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Materials Science and Engineering A 471 (2007) 151–154

Elastic properties of Ca-based bulk metallic glasses studiedby resonant ultrasound spectroscopy

Zhiying Zhang a, Veerle Keppens a,∗, Oleg N. Senkov b, Daniel B. Miracle c

a Department of Materials Science and Engineering, 434 Dougherty Hall, The University of Tennessee, Knoxville, TN 37996, USAb UES Inc., 4401 Dayton-Xenia Rd., Dayton, Ohio, OH 45432, USA

c Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, Ohio, OH 45433, USA

Received 12 March 2006; received in revised form 14 September 2006; accepted 15 January 2007

bstract

We report measurements of the elastic properties and internal friction of Ca-based bulk metallic glasses (BMGs), Ca50Mg20Cu30,a Mg Zn Cu and Ca Mg Zn (numbers indicate at.%), as a function of temperature between 5 and 400 K. Below the glass transition

55 18 11 16 65 15 20

emperature, both Young’s modulus and shear modulus decrease with increasing temperature, and the Poisson ratio increases with increasing tem-erature. Above the glass transition temperature, these trends reverse due to crystallization. At temperatures close to the glass transition temperature,e observe the onset of a peak in the internal friction Q−1, attributed to crystallization. 2007 Elsevier B.V. All rights reserved.

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eywords: Elastic properties; Ca-based bulk metallic glasses; Resonant ultraso

. Introduction

Recently, Novikov and Sokolov [1] reported that the ratio ofnstantaneous shear to bulk modulus in glasses, or, alternatively,he Poisson ratio, is linked to the fragility of the glass-formingiquid, which is in turn an important parameter used to evalu-te the glass-forming ability (GFA) of glasses. Even though thiselation might not hold for bulk metallic glasses (BMGs) [2], aystematic study of the elastic properties and thus the Poissonatio of metallic glasses is expected to yield important infor-ation about their mechanical properties, and can hopefully be

inked to their GFA.Ca-based BMGs are a relatively new class of amorphous

lloys, first reported by Amiya and Inoue in 2002 [3]. Variousystems, including Ca–Mg–Zn, Ca–Mg–Cu, Ca–Mg–Zn–Cu,a–Mg–Ag–Cu, have been formed [3–11]. Unique propertiesave been reported, such as low density (∼2.0 g/cm3) and lowoung’s modulus comparable to the modulus of human bones

11]. In addition, Ca-based BMGs have low glass transition tem-

eratures (∼390 K), which make them very attractive for studiesear the glass transition temperatures.

∗ Corresponding author. Tel.: +1 865 974 3494; fax: +1 865 974 4115.E-mail address: vkeppens@utk.edu (V. Keppens).

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921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2007.01.157

pectroscopy; Internal friction

. Experimental details

Resonant ultrasound spectroscopy (RUS) is a novel techniqueeveloped at Los Alamos National Laboratory for determininghe complete elastic tensor of a solid by measuring its free-bodyesonances [12]. The mechanical resonances can be calculatedor a sample with known dimensions, density, and elastic tensor.n a RUS experiment, the mechanical resonances of a freelyibrating solid of known shape are measured, and an iterationrocedure is used to “match” the measured frequencies withhe calculated spectrum. This allows determination of the fulllastic tensor of the solid from a single frequency scan, whichlearly indicates a main advantage of RUS: there is no need foreparate measurements to probe different moduli, and multipleample remounts and temperature sweeps are avoided. Anotherdvantage lies in the ability of RUS to work with small, mm-ized samples.

Ca-based BMGs, Ca50Mg20Cu30, Ca55Mg18Zn11Cu16 anda65Mg15Zn20 (numbers indicate at.%), were prepared usingethods reported elsewhere [10,11]. The characteristic tem-

eratures (glass transition temperature Tg, crystallization

emperature Tx and liquidus temperature Tl) of these sam-les are shown in Table 1. Samples of approximatelymm × 4 mm × 4 mm were cut from the ingots and then pol-

shed into rectangular parallelepipeds (RP). Samples were

152 Z. Zhang et al. / Materials Science and Engineering A 471 (2007) 151–154

Table 1Glass transition temperature Tg, crystallization temperature Tx, liquidus temperature Tl, supercooled liquid region �Tx, reduced glass transition temperature Trg, γ ,Hruby factor Hr and critical casting thickness dmax for Ca-based BMGs, determined by differential scanning calorimetry (DSC) with the heating rate at 0.667 K/s

Composition Tg (K) Tx (K) Tl (K) Trg �Tx (K) � Hr dmax (mm)

Ca50Mg20Cu30a 401 442 690 0.581 41 0.405 0.165 8

Ca55Mg18Zn11Cu16 392 441 622 0.630 49 0.435 0.271 >10Ca65Mg15Zn20

b 375 410 630 0.595 35 0.408 0.159 6

flMueittGSdfEb

K

E

ν

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3

bFst∼aattdrsoewlec

Fig. 1. Longitudinal modulus L as a function of temperature for Ca50Mg20Cu30,Ca55Mg18Zn11Cu16 and Ca65Mg15Zn20.

Fig. 2. Shear modulus G as a function of temperature for Ca50Mg20Cu30,Ca55Mg18Zn11Cu16 and Ca65Mg15Zn20.

Table 2Atomic volume, VA, density, ρ and elastic constants of elements [13]

Element VA (cm3/mol) ρ (g/cm3) G (GPa) K (GPa) E (GPa) ν

a Data from Ref. [11].b Data from Ref. [10].

at-mounted between the two transducers of the RUS probe.easurements as a function of temperature were performed

sing a specially designed probe that fits in a Physical Prop-rty Measurement System from Quantum Design. Only twondependent elastic constants need to be determined for elas-ically isotropic materials such as BMGs. In crystalline solids,hese two elastic constants would be labeled c11 and c44 (or), where the subscripts refer to the crystallographic axes.ince BMGs have no crystallographic reference axes, longitu-inal (L) and shear (G) directions relative to the RUS referencerame are used here. The bulk modulus K, Young’s modulus

and Poisson ratio ν, can be calculated using the equationselow.

= 3L − 4G

3(1)

= G(3L − 4G)

L − G(2)

= L − 2G

2(L − G)= 1

2− 1

2((K/G) + (1/3))(3)

The internal friction, Q−1, can be determined from the fullidth at half maximum (FWHM) of the resonant frequencies,

.e. Q−1 = �f/f.

. Results and discussions

The longitudinal modulus L and shear modulus G for Ca-ased glasses with three different compositions are plotted inigs. 1 and 2, and bulk modulus, Young’s modulus, and Pois-on ratio are shown in Figs. 3–5. A clear transition in theemperature-dependence of the elastic constants is observed at

362 K for Ca65Mg15Zn20, ∼386 K for Ca55Mg18Zn11Cu16nd ∼400 K for Ca50Mg20Cu30. Below the transition temper-ture, all moduli decrease with increasing temperature, whilehe Poisson ratio increases with increasing temperature. Abovehe transition temperature, the rate of softening is significantlyecreased or is fully arrested. The transition temperatures areoughly equivalent to Tg values for the respective glasses,uggesting that structural relaxations are responsible for thebserved transitions. A systematic influence of composition onlastic moduli is apparent in Figs. 1–5, where moduli increase

ith increasing Cu and decreasing Ca-concentration. This fol-

ows the trend for the elastic properties of the constituentlements (Table 2) [13]. The elastic constants of Ca-based BMGsan be approximated with a weighted average of the elastic con-

Ca 26.20 1.55 7.4 17 20 0.31Mg 14.00 1.74 17 45 45 0.29Zn 9.16 7.14 43 70 108 0.25Cu 7.11 8.92 48 140 130 0.34

Z. Zhang et al. / Materials Science and Engineering A 471 (2007) 151–154 153

Table 3Comparison of measured elastic constants (meas.) at room temperature with the calculated values based on atomic fraction (calat.) and volume fraction (calvol.) ofcomponents

Property Ca50Mg20Cu30 Ca55Mg18Zn11Cu16 Ca65Mg15Zn20

meas. calat. calvol. meas. calat. calvol. meas. calat. calvol.

G (GPa) 12.56 21.5 13.7 11.87 19.5 13.0 10.12 16.0 11.5K (GPa) 29 60 35.9 26 48 30.8 23 32 24.4E (GPa) 33.16 58.0 36.9 30.98 51.8 34.5 26.42 32 30.2ν 0.311 0.315 0.310 0.305 0.305 0.306 0.306 0.295 0.303

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ig. 3. Bulk modulus, K, as a function of temperature for Ca50Mg20Cu30,a55Mg18Zn11Cu16 and Ca65Mg15Zn20.

tants of the alloy components via a linear rule of mixtures:= ∑

icixi, where c is the alloy modulus and ci is the mod-lus of component i. The component fraction xi can represent

ither the atomic fraction [14] or the volume fraction of com-onent i [15]. The calculated moduli based on atomic fractionnd volume fraction of components are compared with the val-es measured by RUS at room temperature in Table 3. These

ig. 4. Young’s modulus, E, as a function of temperature for Ca50Mg20Cu30,a55Mg18Zn11Cu16 and Ca65Mg15Zn20.

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ig. 5. Poisson ratio as a function of temperature for Ca50Mg20Cu30,a55Mg18Zn11Cu16 and Ca65Mg15Zn20.

alculations support the observed composition dependence, andstimates based on constituent volume fraction provide bettergreement with the experimental results.

Internal friction, Q−1, of the Ca-based BMGs as a functionf temperature is shown in Fig. 6. The internal friction gradually

ncreases with increasing temperature, and the increase becomesuite dramatic near the glass transition temperature. This rapidncrease corresponds to the appearance of a prominent peak in

ig. 6. Internal friction, Q−1, as a function of temperature for Ca50Mg20Cu30,a55Mg18Zn11Cu16 and Ca65Mg15Zn20.

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54 Z. Zhang et al. / Materials Science a

−1. A similar peak has been observed by Ichitsubo et al. [16]n Zr-based BMGs.

. Conclusions

A decrease in elastic modulus with increasing temperatures measured for the longitudinal, bulk, shear and Young’s mod-li of Ca-based BMGs below the glass transition temperature.decrease in the softening rate above the glass transition tem-

erature suggests that structural changes are important. Thesetructural changes are also reflected in the rapid increase of inter-al friction Q−1 near Tg. The elastic constants measured by RUSre sensitive to the composition of BMGs, so that higher modulire measured for glasses with higher Cu and lower Ca concen-rations. This trend is in agreement with calculations based onhe volume fraction of the elemental constituents.

cknowledgement

This work was partially supported by the National Scienceoundation, DMR-0506292.

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ngineering A 471 (2007) 151–154

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