Relationship between the heat flow and relaxation of the shear modulus in bulk PdCuP metallic glass

Accepted Manuscript Relationship between the heat flow and relaxation of the shear modulus in bulk PdCuP metallic glass A.N. Tsyplakov, Yu.P. Mitrofanov, V.A. Khonik, N.P. Kobelev, A.A. Kaloyan PII: DOI: Reference:

S0925-8388(14)02073-8 http://dx.doi.org/10.1016/j.jallcom.2014.08.198 JALCOM 32051

To appear in:

Journal of Alloys and Compounds

Received Date: Accepted Date:

5 August 2014 24 August 2014

Please cite this article as: A.N. Tsyplakov, Yu.P. Mitrofanov, V.A. Khonik, N.P. Kobelev, A.A. Kaloyan, Relationship between the heat flow and relaxation of the shear modulus in bulk PdCuP metallic glass, Journal of Alloys and Compounds (2014), doi: http://dx.doi.org/10.1016/j.jallcom.2014.08.198

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Relationship between the heat flow and relaxation of the shear modulus in bulk PdCuP metallic glass A.N. Tsyplakova , Yu.P. Mitrofanova , V.A. Khonika,∗, N.P. Kobelevb , A.A. Kaloyanc a

Department of General Physics, State Pedagogical University, Lenin St. 86, Voronezh 394043, Russia b Institute for Solid State Physics RAS, Chernogolovka, Moscow district 142132, Russia c NBIC-Centre, Kurchatov Institute, Kurchatov Sq. 1, 123182 Moscow, Russia

Abstract We measured the heat flow, shear modulus and density changes occurring upon heating of bulk glassy P d41.25 Cu41.25 P17.5 , which polymorphically crystallizes into tetragonal P d2 Cu2 P with simultaneous decrease of the density. It was found that the heat release (well below the glass transition temperature Tg ) and heat absorption (near and above Tg ) are uniquely linked to the relaxation of the shear modulus through the relaxation change of the concentration of internal ”defects” frozen-in upon glass production. The two models suitable for a quantitative description of this interrelationship are discussed in detail. The obtained results clearly demonstrate an intrinsic connection of the shear moduli of glass and maternal crystal. Keywords: metallic glasses, calorimetry, elasticity 1. Introduction Heat flow occurring upon warming up of metallic glasses was documented already in the first studies of these materials [1, 2]. It is now well known that structural relaxation of as-cast metallic glasses below the glass transition temperature Tg results in the heat release while the attainment of the supercooled liquid region (temperatures T ≥ Tg ) is accompanied by the heat absorption [3, 4], similar to different non-metallic glasses [5]. Clearly, these ∗

Corresponding author Email address: [email protected], Tel/fax:+7-473-239-0433 (V.A. Khonik)

Preprint submitted to Journal of Alloys and Compounds

August 27, 2014

heat reactions reflect basic structural changes in glass upon thermal activation and, therefore, deserve the most detailed and careful investigation. However, after decades-long investigations, the level of understanding of the nature of heat effects seems to be insufficient. The first attempt of quantitative physical interpretation of the heat flow in metallic glasses was performed by van den Beukel and co-workers [6, 7]. Relying on the free volume notions, they argued that annealing out of the free volume yields a release of energy while its production requires energy. They postulated that the change of the internal energy is directly proportional to the free volume change and, thus, the observed heat release/absorption is conditioned by the free volume annihilation/production. It was later experimentally confirmed [8] that there is a direct correlation between the change of the enthalpy and increase of the density upon structural relaxation, which is assumed to a measure of the free volume change. Numerical calculations within the framework of this concept require several fitting parameters and eventually lead to a semi-quantitative agreement with the calorimetrical experiment (e.g. Ref. [9, 10, 11]). This approach was criticized in several directions [12, 13, 14]. In particular, it was suggested that the densification occurring upon structural relaxation can be interpreted not only by the free volume annihilation, but also by the annealing out of interstitialcy-like ”defects” frozen-in from the melt during glass production [14]. Another approach to the understanding of the heat effects was proposed in Ref. [13] on the basis of the Interstitialcy theory [15], which was shown to explain a number of physical phenomena in metallic glasses (see Refs [13, 14] and papers cited therein). The basic idea of this approach consists in the hypothesis that melting of a metallic simple crystal takes place through the rapid generation of dumbbell (split) interstitials (=interstitialcies), which partially remain in the solid glass obtained by melt quenching and determine its structural relaxation upon heat treatment. Using the basic equation of the Interstitialcy theory, which gives an exponential relationship between the shear modulus G of glass and the concentration c of interstitialcy ”defects”, G = Gx exp(−αβc),

(1)

where Gx is the shear modulus of the maternal crystal, dimensionless β is the ”shear susceptibility” and phenomenological parameter α ≈ 1, the authors [13] derived an expression for the heat flow (measured in the heat power per unit mass), 2

  T˙ GRT dGx dG − , W = βρ GRT dT dT x

(2)

where T˙ = dT /dt is the heating rate, ρ the density, GRT and GRT the x shear moduli of glass and maternal crystal at room temperature, respectively. Equation (2) shows that the heat flow is conditioned by the shear moduli of glass and crystal and their temperature derivatives. The underlying reason for this flow is the relaxation of the interstitialcy ”defect” system [16]. It was shown that Eq. (2) gives a quantitative description of the endothermal heat flow in Pd-based glasses near the glass transition [13, 17, 18] as well as describes the exothermal reaction below Tg [17, 18]. The third approach to the understanding of heat reactions in metallic glasses proposed recently [19] is based on the assumption that glass contains quenched-in ”defects” - elastic dipoles, which either disappear (anneal out) below Tg and their elastic energy is released as heat or produced above Tg that requires energy and thus leads to heat absorption. Using a nonlinear elastic representation of the internal energy of glass with quenched-in elastic dipoles, the authors [19] derived an expression for the heat flow,   3T˙ dGx dG W = − , (3) dT βρΩ dT where G, Gx , T˙ , β, ρ have the same meaning as in Eq. (2) and the averaged form-factor Ω = 1.38 takes into account different types of elastic dipoles involved into relaxation. Heat release below Tg is conditioned by relaxation in the system of elastic dipoles (a decrease of their elastic energy or disappearance) while heat absorption above Tg is due to either transitions of elastic dipoles into the states with higher energy or their production. It seen seen that Eqs (2) and (3) are rather similar and the heat flow in both cases is controlled by relaxation of the shear moduli of glass and reference crystal. This seems to be quite natural because, first, the shear modulus is a thermodynamic quantity (being the second derivative of the Gibbs energy with respect to the strain) and currently considered as one of the most important quantities in understanding the physical properties of supercooled liquids and glasses [20, 21, 22]. Second, glass is prepared from the crystal and, therefore, there must be a relationship between the properties of glass and the maternal crystals, as supposed by both expressions (2) and (3). Such a relationship was recently confirmed in a special experiment [16]. Finally, 3

one has to recall that a dumbbell (split) interstitial is just as particular case of an elastic dipole and, thus, Eqs (2) and (3), while derived in fully different ways, should actually describe the same (or very similar) relaxation. These heat flow laws, therefore, require further careful verification on different systems. In general, this the purpose of the present paper. One can notice that both heat flow laws contain derivatives dGx /dT and dG/dT as well as their difference, which are calculated as a function of temperature. This implies that their verification needs very qualitative experimental input data on Gx (T ) and G(T ). Previous shear modulus measurements [13, 17, 18] used for the verification of Eq. (2) were performed using the electromagnetic acoustic transformation method (EMAT). In the present work, we have improved EMAT data pick up and processing procedures that allowed, first, more precise calculations of the shear modulus derivatives and, second, performing measurements deeper in the glass transition region. The second feature of the present work is connected with the choice of the glass for the investigation. Initially, we planned to perform this investigation on bulk glassy P d40 Cu40 P20 , which is unique because its density decreases upon crystallization while the latter occurs polymorphically into the single tetragonal P d2 Cu2 P phase [23, 24]. It is, therefore, interesting to study such unusual behavior in the context of its relaxation properties. We, however, failed to produce bulk glassy P d40 Cu40 P20 using our melt quenching technique. This is why we produced and studied bulk glassy P d41.25 Cu41.25 P17.5 , which has close chemical composition and displays similar crystallization behavior. 2. Experimental Metallic glass P d41.25 Cu41.25 P17.5 (at.%) was produced as 5 × 2 × 60 mm3 bars by melt jet quenching at a rate of ≈ 200 K/s [25]. The initial state was verified to be purely amorphous (Fig.1a) by X-ray diffraction in the transmission mode at λ = 0.055242 nm using a synchrotron radiation facility at the Kurchatov Institute in Moscow. Vacuum annealing at 723 K for 25 min result in the full crystallization, as evidenced by the diffraction pattern shown in Fig. 1b. All Bragg diffraction peaks in this Figure can be ascribed to the tetragonal P d2 Cu2 P , as previously shown in Refs. [23, 24] for bulk P d40 Cu40 P20 . The density was measured by the Archimedian method with distilled water as working liquid. Every sample was tested five times and Fig.2a gives 4

500 Pd

400

Cu

41.25

P

41.25

17.5

a initial

300 synchrotron diffraction

200

=0.05668 nm

5

10

15

25

(324)

(323)

(401)

(411)

(321)

20 2

(104)

(311)

(213)

(212)

(002)

(101)

200

annealed 723 K 25 min

(202)

(200)

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0

(211)

600

(310)

b

(112)

(210)

0

(102)

Intensity (a.u.)

100

30

35

(degrees)

Figure 1: Synchrotron diffraction of bulk P d41.25 Cu41.25 P17.5 in the initial (a) and crystallized (b) states. All Bragg reflections in (b) correspond to the tetragonal P d2 Cu2 P phase.

the average values with the error bars being the standard deviations. Besides that, we used a laboratory-made dilatometer to measure length changes of samples (15 mm long) upon thermal cycling. Differential scanning calorimetry (DSC) was performed using a Hitachi Exstar DSC7020 instrument in flowing Ar atmosphere. All heating procedures were performed at a rate of 3 K/min. Shear modulus measurements were carried out using the EMAT method, which allows precise in situ contactless measurements in a wide temperature range. We performed measurements at frequencies f = 480 − 500 kHz with a data acquisition rate ≈ 0.1 Hz with the relative precision of about 10 ppm in a vacuum of ≈ 0.013 Pa at a heating rate of 3 K/min. Some measurement details are given elsewhere [13, 19].

5

3. Results 3.1. Density The density of initial bulk glassy P d41.25 Cu41.25 P17.5 was found to be 9.40 ± 0.18 g/cm3 . Changes of the room-temperature density of three different samples determined by the Archimedian method after annealing below the glass transition temperature Tg , above the crystallization onset temperature Tx and slightly above the melting temperature Tm = 843 K (measured by DSC) are shown in Figure 2a. It is seen that the density below Tx appears to be about the same within the measurement error. However, dilatometric measurements of the length performed below Tg reliably revealed small decrease of samples’ length L upon thermal cycling implying a density increase ρ − 1 = −3 ∆L up to 0.08 % depending on the annealing temperature, as ρ0 L shown in Fig. 2b. Above Tx , the density first slightly increases and then eventually drops down by about 0.2–0.4 % with respect to the initial state (Fig. 2a). Thus, fully crystallized P d41.25 Cu41.25 P17.5 has smaller density than that in the initial glassy state. 3.2. Differential scanning calorimetry Measurements of the heat flow W (T ) were performed for initial, relaxed glassy and crystallized samples. The following measurement sequence was applied. Run 1: heating of the initial sample up to 575 K (i.e. into the supercooled liquid region), the corresponding heat flow is designated as W1 (T ). Run 2: heating the same glassy sample from room temperature up to 767 K that produces full crystallization. This heat flow curve corresponds to the relaxed state and is referred to as W2 (T ). Run 3: heating up the same sample, this flow curve corresponds to the crystalline state and called W3 (T ) hereafter. To remove the uncertainties related to the baseline of the DSC instrument, we always subtract the heat flow W3 (T ). Figure 3 gives the heat flow curves Wini (T ) = W1 (T ) − W3 (T ) and Wrel (T ) = W2 (T ) − W3 (T ) in the initial and relaxed states (solid and dotted curves), which, in general, demonstrate quite usual behavior. Below Tg in the initial state, one observes an exothermal reaction, which correspond to structural relaxation of glass and disappears in the relaxed state. The attainment of Tg = 540 K (shown by the arrow) is characterized by the beginning of a strong endothermal reaction, which eventually transforms into crystallization-induced exothermal reaction at Tx (shown by the arrow). Crystallization processes are not considered here. 6

0.0010

0.0008

b Pd

0.0006

Cu

41.25

P

41.25

17.5

0.0002

relative density change

/

0

-1

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0.0000

a 0.005

T

m

0.000

T

g

T

x

-0.005 300

400

500

600

700

800

temperature (K)

Figure 2: Changes of room-temperature density determined by the Archimedian method (a) for three different samples after annealing at indicated temperatures. The glass transition Tg and crystallization onset Tx temperatures (measured at T˙ = 3 K/min) as well as the melting temperature Tm are shown by the arrows. (b) - Room-temperature changes of the density below Tg determined by dilatometric measurements of sample’s length. Errors are less than the size of the symbols.

It is important to note that the heat flow W3 (T ) in the crystalline state demonstrates an anomaly, as shown in Fig. 4. Because the heat capacity of a metallic crystal smoothly increases with temperature, one should expect a smooth increase of W3 with temperature as well. However, one observes an increased heat flow rate in the range 460 K≤ T ≤ 490 K. We refer this phenomenon as the ”H-anomaly” hereafter. Presumably, this anomaly reflects some relaxation process or phase transition in the P d2 Cu2 P phase. Equations (2) and (3) relate the measured heat flow with the temperature derivatives of the shear modulus in the glassy and crystalline states, G and Gx . Therefore, we performed precise measurements of G(T ) and Gx (T ) dependences. 7

experimental initial

0.015

experimental relaxed

T

heat flow (W/g)

experimental initial (H-anomaly subtracted)

x

experimental relaxed (H-anomaly subtracted)

0.010 Pd

Cu

41.25

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P

41.25

17.5

T

dT/dt=3 K/min

g

endo

0.000

exo

350

400

450

500

550

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Figure 3: Heat flow of bulk glassy in the initial and relaxed states before and after subtraction the anomaly of the enthalpy in the crystalline state (see Fig.4).

3.3. Shear modulus The heating treatment procedure applied for measurements of the shear modulus consisted of three subsequent runs on the same sample identical to those applied upon measurements of the heat flow described above. Figure 5 gives temperature dependences of the shear modulus of the alloy under investigation alloy in the initial glassy (run 1), relaxed glassy (run 2) and crystallized (run 3) states, designated as Gini , Grel and Gx hereafter, respectively. The shear modulus curves demonstrate a typical pattern, which was earlier documented for Pd- and Zr-based glasses [13, 16, 18, 19], i.e.: (i ) pronounced structural relaxation leads to an increase of the shear modulus over the anharmonic component and, therefore, the shear modulus in the relaxed glassy state is bigger (by ≈ 3.2%) as compared to the initial state; (ii ) very close to the calorimetric Tg , the shear modulus starts to rapidly decrease with temperature indicating the transition into the supercooled liquid state. It is worthy of notice that, in spite of crystallization-induced decrease of the density (Fig. 2), the shear modulus increases by about the same amount as in the case of ”normal” metallic glasses (i.e. which increase their density upon crystallization). This fact is agrees with the calculations [19, 26] showing a small contribution of the dilatation into the observed changes of the shear modulus upon structural relaxation and crystallization of metallic glasses. The shear modulus in the crystalline state (P d2 Cu2 P phase) displays a distinct anomaly, which begins slightly below calorimetric Tg , see Fig. 5. 8

W 0.030

heat flow (W/g)

W

Pd

3

3

(H-anomaly subtracted)

Cu

41.25

P

41.25

17.5

0.025 dT/dt = 3 K/min

0.020 H-anomaly

350

400

450

500

550

temperature (K)

Figure 4: Heat flow in the fully crystallized state. The beginning of the H-anomaly is shown by the upwards arrow. The downwards arrows give the amount of the heat flow subtracted in order to take into account the relaxation structural change occurring upon heating. The dashed curve gives the heat flow after subtraction.

This anomaly is referred to as the ”G-anomaly” hereafter. Similar anomaly was earlier reported for bulk P d40 Cu30 N i10 P20 after full crystallization [16]. It was shown that this G-anomaly is rate dependent and that is why likely reflects a relaxation process in the crystalline structure. Comparing Figs 4 and 5, one can conclude that the G-anomaly is observed at slightly higher temperatures than the H-anomaly described above. However, these anomalies should evidently reflect the same relaxation process. 4. Discussion Both heat flow laws (2) and (3) suggest that the shear moduli G and Gx in the glassy and crystalline state are temperature dependent. These laws also imply that the maternal crystalline state remains the same upon heating. However, the H-anomaly shown in Fig. 4 and the G-anomaly seen in Fig. 5 give the evidence of a certain change occurring in the P d2 Cu2 P phase upon heating. It might be speculated that this change is due to the nonstoichiometry of the phase P d2 Cu2 P occurring upon crystallization. This should result in the appearance of a large number of point defects in this phase. It is to be noted that the H- and G-anomalies are observed approximately in the temperature range, which is close to Tg in the glassy state. This fact might indicate that point defects in the crystal are quite similar the elastic dipoles 9

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ini

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ini

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dT/dt =3 K/min

T

g

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2.8x10

350

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550

600

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Figure 5: Temperature dependences of the shear modulus in the initial, relaxed and crystallized states. The beginning of the anormal G-behavior is indicated. The short arrows give the excess part of the shear modulus due to the relaxation change in P d2 Cu2 P phase.

in the glass. In any case, the nature of this structural change is out of the scope of the present paper. However, the fact of the change has to be taken into account. Formally, this can be done by subtracting the contributions induced by this change into the observed heat flow and shear modulus. The corresponding procedure as applied for the heat flow of P d2 Cu2 P phase is illustrated in Fig. 4, where the arrows give the amount of the heat flow to be subtracted and the blue dashed curve defines the W3 (T ) behavior, which is assumed in the following analysis. After the subtraction, the heat flow curves in the initial and relaxed glassy states transform as shown in Fig. 3. It is seen that the subtraction affects only the heat flow in relatively narrow range below and above Tg . Similar procedure was applied for the shear modulus in the crystalline state as described below. According to Equations (2) and (3), the heat flow is controlled by the derivatives dG/dT and dGx /dT . Besides that, the derivative dGx /dT in the heat flow law (2) is multiplied by the ratio of the room temperature shear moduli for in the glassy and crystalline states, GRT /GRT x . All above quantities are given in Fig. 6. First, one clearly sees a peak in the derivative dGx /dT at about 540 K, which corresponds to the G-anomaly shown in Fig. 5. Above ≈ 590 K, dGx /dT linearly decreases with temperature. Well below the G-peak, in the range 370 K≤ T ≤ 470 K, the dGx /dT -curve was fitted RT dG x by a linear function, so that G = −4.0 × 106 − 3.21 × T [Pa/K]. The GRT dT x extrapolation of this function to higher temperatures up to 590 K is shown 10

7

dG/dT (Pa/K)

-2x10

Pd

Cu

41.25

7

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17.5

dT/dt=3 K/min T (G

7

-6x10

(G

RT

/G

RT

dG dG

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/G

g

RT x

)*dG /dT (G-anomaly subtracted) x

RT x

)*dG /dT x

/dT - relaxed

rel

ini

/dT - initial state

400

450

500

550

temperature (K)

Figure 6: Temperature derivatives of the shear modulus in the initial, relaxed and crystallized states before and after subtracting the G-anomaly.

in Fig. 6. This extrapolation naturally does not contain the G-anomaly and it is the function, which was used for the calculation of the heat flow using Eqs. (2) and (3). Figure 6 also gives temperature dependences of dG/dT in the initial and relaxed glassy states. A strong decrease of dG/dT around calorimetric Tg that reflects the transition of glass into the metastable liquid state. The derivatives dG/dT shown in this Figure were used for the calculation of the heat flow. Figure 7 gives a comparison of experimental heat flow corrected for the H-anomaly (as shown in Fig. 3) with the heat flow calculated within the framework of the Interstitialcy theory using Eq. (2), where the shear modulus data are corrected for the G-anomaly. The shear susceptibility was calculated RT dG T˙ γ x with γ = G − dG taken at T = 565 K (i.e. in the supercooled as β = ρW GRT dT dT x liquid state) that gives β = 20. It is seen that Eq. (2) gives a very good description of the experimental heat flow below and above Tg both for the initial and relaxed states. It is worthy of notice that the calculation correctly describes the peculiarities of the heat release below Tg (two exothermal peaks located at about 390 and 520 K) and gives quite accurate reproduction of the magnitude and temperature position of heat absorption peak (at ≈ 555 K) in the supercooled liquid state as well as its slight shift towards higher temperature in the relaxed state. The shear susceptibility β = 20 accepted in this calculation agrees with the value of β = 17 derived from a special special experiment [17] performed on glassy P d40 Cu30 N i10 P20 . 11

experimental initial (H-anomaly subtracted)

0.015

experimental relaxed (H-anomaly subtracted) calculated - initial

heat flow (W/g)

calculated - relaxed

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Cu

41.25

0.005

P

41.25

17.5

dT/dt=3 K/min

=20 0.000

350

400

450

500

550

temperature (K)

Figure 7: Comparison of the experimental heat flow after the subtraction of the H-anomaly with the calculation of the heat flow using Eq. (2) performed with the shear susceptibility β = 20 and shear modulus data corrected for the G-anomaly. Data on the initial and relaxed states are presented.

A comparison of experimental heat flow corrected for the H-anomaly with heat flow calculated using Eq. (3) with shear modulus data corrected for the G-anomaly for the initial and relaxed states is shown in Fig. 8. In this case, the above procedure for the determination of the shear susceptibility gives β=38, which is exactly the same as determined earlier [19] for glassy Zr46 Cu46 Al8 . It is seen that the agreement between experimental and calculated curves at temperatures above Tg is very good, similar to the case presented in Fig. 7. Below Tg , however, Equation (3) gives systematically underestimated heat flow, although the difference between the experiment and calculation is fairly small. Since this difference is small, one can derive the relationship between the shear susceptibilities in Equations (2) and (3). Designating the corresponding shear susceptibilities as βi and βd , taking into account that the expressions in square brackets of these equations are approximately equal, one arrives at βi ≈ 13 Ωβd . Taking Ω = 1.38 (Ref. [19]) and βd = 38, one gets βi = 17.5, which is fairly close to the present calculation (βi = 20). Thus, upon appropriate correction for the H- and G-anomalies occurring in crystalline P d2 Cu2 P upon heating, both equations (2) and (3) provide a quantitative description of the heat release and heat absorption in glassy P d41.25 Cu41.25 P17.5 . Equation (2) gives a very good interpretation of the heat flow in the whole temperature range, from room temperature to the 12

0.015

experimental initial (H-anomaly subtracted) experimental relaxed (H-anomaly subtracted) calculated - initial

heat flow (W/g)

calculated - relaxed

0.010 Pd

Cu

41.25

0.005

P

41.25

17.5

=38

dT/dt=3 K/min 0.000

350

400

450

500

550

temperature (K)

Figure 8: Comparison of the experimental heat flow after subtraction of the H-anomaly with the calculation of the heat flow using Eq. (3) with the shear susceptibility β = 38 and shear modulus data corrected for the G-anomaly.

supercooled liquid region above Tg . The quality of the fit given by Eq. (3) is equally high near and above Tg . Below Tg , this equation gives slightly worse fit. It should be noted that failure to take account of H- and G-anomalies in the reference crystalline P d2 Cu2 P leads to a significant deterioration of both fits, supporting thus the aforementioned basic idea on intrinsic relationship between the properties properties of glass and maternal crystal. This idea lies in both approaches [15] and [19], which lead to Eqs (2) and (3), respectively. The physical mechanisms of relaxation and related heat flow underlying Eqs (2) and (3) are also quite similar. The heat release and heat absorption as described by the Intersititaly theory (Eq. (2)) originates from relaxation decrease (below Tg ) and increase (above Tg ) of the concentration of interstitialcy ”defects” [13]. Within the framework of the approach presented in Ref. [19] that leads to Eq. (3), these ”defects” are elastic dipoles. As mentioned above, the interstitialcy defect represents in fact a particular case of an elastic dipole. Macroscopically, the relaxation change of the concentration of ”defects” in both cases is revealed as the relaxation of the shear modulus, which defines their formation enthalpy. Within the framework the Intersitialcy theory the relaxation is directly governed by the explicit relationship connecting the ”defect” concentration and shear moduli of glass and maternal crystal given by Eq. (1). In the ”elastic dipole” approach [19], this relationship implicitly comes through the relaxation of the ”defect” elastic energy, which is in turn controlled by the shear modulus. The ideology of 13

both approaches directly agrees with the common current understanding of the shear modulus as one of the main thermodynamic parameters of noncrystalline materials [20, 21, 27, 28, 29]. The quality of the fits given by both equations actually with no fitting parameter is quite impressive. Thermoactivated relaxation of the ”defect” system in glass should be associated with its volume changes. It is interesting to note that both increase of the density (below Tg ) of the glass under investigation and its decrease (due to crystallization above Tg ) lead to an increase of the shear modulus, as clearly demonstrated by Figs. 2 and 5. This fact suggests that volume changes occurring upon structural relaxation of a metallic glass do not play any constitutive role in changes of the shear modulus, in agreement with the calculations [19]. 5. Conclusions Detailed density, shear modulus and heat flow measurements performed on bulk glassy P d41.25 Cu41.25 P17.5 led to the following conclusions. 1. The density of the glass under investigation increases by up to ≈ 0.08% upon structural relaxation below the glass transition temperature Tg . Continued heating leads to the crystallization into tetragonal P d2 Cu2 P phase with no X-ray signs for any other crystalline phases. The density decreases upon crystallization by about 0.3% − 0.4% so that the initial glass has bigger density with respect to its maternal crystal. In spite of the fact that the density changes have different signs upon structural relaxation and crystallization, the room-temperature shear modulus always increases suggesting that the volume change is not determinative for the shear modulus change. The shear modulus and heat flow data display distinct anomalies upon heating of crystalline P d2 Cu2 P , which indicate certain structural changes. 2. Despite of unusual density behavior, the heat flow and shear modulus temperature dependences are quite similar to those for other metallic glasses. We performed a detailed analysis of heat flow and shear modulus data within the framework of the Interstitialcy theory and elastic dipole approach, which lead to the expressions for the heat flow given by Equations (2) and (3), respectively. It is found that if appropriate corrections for the heat flow and shear modulus anomalies in crystalline P d2 Cu2 P are applied, both Equations in general quite correctly describe the experimental heat flow. The elastic dipole approach provides a very good description of the heat flow data near and above Tg but slightly underestimates the heat flow well below Tg . The 14

Interstitialcy theory provides a very good description of the heat flow data in the whole temperature range. 3. The Interstitialcy theory and elastic dipole approach both imply that the heat flow is conditioned by the relaxation change of the concentration of structural ”defects” frozen-in upon glass production. Macroscopically, this concentration changes is revealed as relaxation change of the shear modulus. Thus, the heat flow is intrinsically connected with shear modulus relaxation. The latter depends on the shear modulus of the maternal crystal. Thus, the obtained data confirm generic connection between properties of glass with those of the maternal crystal. 6. Acknowledgements V.A.K. thanks Prof. A.V. Granato and Dr. D.M. Joncich (University of Illinois at Urbana-Champaign, USA) for the long-standing cooperation and numerous discussions. Financial support from the Ministry of Education and Science of Russia (project 3.114.2014/K) is acknowledged. References [1] H.S. Chen, D. Turnbull, J. Chem. Phys. 48 (1968) 2560-2571. [2] H.S. Chen, E. Coleman, Appl. Phys. Lett. 28 (1976) 245-247. [3] H.S. Chen, Rep. Prog. Phys. 43 (1980) 353-432. [4] C. Suryanarayama, A. Inoue, Bulk metallic glasses, CRC Press, Boca Raton, London, New-York, 2011. [5] S.R. Elliott, Physics of amorphous materials, Longmann, London, NewYork, 1983. [6] A. van den Beukel, S. Radelar, Acta Metall. 31 (1983) 419-427. [7] A. van den Beukel, J. Sietsma, Acta Metall. Mater. 38 (1990) 383-389. [8] A. Slipenyuk, J. Eckert, Scr. Mater. 50 (2004) 39-44. [9] Z.D. Zhu, E. Ma, J. Xu, Intermetallics 46 (2014) 164-172. [10] J. B¨ unz, G. Wilde, J. Appl. Phys. 114 (2013) 223503. 15

[11] Y. Zhang, H. Hahn, J. Alloys and Comp. 488 (2009) 65-71. [12] Y.Q. Cheng, E. Ma, Appl. Phys. Lett. 93( 2008) 051910. [13] Yu.P. Mitrofanov, A.S. Makarov, V.A. Khonik, A.V. Granato, D.M. Joncich, S.V. Khonik, Appl. Phys. Lett. 101 (2012) 131903. [14] V.A. Khonik, N.P. Kobelev, J. Appl. Phys. 115 (2014) 093510. [15] A.V. Granato, Phys. Rev. Lett. 68 (1992) 974-977. [16] A.S. Makarov, V.A. Khonik, Yu.P. Mitrofanov, A.V. Granato, D.M. Joncich, S.V. Khonik, Appl. Phys. Lett. 102 (2013) 091908. [17] A.S. Makarov, V.A. Khonik, Yu.P. Mitrofanov, A.V. Granato, D.M. Joncich, J. Non-Cryst. Sol. 370 (2013) 18-20. [18] A.S. Makarov, V.A. Khonik, G. Wilde, Yu.P. Mitrofanov, S.V. Khonik, Intermetallics 44 (2014) 106-109. [19] N.P. Kobelev, V.A. Khonik, A.S. Makarov, G.V. Afonin, Yu.P. Mitrofanov, J. Appl. Phys. 115 (2014) 033513. [20] S.V. Nemilov, J. Non-Cryst. Sol. 352 (2006) 2715-2725. [21] S.V. Nemilov, J. Non-Cryst. Sol. 353 (2007) 4613-4632. [22] J. Dyre, Rev. Mod. Phys. 78 (2006) 953-972. [23] T.D. Shen, U. Harms, R.B. Schwarz, Appl. Phys. Lett. 83 (2003) 45124514. [24] D.J. Safarik, R.B. Schwarz, Acta Mater. 55 (2007) 5736-5746. [25] S.V. Khonik, L.D. Kaverin, N.P. Kobelev, N.T.N. Nguyen, A.V. Lysenko, M.Yu. Yazvitsky, V.A. Khonik, J. Non-Cryst. Sol. 354 (2008) 3896-3902. [26] N.P. Kobelev, V.A. Khonik, N.A. Afonin, E.L. Kolyvanov, submitted to Intermetallics. [27] J.C. Dyre, N.B. Olsen, and T. Christensen, Phys. Rev. B 53 (1996) 2171-2174. 16

[28] J.C. Dyre, Phys. Rev. B 75, 092102 (2007). [29] W.L. Johnson, K. Samwer. Phys. Rev. Lett. 95 (2005) 195501.

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We studied unusual PdCuP glass, whose density decreases upon crystallization. We found that heat effects are uniquely linked to shear modulus relaxation. Equations describing this relationship are discussed. There is an intrinsic connection between the shear moduli of glass and crystal.