL/(10-5 cm·s-1)vT/(10-5 cm·s-1)BT/(10-11 dyne·cm-2)G/(10-11 dyne·cm-2)σY/(10-11 dyne·cm-2)θD/K
HBH1.43910.83080.58410.35040.25000.876192.35
T0.27310.15760.02100.01260.25030.031517.52
IU1.18270.68290.39450.23670.24990.591875.90
F1.14560.66140.37010.22210.25000.555273.51
S1.44280.83300.58710.35220.25000.880692.58
TGH1.76370.73821.21030.27660.39380.771183.59
T1.39640.92200.41450.43160.11350.9612101.04
IU1.73330.91590.95720.42590.30631.1127102.51
F1.74110.93990.94090.44850.29441.1610105.03
S2.15820.46862.21590.11150.47530.328953.61
BSH5.85013.265610.15545.41390.273713.7909363.99
T6.21373.542111.10806.36950.259316.0422394.13
IU6.22583.534511.22126.34200.262216.0098393.41
F6.18873.504211.13156.23380.264015.7595390.13
S6.23653.574111.09876.48490.255516.2834397.50
Tab.4  Thermodynamic and elastic properties of CuY glass.
App.SCRvL/(10-5 cm·s-1)vT/(10-5 cm·s-1)BT/(10-1 dyne·cm-2)G/(10-11 dyne·cm-2)σY/(10-11 dyne·cm-2)θD/K
HBH2.16931.25251.25710.75430.24991.8856155.59
T1.57120.90720.65950.39570.24990.9892112.70
IU1.95571.12911.02170.61300.25001.5326140.27
F1.93781.11881.00310.60190.24991.5046138.99
S1.77761.02630.84410.50640.24991.2661127.50
TGH2.72321.14202.72960.62700.39331.7473144.52
T2.38851.36381.55080.89430.25822.2503169.59
IU2.72881.37192.37370.90490.33092.4087172.16
F2.75061.39902.38300.94100.32552.4948175.44
S1.92141.16290.90820.65030.21101.5749143.83
BSH7.86843.846720.28217.11460.343019.1095483.49
T8.32984.257221.74318.71440.323223.0623533.70
IU8.35404.258821.92798.72090.324423.1002533.98
F8.31734.225221.81708.58390.326122.7660529.89
S8.34634.288821.70228.84430.320623.3597537.48
Tab.5  Thermodynamic and elastic properties of CuTi glass.
App.SCRvL/(10-5 cm·s-1)vT/(10-5 cm·s-1)BT/(10-11 dyne·cm-2)G/(10-11 dyne·cm-2)σY/(10-11 dyne·cm-2)θD/K
HBH1.29210.74600.51070.30640.24990.766194.92
T1.15390.66620.40730.24440.25000.611084.77
IU1.49880.86530.68710.41230.25001.0307110.10
F1.48860.85940.67780.40670.25001.0167109.35
S1.04430.60290.33360.20020.25000.500476.72
TGH1.53240.59251.03520.19330.41210.545977.00
T1.56110.79010.88360.34370.32780.9128101.51
IU1.80430.84531.26800.39340.35941.0697109.06
F1.81280.85821.26880.40560.35561.0995110.67
S1.51210.72590.87210.29010.35030.783493.53
BSH5.41932.313512.24132.94710.38868.1844299.68
T6.34593.227814.52435.73670.325515.2079414.56
IU6.45443.303114.92846.00750.322615.8909424.07
F6.44093.282714.93105.93330.324615.7179421.56
S6.23353.156614.07935.48650.327614.5672405.53
Others [12]5.245.372.943.071.061.08396.98 413.89
Tab.6  Thermodynamic and elastic properties of CuTi glass.
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