On the stability limits of the undercooled liquid state of Pd-Ni-P

MATERIALS SCIENCE & ERiGl WEERiNG Materials Scienceand Engineering A226-228 (1997) 434-438

A

On the stability limits of the undercooled liquid state of Pd-Ni-P G, Wilde a, S.G. Klose b, W. Soellner a, G.P. Giirler a, K. Jeropoulos c, R. Willnecker a, H.J. Fecht c a DLR, Institut ftir Raumsimulation, 51147 K&, Germany b Awdi A G, Ingoistadt, Germany ’ TU Berlin, Institut fiir Metallische Werkstoffe, 10623 Berlin, Germany

Abstract

The easyglass-formingmetallic alloy Pd-Ni-P exhibitsan exceptionalresistanceagainstcrystallization in the deeplyundercooled liquid state. In the presentwork, the absenceof crystallization was utilized to equilibrate bulk amorphous samples at different temperaturesbelow the glasstransition by extendedisothermalannealing.Specificheat data and equilibrium viscosity data could be obtained in the glasstransition region. From density and volume expansion measurements the thermal expansion coefficient of the undercooledliquid could be derived. The free volume frozen-in at typical cooling rates could be determinedto be in the order of 0.3%. The resultsare discussed with regard to stability criteria of the undercooledliquid state. 0 1997Elsevier Science S.A. Keywords: Bulk metallicglass;Structuralrelaxation;Specificheat;Viscosity;Density;Stabilitylimits

1. Introduction

Since the first studies of Klement, Willens and Duwez on Au-Si [l] it is known that a variety of metallic alloys can be quenched from the melt to form a glass. Today, the easy glass forming Pd-, Al-, or Z--based metals have caused outstanding scientific interest, because of their remarkable resistance against crystallization, which offers the opportunity to produce bulk amorphous samples [2-41. In contrast to the network building oxide glasses or polymers these molecular glasses are thought of as model systems for studies on the glass transition. Pd40Ni$,,P20 belongs to this group of alloys and can be vitrified by applying a cooling rate as low as 0.16 K s-l [5], thus giving rise to the direct measurement of the specific heat of the undercooled liquid state throughout the entire undercooling range [6]. The pronounced stability of the undercooled state of this alloy allows for extensive experimental diagnosis of this metastable phase. Recently, it was demonstrated that by thermal heat treatment at temperatures below the gIass transition amorphous alloys can be fully relaxed into the metastable equilibrium state thus considerably lowering the glass temperature of the specimens [7]. By this 0921-5093/97/$17.00 0 1997ElsevierScience S.A. All rightsreserved. PIISO921-5093(96)10659-6

method, experiments on the specific heat and equilibrium viscosity measurements could be extended into the vicinity of the isentropic regime. In this work, further experiments taking advantage of this method are reported with emphasis on new results of density measurements of the undercooled liquid. The results are discussed in the context of proposed stability limits for the undercooled liquid state. 2. Experimental

J%,Ph&~ samples were prepared by alloying premelted N&P samples (99.5% pure) with a Pd ingot (99.9% pure) in a resistance furnace under argon flow. Amorphous rods of 3.5 mm in diameter and up to 35 mm in length were produced by either flow casting or die casting in argon atmosphere. For density measurements the entire rods of about 3 g in weight were used. Small discs of about 100 mg were cut for the relaxation experiments and subsequent DSC measurements. The samples used for the creep measurements were stripshaped (0.5 x 0.5 mm) at a length of 10 mm. Measurements on the coefficient of thermal expansion were performed on cylindrical samples of 3.5 mm in diameter and 10 mm in length.

G. Wilde et al. /Materials

Science and Engineering A226-228

Amorphous samples were relaxed in the temperature range between 537 and 561 K using a high-precision isothermal vacuum furnace. The procedure to monitor the approach of the equilibrium state is described in detail elsewhere [S]. Using a commercial Dynamic Mechanical Analyzer (Perkin-Elmer DMA-7) isothermal creep measurements under constant flow of argon were performed at different temperatures between 540 and 578 K. Temperature calibration was carefully done using the melting temperatures of indium and zinc. The momentary sample length 1 was measured for each specimen at a constant tensile stress level gI = 2.16 MPa as a function of time t. By measurements of the dependence of the strain rate on the stress it was proven that the viscous flow is Newtonian at this tensile stress level. The corresponding shear viscosity q = ~,/(3 de/ dt) then is a function of the applied stress and the elongation rate dE/dt = 1-i dlldt, which can be taken directly from the isothermal creep data. The linear thermal expansion coefficients of amorphous and crystalline Pd,,,Ni,,P,, samples were measured by using the DMA in the dilatometric mode. The applied load on the sample amounted to only 10 mN to prevent massive deformation of the amorphous samples in the vicinity of the glass transition. The crystalline specimens were equilibrated at temperatures about 20 K below the eutectic temperature, to ensure that the measurements on the crystalline state are not affected by remaining metastable phases. The density of structurally relaxed samples was determined at room temperature by the fluid displacement method in ethanol and in water using a microbalance (Sartorius 2504). Such annealing temperatures were choosen, that a low annealing temperature was followed by a high annealing temperature (with subsequent rapid cooling) and vice versa, to ensure the reversibility of the measured density changes. The accuracy in the density measurements was about t- 0.0005 g cmw3. The measured absolute values were always checked by calibration measurements on a 2.5 g sapphire rod of 3.9850 g cms3 in density.

(1997) 434-438

435

liquid. In the case of calorimetric measurements glass temperature is defined by Eq. (l),

the

[c,,d?=[r;di+[c;dT

(1)

where c’, and c; are the extrapolated courses of the specific heat of liquid and glass respectively, cp denotes the ‘apparent specific heat’ measured during heating across the glass transition and T1 and T2 are temperatures well below and well above the glass transition. Consequently, the glass temperature Tg for fully relaxed samples coincides with the annealing temperature. Thus, by use of Eq. (1) and with knowledge of T6, the concept of the limiting fictive temperature offers the possibility to follow the course of the deeply undercooled liquid from the known high temperature values to Tg. The results of these measurements as well as the ck curve covering the entire undercooling range [6] is shown in Fig. 1. The continuous curve was measured by using a differential heat flow calorimeter (Netzsch DSC 404) and applying a cooling rate of - 10 K min- ‘. Thus, the resulting glass temperature of the sample amounted to Tg = 568.5 K. After a relaxation period of 22 days the lowest value of Tg was reached at 537 K. The absence of crystallinity in the annealed samples was confirmed by subsequent measurements of the crystallization enthalpy. Using the measured values of CL, the specific heat of the crystalline state c; and the melting entropy AS,= AHf/T, the enthalpy difference (not shown) and the entropy difference (Fig. 2) between undercooled melt and crystal could be calculated. The isentropic (Kauzmann) temperature was determined as TK = 500 I 5 K. This temperature defines the low temperature limit of the liquid state. The hypothetical isenthalpic temperature was found to be about 120

3. Results 3.1. Calorimetric

investigations

The principle of the method used to determine the calorimetric data of the undercooled liquid below 600 K goes back to the concept of Tool [9], who defined the glass temperature as a ‘limiting fictive temperature’ of the sample. This temperature is characterized by the projection of a thermodynamic potential (e.g. enthalpy or specific volume) of the final glassy state towards the equilibrium curve of the metastable undercooled liquid and characterizes the frozen-in state of the equilibrium

0.1 E-

AH,= 130 J/g i 0 ~,,,,,,,,,,,,.,,,.,,,,,Y,,,,,,,,,,~ 400 SO0 600 700 800 903 Temperature [K]

1000

1100

Fig. 1. The specific heat of Pd,,Ni,,P,, in the crystalline, glassy and liquid state. The continuous curves were measured directly, the circles correspond to DSC measurements on samples fully relaxed at the corresponding annealing temperatures.

436

G. Wilde

et al. /Matedds

Science

and Engineering

TK

0

It*,

400

~,~~“~‘(““S’~~(~

500

600 700 Temperature [K]

800

900

Fig. 2. The derived entropy difference between undercooled liquid and crystalline phase. The continuous curve corresponds to the direct cp measurements: the circles mark the approach to the Kauzmann temperature TK by the annealing treatments.

K beiow TK. The residual excess entropy persistent in the sample is continuously lowered by the annealing treatments from 0.31 AS, at T, = 568.5 K to only 0.18 AS’, at T, = 537 K. From this result it is obvious that a further approach to the ideal glassy state (AS= 0) becomes possible with increasing relaxation time. 3.2. Thesmomechnnicalanalysis

Isothermal creep measurements were performed on samples which were fully equilibrated at different annealing temperatures. The results directly yielded the equilibrium viscosity data [lo]. Fig. 3 shows the equilibrium viscosity &T) thus obtained for Pd-Ni-P on a reduced temperature scale (Angel1 plot [ll]). The measured viscosity values of 10'5 10' 3

1011 ~ F 109 g 107 /r

105

i2

103

Pd4$\ii4opzo

~4lTil3NilOCU

13%3

Fig. 3. The measured and extrapolated viscosities of Zr-Ti-Ni-&Be, Pd-Ni-P and Au-Pb-Sb on a reduced temperature scale (Angel1 plot). T* ( = 560 K for Pd-Ni-P) is choosen as the temperature, where the equilibrium viscosity amounts to lo’* Pa.s. The three metallic glasses can be characterized as strong, intermediate and fragile, respectively.

AZ%-228

(1997)

434-438

Pd-Ni-P cover about four orders in magnitude. This demonstrates that the arbitrary definition of the glass temperature, at which qes = 1012 Pass is not applicable in the case of isothermal measurements performed on a time scale in the order of the sample relaxation time. The comparison with the viscosities of the easy glass forming alloys Zr-Ti-Ni-Cu-Be and Au-Pb-Sb indicates that Pd-Ni-P takes an intermediate position between rather strong (Zr-Ti-Ni-Cu-Be) and rather fragile (AuPb-Sb) glass formers. The temperature dependence of qecl in the temperature range of the glass transition can be well described by either the Vogel-Tammann-Fulcher (VTF) equation qes = vi exp[B/(TTO)] or the ‘hybrid equation’ yes = y,T exp[Q,j/(RT)] exp[B/(TTO)]. At elevated temperatures, however, only the hybrid equation leads to a good agreement with available experimental values near the melting regime [12]. Using TO= 495 K = TK (within experimental accuracy) and B = 500 K, the remaining parameters are obtained as v,, = 2.5 x 100 lg Paas*K-’ and Q,=260 kJ moi- i. Thus the measured equilibrium viscosity could be well fitted by the use of the (calorimetrically obtained) Kauzmann temperature as the temperature of diverging viscosity. This result further suggests that the ideal glass transition sets a limit to the stability range of the undercooled liquid. 3.3. Density measurements

The temperature dependent equilibrium density of structurally relaxed amorphous samples was determined by measuring the room-temperature density and the linear thermal expansion coefficient of the glass clg. By this method, the interference from viscous flow of the sample in the glass transition regime was avoided. The same procedure was applied on the crystalline samples, yielding the density at ambient temperature and the linear thermal expansion coefficient of the crystalline phase cr,. In accordance with literature [13] it was found E,~= 13 x 10B6 K-i, a, =29 x IOU6 K-’ and a6 = 17 x lO-‘j K-l in the glass transition region. Fig. 4 shows the resulting specific volume of crystal, glass and undercooled liquid as a function of temperature. The extrapolation of the specific volume of the liquid towards elevated temperatures yields a reasonable agreement with available experimental data in the vicinity of the melting regime [ 141. The free volume theory is based on the assumption that the production of free volume (vr) starts at TK. Thus, assuming the difference in the thermal expansion coefficients of undercooled liquid and glass to be constant in the temperature range above TK, the free volume can be calculated as a function of temperature according to:

G. Wilde et al. /Materials

Science and Engineering A226-228

0.107’ t ( ’ ” I t * I I’ t I ’ ” 8 I r 1 ’ ” ’ I I ’ I I ’ 550 600 500 Temperature [K] Fig. 4. The specific volumes of crystalline, glassy and undercooled liquid Pd-Ni-P obtained from room-temperature density measurements and by determination of the respective thermal expansion coefficients.

This leads to a fraction of I&, = 0.003 free volume at T, = 568.5 K. At the eutectic temperature T, = 8X4 K the free volume amounts to 1.494. This value is about one order of magnitude lower than values often taken in model calculations [15,16], but seems to be more realistic. The measured values indicate that the equilibrium specific volume of undercooled liquid Pd40Ni4,,P20 at the isentropic temperature would still be larger than the corresponding value of the crystalline state. Thus, the isochoric point can not be reached with this alloy. The result is in accordance with previous findings on bulk amorphous Zr-Ti-Ni-Cu-Be samples [17]. Following the arguments of Tallon [18], at least in the case of systems with a close-packed crystalline phase, it is expected that the isochoric temperature T(AV= 0) should be higher than the isentropic temperature T(AS= 0) and the isenthalpic temperature T(AH= 0) [19]. Obviously, this relation is not applicable in the case of the investigated bulk glass-forming alloys. From experimental data the sequence of stability limits is received as: T(AH = 0) < T(AV= 0) < T(AS = 0).

4. Conclusions The present investigations show that the concept of the fictive temperature is well suited to describe the thermodynamic and thermomechanic behaviour of a metallic glass. By applying this method, the specific heat and the equilibrium viscosity of the deeply undercooled liquid as well as the equilibrium specific volume of this state could be determined at high accuracy for a temperature interval1 extended below 600 K.

(1997) 434-438

431

The comparison of the equilibrium viscosity data of Pd-Ni-P, Zr-Ti-Ni-Cu-Be and Au-Pb-Sb shows that Pd-Ni-P takes an intermediate position between fragile and strong glassformers. Glasses of this type are well suited to monitor the approach of the Kauzmann temperature. Their relaxation times are not diverging too fast and the effects due to structural relaxation can be measured accurately. The temperature dependence of the viscosity could be fitted adequately by the VTF equation and by the hybrid equation taking the calorimetrically determined T, as the temperature of the viscosity divergence. From the measurements of the specific volume of crystalline, glassy and deeply undercooled liquid Pd-NiP the fraction of free volume at the typical glass temperature Tg = 568.5 K was determined as 0.3%. The extrapolation of the measured values towards lower temperatures indicates that the isochoric point is well below TK and thus can not be reached for this alloy. This is in contrast to the hierarchy of stability criteria proposed by Tallon. However, further investigations on closed packed systems are needed to test the validity of this concept. The present results support the recent suggestion that the glass transition is a kinetic freezing process concealing an underlying entropic stability limit at TK [20].

Acknowledgements The financial support by the Deutsche Forschungsgemeinschaft, Project No. Wi 1350/l-2 is gratefully acknowledged.

References [I] W. Klement, R.H. Willens and P. Duwez, Nature, 187 (1960) 869. [2] H.W. Kui, A.L. Greer and D. Turnbull, Appl. Phys. Lett., 45 (1984) 615. 131 A. Inoue, T. Nahamara and T. Masumoto, Mat. Trans. JIM, 31 (1990) 425. [4] A. Peker and W.L. Johnson, Appl. Phys. Lett., 63 (1993) 2342. [S] R. Willnecker, K. Wittmann and G.P. GGrler, J. Non-Cryst. Solids, 156- 158 (1993) 450. [6] G. Wilde, G.P. GBrler, R. Willnecker and G. Die&, Appl. Phys. Lett., 65 (1994) 397. [73 C. Mitsch, G.P. Giirler, G. Wilde and R. Willnecker, to be published. [S] G. Wilde, G.P. Giirler, R. Willnecker, S.G. Klose and H.J. Fecht, Mat. Sci. Forum, 225-227 (1996) 101. [9] A.Q. Tool, J. Amer. Cemn. Sot., 29 (1946) 240. [lo] C.A. Volkert and F. Spaepen, Mnt. Sci. Eng., 97 (1988) 449. [ll] C.A. Angell, J. Phys. Chenz. Solids, 49 (1988) 563. [12] K.H. Tsang, S.K. Lee and H.W. Kui, J. Appl. PIERS.,70 (1991) 4837. [13] H.S. Chen, J.T. Krause and E.A. Sigety, J. Non-Cryst. Solids, 13 (1973174) 321.

438

G. Wilde et al. /Materials

Science

and Engineering

[14] K.C. Chow,% W0ngandH.W. Kui,J. Appl.Phys., 74(1993) 5410. [15] P. Ramachandrarao, 3. Cantor and R.W. Cahn, J. Mat. Sci., 12 (1977) 2488. [16] A.E. Owen, in N.H. March, R.A. Street and M. Tosi teds.), Amorphous Solidsaandthe LiquidState, PlenumPress, 1985, pp. 395.

A226-228

(1997)

434-438

[17] S.G. Klose, M.P. Macht and H.J. Fecht, Mat. Sci. Forum, 225-227 (1996) 51. [18] J.L. Tallon, Nnlzve, 342 (1989) 658, [19] H.J. Fecht and W.L. Johnson, Nature, 334 (1988) 50. [20] H.J. Fecht, Mat. Trans. JIM, 36 (1995) 777.