Nucleation, the initial formation of a new phase from a parent phase, plays an important role in the eventual microstructure and properties of materials. Theories and models of nucleation have been integral to materials science for close to a century. These models assume that the parent material is compositionally homogeneous on length-scales relevant to nucleation. However, in certain materials – such as thin films or reactive nanolaminates – sharp gradients in the composition may influence nucleation. Models and theories exploring these impacts are based on little direct experimental data. Here we present means of producing and characterizing samples with composition gradients to measure the impacts of gradients on nucleation. We fabricate amorphous Cu-Zr films with known composition gradients through their thicknesses; we perform isochronal nanocalorimetry to measure the impact of the gradients on nucleation and growth; and we characterize the samples before and after reaction. We see evidence of phase separation of the vapor-quenched Cu-Zr amorphous films. While we measure differences between the samples with gradients and those without, the gradients relax sufficiently during heating such that nucleation (the onset of crystallization) occurs at the same temperatures. For both sets of samples we find three distinct regions of heat release: the first we attribute to local ordering, the second to extended phase separation and interdiffusion, and the third to nucleation and growth of the Cu10Zr7 crystalline phase. This work represents a first step towards investigating the impact of gradients on nucleation, as well as growth.

The fabrication of many metallic alloys – both thin film and bulk – relies on the nucleation and subsequent growth of intermetallic phases from a solid solution. In bulk materials, this can take the form of precipitation hardening – where intermetallic particles precipitate from a super-saturated solid solution. Evaporated or sputtered thin films can undergo similar processes when they interdiffuse and nucleate a new phase (such as aluminization of nickel1,2) or through intermixing, formation of solid solutions, and subsequent nucleation of intermetallics such as in various nanoscale multilayer films.3–5 Due to the initial structure of these films, significant composition gradients still exist within the films at the point of nucleation, even after intermixing has occurred. Both theoretical treatises6–10 and recent experimental work11,12 imply that these compositional gradients can inhibit nucleation when the gradient is above a critical threshold. This gradient effect is not captured in classical nucleation theory (CNT), which assumes that the parent material is compositionally homogenous.

A thermodynamic model for the gradient effect on nucleation has been developed by Desré, and Yavari8 and Gusak.9 For a nucleus of radius r, this model includes not only the expected r2 and r3 terms from CNT, but also a r5 term which depends on the composition gradient ∇c2. As the gradient increases from homogeneity, the nucleation barrier increases and the nucleation rate decreases. Above a critical value for the gradient, ∇c*, nucleation is fully inhibited. This model has been used to calculate the critical gradients for specific systems, such as ∇c* = 5 × 108 m-1 for a Ni/Zr multilayers.6,7 An animation demonstrating the effect of this term on the ΔG versus nucleus radius plot for Ni/Zr using the values in Refs. 6 and 7 is included in the supplementary material, Figure 2 (Multimedia view).

A recent study demonstrated a gradient effect in 3Al:Ni thin films using nanocalorimetry, a chip-based calorimetric method which can heat small samples at very high heating rates.11 For these films, it was determined that a steep composition gradient can inhibit nucleation of Al3Ni until sufficient intermixing – as measured by the extent of reaction progression – occurs to reduce the gradient below a critical threshold. Similar results have been shown in molecular dynamics simulations of AlNi crystallization from a liquid with a controlled composition gradient.12 

In general, experimental studies of this gradient effect are challenging because the reactions necessarily occur in inhomogeneous systems and because decoupling the thermodynamic and the kinetic processes impacting nucleation upon heating multilayers is challenging. The molecular dynamics studies allow for a degree of control over the composition gradient which is lacking in experiments, where the as-deposited gradients at layer interfaces are frequently unknown and where measurement of their evolution on heating is very challenging.

In order to explore the effects of gradients on nucleation in a more controlled system, we have begun a program wherein our goal is to determine the feasibility of fabricating amorphous thin films with composition gradients for use in thermal investigations of the gradient effect on nucleation, as well as on growth. As a first step in that program, our goals are twofold: to demonstrate that we can deposit and characterize amorphous films with known, controlled initial composition profiles, and to determine whether these gradients impact the nucleation process, in regard to nucleation temperatures (the onset of crystallization), final crystallite sizes, and activation energies for both nucleation and growth, during isochronal heating experiments. To our knowledge, this is the first attempt to control as-fabricated composition gradients in order to investigate their impact on nucleation and growth in amorphous films. With the knowledge gained by this study, we will proceed towards isothermal characterizations to further investigate and better measure the impacts of composition gradients on nucleation and growth.

Nanocalorimeters are micromachined, chip-based calorimeters capable of heating small (ng-μg) samples at heating rates ranging from 100 K/s to 105 K/s while measuring the heat released or absorbed by the samples. This is accomplished by heating a thin (100nm) low-stress silicon nitride membrane using a Ta/Pt heating strip which doubles as a resistance thermometer. The waveform used to heat the chip can be arbitrarily generated, giving wide flexibility to the range of thermal histories that can be imposed. Each heating strip has three 20 μm Transmission Electron Microscope (TEM) windows, allowing for plan-view imaging or diffraction through the amorphous silicon nitride.

The nanocalorimeters used in this study were fabricated following the procedure described in depth in Refs. 13 and 14, and summarized in supplementary material Section 1. Calibration followed the optical method described in Ref. 15 after annealing the sensors in clean air.

To create samples with large composition gradients, one must deposit a large compositional range, very thin films, or a combination of both. Amorphous films offer a much larger range of compositional stability than their crystalline counterparts, allowing for thicker films for a given gradient and a larger range of possible gradients to be deposited. To validate the experimental principle, we desire a system known to form amorphous films across a large range of compositions and which contains several crystalline phases which are isolated within a relatively large composition range and are known to form first on heating. Ideally, these phases should also have moderate heats of mixing to provide a strong calorimetric signal. Systems with very large heats of mixing will have a stronger driving force for nucleation, which may reduce the barrier to nucleation significantly and thereby offset the gradient effect in retarding nucleation.16 Copper-zirconium was selected as the first model system, as it has moderate heats of mixing, excellent glass-formability, particularly in sputtered films,17–19 and provides two promising stable phases for investigation: Cu10Zr7 and CuZr2.20,21

Of these two phases, Cu10Zr7 was selected to investigate. It is known to be the first phase to form from amorphous solutions, particularly those rich in Cu, where CuZr2 forms first or concurrently in Zr-rich solutions.20–23 We selected a range of composition from 34 atomic percentage (at%) to 48 at% of Zr for the gradient films, such that we are in the Cu-rich regime. We therefore expect Cu10Zr7 to form first, which should aid in avoiding the formation and subsequent decomposition of other Cu/Zr intermetallics such as CuZr. This composition range equates to approximately ±7 at% Zr from the bulk composition of Cu10Zr7 (≈41 at% Zr). Samples without a gradient are deposited at the bulk composition of Cu10Zr7 for comparison. Following the methods in Refs. 7 and 8 and using values acquired or calculated from Refs. 24–27, we calculate the critical gradient for the formation of Cu10Zr7 from an amorphous phase to be ∇c* = 7 × 107 m-1. A more detailed outline of the model and parameters used can be found in the supplementary material, Section 2.

As shown in Figure 1(b), samples for this study consist of 100 nm thick amorphous Cu-Zr films deposited onto the backs of the silicon nitride membranes of the nanocalorimeters, capped on either side by 10 nm of Al2O3. The samples were sputter deposited in a Denton Vacuum Discovery 550 sputtering chamber evacuated below 8 × 10-4 Pa prior to deposition. The samples were deposited through a machined shadow-mask which limits the deposition to the sensitive region of the nanocalorimeter. The composition throughout the thickness of the Cu-Zr film is controlled by co-sputtering Cu (Kurt J. Lesker, nominal 99.999 at% purity) and Zr (Kurt J. Lesker, grade 702, nominal 97.52 at% purity) and modulating the power to each magnetron throughout the deposition. Non-graded samples are deposited using constant power to both the Cu and Zr targets. In both cases, 10 nm of Al2O3 (Kurt J. Lesker, nominal 99.99 at% purity) is deposited on either side of the Cu/Zr film through the same shadow mask. The sample platen is rotated during deposition to ensure uniformity across samples.

FIG. 1.

(a) Schematic cross-section of nanocalorimeter chips used in this study, showing a 100 nm Cu-Zr film capped on either side by 10 nm of Al2O3. (b) Plan view optical image of a nanocalorimeter, highlighting the dimensions and layout of the sensors and the sample. A white dashed line marks the borders of the measurement area.

FIG. 1.

(a) Schematic cross-section of nanocalorimeter chips used in this study, showing a 100 nm Cu-Zr film capped on either side by 10 nm of Al2O3. (b) Plan view optical image of a nanocalorimeter, highlighting the dimensions and layout of the sensors and the sample. A white dashed line marks the borders of the measurement area.

Close modal

Witness substrates of SiO2 are used in the deposition process to validate film thicknesses and composition gradients. The thicknesses were verified by stylus profilometry (Bruker Dektak XT) measuring film step height. The compositions of as-deposited samples were confirmed by depth-profiling X-ray Photoelectron Spectroscopy (XPS). XPS spectra were gathered using a Mg source probing a sample area of 800 μm × 800 μm, with a step size of 0.5 eV, averaging over 10 sweeps for each peak. The peaks measured were Cu 2p (974 eV - 924 eV), Zr 3d (194 eV - 174 eV), Al 2s (133 eV -113 eV), O 1s (539 eV - 525 eV), Si 2P (111 eV - 91 eV), and N 1S (406 eV - 388 eV). Depth profiling was accomplished by 165 second Ar sputter steps covering a 7 mm × 7 mm area of sample. The acquired XPS spectra were analyzed using CasaXPS. Each peak was integrated using a Shirley background, with the integrated area normalized by relative intensity factors supplied by Physical Electronics, Inc. The Al 2s peak was deconvolved from the neighboring Cu 3s manually using CasaXPS – since the composition of the Al2O3 layer is not of concern, this was deemed sufficient. Due to the geometry of the films deposited on nanocalorimeters and of the XPS system used, it was not feasible to perform XPS on samples on nanocalorimeters, thus witness substrates of SiO2 are used instead.

Plan-view Transmission Electron Microscope (TEM) imaging (bright and dark field) and electron diffraction were performed on samples deposited onto nanocalorimeters before and after reaction using a custom TEM holder designed for ex-situ analysis in a Tecnai TF-30 TEM. The diffraction patterns were radially averaged using CrysTBox.28 Background subtraction was done in two steps as reported previously.29 First, a representative radially averaged diffraction pattern through a nanocalorimeter window with no sample is subtracted, to remove the contributions of the amorphous silicon nitride membrane, using an arbitrary scaling factor to account for any differences in thickness and signal intensity. Then a secondary baseline, which approximates an exponential decay function, is manually fitted with care taken to avoid the introduction of artifacts. A combination of diffraction data and dark field images were used to verify the presence of crystallites at various quench points throughout the reaction sequence.

All heating experiments were performed in a custom turbomolecularly pumped chamber fitted with a modified JEOL TEM side-entry stage to accept a custom TEM holder made for nanocalorimetric investigations.30 The vacuum for all experimental runs was better than 1.4 × 10-4 Pa. The waveforms used for each heating rate were calculated using the method described in detail in Ref. 11 to generate approximately constant heating rates. The applied waveform was output by a high-resolution digital to analog converter (National Instruments PXI-4461) and buffered by a unity-gain amplifier (Burr-Brown BU634). A minimum of two samples were tested for each heating rate and each gradient condition at nominal heating rates of 1 000 K/s, 2 500 K/s, 10 000 K/s, 25 000 K/s, 50 000 K/s, and 100 000 K/s.

In all experiments, the only measured quantities are the voltage across a sense resistor and the voltage across the central region of the heater of the nanocalorimeter. The voltage drop across the sense resistor is divided by the sense resistance to yield the instantaneous current flow during the experiment. This current is divided into the voltage across the heater to yield the instantaneous heater resistance, and thus the sample temperature based upon the calibrated TCR. The current is also multiplied by the voltage across the heater strip to determine the power applied to the sample, Q̇App. The calculated temperature yields the instantaneous heating rate through a time derivative. To improve experimental noise generated by this numerical derivative, the data is smoothed by a binned averaging algorithm, wherein the data is divided into bins of a characteristic size (the downsampling ratio) and averaged. The downsampling ratio is determined individually for each heating rate, decreasing with increasing heating rates. For a graphical depiction of this process, see Ref. 11.

Each sample was run first to obtain reaction signal data, then twice more for sample and sensor-specific baseline heat-flow data. No further reaction signal was evident during the baseline runs, indicating that the reaction is completed and irreversible. To analyze the reaction data in the most accurate way, we follow the method described in further detail in Ref. 11 and briefly summarized in the supplementary material, Section 3. This results in a baseline subtracted reaction power, which is used in turn to calculate a dimensionless extent of reaction, α, and subsequently the reaction rate.

A significant benefit of calculating the extent of reaction and reaction rate is that we can apply an isoconversion analysis following Friedman,31 a kinetic treatment similar to a Kissinger analysis,32 but applied to the datasets at multiple, distinct values of reaction progression, α, rather than solely at a single reaction peak as done in the Kissinger analysis. Because the heating rates for nanocalorimetry experiments are not constant, a traditional Kissinger analysis is more challenging than for traditional DSC experiments, however the isoconversion analysis is very well suited to these datasets. Grapes et al11 previously determined that there was negligible difference between the Friedman method and other advanced integral methods33 for similar nanocalorimetric experiments, and thus we apply only the simpler Friedman method.

For the isoconversion analysis, we take the natural logarithm of both sides of the reaction rate equation found in supplementary material, Section 3 (Equation (9)) at constant values of reaction progression (α) to arrive at Equation (1).11 The α subscripts in (1) indicate that these values hold only for a constant value of reaction progression, where the i subscripts indicate the experimental data. For each heating rate and each gradient condition, we have at least two data points for the reaction rate and the temperature at a given α.

lndαdtα,i=lnfαAαEaαRTα,i
(1)

The analysis is performed by generating and plotting the appropriate values of ln(dα/dt)α and (1/Tα) for a given value of α. A linear regression is then fit to the data, where the slope yields the effective activation energy, Ea, and the intercept yields lnfαAα. As in Ref. 11 we repeat this procedure over a range of values of α to create a dataset of effective activation energies as a function of α.

Following the procedure outlined in Section II C, composition profiles were characterized for two samples as a function of depth: one where the composition varies from 34 at% to 48 at% Zr over 100 nm and one with no gradient. Both have the average composition of 41 at% Zr, which matches the composition of Cu10Zr7. The results are presented in Figure 2, as a function of etch time. In this configuration, the relative thickness of the regions is distorted by their relative sputter rates, thus the Al2O3, which sputters much slower, appears thicker than it is. The composition profiles for the Cu/Zr region of the films show an excellent agreement to the desired film properties which are overlaid as dashed lines in Figure 2. The gradient produced by this composition range and thickness is ∇c = 1.4 × 106 m-1, well below the calculated critical gradient of ∇c* = 7 × 107 m-1.

FIG. 2.

(a-b) Composition versus etch time from depth-profiling XPS. (a) 100 nm Cu-Zr film with gradient from 34 at% to 48 at% Zr, capped on both sides with 10 nm Al2O3 deposited on SiNx. Dashed overlay shows desired composition profile. (b) 100 nm Cu-Zr film with no gradient capped on both sides with 10 nm Al2O3 deposited on SiNx. Dashed overlay shows desired composition profile. (c) TEM selected area diffraction pattern of a Cu-Zr film with gradient 34 at% to 48 at% Zr, as deposited on a nanocalorimeter.

FIG. 2.

(a-b) Composition versus etch time from depth-profiling XPS. (a) 100 nm Cu-Zr film with gradient from 34 at% to 48 at% Zr, capped on both sides with 10 nm Al2O3 deposited on SiNx. Dashed overlay shows desired composition profile. (b) 100 nm Cu-Zr film with no gradient capped on both sides with 10 nm Al2O3 deposited on SiNx. Dashed overlay shows desired composition profile. (c) TEM selected area diffraction pattern of a Cu-Zr film with gradient 34 at% to 48 at% Zr, as deposited on a nanocalorimeter.

Close modal

As discussed elsewhere11,13,34 the heating rates during nanocalorimetry experiments are not truly constant, partially due to the imperfect calculations of the voltage waveforms used for the experiments and partially because the exothermic reactions create a spike in heating rate which increases the mean heating rate. The ranges of actual heating rates for the experiments are presented in Table I.

TABLE I.

Experimental mean and maximum heating rates for each nominal heating rate used in isochronal nanocalorimetry experiments. The maximum values exceed the nominal rates due to spikes caused by exothermic reactions.

Experimental Heating Rates (K/s)
Nominal Heating Rate (K/s)MeanMaximum
1000 985 1 588 
2 500 2 463 3 692 
10 000 10 240 15 249 
25 000 26 186 38 718 
50 000 56 396 87 063 
100 000 114 076 184 695 
Experimental Heating Rates (K/s)
Nominal Heating Rate (K/s)MeanMaximum
1000 985 1 588 
2 500 2 463 3 692 
10 000 10 240 15 249 
25 000 26 186 38 718 
50 000 56 396 87 063 
100 000 114 076 184 695 

For both gradient conditions and for all six heating rates the resulting reaction powers and reaction rates are plotted in Figure 3. To compare the results for such a large range of heating rates, we normalize the reaction powers and reaction rates to their maximal values. There is good agreement in reaction power between the two samples tested, for both gradient and non-gradient cases, for heating rates of 1 000K/s, 10 000 K/s, 25 000 K/s, 50 000 K/s and 100 000 K/s. Because there was more variability for 2 500 K/s, a larger number of samples were tested for this heating rate – three for samples with a gradient and five for samples without. For this rate we show the average with shading marking the standard deviation.

FIG. 3.

(a) Normalized reaction power versus reaction temperature and (b) normalized reaction rate versus reaction progression, α, for 1 000 K/s (black), 2 500 K/s (blue), 10 000 K/s (light green), 25 000 K/s (gold), 50 000 K/s (pink), and 100 000 K/s (forest green). Dashed lines indicate samples with no gradient, and solid lines indicate samples with a gradient of 34 at% to 48 at% Zr over 100 nm. 2 500 K/s curves are averages of 3 (gradient) and 5 (non-gradient), with standard deviations shown as shaded regions. All other heating rates show both experiments for each composition case. Successive heating rates are offset vertically by 1 to aid in visualization.

FIG. 3.

(a) Normalized reaction power versus reaction temperature and (b) normalized reaction rate versus reaction progression, α, for 1 000 K/s (black), 2 500 K/s (blue), 10 000 K/s (light green), 25 000 K/s (gold), 50 000 K/s (pink), and 100 000 K/s (forest green). Dashed lines indicate samples with no gradient, and solid lines indicate samples with a gradient of 34 at% to 48 at% Zr over 100 nm. 2 500 K/s curves are averages of 3 (gradient) and 5 (non-gradient), with standard deviations shown as shaded regions. All other heating rates show both experiments for each composition case. Successive heating rates are offset vertically by 1 to aid in visualization.

Close modal

As shown in Figure 3, almost all curves have two distinct exothermic peaks: a small one between 430 K and 630 K and a much larger peak between 830 K and 1 050 K that is attributed to crystallization. As expected, the temperatures for these two peaks rise with heating rate. There is also a region of heat release between the two peaks which varies with heating rate. For most heating rates, the normalized reaction powers and rates were higher for the graded samples in this middle region. Focusing on Figure 3(b), one can see that the onset of the final and largest exothermic peak occurred at higher values of reaction progression, α, for the graded samples compared to the homogeneous samples. This indicates that a larger fraction of the total heat is released prior to the final peak in the graded samples.

TEM analysis of as-deposited films, both with and without gradients, revealed no discernable crystalline phases via dark field imaging or diffraction, strongly suggesting that the as-deposited films are amorphous. The brightest amorphous ring in Figure 4(b–d) and Figure 2(c) corresponds to SiN, as evidenced in prior studies.30 The two large and broad peaks in the as-deposited diffraction pattern (Figure 4(a)) indicate that our sample may be phase-separated upon deposition, as seen in previous vapor quenched Cu-Zr films.19 The broad peaks are likely representative of Zr-rich (lower angle) and Cu-rich (higher angle) phases.17,19,35,36 Based on prior diffraction data for Cu/Zr amorphous phases,17,19,36 we estimate the composition of the Zr-rich phase at 80-90% Zr, and the Cu-rich phase at 15-25 % Zr. The second set of much smaller peaks are consistent with second order reflections from the amorphous phases.36 (Note: phase separation is most likely to occur through the thickness of the film and is not obvious in plan-view images, particularly given the additional signal from the silicon nitride and alumina layers.) Samples quenched after the first exothermic peak (550 K when heated at 2 500 K/s) reveal neither crystalline diffraction rings, nor any crystallites in dark-field imaging. Samples quenched immediately prior to the main exothermic peak (800 K when heated at 2 500 K/s) similarly have no evidence of crystallites in either diffraction or dark-field imaging. The one notable change in the radially-integrated and baseline-subtracted diffraction patterns in Figure 4(a) is the slight growth of the hump on the second broad peak for the 800 K sample, compared to the as-deposited case.

FIG. 4.

(a) Radially integrated and baseline subtracted diffraction patterns throughout the reaction sequence, solid lines indicate gradient samples and dotted lines indicate non-gradient samples. (b)-(d) TEM dark field images with inset 500 mm camera length diffraction patterns of 100 nm Cu/Zr films that were quenched after heating at 2 500 K/s to (b) 550 K and (c) 800 K, and (d) that were quenched after complete reaction and subsequent baseline analysis. The TEM figures shown are of samples with an initial gradient but are representative of results for those without as well.

FIG. 4.

(a) Radially integrated and baseline subtracted diffraction patterns throughout the reaction sequence, solid lines indicate gradient samples and dotted lines indicate non-gradient samples. (b)-(d) TEM dark field images with inset 500 mm camera length diffraction patterns of 100 nm Cu/Zr films that were quenched after heating at 2 500 K/s to (b) 550 K and (c) 800 K, and (d) that were quenched after complete reaction and subsequent baseline analysis. The TEM figures shown are of samples with an initial gradient but are representative of results for those without as well.

Close modal

After a complete heating ramp, both sets of samples demonstrate strong nano-crystalline diffraction, as seen in the inset of Figure 4(d); the dark-field images indicate that the crystallites are on the order of 2-14 nm in diameter. All the Cu-Zr intermetallics have a large number of diffraction peaks, many of which have similar d-spacings making identification challenging. Furthermore, the nanocrystalline diffraction gives rise to relatively broad peaks. Each peak was considered individually and the closest match was considered amongst the phases that are likely to form (Cu10Zr7, CuZr2, Cu51Zr14, CuZr, Cu8Zr3). The expected Cu10Zr7 phase offers the best match for the observed peaks and there is no indication that we have formed more than one intermetallic phase.

Dark field images of fully reacted samples taken at different orientations suggest that the samples are completely crystalline and lack strong texture after a single, complete heating ramp. Using ImageJ we measured the average crystallite area for continuous particles and converted the areas to approximate crystallite radii by assuming spherical crystallites. The largest observed crystallites were below 12 nm, suggesting they do not extend across the 100 nm thickness of the heated samples. The largest crystallites observed were greater in samples heated at 2 500 K/s (11 nm) compared to those heated at 100 000 K/s (8 nm), and there was a commensurate shift in the distribution of crystallites to larger sizes for 2 500 K/s. Since the growth of these crystalline grains can release a significant amount of energy,37,38 we suggest that the extended period of time at elevated temperatures in the slower scans accounts for the slightly larger total heat release measured at lower heating rates.

We determined a temperature for the onset of crystallization (nucleation) for every experiment from the reaction power versus temperature plots (Figure 3(a)) by identifying the temperature at which there is a discontinuous change in slope at the start of the second distinct exotherm. While we cannot strictly follow governing standards (such as ASTM 3418) for this analysis due to the limitations of nanocalorimetry, we apply the same approach with regards to the change in slope of reaction power versus temperature to determine the crystallization temperatures. Further description of this method can be found in literature,39 and an example is shown in the inset to Figure 5. As this temperature marks the initial onset of the exotherm associated with nucleation and growth of the crystal phase, we suggest that the crystallization temperatures are equivalent to the temperatures at which nucleation first occurs, recognizing that nucleation will continue along with growth of the initial nuclei.

FIG. 5.

Crystallization onset (nucleation) temperatures versus the logarithm of heating rate for both gradient (red circles) and non-gradient (black squares) samples compared to literature values for other Cu/Zr amorphous samples. The shaded regions demonstrate the standard error of the regression for gradient (red) and non-gradient (black) samples. The inset demonstrates the method of determining Crystallization temperatures, with the single half-filled red circle data point corresponding to the value in the main plot.

FIG. 5.

Crystallization onset (nucleation) temperatures versus the logarithm of heating rate for both gradient (red circles) and non-gradient (black squares) samples compared to literature values for other Cu/Zr amorphous samples. The shaded regions demonstrate the standard error of the regression for gradient (red) and non-gradient (black) samples. The inset demonstrates the method of determining Crystallization temperatures, with the single half-filled red circle data point corresponding to the value in the main plot.

Close modal

We take a linear regression of these values versus the logarithm of the heating rate to extrapolate crystallization temperatures to traditional DSC heating rates (1 K/s). The results are compared below in Figure 5, plotted with literature values for similar crystallization experiments. The most relevant literature values20,23,40–45 are those close to the composition of the non-graded films at 41 at% Zr, as the crystallization temperature of Cu10Zr7 is dependent on composition and processing techniques.42,45–47 We also determine the extent of conversion at the onset of the major reaction peak and plot it against the crystallization temperature in supplementary material, Figure 3.

With the reaction rates, we apply the isoconversion method of Friedman11,31 to determine effective activation energies during the major crystallization peak as a function of reaction progression for α values ranging from 0.01 to 0.99 with a step size of 0.01. Using only regressions with an R2 > 0.80, activation energies are plotted in Figure 6. The differences in activation energy between the gradient and non-gradient samples are within the experimental error.

FIG. 6.

Effective Activation Energy vs reaction progression, α, for 100 nm thick Cu/Zr films with a composition gradient from 34 at% to 48 at% over 100 nm (blue) and Cu/Zr films with the same average composition and no gradient (red). Bounds indicate one standard error, only data where the linear fit has an R2 > 0.80 are shown.

FIG. 6.

Effective Activation Energy vs reaction progression, α, for 100 nm thick Cu/Zr films with a composition gradient from 34 at% to 48 at% over 100 nm (blue) and Cu/Zr films with the same average composition and no gradient (red). Bounds indicate one standard error, only data where the linear fit has an R2 > 0.80 are shown.

Close modal

As indicated by TEM and XPS, the as-fabricated samples appear to be fully amorphous with the desired composition profile through their thickness. Though there is exothermic activity in both sets of samples starting at temperatures as low as 430 K, we do not see evidence of crystallization in TEM analysis after heating to and quenching from 550 K or 800 K. The heat release in this temperature range may be caused by local ordering,48 by a growth of the phase separated regions within the samples, and by a reduction of the compositional gradient in the graded samples. For both graded and non-graded samples, the final product is nano-crystalline, with crystallites much smaller than the total film thickness.

For analysis, we divide the full exothermic reaction into three regions. The first region has a small but distinct peak with onset temperatures ranging from 430 K to 550 K. The second region provides a more gradual heat release with some evidence of a more distinct exotherm around 800 K at 1 000 K/s and around 700 K at the highest heating rate. The third region has the largest and most distinct exotherm in Figure 3(a), with onset temperatures ranging from 870 K to 960 K. In each region we integrate the heat flow and divide by the total integrated heat of reaction to determine the relative contribution of that region to the total measured value. The calculated values are shown in supplementary material, Figure 1.

Across all heating rates, for both graded and non-graded samples, the heat release in the first region remains fairly constant at approximately 10% of the total value, as shown in Table II. No difference is seen between the samples with gradients and those without. We are unsure of the cause of the exothermic heat release in this region. Oxidation of the Zr due to transfer of oxygen from the Al2O3 is not a favorable reaction until much higher temperatures.49 The calorimeters used in this study have been extensively used in previous work without a similar effect50–52 and are heated several times prior to sample deposition to avoid thermal artifacts. The TEM data does not show evidence of crystallization in this temperature region, nor is there a significant change in the phase-separated amorphous state of the film. However, local ordering could be occurring in both sets of samples, which would produce heat. Such local ordering has been reported to produce heat in other amorphous metal samples with no apparent nucleation,48 and high-resolution TEM studies have resolved these locally ordered regions.53 In this study a Kissinger analysis32 of the first peak yields activation energies of 127kJ/mol for both graded and non-graded samples (σ = 3 kJ/mol, N = 13 for graded, σ = 3 kJ/mol N = 15 for non-graded), which is in keeping with fast, short-range diffusion.

TABLE II.

Average energy released, in kJ/mol, during each stage of reaction for gradient and non-gradient samples. Uncertainties given are standard deviations, with N = 13 for graded samples and N = 15 for non-graded samples.

First RegionSecond RegionThird RegionTotal
Gradient 0.37 ± 0.03 kJ/mol 2.44 ± 0.30 kJ/mol 2.01 ± 0.08 kJ/mol 4.81 ± 0.39 kJ/mol 
No Gradient 0.37 ± 0.05 kJ/mol 1.59 ± 0.27 kJ/mol 2.01 ± 0.17 kJ/mol 3.97 ± 0.48 kJ/mol 
First RegionSecond RegionThird RegionTotal
Gradient 0.37 ± 0.03 kJ/mol 2.44 ± 0.30 kJ/mol 2.01 ± 0.08 kJ/mol 4.81 ± 0.39 kJ/mol 
No Gradient 0.37 ± 0.05 kJ/mol 1.59 ± 0.27 kJ/mol 2.01 ± 0.17 kJ/mol 3.97 ± 0.48 kJ/mol 

In the second, broad region, heat release decreases in relative magnitude as heating rate increases, mainly above 10 000 K/s. In addition, approximately 50 % more heat is released in the graded samples compared to the homogeneous samples, as shown in Table II. We attribute the majority of this heat release to enhancement of phase separation or structural relaxation, and we attribute the difference between the graded and non-graded samples to a reduction of the chemical gradient. To estimate the heat release by the gradient reduction, we calculate the enthalpy difference between the amorphous phase with and without a composition gradient using the enthalpies of formation for amorphous Cu/Zr calculated by Turchanin et al.24 We discretize the gradient into 100 increments (each nominally 1 nm) and calculate the enthalpy of formation for each thin layer. The sum of these is subtracted from the expected enthalpy of formation for an equivalent non-graded film, yielding an estimated enthalpy difference of 0.4 kJ/mol. Given the enthalpy of crystallization at this composition is expected to be around 4.5 kJ/mol (σ = 0.7 kJ/mol, N = 8),25 diffusional intermixing that removes the gradient could produce a 10 % higher heat release in the graded samples. This is somewhat lower than the difference measured in the heat released in the second region of 0.85 kJ/mol, although the errors in thermal measurement and in sample mass estimation can account for this discrepancy.

The third region, characterized by the major peak in the reaction signal, contributes a majority of the total signal at high heating rates as shown in supplementary material, Figure 1. At the lower heating rates its contribution is comparable to the second region for non-gradient samples, and smaller for gradient samples. Taking averages across all heating rates, Table II shows that the heat released in the third region is identical for the graded and non-graded samples, as it is for the first region. The major difference in the average heat release between the gradient and non-gradient samples arises in the second region, where the gradient is thought to be reduced by intermixing. The total heat of reaction measured for both sample sets fall within the range of previously reported values for similar compositions of 4.5 kJ/mol (σ = 0.7 kJ/mol, N = 8).25 

As mentioned above, a Kissinger analysis32 of the first peak yields consistent results of 127kJ/mol across both gradient and non-gradient samples. Since the second reaction region has no distinct peak, a Kissinger analysis cannot be performed. Attempts to apply the isoconversion method of Friedman yield poor regression fits for a broad range of the reaction and are therefore unreliable and are not included. The only results of note from that analysis is that the beginning of the second reaction region has an apparent activation energy of approximately 170 kJ/mol, similar to the first peak, while the end of the region has an apparent activation energy of approximately 315 kJ/mol, similar to the start of the main nucleation and growth peak. This is consistent with an evolution in the active processes in which the ones with the lowest thermal barriers (local atomic rearrangement and atomic intermixing) dominate early and those with higher thermal barriers (crystal nucleation and growth) appear later.

The isoconversion analysis of the crystallization peak in Figure 6 yields results within the error of the calculation between the sample conditions. This indicates that there is minimal effect of the initial gradient on the main reaction peak that is associated with the nucleation and growth of Cu10Zr7. Both curves are marked by an initial value of around 300 kJ/mol, which rises rapidly to approximately 375 kJ/mol, where it stays relatively constant for the rest of the peak. The initial value around 300 kJ/mol can be attributed to nucleation of the crystalline phase in the amorphous film, while the long, relatively-constant region suggests that the reaction process is consistent during this stage and is likely dominated by growth of Cu10Zr7 nuclei.

The measured activation energies are consistent with those obtained from slow heating DSC experiments on other Cu/Zr systems. In Cu/Zr multilayers, where there exist a series of reactions, individual activation energies have been measured to range from 190 kJ/mol to 260 kJ/mol.38 For crystallization from bulk amorphous Cu/Zr samples, activation energies have been measured for various compositions such as 315 kJ/mol (CuZr2),54 518 kJ/mol (Cu62Zr38),55 or 400 kJ/mol (Cu56Zr44).21 Nanocalorimetric results for crystallization of Cu/Zr thin films range from 100 kJ/mol to 380 kJ/mol.23 These activation energies were determined by traditional Kissinger analysis and if we apply a traditional Kissinger analysis to the third, large peak, we find lower but equally consistent activation energies of 290 kJ/mol for graded samples and 305 kJ/mol for homogeneous samples.

When we plot reaction power versus temperature (Figure 3(a)), we do not see a clear indication of a glass transition in our samples. Previous work involving binary Cu-Zr glasses have shown that the glass transition temperature is generally very close to the crystallization temperature18,21–23,42 and in some cases it was not seen at all.18 When we extrapolate the crystallization onset (nucleation) temperatures measured here to those from low heating rates experiments using similar compositions, we find slightly lower crystallization temperatures than those reported in literature. Figure 5 shows this extrapolation, along with the standard error of the regression. We suggest that the difference is insignificant given we are extrapolating over several orders of magnitude in heating rate. We also find somewhat higher extrapolated crystallization temperatures for samples with gradients, compared to non-gradient samples. However, the difference is not statistically significant.

Given that we have demonstrated the ability to produce amorphous, compositionally graded samples and the capability to characterize them and measure the impacts of gradients in isochronal experiments, we see this work as a first step in directly investigating the effects of composition gradients on nucleation. Future films will be deposited with sharper gradients by reducing the thickness over which the composition changes to values as small as 10 nm. A film with the same overall chemistry but changing in composition from 34 at% to 48 at% Zr over 10 nm yields a gradient of ∇c = 1.4 × 107 m-1. In addition to the isochronal scans, we aim to apply in-situ isothermal TEM experiments using nanocalorimetry to obtain more direct measures of the effects of gradients on nucleation rate.

We present the first results of what is, to the best of our knowledge, a first attempt to directly control initial composition gradients in order to measure their effects on nucleation and growth. After depositing amorphous Cu-Zr thin films onto nanocalorimeters with a compositional gradient of ∇c = 1.4 × 106 m-1 through their thickness, we performed isochronal experiments at heating rates ranging from 1 000 K/s to 100 000 K/s, but did not see distinct differences in crystallization with samples deposited with the same average composition of 41 at% Zr but no composition gradient. All samples exhibit signs of amorphous phase separation prior to reaction, a phenomenon which has previously been seen in other vapor-quenched Cu-Zr films but is not frequently reported. For both sets of samples we found three distinct regions of heat release: a small but sharp exotherm at temperatures ranging from 430 K to 630 K that is attributed to local ordering, gradual heat release over the next 300 K to 400 K that is attributed to extended phase separation and interdiffusion, and a large exotherm between 830 K and 1 050 K that is attributed to nucleation and growth of the Cu10Zr7 crystalline phase. Combining Kissinger analysis and isoconversion analysis, we find the activation energies of the first and third regions. The effective activation energy rises from the first region to the third and evidences a sharp rise to a plateau during region 3, indicative of nucleation of the crystalline phase giving way to growth. The transition to region 3 occurs at a higher value of α for samples with a gradient, which is attributed to a reduction of the concentration gradient due to interdiffusion within region 2. The graded samples produce a slightly higher total heat release, as expected, but the crystallization temperature of samples with gradients do not differ significantly from those of samples without gradients. The measured activation energies, crystallization temperatures, and total heats match those reported in literature. We conclude that the gradients deposited in this study are not steep enough to affect nucleation in an isochronal experiment, given that diffusion through the amorphous film can relax the gradient during heating to crystallization temperatures. Future studies will utilize samples with sharper composition gradients and in situ characterization of nucleation rates during isothermal TEM experiments, and will also consider other material systems where amorphous phase separation may be avoided.

See supplementary material for further detail on nanocalorimeter sensor fabrication, the full calculation of the critical gradient for nucleation in Cu-Zr, an expanded explanation of the method employed to analyze nanocalorimeter data, a figure demonstrating the relative magnitudes of each reaction region and of the total heat of reaction as a function of heating rate, a video demonstrating the effect of concentration gradients on the critical nucleus size, and a figure plotting the extent of reaction at the onset of crystallization for each experiment.

Certain commercial equipment, instruments, or materials are identified in this document. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products identified are necessarily the best available for the purpose. Nanocalorimeter fabrication was performed in part at the NIST Center for Nanoscale Science & Technology (CNST). This research was supported in part by the National Science Foundation through Grant No. DMR-1308966, and in part by the Department of Energy through Grant No. DE-SC001910777. SQA gratefully acknowledges support through a Draper Fellowship from the Charles Stark Draper Laboratory and useful conversations with Professors Todd Hufnagel, Evan Ma, and Michael Falk.

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Supplementary Material