Introduction

Professor Kamanio Chattopadhyay was creating knowledge at least two years before I took up doctoral research. His first paper in 1974, dealt with the structure of a eutectic alloy solidified over a heat pipe that he constructed himself (Fig. 1). The pipe has a chilling effect on any hot object that it comes into contact with; significantly, it is able to mitigate any unintended temperature excursion, such as might follow recalescence during solidification. The equipment therefore enabled large undercoolings to be achieved below the equilibrium freezing temperature [1].

Figure 1
figure 1

Original diagram of the heat pipe, ‘a versatile heat transfer device’, constructed for the experiments on an aluminium–copper eutectic. Its assembly involved some scavenging of a junk yard to harvest bits and pieces needed to build a respectable device [2]. Image from Chattopadhyay and Ramachandrarao [3] reproduced with permission of Elsevier.

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That study was followed up a couple of years later, with publications on splat cooling experiments [4] and vapour deposition, aimed again at achieving greater undercoolings and extending the range of solubility of the nickel in aluminium, beyond that permitted by equilibrium. These were the heady days of battling thermodynamic constraints. The vapour deposited samples revealed, for the first time, multiple twinned particles in aluminium alloys, particles that were not too stable when subjected to examination in an 80 kV beam of electrons [1].

There was a brief excursion into the rapid cooling of a tool steel, ordered structures in a melt spun Fe–Si alloy, austenitic ductile iron, icosahedral FeTi\(_2\), the iron–germanium system, but much of the subsequent work involved anything other than iron, or iron as a supplement. I felt therefore that Professor Chattopadhyay would be especially interested in an article on undercooled pure iron. He has written on the special behaviour of nanoparticles [5] and small particles [6]—glassy pure iron is limited to these length scales so I imagine that will intensify his interest. Pure amorphous iron is difficult to make in any sizeable quantities, so practical applications are unlikely—it nevertheless is a stimulating topic.

Pure iron prefers to crystallise so to induce it into an amorphous solid necessitates cooling rates that we shall see are unachievable in practice. It is possible to precipitate slightly impure amorphous iron particles that are tiny, or films that are thin. Calculations that are revealing not only of the atomic configuration of the disordered solid, but which explain its magnetic and other characteristics, are possible. The caveat is that they should verifiably demonstrate configurationally frozen disorder.

Pair correlation functions

Any simulation of the atomic structure of amorphous iron must reproduce the experimental function describing the distribution of distances between a reference atom and another, in a given volume; it must also achieve a packing fraction that is close to the crystalline state [7]. If a reference atom sits at the origin \(r=0\), the pair correlation function \(g\{r\}\) gives the probability \(g\{r\}4\pi r^2\,\textrm{d}r\) for another atom to be located at a distance r and \(r+\textrm{d}r\) [8]. The particular characteristic of this function for glassy iron is that the peak representing the second neighbours is split into two subsidiary maxima (Fig. 2). This splitting is a reflection of the atomic packing, best described in terms of Voronoi polyhedra and their connections. The stronger first sub-peak is attributed to polyhedra that share three atoms, the second where they share one atom and the dip in the middle to two-atom shared connections [9]. This splitting and the relative intensities of the two sub-peaks are regarded as an important validation of any model for the structure of amorphous iron when compared against experimental pair correlation functions. Thus, the random packing model originally representing the liquid state with the irregular and dense piling of spheres [10] fails in this respect. Other computations involving hard-sphere random-stacking fare better using specific criteria by which an amorphous cluster is built up from a seed onto which other atoms are attached in a stepwise manner [11, 12].

Figure 2
figure 2

A pair correlation function for an iron-based metallic glass (Fe-B). Schematic diagram using selected data from [13]. The distance r is with respect to a reference atom and the vertical distance could be identified with the number of atoms per unit volume.

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Simulations

A technique used to study the pair correlation functions of the different states of iron is a molecular dynamics simulation, which begins with a cubic arrangement of thousands of atoms. Furthermore, the notional assembly of atoms can be heated or cooled to examine transitions. The real-time scales in such simulations are incredibly small so it is ‘easy’ to implement very large temperature changes. The molten assembly can be cooled so rapidly that the iron assumes a glassy state. Referring to Fig. 3, the calculated pair correlation function for the liquid generated at 2000 K and zero pressure shows a monotonic second peak, but on quenching to 300 K (zero pressure) the second neighbour peak splits into the sub-peaks characteristic of a glass.

Figure 3
figure 3

Pair correlation functions calculated using molecular dynamics simulations. The data for 2000 K are consistent with the liquid state of pure iron. The cooling rate \(\vert \dot{T}\vert\) to 300 K was \(10^{13}\,\mathrm{K\,s^{-1}}\). The arrows highlight the splitting of the second peak of the amorphous solid iron into two sub-peaks, to be compared against the function for the liquid where the second peak is a single maximum. The vertical origin of each set of data is arbitrary. Selected data from Mo et al. [14].

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Voronoi polyhedra can be expressed as \(\langle n_3,n_4,n_5,n_6\rangle\) where \(n_i\) refers to the number of i-edged faces. Simulations indicate that the distribution of atoms in amorphous iron, have polyhedra corresponding to \(\langle 0,2,8,4\rangle\), \(\langle 0,3,6,4 \rangle\), \(\langle 0,1,10,2\rangle\) (Fig. 4) as the dominant construction blocks at ambient pressure [14], and some further data are shown in Table 1. Although some of these parameters can be similar for the amorphous and body-centred cubic forms of iron, the polyhedra in the former are likely to be distorted when compared against the regular ones in the crystalline form.

Figure 4
figure 4

Dominant polyhedra (construction blocks) indicating the spatial distribution of atoms in amorphous iron.

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The simulations indicate that liquid iron would need to be quenched at \(\vert \dot{T}\vert \approx 10^{13}\,\mathrm{K\,s^{-1}}\) to solidify as a glass; this applies for pressures up to about 20 GPa. Pressures in excess of 20 GPa favour solidification to the crystalline state which has a smaller specific volume, giving rise to the peaks in the pair correlation function corresponding to the long-range periodicity of the structure [14]. It does not therefore seem possible to obtain sizeable chunks of pure, glassy iron.

The simulation cannot be replicated experimentally. But solids other than iron are known to undergo an amorphous to a denser amorphous state, apparently a first-order transformation induced by pressure. Low-density, amorphous ice when compressed at a pressure of about 10 atmospheres undergoes a sharp transition into another form of denser amorphous ice [15]. However, an amorphous\(\rightarrow\)crystal transition under pressure is rare, but it does occur in silicon. High-density amorphous silicon crystallises into the presumably denser primitive hexagonal crystal structure at a pressure of about 14 GPa [16]. Similar transitions occur in amorphous Zr-based alloys [17] and amorphous selenium [18]. It is reasonable therefore, to accept the simulation result that at sufficiently large (hydrostatic) pressures, pure amorphous iron should crystallise.

From an experimental point of view, uniaxial compression of certain bulk metallic glass causes quasicrystals to germinate in shear bands, but this amorphous\(\rightarrow\) crystalline transformation has been attributed to adiabatic heating due to the rate of deformation within those bands [19].

Another molecular dynamics simulation dealt with the quenching of liquid iron to 50 K; a completely amorphous state could be achieved when \(\vert \dot{T}\vert \ge 10^{12.3}\,\mathrm{K\,s^{-1}}\) [20]; this is consistent with the simulation in [14]. An examination of the atomic configurations indicated that a mixture of amorphous and \(\upalpha\)-iron crystals forms when \(10^{11.98} \le \vert \dot{T}\vert \le 10^{12.3}\,\mathrm{K\,s^{-1}}\)Footnote 1 and completely crystalline at any slower rates. A latent heat of transformation was observed only when the liquid crystallised. Interestingly, the cooling rate below which crystallisation sets in was estimated using independent homogeneous nucleation theory of the solidification of pure liquids [21] and agrees with the molecular dynamics simulations. Indeed, laser pulsing of pure iron is estimated to cool the surface at \(\vert \dot{T}\vert \approx 10^{10}\,\mathrm{K\,s^{-1}}\) but careful characterisation shows that the surface maintains crystallinity [22].

The molecular dynamics method [14] has been used to simulate the stress versus strain behaviour of pure iron metallic glass during uniaxial compression. Recalling that the method starts with a cubic arrangement of thousands of iron atoms, the box was compressed along one of its edges at a huge strain rate of \(1\times 10^{10}\,\textrm{s}^{-1}\). The yield strength was found to be very large at \(\approx 5\,\)GPa, followed by a decrease in the stress required to propagate deformation to about 3.5 GPa, which remained about constant to a plastic strain of 0.5. However, the Young’s modulus was recorded at just 90 GPa, which is much smaller than observed for iron-based bulk metallic glasses where it is in the range 192–213 GPa [23], close to the isotropic modulus for crystalline \(\upalpha\)-iron (210 GPa). Experimental stress–strain curves from uniaxial compression [23] do not show the maximum recorded in the simulation [14] (Fig. 5). It is probable that much of the simulated curve beyond yield is an artefact of the method.

Figure 5
figure 5

Metallic glasses uniaxially compressed. The curve with the larger modulus is from a bulk metallic glass of composition \(\mathrm{Fe_{64.5}Mo_{14}C_{15}B_6Er_{0.5}}\) [23], whereas the other one is a simulation of the uniaxial compression of amorphous pure iron using selected data from [14].

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Experimental

An amorphous configuration of atoms in a solid alloy was first discovered in a gold–silicon alloy that was quenched from the liquid state [24]. That work stimulated an entire field of research on metallic glasses. Whereas iron has formed the basis of many metallic glasses, it is not feasible to obtain sizeable samples of pure iron in a glassy state.

However, small particles about 30 nm in size can be produced by subjecting an organometallic iron pentacarbonyl Fe(CO)\(_5\) to intense ultrasound (20 kHz, 80 W cm\(^{-2}\)) that causes cavities in the liquid to form and collapse, processes associated with momentary high temperatures and pressures. The effective heating and cooling rates in such events exceed \(10^9\,\mathrm{K\,s^{-1}}\), resulting in the generation of amorphous iron particles that for further studies are filtered and washed in dry pentane while being kept away from oxygen and moisture [25, 26].

The particles are found to be ferromagnetic under ambient conditions with a magnetic moment of 1.7 \(\mu _{\textrm{B}}\) per atom. The Curie temperature based on an assessment of a large quantity of data is \(\approx 200\) K [27]. This compares with 2.22\(\,\mu _{\textrm{B}}\) per atom of crystalline \(\upalpha\)-iron, which has a much greater Curie temperature of 1042 K. The reduction in magnetic moment in the amorphous condition is probably because there is a distribution of exchange interactions that can lead to mixed magnetism, with confusion between ferro- and antiferromagnetic coupling [28].Footnote 2 The amorphous iron cannot strictly be defined as ferromagnetic; because of the disorderly arrangement of atoms, the ferromagnetic axis ‘wanders under the influence of the local balance of exchange’, a phenomenon defined as asperomagnetism [29]. The evidence for the asperomagnetic state comes from calculations where the density of amorphous iron is unfortunately set at only 7.39 g cm\(^{-3}\) [30]. A value closer to 7.6 g cm\(^{-3}\) is realistic [31] and consistent with an atomic packing density of about 0.66 obtained in a model of the amorphous state that correctly reproduces the pair correlation function shown in Fig. 3 [7]. It may still therefore be reasonable to regard glassy iron with its large magnetic moment per atom as ferromagnetic below \(T_{\textrm{C}}\) [27, 31, 32].

Small amorphous iron particles can also be produced from a ferric chloride solution that is treated with NaBH\(_4\) to reduce Fe\(^{3+}\) directly into iron [33], followed by magnetic separation and washing (Fig. 6). Ingenious experiments have been conducted on such particles using in situ heat treatment in a transmission electron microscope, to cause the particles to crystallise. The \(\upalpha\)-iron crystals that form on heating to 773 K grow rapidly until the amorphous phase is consumed in its entirety.

Figure 6
figure 6

Amorphous iron particles obtained from a solution by the chemical reduction of Fe\(^{3+}\). The diffuse electron diffraction pattern is consistent with an amorphous state. Image adapted from Falqui et al. [33] under the CC BY 4.0 licence, https://creativecommons.org/licenses/by/4.0/.

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The crystallisation occurs in the range 585–775 K as the iron atoms become mobile. Nothing much is known about the evolution of the crystals within the amorphous matrix, or whether the particle surfaces play a significant role. For reasons that are not clear, small particles (\(\approx 200\,\)nm) crystallise at a higher temperature during continuous heating, all other things being equal [34], with transformation monitored using differential scanning calorimetry. The amorphous nanoparticles are magnetically soft (narrow hysteresis loop), so much so that the magnetic coercivity is close to zero at 300 K; it is only 190 Oersteds at 5 K but even this might be an artefact of the rate of the experiment (Fig. 7) [26]. The nanoparticles are unlikely to contain domain boundaries, so the magnetic softness is because there is no favoured direction along which the magnetic moments would prefer to be oriented [35], unlike the case for \(\upalpha\)-crystals.

Fig. 7
figure 7

Hysteresis loops for amorphous iron (a) at 300 K. (b) At 9 K. One Tesla equals 10\(^4\) Oersteds assuming a magnetic field in free space; 1 emu g\(^{-1}\equiv 1\,\mathrm{A\,m^2\,kg^{-1}}\). Reprinted with permission from Grinstaff et al. [26], copyright 1993 by the American Physical Society.

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The presence of carbon in otherwise pure iron makes it easier to obtain the glassy state. A steel containing \(\approx 4.3\)C wt% displayed substantial quantities of glass that could then be induced to crystallise on heating [36]. This is relevant to the amorphous iron produced using the pentacarbonyl method, because this iron is found to contain up to 3C wt% and up to 1 wt% of oxygen, perhaps from the pentane used to wash the reactive powder after synthesis [26, 37]. With a different preparation method involving the pentacarbonyl, about 2.6 wt% of carbon has been reported within the amorphous iron [38]. When such particles are heated, they crystallise into a mixture of cementite and \(\upalpha\)-iron [39]. Films 1–2\(\,\upmu\)m thick of amorphous iron containing between 20–65C at.% can be made by sputtering [40]; these are much thicker than achieved for pure iron in the amorphous state (Sect. 7), confirming the role of carbon in stabilising the state.

Table 1 Properties of pure, amorphous iron.
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Colloidal suspensions of amorphous iron

Dispersions of iron particles can be produced by heating Fe(CO)\(_5\) to \(\approx 150\,\) \(^\circ\)C in dilute solutions of polymers in an oxygen-free environment [41]. Particles smaller than \(\approx 10\) nm tend to be amorphous and some of the larger particles can contain amorphous cores surrounded by crystalline \(\upalpha\)-iron. They are magnetically single domain, with the magnetic moments within each particle aligned at ambient temperature. However, in a collection of particles, the net magnetic moment of each particle can point in any direction, rather like paramagnetism, but since each ferromagnetic particle has very many coupled atomic moments, the phenomenon is known as superparamagnetism, illustrated in Fig. 8. The average magnetisation of this collection of particles sums to zero. When an external field is applied, the moments of the particles align to that, but the saturation magnetisation is less than found with the crystalline form, the discrepancy attributed to crystalline disorder and surface effects [41].Footnote 3

Figure 8
figure 8

Illustration of the difference between paramagnetism where the individual magnetic moments are randomly aligned, and superparamagnetism where clusters of moments are randomly aligned in a suspension of nanoparticles.

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Thin films of amorphous iron

Thin objects can have different properties than bulk samples. Just to set this into context, there are two special magnetic effects associated with crystalline thin films of iron [44, p.43, ]. First, the magnetic moment per atom becomes especially large (3.1 \(\mu _{\textrm{B}}\)) when compared with bulk iron (2.2 \(\mu _{\textrm{B}}\)). Secondly, there exists a large magnetic anisotropy in thin epitaxial films of iron. The increase in the magnetic moment per atom is due to the smaller coordination number for atoms in a thin film. The atoms of the substrate used to produce the thin film do not contribute to the coordination number because there is a lack of hybridisation between the electronic states of the iron layer and the substrate [45, 46]. The d-bands in bulk ferromagnets are much broader than they would be for a single atom because of hybridisation between atoms. In reducing the number of nearest neighbours, the hybridisation is reduced so the bands become ‘atom-like’. This squashing of the d-bands increases the density of states at the Fermi level and resolves the majority spin-up band from the minority spin-down band. A low-coordination atom therefore has more electrons in its majority spin-up band, and so a larger moment per atom. An isolated atom has the highest moment and the bulk material the lowest. Reducing the coordination makes the material less bulk-like and more single atom-like.

The magnetic anisotropy seen in thin films is a general feature found even in bulk iron where it is more readily magnetised along the \(\langle 100 \rangle\) axis [47]. Anisotropy is caused by the coupling of the directions of the spin magnetic moments and orbital magnetic moments. For a thin film of iron, the net effect is often such that it causes the spins to align in a direction normal to its plane. Thin layers of iron separated by intervening layers of chalcogenides have been found to be highly anisotropic with the internal field perpendicular to the plane [48]. Such materials show a large change in resistance as the magnetic field is altered and could conceivably have applications in recording devices.

Thin film effects pervade in other materials. In recent work, Chattopadhyay and co-workers showed that manganese–telluride thin films prepared by exfoliating liquid exhibited huge magnetic saturation when compared with the bulk material at ambient temperature [49]. At the same time, the antiferromagnetic behaviour of bulk samples was replaced by paramagnetism in the thin film form. The Néel temperature shifted from 307 K to 290 K in the two-dimensional form, which is consistent with its paramagnetic behaviour at ambient temperature (\(\approx 300\,\)K).

Focusing now on iron, there are multiple ways of depositing thin films, one being the evaporation of iron onto a thick amorphous carbon substrate at a pressure of \(8\times 10^{-3}\) Pa, with the thickness of the film increasing at \(\approx 0.5\mathrm{\,nm\,s^{-1}}\) [50]. Each film was deposited as a circular disc of uniform thickness but tapering to zero at the edge. With the substrate at liquid helium temperature (4.2 K), the film evolves in an amorphous state but crystallises spontaneously at that temperature, by islands of amorphous material transforming suddenly into single crystals. This happened on reaching a critical film thickness which is 3.4 nm or 25 nm for deposited disc radii of 25 \(\upmu\)m and \(5\,\upmu\)m, respectively. This dependence on disc radius has its origins in the stress generated either by the crystallisation event that leads to densification, effectively of a constrained film, and possibly magnetostriction effects.

Only crystalline \(\upalpha\)-iron is obtained when deposited with a substrate temperature of 300 K, with a grain size that is much finer than obtained during the spontaneous crystallisation of the sample deposited at 4.2 K. It is possible that the larger grain size in the latter case is due to local heating during sudden crystallisation [50].

Sputtering has been used to produce structures that have alternating layers of iron and another element such as gadolinium and dysprosium [51, 52]. The iron when first deposited remains amorphous, but on reaching a certain thickness, the entire layer crystallises. It is suggested that this has to do with the misfit between iron and the dissimilar layers, which accumulates as its thickness increases, until the influence of the interface diminishes to the point where crystallisation sets in.

Summary

Pure iron is interesting—it occurs as a liquid, vapour, crystalline form (body-centred cubic, cubic close-packed, hexagonal close-packed, trigonal and tetragonal crystal structures) and has been produced as an amorphous solid. However, the amorphous state is not achieved easily, and when samples are successfully made, they are very small in size, either as small particles or as thin films. There is no application as yet, in spite of the good intentions of the opening paragraphs of many publications. The subject nevertheless is fascinating and has inspired considerable theoretical efforts ranging from the random physical arrangement of hard balls, to computational simulations that deal with many thousands of atoms. These simulations have rather nicely identified the conditions needed to produce pure iron in an amorphous state, disclosing the locations of atoms and images indicating the coexistence of the glassy and crystalline states under appropriate circumstances. There has even been a daring attempt to simulate the stress–strain curve in uniaxial compression of glassy iron to very large plastic strains, but there remain many unexplained features in the predicted behaviour.

Finally, it is a veritable pleasure to acknowledge Professor Kamanio Chattopadhyay, whose presence I have felt in both India and the UK. One of the nicest people I have had the privilege to meet and a brilliant scientist to boot.