ARL-TR-7985 ● MAR 2017

US Army Research Laboratory

Field-Induced Texturing of Ceramic Materials 

for Unparalleled Properties

by Raymond Brennan, Victoria Blair, Nicholas Ku, 

Krista Limmer, Tanya Chantawansri, Mahesh Neupane, 

Berend Rinderspacher, Jennifer Elward, Constantine 

Fountzoulas, Michael Kornecki, Selva Vennila Raju, Carli 

Moorehead, Erik Nykwest, Joseph Marsico, Dinesh Agrawal, 

Gerard Ludtka, Orlando Rios, and Shenqiang Ren

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Destroy this report when it is no longer needed. Do not return it to the originator.
ARL-TR-7985 ● MAR 2017

US Army Research Laboratory

Field-Induced Texturing of Ceramic Materials 

for Unparalleled Properties

by Raymond Brennan, Victoria Blair, Nicholas Ku, 

Krista Limmer, Tanya Chantawansri, Mahesh Neupane, Berend 

Rinderspacher, Jennifer Elward, Constantine Fountzoulas,

Michael Kornecki, and Selva Vennila Raju

Weapons and Materials Research Directorate, ARL

Carli Moorehead

Drexel University, Philadelphia, PA

Erik Nykwest

University of Connecticut, Storrs, CT

Joseph Marsico 

Rochester Institute of Technology, Rochester, NY

Dinesh Agrawal

Pennsylvania State University, University Park, PA

Gerard Ludtka and Orlando Rios

Oak Ridge National Laboratory, Oak Ridge, TN

Shenqiang Ren

Temple University, Philadelphia, PA

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1. REPORT DATE (DD-MM-YYYY)

March 2017

2. REPORT TYPE

Director’s Strategic Initiative (DSI)

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October 2014–September 2016

4. TITLE AND SUBTITLE

Field-Induced Texturing of Ceramic Materials for Unparalleled Properties

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Raymond Brennan, Victoria Blair, Nicholas Ku, Krista Limmer, 

Tanya Chantawansri, Mahesh Neupane, Berend Rinderspacher, 

Jennifer Elward, Constantine Fountzoulas, Michael Kornecki, Selva Vennila 

Raju, Carli Moorehead, Erik Nykwest, Joseph Marsico, Dinesh Agrawal, 

Gerard Ludtka, Orlando Rios, and Shenqiang Ren

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

US Army Research Laboratory

ATTN: RDRL-WMM-D

Aberdeen Proving Ground, MD 21005-5069

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ARL-TR-7985

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14. ABSTRACT

The objective of this research was to characterize and exploit effects of energetic fields (microwave, magnetic, etc.) on 

microstructural development of materials to formulate a physical explanation of the fundamental mechanisms dictating material 

interactions during processing. This strategy was used to develop processing methods and computational modeling capabilities 

for synthesizing transparent noncubic alumina (Al2O3) through magnetic alignment of particles during forming and heat 

treatment, microwave-enhanced densification, and high-energy field microstructure and crystalline phase transformation 

control. The influence of dopant addition on phase formation, grain alignment, and enhancement of material response to applied 

fields was also assessed. These interactions were explored by utilizing external fields to initiate simultaneous grain size reduction 

and crystallographic texturing enhancement.

15. SUBJECT TERMS

Director’s Strategic Initiative (DSI), alumina, rare-earth dopants, magnetic field, microwave field

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Raymond Brennan

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(410) 306-0913

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Contents

List of Figures v

List of Tables viii

Acknowledgments ix

1. Introduction and Background 1

1.1 Materials Synthesis and Processing 1

1.2 Field-Enhanced Processing and Crystallographic Texturing 3

2. Synthesis and Processing of Er-Doped Alumina 5

2.1 Powder Synthesis 5

2.2 Initial Powder Characterization 7

2.3 Powder Morphology 10

2.4 Undoped Alumina vs. Er-Doped Alumina 12

2.5 Lanthanide-Doped Alumina Series Preparation 15

3. Advanced Characterization of Dopants Effects on Alumina 16

4. Density Functional Theory Modeling and Simulation 23

5. Microwave Sintering of Rare-Earth-Doped Alumina 27

6. Magnetic Field Processing of Rare-Earth-Doped Alumina 34

6.1 DFT Modeling of Magnetic-Field Effects 34

6.2 High-Temperature DSC Characterization under Applied Magnetic 

Field 43

6.3 Magnetic Field Texturing of Epoxy Samples 45

6.4 Magnetic Field Texturing of Gel Cast Samples 55

7. Conclusions 59

8. Transitions 62
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9. References 64

10. Bibliography 69

List of Symbols, Abbreviations, and Acronyms 72

Distribution List 74
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v

List of Figures

Fig. 1 Estimated transitions of Al2O3 from crystallized aluminum hydroxide 2

Fig. 2 Schematic of the magnetic alignment mechanism.................................5

Fig. 3 Schematic of principle described by Eq. 1.............................................5

Fig. 4 Schematic representation of rare-earth-doped alumina sample 

preparation .............................................................................................7

Fig. 5 Heating schedule used for the dried precipitate AACH samples in HTXRD.......................................................................................................8

Fig. 6 DSC data showing the heat flow vs. temperature where exothermic 

reactions are down and endothermic reactions are up ...........................9

Fig. 7 Flow chart of the precipitated powder phase development .................10

Fig. 8 TEM image of the precipitate calcined at 230 °C to obtain boehmite, 

AlO(OH) ..............................................................................................10

Fig. 9 TEM image of the precipitate calcined at 1050 °C to obtain θ-Al2O3.11

Fig. 10 TEM image of powder calcined at 1350 °C to obtain α-Al2O3 ...........11

Fig. 11 SEM image of the powder calcined at 1350 °C to obtain α-Al2O3 .....12

Fig. 12 High-temperature DSC data comparing Er-doped Al2O3 to undoped 

Al2O3 (heating rate 3 °C/min)..............................................................13

Fig. 13 HT-XRD of undoped AACH. The figure identifies where specific 

transformations occur as well as the specific space groups of each 

phase. ...................................................................................................14

Fig. 14 HT-XRD of Er-doped AACH. The figure identifies where specific 

transformations occur as well as the specific space groups of each 

phase. ...................................................................................................15

Fig. 15 SEM images of Ln-doped alumina. The scale bar is 1 μ.....................15

Fig. 16 a) Overlay of 1-D 27Al MAS NMR spectra for Al2O3, Er-doped Al2O3, 

undoped α-Al2O3 phase and undoped θ-Al2O3 phase. The MAS rate 

was equal to 10 kHz. b) 2-D 27Al MQ-MAS spectra of undoped Al2O3; 

c) 2-D 27Al MQ-MAS spectra of Er-doped Al2O3...............................17

Fig. 17 a) High-temperature DSC curves of Al2O3 (purple) and Er-Al2O3 (red); 

b) SEM image of Er-doped Al2O3 .......................................................19

Fig. 18 2-D MQ-MAS spectra of Ln-doped Al2O3 ..........................................20
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vi

Fig. 19 a) Low-angle HR-XRD data of the Ln-doped alumina. From top to 

bottom: Ln = Pr, Er, La, Gd, Yb, Nd, Tm, Lu, Dy, respectively. The 

data were sequentially offset by a factor of 10 for clarity. The peaks 

denoted “*” represented the α-phase and the peaks denoted “o” 

symbols represented the θ-phase. b) Graphical representation of the αand θ-phase populations at ~1300 °C. The Dy- and Lu-doped alumina 

exhibited only α-phase. c) Graphical representation of Ln-cationic 

phase fraction, octahedral coordination radius and phase diameters. 

The data points represented Ln-series elements in decreasing order of 

atomic number, moving from left to right (Lu, Yb, Tm, Er, Dy, Gd, 

Nd, Pr, and La). The diameter was represented by the orange data 

points and the phase fraction was represented by the blue data points. 

A refinement summary of all Ln3+ doped alumina was included. d) 

SEM images of Dy- and Tm-doped alumina. ......................................22

Fig. 20 Schematic representation of Al2O3 unit cells a) α-Al2O3 and b) θ-Al2O3

with atomic coloring of the smaller Al (blue) and larger O (red)........23

Fig. 21 Changes in local structural properties: a) Ln-O bond length (solid) and 

change in substitutional site volume (dashed), and b) quadratic 

elongation (solid) and bond angle standard deviation (dashed), as a 

function of dopant ionic radius (octahedral, 3+) for Ln-doped α- and θAl2O3 at different lattice sites. The error bars (A) represent the range 

of Ln-O bond distances........................................................................25

Fig. 22 DFT calculated a) cohesive energy (Ecoh) and b) defect formation 

energy (Edefect) for Ln-doped α- and θ-Al2O3 with composition 

Al47LnO72 .............................................................................................26

Fig. 23 XRD patterns for calcined Er-doped Al2O3 powder and microwave 

sintered sample SM-30:70. The inset shows the (420) peak of the 

Er3Al5O12 phase and the (104) peak of the Al2O3 phase, which were 

used to determine the peak-height ratios given in Table 2. .................30

Fig. 24 Ratio of magnetic to electric field strength vs. density of all 

microwave-sintered Er-doped Al2O3 (dashed line represents density of 

conventionally sintered Er-doped Al2O3) ............................................31

Fig. 25 Ratio of magnetic to electric field vs. equivalent vol% of ErAG of all 

microwave sintered Er-doped Al2O3 (dashed line represents equivalent 

wt% of conventionally sintered Er-doped Al2O3)................................32

Fig. 26 SEM images of sample MM using secondary electrons. A high degree 

of porosity can be seen in the region which was ion-polished. ...........33

Fig. 27 a) SEM images of sample SM-30:70 using secondary electrons, and b) 

back-scattered electrons. Regions of differing Z-contrast are very clear 

in b. ......................................................................................................33
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Fig. 28 DFT-calculated magnetic moment of Ln-doped Al2O3. a) Magnetic 

moment of Ln-dopant as a single atom in vacuum, the full α-Al2O3:Ln 

supercell, and localized on the Ln-dopant within the α-Al2O3:Ln 

supercell. b) 1/4 supercell of α-Al2O3:Gd, and c) 1/4 supercell of θAl2O3:Yb with arrows indicating the localization and magnitude of the 

magnetic moment for each atom, with atoms colored as O (red), 

Al (blue), Gd (green), and Yb (yellow). ..............................................36

Fig. 29 Collinear vs. noncollinear spin-orbit coupled cohesive energy for αphase RE-doped and undoped alumina................................................38

Fig. 30 Collinear vs. noncollinear spin-orbit coupled cohesive energy for 

θ-phase (octahedral site) RE-doped alumina .......................................39

Fig. 31 Collinear vs. noncollinear spin-orbit coupled cohesive energy for 

θ-phase (tetrahedral site) RE-doped and undoped alumina .................39

Fig. 32 Change in total energy as a result of the addition of spin-orbit 

coupling. Energy change is given in eV and shown for each RE-dopant 

and material phase................................................................................40

Fig. 33 MAE interpolated surface plots for Pr-doped Al2O3 ...........................40

Fig. 34 MAE interpolated surface plots for Er-doped Al2O3 ...........................41

Fig. 35 MAE interpolated surface plots for Gd-doped Al2O3 ..........................41

Fig. 36 The magnetic susceptibility of α-phase and θ-phase (octahedral, 

tetrahedral) RE-doped alumina...........................................................43

Fig. 37 DSC data comparison between ARL DSC data and ORNL DSC data, 

both data sets measured at a heating rate of 10 °C/min .......................44

Fig. 38 DSC data collected at ORNL at both 0 T and 9 T magnetic field, both 

data sets measured at a heating rate of 10 °C/min ...............................45

Fig. 39 Aligning epoxy and slurry casts within a 1.8 T magnetic field ...........47

Fig. 40 Cutting and mounting pattern of epoxy pucks cured in magnetic 

field ......................................................................................................47

Fig. 41 Idealized rhombohedral unit cell illustrating the (006) and (110) 

crystal planes........................................................................................48

Fig. 42 a) LF as a function of field strength and dopant type with respect to the 

(006), LF(006) and b) LF as a function of field strength and dopant type 

with respect to the (110), LF(110)..........................................................49

Fig. 43 XRD example spectra of Yb:Al2O3 samples with increasing magnetic 

field strength ........................................................................................50

Fig. 44 Percentage alignment values for each dopant type ..............................54

Fig. 45 Percent alignment values for each powder type of green gel-cast 

specimens.............................................................................................57

Fig. 46 XRD spectra of the unaligned green body, aligned green body, and 

sintered aligned body. As can be seen, the (006) peak at ~41.5 °2Θ 

increases with alignment......................................................................58
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viii

Fig. 47 SEM image of a polished cross section from a sintered, aligned gelcast part ................................................................................................58

List of Tables

Table 1 Compositions synthesized for this study................................................6

Table 2 List of sintering conditions, density and phase quantification for all 

samples.................................................................................................29

Table 3 Cohesive energy (eV) of rare-earth-doped alumina with z-axis oriented 

spins from collinear and noncollinear spin orbit coupled calculations37

Table 4 Energetic contribution (eV) of the rare-earth dopant spin-orbit 

coupling for z-axis oriented spins from nonself-consistent 

calculations ..........................................................................................38

Table 5 DFT calculated easy magnetic axis and maximal MAE (meV) 

indicating degree of magnetic anisotropy in the Ln-doped supercell for 

Ln-dopants in the Al-octahedral site of α- and θ-Al2O3 ......................41

Table 6 LFs calculated from (006) and (110) planes for magnetically aligned 

ceramic composite samples..................................................................49

Table 7 Quantification of alumina polymorphs in the materials examined, 

determined by Rietveld refinement of synchrotron X-ray diffraction.52

Table 8 Average percentage alignment values ± standard deviation for phasepure α-alumina epoxy samples. Third column also lists the percentage 

alignment values recalculated using the average facial angle method 

from the previous mixed-phase alumina epoxy alignment samples for 

comparison...........................................................................................53

Table 9 Alignment directions identified previously through DFT and their 

corresponding XRD alignment peak based on a dot product equal to 

zero. Some directions had no measurable XRD peaks. .......................55

Table 10 Average percentage alignment values ± standard deviation for phasepure α-alumina gel casting samples.....................................................56
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ix

Acknowledgments

Carli Moorehead (Drexel University, Philadelphia, Pennsylvania) and Joseph 

Marsico (Rochester Institute of Technology, Rochester, New York) were funded 

through a contract with the College Qualified Leaders program.
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1

1. Introduction and Background

The objective of this research was to characterize and exploit effects of energetic 

fields (microwave, magnetic, etc.) on microstructural development of materials to 

formulate a physical explanation of the fundamental mechanisms dictating material 

interactions during processing. This strategy was used to develop processing 

methods and computational modeling capabilities for synthesizing transparent 

noncubic alumina (Al2O3) through magnetic alignment of particles during forming 

and heat treatment, microwave-enhanced densification, and high-energy field 

microstructure and crystalline phase transformation control. The influence of 

dopant addition on phase formation, grain alignment, and enhancement of material 

response to applied fields was also assessed. These interactions were explored by 

utilizing external fields to initiate simultaneous grain size reduction and 

crystallographic texturing enhancement.

1.1 Materials Synthesis and Processing

Transparent ceramic materials have made an impact on a wide range of 

applications, including optically transparent armor, windows, and sensors.1–4

Current research has focused on transparent polycrystalline materials for highenergy lasers (HELs), as ceramics typically have higher strengths than single 

crystals, glasses, and polymers.5 Additionally, processing polycrystalline ceramics 

can provide cost savings when compared to growing large single crystals, and 

fosters a more homogenous chemical composition across the part. One of the major 

challenges for HELs is the difficulty of removing waste heat from laser gain media 

during lasing. Current polycrystalline ceramics such as neodymium-doped yttrium 

aluminum garnet (Nd:YAG) have a significantly lower thermal conductivity, and 

result in low-thermal efficiency during operation, thus limiting the total power from 

the laser. However, replacement materials with high-thermal conductivity 

properties can enable more rapid dissipation of heat from the laser source. 

Transparent polycrystalline Al2O3 could potentially replace Nd:YAG due to its 

improved strength and thermal conductivity properties. However, major challenges 

exist, as the material must be doped with a critical lasing ion (i.e., rare-earth cation) 

and exhibit transparency.

Significant materials research has been conducted on Al2O3, which has several 

structural polymorphs contributing to its versatility. The thermodynamically stable 

phase is alpha-alumina (α-Al2O3), and the transition is irreversible once it has been 

formed. Grain growth is rapid once the α-phase has been achieved. Most other 

phases of alumina are metastable, as described in Fig. 1.
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Fig. 1 Estimated transitions of Al2O3 from crystallized aluminum hydroxide

During chemical synthesis of alumina, for example, the phases develop at different 

temperatures as a function of the synthesis and processing techniques used.6,7 It is 

possible to seed α-Al2O3 with a polymorph transition alumina (i.e., theta or 

gamma), which can lead to changes in the densification process.6,8 Using a dualphase alumina mixture that includes a majority of theta polymorph and an addition 

of alpha polymorph seeds allows for full densification of the sample while keeping 

the grain size small. Since alumina grains grow quickly once the material reaches 

the alpha polymorph, the sample is almost completely dense by the time the 

material is purely alpha phase. 

Materials research on alumina has examined transition behavior and phase stability 

extensively. For example, transition metal and lanthanide cations have been doped 

into alumina, resulting in stability of metastable phases.9–13 However, addition of 

rare-earth dopants in bulk alumina continues to be a challenge, as most of the work 

has focused on thin films.14 The rare-earth dopant is more difficult to incorporate 

into the crystal structure due to the cation size mismatch with aluminum, but can 

be aided by working with thin films and nanoparticles via wet chemical synthesis 

methods. A study by Thompson et al. showed that the rare-earth cation typically 

segregates to the grain boundaries.15 Clustering of rare-earth cations reduces the 

efficiency and power of a laser.

14,16 Penilla et al. demonstrated successful terbium

doping of transparent alumina through field-assisted sintering of mixed materials. 

However, their spectroscopic data showed broadening of the emission lines, which 

could lead to a decrease in overall efficiency. Novel research in synthesis and 

processing of alumina by Sanamyan et al. led to production of transparent Erbium 

(Er)-doped Al2O3 using a nanoprecipitation technique combined with spark plasma 

sintering.

16 The subsequent spectroscopic results indicated that the Er3+ dopant was 

trapped in the lattice, giving rise to single-site activation with a concentration of 
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0.1–0.3 atom percent. Recent work published by the US Army Research Laboratory 

(ARL), which will be detailed in this report, revealed the presence of localized 

structural distortions in alumina that drastically affect the phase development of 

rare-earth-doped alumina. 17

1.2 Field-Enhanced Processing and Crystallographic Texturing

High-energy magnetic, electric, acoustic, and other fields applied during processing 

have been shown to influence grain and interphase boundary-related phenomena 

such as texturing, nucleation, grain growth, phase transformation, grain boundary 

migration, segregation, atomic diffusion, and sintering.

18 By taking advantage of 

these effects, microstructures can be manipulated to harness otherwise unattainable 

physical properties that are beyond the current state-of-the-art. Although 

electromagnetic (EM) fields are currently being implemented during materials 

processing, a fundamental understanding of the underlying physics responsible for 

microstructural modification is lacking. In this effort, the influence of microwave 

and magnetic fields on the behavior of rare-earth-doped alumina was explored, 

emphasizing the effects on phase formation and crystallographic texturing.

Texture has been shown to have a profound influence over many properties, such 

as optical transparency, strength, electrical conductivity, and piezoelectricity.19

Highly textured materials are desired for a variety of DOD-relevant applications 

including microactuators, nonvolatile memories, tunable microwave devices, and 

battery membranes, since they often possess significantly improved properties 

compared to their randomly oriented polycrystalline or single crystal counterparts.

Many techniques have been explored to produce grain alignment, including platelet 

seeding for anisotropic grain growth, hot pressing, incorporating sintering 

additives, and magnetic alignment, the last of which has not been well 

researched.

20–32 Magnetic manipulation of liquid metals has been used for some 

applications, but those techniques are of limited use in ceramics because liquid 

metals usually have an inherently strong magnetic susceptibility while ceramics do 

not.

24,31,33,34 Ceramics are often paramagnetic or diamagnetic, and respond weakly 

to magnetic fields, thus requiring much stronger fields to produce 

effects.

22–24,26–27,30 Additionally, many ceramics have slightly different magnetic 

susceptibilities associated with each crystallographic plane.

24–27,30,32,34 The 

magnetic response of ceramics is governed by 2 main equations:

∆EE = VV�χχcc − χχaa,bb� 1

2 μ0BB2 > kkBBTT (1)
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tt = −μ0

30ηη+rr2σσBB2

5�χχcc−χχaa,bb�BB2 ln � tt tttt

tt tt 0

� , (2)

where ΔE is the anisotropic magnetic energy, V is the primary crystal volume, χχa,b, 

and χχc are the magnetic susceptibilities of the crystallographic plains perpendicular 

and parallel to the magnetic field, respectively, μ0 is the permeability of free space, 

B is the externally imposed magnetic flux density, kB is Boltzmann’s constant, T is 

the absolute temperature, t is the time needed for a crystal to rotate a certain amount 

(assuming no steric hindrance), ηη is the viscosity of the melt or fluid surrounding 

the crystal, r is the crystal radius (particle radius), σ is the electrical conductivity of 

the particle, and Θ0 and Θ are the initial and final angles of the crystal in relation to 

the magnetic field, respectively. For alignment to occur, the magnetic torque on a 

crystal must be higher than the thermal energy.24 The magnetic energy is a function 

of the crystal size (larger crystals have higher magnetic torque), the difference in 

magnetic susceptibility across different crystallographic planes (more magnetically 

anisotropic crystals will respond more effectively to a magnetic field), and the 

magnetic field strength (higher magnetic fields lead to higher magnetic torque), as 

demonstrated in Figs. 2 and 3. Furthermore, there is a time dependence on magnetic 

alignment related to the environment around the particles and their own magnetic 

energy. From Eq. 2, it is evident that this is a function of the viscosity of the fluid 

phase (less viscous fluids allow particles to rotate faster),32 particle conductivity 

(materials that are more electrically active have a larger response to magnetic 

fields), degree of rotation necessary (partially aligned particles will align more 

rapidly in the presence of a magnetic field), and magnetic energy of the crystals. 

Based on those factors, it is anticipated that an extremely strong magnetic field on 

the order of several Tesla will be necessary to produce the required magnetic torque 

for achieving magnetic alignment in nanosized particles. Additionally, it is 

imperative to use a green body forming system with a liquid phase that contains as 

low of a viscosity as possible. For that reason, almost all magnetic alignment studies 

of ceramic particles involve some form of colloidal processing or gel casting, which 

gives particles the mobility of a low-viscosity liquid phase in the absence of a 

melt.20–21,25–28,30,32 In this study, gel casting has been selected as the most 

advantageous processing route for successfully achieving magnetic alignment of 

the rare-earth-doped alumina materials.
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Fig. 2 Schematic of the magnetic alignment mechanism

Fig. 3 Schematic of principle described by Eq. 1

2. Synthesis and Processing of Er-Doped Alumina

2.1 Powder Synthesis

An in-situ nanoprecipitation method was used to synthesize amorphous prealumina 

powder in an aqueous environment. Prior to precipitation, 2 solutions were 

prepared, including an acidic solution (solution A) and a basic solution (solution 

B). The acidic solution consisted of aluminum nitrate, magnesium nitrate, and a 

rare-earth nitrate in stoichiometric amounts to achieve a composition of 

RE0.002Al1.998O3 with 250 ppm of MgO. Adding magnesium to the alumina served 

the dual purpose of creating a structural distortion to assist in dissolving the rareearth nitrate into the Al octahedral site, and acting as a grain–growth inhibitor. 

Deionized (DI) water was added to the mixed nitrates to get a 7.5-M solution 

composed of Al(NO3)3, as the rare earth and magnesium nitrates were not included 

in the calculation. The basic solution consisted of 11-wt% ammonium bicarbonate 
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and 3-wt% ammonium hydroxide in DI water. Both solutions were stirred until all 

the crystals had dissolved, adding heat when necessary.

Once solutions A and B were prepared, a third solution, referred to as the buffer 

solution, was mixed in to initiate the reactions. The amount of buffer solution 

(2-wt% ammonium bicarbonate in DI water) was dictated by the batch size. The 

pH of the buffer was adjusted to approximately 7 with a small amount of nitric acid. 

Finally, solutions A and B were added drop-by-drop to the buffer solution while 

maintaining a pH value of approximately 7 during the entire precipitation step. 

When solution A was exhausted, the resulting suspension was allowed to age while 

stirring vigorously overnight.

On the following day, the suspension was filtered out of the salty solution. The 

resulting powder was washed twice with DI water and once with isopropyl alcohol. 

After washing, the powder was put into an oven to dry. The dry powder was gently 

crushed and calcined at various temperatures for 30 min. A list of the synthesized 

compositions is included in Table 1, and the synthesis process is depicted in Fig. 4.

Table 1 Compositions synthesized for this study

Composition Mg 

(ppm)

Al2O3 250

Al1.998Yb0.002O3 250

Al1.998Er0.002O3 250

Al1.998Gd0.002O3 250

Al1.998Nd0.002O3 250

Al1.998Pr0.002O3 250
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Fig. 4 Schematic representation of rare-earth-doped alumina sample preparation

2.2 Initial Powder Characterization

Particle and powder morphology were analyzed via transmission electron 

microscopy (TEM) and scanning electron microscopy (SEM). The particle size 

distributions were measured by laser scattering. Exothermic and endothermic 

reactions of the precipitate were measured using a digital scanning calorimeter 

(DSC) from room temperature up to 1400 °C under flowing argon gas at varying 

heating rates. Powder X-ray diffraction (XRD) was completed using Cu-Kα 

radiation at 30 kV, 15 mA (Rigaku MiniFlex II), and the resulting patterns were 

analyzed using Jade 8 software, including crystallite size calculations. Hightemperature X-ray powder diffraction (HT-XRD) was completed on a Siemens 

D5000 XRD with a custom high-temperature attachment and Vantec-1 high-speed 

particle size distribution detector. The X-ray beam was produced using a Co anode 

X-ray tube and shaped by a Göbel Mirror. The uncalcined powders were packed 

onto single crystal sapphire, zero background sample holders. The heating schedule 

of the HT-XRD furnace is displayed in Fig. 5.
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Fig. 5 Heating schedule used for the dried precipitate AACH samples in HT-XRD

Once the final rinsing and drying steps had been completed, the resulting precipitate 

was identified as a combination of NH4(RE,Al)(OH)2CO3 and ammonium 

aluminum hydroxycarbonate (AACH) by X-ray powder diffraction. Additionally, 

the crystallinity and water content was dictated by the drying temperature and 

relative humidity. The AACH precipitate retained its structure until approximately 

150 °C, beyond which the ammonia, carbonate, and adsorbed water began to 

dissociate and form boehmite, AlO(OH). The major exotherm at 180 °C was a result 

of ammonia and carbon burn off. The material fully formed boehmite at 230 °C. 

These temperatures were confirmed by DSC measured at 3 °C/min, as shown in 

Fig. 6.
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Fig. 6 DSC data showing the heat flow vs. temperature where exothermic reactions are 

down and endothermic reactions are up

At approximately 850 °C, the small endotherm indicated that crystallization had 

occurred. According to Fig. 1, this phase should be representative of gammaalumina (γ-Al2O3). The knee of the DSC curve at approximately 1080 °C should be 

indicative of δ-alumina or θ-alumina crystallization, while the endotherm at 

approximately 1240 °C should represent α-alumina crystallization. These phases 

were confirmed by heating the precipitated powder at varying temperatures and 

cooling to room temperature at 10 °C/min. The resulting calcined powders were 

characterized by powder X-ray diffraction and subjected to phase identification. 

From these X-ray measurements, the flow chart in Fig. 7 was generated. The 

temperatures obtained from the X-ray diffraction measurements corresponded well 

with the DSC data. Repeated measurements of the same powder batch from the 

DSC indicated that the crystallization temperatures did not vary more than 2 °C. 

Repeated batch synthesis also indicated that the crystallization temperature did not 

vary more than 4 °C around the average temperature.
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Fig. 7 Flow chart of the precipitated powder phase development

2.3 Powder Morphology

A more detailed morphological study of the calcined materials was completed using 

TEM and SEM. Starting with the boehmite materials calcined at 230 °C, the 

particles had high-aspect ratios with rounded edges, as shown in Fig. 8. There was 

some degree of localized crystallinity, which led to broadening of the AACH XRD 

peaks.

Fig. 8 TEM image of the precipitate calcined at 230 °C to obtain boehmite, AlO(OH)

The γ-Al2O3 phase could not be isolated during the traditional calcination process, 

as it was highly unstable. Figure 9 shows a TEM image of the θ-Al2O3 material. 

The morphology was drastically different from boehmite, as the space group of the 

crystallite changed from Amam for boehmite to C2/m for θ-Al2O3, leading to a 
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drastic unit cell change. The morphology of θ-Al2O3 consisted of small hexagonal 

platelets approximately 10 nm in diameter. The final isolated phase was α-Al2O3. 

Figure 10 shows the particles after calcination at 1350 °C, which were round and 

smooth, and ranged in size from 500 nm to 1 μm. The TEM image also showed that 

some degree of necking occurred between the particles, indicating that some form 

of milling would be necessary to deagglomerate them. Figure 11 shows an SEM 

image of the same powder, confirming a high degree of particle agglomeration.

Fig. 9 TEM image of the precipitate calcined at 1050 °C to obtain θ-Al2O3

Fig. 10 TEM image of powder calcined at 1350 °C to obtain α-Al2O3
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Fig. 11 SEM image of the powder calcined at 1350 °C to obtain α-Al2O3

2.4 Undoped Alumina vs. Er-Doped Alumina

While the milestone of successfully doping alumina with a rare-earth cation

(erbium) via the coprecipitation process was achieved, a direct comparison had not 

yet been made to undoped Al2O3. Patel et al.17 showed that the type of rare-earth 

cation introduced into the alumina lattice had varying effects on the transformation 

temperature from θ-Al2O3 to α-Al2O3. This was investigated by first establishing a 

baseline comparison to undoped Al2O3, and later exploring the difference between 

Er-doped Al2O3 and 8 other rare-earth lanthanide series-doped (Ln-doped) Al2O3

materials. In order to maintain consistency, the erbium dopant was removed while 

including 250 ppm of Mg2+ for all undoped materials. High-temperature DSC and 

HT-XRD data were collected for undoped and Er-doped Al2O3 samples. Figure 12 

shows high-temperature DSC data, with the most notable difference indicated by a 

missing endotherm for the undoped sample around 850 °C. After repeated DSC 

measurements of the undoped alumina using different material amounts and 

varying heating rates, an 850 °C endotherm was still not detectable, confirming that 

gamma crystallization did not occur. The next sets of endotherms at 1025 °C and 

1280 °C for undoped Al2O3 were significantly different than Er-doped Al2O3, 

providing an initial indication that the erbium cations in the alumina lattice were 

affecting crystallization behaviors and temperatures.
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Fig. 12 High-temperature DSC data comparing Er-doped Al2O3 to undoped Al2O3 (heating 

rate 3 °C/min)

HT-XRD data was also compared for undoped and Er-doped Al2O3. Figure 13 

shows in-situ HT-XRD data collected from the undoped AACH precipitate. The 

temperature change was minimal until approximately 150 °C, at which point the 

AACH began to decompose and form boehmite, AlO(OH). The boehmite remained 

the majority phase until approximately 800 °C when gamma-alumina began to 

form. The gamma-alumina peaks were small and broad, suggesting that this phase 

had small particles with relatively low crystallinity in comparison to the boehmite 

and AACH. It was not until approximately 1100 °C that the theta-alumina began to 

crystallize, with the alpha-alumina peaks appearing around 1325 °C.
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Fig. 13 HT-XRD of undoped AACH. The figure identifies where specific transformations 

occur as well as the specific space groups of each phase.

When comparing these temperatures to the DSC crystallization temperatures for 

the same materials, the data collection process was considered. While DSC 

collected data continuously, measuring the electrical signal from the reference and 

sample concurrently, the HT-XRD furnace underwent a ramp and dwell cycle 

before the XRD pattern was collected, making it less of an in-situ method than hightemperature DSC. This explained some of the differences in phase formation 

temperatures between the 2 methods.

Figure 14 shows HT-XRD data for the Er-doped AACH. The main difference with 

this sample was that the boehmite phase did not appear to form. This was an 

important difference to note, since the boehmite phase did not experience enough 

of a dwell time to crystallize, leading to a region between 200 °C and 700 °C with 

no diffracted peaks. It was possible that the erbium dopant was creating enough of 

a structural distortion that it required more time to fully crystallize Er-doped 

boehmite. The Er-doped Al2O3 transformation temperatures from HT-XRD did not 

vary significantly from the undoped Al2O3, likely due to the nature of HT-XRD in 

comparison to DSC, as it was less of an in-situ experiment.
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Fig. 14 HT-XRD of Er-doped AACH. The figure identifies where specific transformations 

occur as well as the specific space groups of each phase.

2.5 Lanthanide-Doped Alumina Series Preparation

After synthesizing and characterizing undoped baseline alumina and Er-doped 

alumina, a series of 8 additional Ln-doped alumina samples was prepared to 

observe dopant effects on alumina nanocrystals. The effects of sparse Ln3+ dopants 

(Lanthanum [La], Praseodymium [Pr], Dysprosium [Dy], Neodymium [Nd], 

Erbium [Er], Thulium [Tm], Lutetium [Lu], Gadolinium [Gd], and Ytterbium [Yb])

on phase transition and structural geometry of alumina were investigated. The 

concentrations of Ln-dopants were kept at a constant level of Ln0.002Al1.998O3 (e.g.,

the weight concentration of Er-dopant was ~0.03271 wt% [or 400 ppm] in the 

alumina lattice) to avoid any potential formation of LnAlO3 and/or Ln2O3 phases.

Figure 15 shows SEM images that highlight the contrasting morphologies of 

various Ln-doped samples, which were a consequence of the Ln3+ dopants, since 

they share the same oxidation state as aluminum. 

Fig. 15 SEM images of Ln-doped alumina. The scale bar is 1 μ.
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3. Advanced Characterization of Dopants Effects on Alumina

A suite of state-of-the-art structural probes was used to test the hypothesis that the 

local structure and positioning of Ln-ions could largely influence the structural 

transition and phase composition of doped alumina due to their interactions with 

the Al2O3 host lattice. One-dimensional magic angle spinning (MAS) and 2-D 27Al 

multiple quantum magic angle spinning (MQ-MAS) solid-state nuclear magnetic 

resonance (ss-NMR) spectroscopy techniques, together with high-resolution X-ray 

diffraction (HR-XRD [Synchrotron 11-BM at the Advanced Photon Source of 

Argonne National Laboratory]), were employed to examine the Ln-dopant effect 

on Al2O3 phase composition. The structural characteristics and phase evolution of 

Ln-doped Al2O3 were further confirmed through SEM and high-temperature DSC.

Undoped alumina samples, including pure α-Al2O3 and pure θ-Al2O3, were 

prepared for initial comparison with Er-doped alumina, which had undergone the 

most extensive initial characterization during this study. These samples were 

characterized using 1-D 27Al MAS ss-NMR with a spin rate of 10 kHz (Fig. 16a). 

The α-Al2O3 was represented by hexagonal packing of oxygen anions. The 

distribution of Al cations for this phase was limited to octahedral sites, and was 

represented by a single peak at approximately 13.9 ppm in the MAS spectrum. The 

θ-Al2O3 phase, on the other hand, was represented by monoclinic arrangements of 

the oxygen, and distribution of Al cations in tetrahedral and octahedral sites. This 

arrangement led to 2 distinct inhomogeneously broadened peaks at approximately 

59.3 and approximately 8.8 ppm for tetrahedral and octahedral sites, respectively. 

Upon doping Al2O3 with 400 ppm Er3+, the MAS spectrum changed relative to 

undoped Al2O3. Most notably, there was significant attenuation, which reduced the 

intensity of the peak at around 13.9 ppm. 
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Fig. 16 a) Overlay of 1-D 27Al MAS NMR spectra for Al2O3, Er-doped Al2O3, undoped 

α-Al2O3 phase and undoped θ-Al2O3 phase. The MAS rate was equal to 10 kHz. b) 2-D 27Al 

MQ-MAS spectra of undoped Al2O3; c) 2-D 27Al MQ-MAS spectra of Er-doped Al2O3.
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Multidimensional ss-NMR was used to further explore these results, as 2-D 27Al

MQ-MAS spectra were collected on undoped and Er-doped Al2O3, as shown in 

Figs. 16b and 16c. There were 3 clear peaks in the MQ-MAS spectrum of Al2O3 at 

approximately 59.3, 13.9, and 8.8 ppm, respectively, in the F2 dimension. The 

intensity of the peak at approximately 13.9 ppm in F2 in the MQ-MAS spectrum 

was reduced significantly upon doping with Er3+, which was in agreement with the 

results of the 1-D MAS spectra. Taken together, these results suggested that, given 

the approximately 0.03271% weight percentage of dopant, changes in the NMR 

spectra were not attributed to Er3+ induced changes from anisotropic spin 

interactions, but rather an alteration in alumina phase composition caused by the 

doping procedure.

To further analyze the Er-dopant effect on the phase composition and structure of 

alumina, high-temperature DSC was used to investigate the phase transition of 

alumina before and after Er doping. Despite limited solubility, Ln-dopants 

effectively altered the phase transition temperature of alumina, as more thermal 

energy was necessary to convert to the α-Al2O3 phase, the most thermodynamically 

stable phase, after Er doping.

35,36 The phase transition took place at a temperature 

(Tc) of approximately 1280 °C for the pristine Al2O3 and approximately 1325 °

C 

for the Er-doped Al2O3 (Fig. 17a), suggesting that doping alumina with erbium 

increased the transition temperature significantly. SEM images of Er-doped Al2O3

(Fig. 17b) calcined at 1300 °

C, which was lower than the alpha-alumina transition 

temperature, showed a mixture of particle morphologies. θ-Al2O3 has been known 

to have a smaller particle size than α-Al2O3, as the grains will not grow until the 

final alpha-alumina phase has been developed. It has been theorized that the larger 

grains represented α-Al2O3 and the smaller grains represented θ-Al2O3. These 

observations further confirmed the NMR spectra of Er-doped Al2O3 discussed 

above. Loading of large Er3+ ions into alumina forced the lattice to expand, 

distorting the neighboring tetrahedral and octahedral locations. Consequently, the 

distorted lattice conversion into octahedral sites and rearrangement into stable 

structures for the phase transformation from θ-Al2O3 to α-Al2O3 required a higher 

thermal energy, leading to a phase transformation temperature shift. 
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Fig. 17 a) High-temperature DSC curves of Al2O3 (purple) and Er-Al2O3 (red); b) SEM 

image of Er-doped Al2O3

After evaluating the Er-doped alumina samples, samples doped with identical 

amounts of La, Pr, Dy, Nd, Tm, Lu, Gd, and Yb, respectively, were characterized 

using ss-NMR. Each dopant had a unique effect on alumina, as shown in Fig. 18.

The 2-D MQ-MAS spectrum of Pr-doped Al2O3 included 3 clear transitions at 

approximately 59.3, 13.9, and 8.8 ppm, respectively. The 2-D MQ-MAS of La- and 

Yb-doped Al2O3 also showed 3 transitions with weaker downfield peaks. The 2-D 

MQ-MAS results for Tm-, Nd-, Lu-, Dy-, Gd-, and Yb-doped Al2O3 exhibited 2

upfield peaks at various intensities. The presence of the dopants in the lattice 

generated stress in the geometry of arranged alumina, leading to changes in the 

system configurations. Pr-doped alumina showed a significant increase in θdomains (~59.3 ppm), whereas the Dy and Lu dopants showed no indication of θdomains. Since the ratio of Al to Ln was constant, it was assumed that an increase 

in one type of domain was followed by the decrease of another type of domain by 

the same amount. Whether or not the dopant favored formation of the θ-domain or 

α-domain at a given temperature was dictated by the size of the dopant and the size 

of the site it was being doped into.
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Fig. 18 2-D MQ-MAS spectra of Ln-doped Al2O3

Final confirmation of the presence of α- and θ-phases in various ratios for each Lndopant was determined using data obtained from HR-XRD, which quantitatively 

reinforced conclusions drawn from the ss-NMR results. HR-XRD spectra of each 

Ln-dopant indicated notable differences in α- and θ-peaks, with Dy-doped and 

Lu-doped alumina exhibiting only α-phase, and Pr-doped alumina revealing the 

θ-phase in extremely high quantities (Fig. 19a). All of these doped Al2O3 samples 
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were prepared at the same calcination temperature of approximately 1300°C for 30 

min. As observed in the case of Er-doped alumina, the transition temperature of αAl2O3 increased to approximately 1325 °C. Therefore, the θ-Al2O3 domains in the 

sample prepared at approximately 1300 °

C were expected to be present, since the 

material was calcined at a temperature lower than the transition temperature for 

alpha alumina. These spectra indicated the presence of uneven phase percentages

in each Ln-doped Al2O3 sample. The graphical representations of phase populations 

for each dopant in Fig. 19b were generated using Rietveld refinement data from the 

HR-XRD, which were analyzed using X-ray refinement software, GSAS-II.37 They 

provided a quantitative summary of phases in each sample doped with lanthanide 

elements. With the exception of Dy-doped and Lu-doped alumina, the θ-Al2O3

phase was present in all of the other samples. This suggested that the Dy dopant 

decreased the α-θ phase transition temperature when compared to the pure-alumina 

phase.

The lanthanide ionic size effect appeared to play a role in the transition temperature 

shift as well. There was a notable variation in the phase population of θ- and αdomains, as observed in Fig. 19c. It was possible that elements from the second 

half of the lanthanide series (Gd, Dy, Tm, Lu, Yb), which were smaller in size due 

to lanthanide contraction, could have led to a lower percentage of θ-phase when 

compared to elements from the first half of the series (La, Pr). The smaller dopant 

sizes could have resulted in less distortion of the neighboring lattice, leading to a 

lower energy requirement for atomic rearrangement. Furthermore, the Ln-dopant 

effects were purely intrinsic, and did not lead to formation of any undesirable 

LnAlO3 or Ln2O3 phases, which was confirmed by both ss-NMR and HR-XRD 

spectra. The refinement summary from HR-XRD also provided the geometry and 

dimensions of the domains, indicating that the ionic size effect of Ln-dopants was 

responsible for delaying the phase transformation of θ-domains into α-domains 

(Fig. 19c). The θ-Al2O3 particle morphology was anisotropic (ellipsoid-like) 

whereas the alpha alumina particles were isotropic (cube or sphere-like). The SEM 

images of 2 representative Ln-doped alumina samples (i.e., Dy-doped and Tmdoped alumina), shown in Fig. 19d, were consistent with the structural conclusions 

from the refinement summary, verifying that contrasting morphologies of the 

samples were clearly present.
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Fig. 19 a) Low-angle HR-XRD data of the Ln-doped alumina. From top to bottom: Ln = Pr, 

Er, La, Gd, Yb, Nd, Tm, Lu, Dy, respectively. The data were sequentially offset by a factor of 

10 for clarity. The peaks denoted “*” represented the α-phase and the peaks denoted “o” 

symbols represented the θ-phase. b) Graphical representation of the α- and θ-phase 

populations at ~1300 °C. The Dy- and Lu-doped alumina exhibited only α-phase. c) Graphical 

representation of Ln-cationic phase fraction, octahedral coordination radius and phase 

diameters. The data points represented Ln-series elements in decreasing order of atomic 

number, moving from left to right (Lu, Yb, Tm, Er, Dy, Gd, Nd, Pr, and La). The diameter 

was represented by the orange data points and the phase fraction was represented by the blue 

data points. A refinement summary of all Ln3+ doped alumina was included. d) SEM images 

of Dy- and Tm-doped alumina.
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The advanced characterization study demonstrated that Ln doping (400 ppm) in 

alumina had a significant influence over structural and phase evolution. Ln dopants 

served as structural promoters to increase the phase transformation temperature 

(θ →α) by a notable magnitude, which delayed the onset of alumina lattice phase 

transformations. Lanthanide doping in alumina enabled control of the phase 

population with no additional unwanted phases (i.e., LnAl2O3 or Ln2O3) observed. 

Additionally, it was determined that the lanthanide dopants resided in the vacant 

octahedral locations within the alumina lattice. The formation of 100% α-phase was 

also observed in the case of Dy- and Lu-doped alumina. This study revealed a new 

perspective on the significance of Ln-doping in alumina.

4. Density Functional Theory Modeling and Simulation

Density functional theory (DFT) was used to provide insight into the effect of rareearth dopants on structure and phase stability of α- and θ-Al2O3. Lanthanide series 

rare-earth dopants, including Er, Yb, Nd, Gd, and Pr selected for evaluation. The 

α-Al2O3 and θ-Al2O3 were modeled. The α-Al2O3 unit cell contained 30-atoms in a 

corundum structure with space group symmetry RR3�cc as shown in Fig. 20a. The

oxygen ions (O2-) were arranged in a distorted HCP lattice, while the aluminum 

ions (Al3+) were located in 2/3 of the equivalent octahedral interstitial positions. 

The θ-Al2O3 unit cell contained 20 atoms and belonged to the monoclinic C2/m 

space group, as shown in Fig. 20b. The O2- ions were arranged as an FCC array, 

yielding 2 nonequivalent Al3+ sites in the θ-phase, an octahedral and tetrahedral 

site, on which the Al3+ ions were evenly distributed. To study the doping effect, a 

supercell approach was adopted, where supercells were generated by repeating unit 

cells: 2 × 2 × 1 and 1 × 3 × 2 for α-Al2O3 and θ-Al2O3, respectively. These 

asymmetric repetitions of the lattice vectors created similarly sized supercells for 

both phases composed of 120 atoms each (i.e., 24 Al2O3 formula units).

Fig. 20 Schematic representation of Al2O3 unit cells a) α-Al2O3 and b) θ-Al2O3 with atomic 

coloring of the smaller Al (blue) and larger O (red)
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Ln-doped supercells were modeled by substituting one of the Al3+ ions with the Lndopant near the center of the supercell, resulting in a composition of 

Al1.958Ln0.042O3. All symmetry equivalent Al3+ sites were examined (i.e., octahedral 

sites in α-Al2O3; octahedral and tetrahedral sites in θ-Al2O3). The spacing between 

Ln-dopants and their periodic image was approximately 1 nm. This spacing was 

found to be sufficient to avoid Ln–Ln interactions in an Er-doped supercell, where 

increasing the Er–Er spacing to greater than 1 nm affected the defect formation 

energy by less than 0.3 meV. Further, similar studies on doped alumina38–43 and 

doped oxides44–45 confirmed that a distance of 1 nm was sufficient to minimize

dopant–dopant interactions.

The calculated lattice parameters of undoped α-Al2O3 (a = b = 4.81 Å and 

c = 13.12 Å) and θ-Al2O3 (a = 11.77 Å, b = 2.92 Å, c = 5.62 Å, and β = 104.0°) 

were consistent with other theoretical values,

39 and were also within 1% of reported 

experimental values.

46–47 Local distortion of the Al3+ sites were also in good 

agreement with experimental values. In particular, Al-O bond distances associated 

with the distorted Al3+ sites compared well with experimental values given in 

parenthesis, for α-Al2O3 octahedral sites of 1.87–1.99 Å (1.86–1.97 Å),

48 θ-Al2O3 

octahedral sites of 1.87–2.00 Å (1.86–1.99 Å)47 and θ-Al2O3 tetrahedral sites of 

1.76–1.80 Å (1.73–1.82 Å).

47

Substitution of an Al-atom with an Ln-dopant increased the lattice parameters and 

enhanced the local structural distortion around the substitution site. Local distortion 

was quantified as a function of Ln-O bond distance, Ln-site volume, quadratic 

elongation, and standard deviation of the internal bond angles.

49 Substitution by the 

large Ln-dopants led to an increase in the lattice parameters by approximately 0.5% 

for all sites and dopants considered. Substitutional site volume and Ln-O bond 

distances increased with increasing ionic radii, as shown in Fig. 21a. The increase 

in Ln-O bond length with respect to dopant radii was approximately linear and of 

the same magnitude for the octahedral and tetrahedral sites. Due to the smaller size 

of the tetrahedral site, this manifested as a larger percentage change in the site 

volume (Fig. 21a). Interestingly, the θ-Al2O3 octahedral site volume also increased 

more substantially than that of the α-Al2O3 octahedral site. This may be explained 

in part by the substitutional site quadratic elongation and bond angle standard 

deviation shown in Fig. 21b. The α-Al2O3 octahedral site had the largest geometric 

site distortion, indicating that the Ln-O bond length increase was primarily 

accommodated by octahedral distortion rather than expansion. Undoped θ-Al2O3 

had a lower calculated density than α-Al2O3, 3.62 versus 3.87 g/cm3, respectively, 

allowing for the volumetric expansion of its octahedral and tetrahedral sites to be 

more easily accommodated within the less dense structure. This was exaggerated 

in the θ-Al2O3 tetrahedral site, which had negligible change in the quadratic 
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elongation and bond angle standard deviation after doping but exhibited large 

volumetric expansion. 

Fig. 21 Changes in local structural properties: a) Ln-O bond length (solid) and change in 

substitutional site volume (dashed), and b) quadratic elongation (solid) and bond angle 

standard deviation (dashed), as a function of dopant ionic radius (octahedral, 3+) for Lndoped α- and θ-Al2O3 at different lattice sites. The error bars (A) represent the range of LnO bond distances.

The relative phase stability was determined by comparing the cohesive energies 

(Ecoh) of the undoped and doped supercells

Ecoh = E(Al47LnO72) − [47 ∙ E(Al) + E(Ln) + 72 ∙ E(O)], (3)

where E(Al47LnO72), E(Al48O72), E(Al), E(O) and E(Ln) represent total energies of 

the doped supercell, undoped supercell, Al-atom, O-atom, and Ln-atom, 

respectively. The Ecoh of undoped α-Al2O3 was found to be 31.1 eV/f.u., which 

compared well with the experimental value of 31.8 eV/f.u.46 Cohesive energy 

comparison indicated stability of α-Al2O3 over θ-Al2O3, with a cohesive energy 

difference of 0.08 eV/f.u., in good qualitative agreement with earlier theoretical and 

experimental studies.

38,50 As shown in Fig. 22, α-Al2O3 remained the most stable 

phase for all Ln-dopants considered. Doping in the θ-Al2O3 tetrahedral site resulted 

in the lowest phase stability, with the highest Ecoh for each Ln-dopant studied. The 

Ecoh difference for Ln-dopants in octahedral sites of α- and θ-Al2O3 were 0.53, 0.32, 

0.24, 0.15, and 0.07 eV for Yb, Er, Gd, Nd, and Pr, respectively, indicating an 

increasing relative stability of θ-Al2O3 with increasing dopant radii. 
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Fig. 22 DFT calculated a) cohesive energy (Ecoh) and b) defect formation energy (Edefect) for 

Ln-doped α- and θ-Al2O3 with composition Al47LnO72

The ease of doping was calculated as the defect formation energy

Edefect = E(Al47LnO72) + E(Al) − [E(Al48O72) + E(Ln)], (4)

defined as the change in energy between the respectively optimized doped and 

undoped supercells. Edefect decreased with increasing number of unpaired electrons. 

For Gd in the θ-Al2O3 octahedral site, a negative Edefect was observed, suggesting 

favorable substitution of Al by Gd for the model concentration and site substitution. 

Substitution of Al with Gd had also recently been shown to be energetically 

favorable in Al2O3 clusters through a similar DFT study.

51 In general, Edefect was 

higher in α-Al2O3 than in θ-Al2O3 for each of the lanthanide dopants considered, 

with the θ-Al2O3 octahedral site having the lowest Edefect. This observation was 

consistent with a study in which large transition metal dopants were found to prefer 

the θ-Al2O3 octahedral site, increasing the relative stability of θ-Al2O3 over αAl2O3.

39 As discussed earlier, the volume expansion of the sites in θ-Al2O3

(Fig. 21a) occurred with less distortion (Fig. 21b) than in α-Al2O3, which was now 

found to occur at a lower energetic cost as well. This energetic preference for 

substitution into θ-Al2O3 may have affected the θ to α phase transformation 

temperature during processing.

52–54

As a result of the DFT studies, the lattice parameters and dopant site volumes were 

generally found to increase with increasing Ln-dopant ionic radii, regardless of the 

phase and doping site. Greater local distortion was consistently observed for the 

octahedral sites compared to tetrahedral, and was most pronounced in α-Al2O3. For 

a given dopant, α-Al2O3 remained the most stable phase, with doping in the 

tetrahedral site of θ-Al2O3 being the least stable. The relative stability of θ-Al2O3 
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with an octahedral site dopant increased with increasing dopant radii, as observed 

in Ecoh differences. The octahedral site of θ-Al2O3 was also found to be the preferred 

substitutional site for all Ln-dopants considered, where the defect formation energy 

decreased with an increasing number of unpaired electrons.

After thorough characterization and initial DFT modeling demonstrated the effect 

of rare earth dopant addition on alumina structure and phase, investigation of 

external field interactions with rare-earth doped alumina samples were also 

explored. In this phase of the program, microwave sintering and magnetic field

processing were studied in relation to densification and crystallographic texturing 

behavior.

5. Microwave Sintering of Rare-Earth-Doped Alumina

Microwave sintering is a technique that converts microwave energy of different 

frequencies and fields into heat. In multimode microwave sintering—the most 

common microwave technology used in materials processing—microwave 

radiation is emitted into a reflective cavity that is much larger than the wavelength, 

and multiple modes are excited within the cavity. This design is intended to produce 

a mixed-EM energy within the cavity. While this is beneficial for heating large 

objects uniformly, it inherently limits fundamental studies of the mechanisms by 

which microwave energy interacts with matter, since many modes are active in the 

chamber and the effects of electric and magnetic fields cannot be separated. In 

contrast to multimode systems, single-mode microwave sintering systems have 

been developed through careful design of the applicator to form a standing wave, 

in which only a single mode is excited. One advantage of this design is the 

significantly lower power requirement, since microwave energy is concentrated on 

1 or 2 modes in a small area of the cavity. Another advantage is the ability to fully 

separate the electric and magnetic field components of EM waves at specific cavity 

locations. Single-mode microwave heating, therefore, holds great promise for 

fundamental research in microwave processing, since the electric and magnetic 

field maxima are separated spatially in the chamber. Depending on the sample 

position, the sample can be subjected to 100% electric and 0% magnetic energy and 

vice versa. Earlier reports55–57 have demonstrated that processing materials in the 

regions of electric field and magnetic field maxima in a single-mode microwave 

system can produce unique microstructures and phase transformations, enabling the 

processing of a wider range of materials.

While many studies have been performed in the regions of electric or magnetic 

maxima using single-mode microwave systems, the potential benefits of using 

mixed-component microwave fields have been largely unexplored. In addition to 
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28

the 100%:0% field ratios, the sample may be placed such that it experiences a 

nonzero percentage of both fields: a mixed-field mode (e.g., 30% electric field and 

70% magnetic field). This unique experimental parameter afforded by single-mode 

microwave sintering may provide insight into how the different fields affect crystal 

structure and microstructure-controlling mechanisms during such heat treatment. 

In addition, the ability to adjust the relative amounts of applied electric and 

magnetic fields may be especially useful for materials such as Al2O3, which is 

diamagnetic, and does not couple to the magnetic field, so the 100% magnetic field, 

0% electric-field condition does not heat the sample. Therefore, by using the mixedfield condition, one field can be used to heat the sample and the other field can be 

varied to study its effects on the material microstructure quasi-independently. 

In this effort, Er-doped Al2O3 was sintered using both multi- and single-mode 

microwave systems. Powders and sintered pellets were characterized via 

Archimedes density measurements, XRD, SEM, and energy dispersive 

spectroscopy (EDS). The focus was centered on the single-mode microwave 

sintering system, and the effect of placing the sample in different positions along 

the cavity for exposure to varying proportions of electric field and magnetic field. 

To study how the EM field at microwave frequencies (2.45 GHz) affected sintering 

behavior of rare-earth-doped Al2O3, microwave sintering parameters including the 

temperature, microwave frequency, and sintering atmosphere were held constant. 

The results showed that the mixed-field parameters had an effect on both the density 

of the sintered ceramic, as well as the dopant migration. 

Pellets of Er-doped Al2O3 13 mm in diameter were cold isostatically pressed to 

400 MPa, and either conventionally sintered or microwave sintered. To obtain 

baseline materials, 2 samples were pressure-less sintered, using a ramp rate of 

15 °C/min and a hold time of 2 h. Microwave sintering was performed using either 

a 2-kW, 2.45-GHz multimode system or a 2-kW, 2.45-GHz single-mode system. 

The details of single-mode microwave systems are provided by other resources.

56

The microwave sintering parameters, as well as the sintering parameters for the 

baseline samples, are shown in Table 2 (where SM stands for single-mode 

microwave sintered, BL stands for baseline conventionally sintered, and MM 

stands for multimode microwave sintered). The SM samples also included the 

relative amounts of the electric and magnetic field. For example, SM-100:0 was 

sintered at the center of the electric field maximum, where magnetic field was zero,

while SM-30:70 was situated along the chamber axis where the ratio of electric and 

magnetic fields was estimated to be 30:70. All samples were sintered in air at 

1400 °C (with a 2-h hold). The temperature measurement was made using an optical 

pyrometer (Leeds and Northrup Company, Philadelphia, PA, USA) focused on the 

surface of the sample. 
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29

A typical heating schedule for the sample sintered at 1700 °C was 30 °C/min from 

room temperature to 1200 °C, and 20 °C/min from 1200 °C to 1700 °C.

Table 2 List of sintering conditions, density and phase quantification for all samples

Sample Temp 

(°C) Microwave conditions Density(g/cm3)

Peak height 

ratio

Equivalent vol%a

Er3Al5O12

BL 1400 No microwave 2.80 7.31 2.62

BL-HT 1700 No microwave 3.88 7.32 2.61

MM 1400 Multimode 2.93 7.30 2.62

SM-100:0 1400 Single mode 100%E:0%H 2.75 7.38 2.59

SM-60:40 1400 Single mode 60%E:40%H 2.64 7.69 2.45

SM-30:70 1400 Single mode 30%E:70%H 3.88 8.23 2.25

a Equivalent volume percent was calculated using calibration curves from Y3Al5O12/Al2O3 mixed-phase powders.

After sintering, XRD patterns were measured on sintered pellets and ground 

powder samples using a Rigaku MiniFlex powder XRD, and the spectra were 

analyzed using the commercial software, Jade 8. The peak heights of the (420) 

plane for the Er3Al5O12 phase and the (104) plane for the Al2O3 phase were 

carefully measured to determine relative second-phase content (also given in Table 

2). Samples were prepared for electron microscopy by polishing down to 6 μm with 

successively finer diamond films. Following the mechanical polishing step, the 

samples were ion-polished using a Leica TIC 3X ion beam slope cutter on a rotary 

stage with a beam energy of 6 kV and a milling time of 1 h. Ion polishing was used 

to remove any residual surface scratches from mechanical polishing, and to ensure 

that the pores did not become filled in with polishing compounds, which would 

obscure the appearance of the microstructure. The ion polishing step was especially 

useful in preparing the lower density samples, which contain many pores. The 

sintered ceramic pellets were observed using either a Hitachi 4700 FESEM at 1.5 

kV or an FEI Nova NanoSEM 600 using the low-vacuum option (80 Pa), which 

was equipped with an Oxford EDS system. 

Figure 23 shows the XRD patterns for the starting (unsintered) powder as well as 

sample SM-30:70. The starting powder was composed primarily of α-Al2O3, with 

minor amounts of ErAlO3 and θ-Al2O3. The presence of ErAlO3 confirmed that the 

solubility of erbium had been exceeded, and that some erbium, even at the low 

calcination time and temperature, had been allowed to diffuse out of the lattice and

form an Er-rich second phase. The SM-30:70 sample showed peaks corresponding 

to α-Al2O3 as well as Er3Al5O12. The inset showed the (420) plane for the Er3Al5O12
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30

phase and the (104) plane for the Al2O3 phase, which were used for phase content 

calculations.

Fig. 23 XRD patterns for calcined Er-doped Al2O3 powder and microwave sintered sample 

SM-30:70. The inset shows the (420) peak of the Er3Al5O12 phase and the (104) peak of the 

Al2O3 phase, which were used to determine the peak-height ratios given in Table 2.

To establish a baseline material, Er-doped Al2O3 powder was initially sintered 

using conventional (pressure-less) sintering (sample BL was sintered at 1400 °C 

for 2 h and sample BL-HT was sintered at 1650 °C for 5 h). As shown in Table 2, 

the density for BL was quite low at 2.80 g/cm3, which was approximately 70% of 

the theoretical density. Without the benefit of applied pressure or wet powder 

processing, this low density was not surprising. Most microwave-processed 

samples had similar densities. SM-60:40 and SM-100:0 had similar densities 

compared to the conventionally sintered sample, with the densities of these 2

microwave-sintered samples within 5% of the baseline sample. MM was slightly 

more dense (2.93 g/cm3). SM-30:70, however, was significantly more dense (3.88 

g/cm3

, or about 97% of the theoretical density of Al2O3). The density value of 

SM-30:70 was highly encouraging, as it was comparable to values achieved by hotpressing Er-doped Al2O3 at 1350 °C. Therefore, by using the 30%E:70%H 

microwave sintering condition, the need for hot-pressing could potentially be 

eliminated, and the only compromise would be an increased sintering temperature 

of 50 °C (1350 °C to 1400 °C). In fact, SM-30:70 was similar in density to BL-HT 

despite the 250 °C difference in temperature. If it was assumed that BL-HT 

represented the maximum density possible within the sample set (as limited by the 

particular powder and particle packing characteristics), SM-30:70 achieved 
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31

maximum density under thermal conditions that would otherwise produce 70% 

dense samples.

Another way to consider the effect of sintering conditions on densification was to 

describe the samples in terms of relative intensity of magnetic field present during 

heat treatment. The microwave heating of ceramics was thought to be mainly due 

to the dielectric loss of the material, and the electric field component was thought 

to dominate the heating process. However, it has been suggested that at elevated 

temperatures, the heating mechanism of ceramics may have been due to a 

combination of factors, including dielectric loss, eddy current, and magnetic loss.

58–

59 Figure 24 shows sample density plotted as a function of the ratio of magnetic to 

electric field. For example, SM-100:0 had a ratio of zero (or 0/100) while SM-30:70 

had a ratio of 2.33 (or 70/30). The multimode sample was assumed to have a ratio 

of one. These results suggested that the amount of magnetic energy present may 

have had a significant effect on densification, despite the fact that magnetic fields 

coupled very weakly with Al2O3 but strongly with erbium (having unpaired 

electrons and hence high magnetic moment).

Fig. 24 Ratio of magnetic to electric field strength vs. density of all microwave-sintered Erdoped Al2O3 (dashed line represents density of conventionally sintered Er-doped Al2O3)

To investigate the effect of microwave parameters on erbium stability and 

diffusion, the phase content of each sample was studied using XRD. All samples 

contained Er3Al5O12 (ErAG) after sintering. There was no remaining ErAl2O3. The 

peak height ratios were converted to ErAG concentrations using a calibration curve 

generated by precise mixtures of commercial Y3Al5O12 (YAG) and Al2O3 powders. 

Although the analysis was semiquantitative, since ErAG and YAG are isostructural 

and erbium and yttrium have similar mass attenuation coefficients, the 

approximation of volume percent ErAG and YAG should be nearly identical. Thus, 
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32

the ErAG concentrations are referred to as equivalent concentrations, and these are 

indicated by an asterisk in Table 2.

While phase composition did not vary as widely as density across the sample set, 

there was still an observable effect. The baseline samples at both temperatures, as 

well as SM-100:0 and MM, were composed of approximately 2.6 volume percent 

ErAG. This amount of second-phase ErAG corresponded to an overall Er:Al cation 

ratio of approximately 0.54%, which matched the initial concentration quite well. 

This indicated that all Er in these samples had formed second-phase precipitates, 

and that very little, if any, remained in the crystal structure. The SM-30:70 sample 

had an ErAG concentration of 2.25, making it the most favorable for preventing 

erbium from diffusing out of the crystal structure. If the remaining erbium was still 

in solution within the Al2O3, approximately 0.08% Er doping was achieved. The 

phase composition data is shown in Fig. 25, and the equivalent volume percent of 

ErAG was plotted as a ratio of magnetic to electric field intensity. In this plot, the 

results suggested that increasing the magnetic component of the microwave field 

decreased second-phase formation.

Fig. 25 Ratio of magnetic to electric field vs. equivalent vol% of ErAG of all microwave 

sintered Er-doped Al2O3 (dashed line represents equivalent wt% of conventionally sintered 

Er-doped Al2O3)

The microstructure of the MM sample is shown in Fig. 26. A high degree of 

porosity was observed, as suggested by the density results. The average grain size 

of the sample was approximately 250–300 nm, and the grain size distribution was 

very uniform. SEM micrographs of samples BL, SM-100:0, and SM-60:40 were all 

very similar to Fig. 26. The microstructure of SM-30:70, however, was quite 

different, as shown in Fig. 27. As observed in the secondary electron image of Fig.

27a, SM-30:70 had much less porosity, which confirmed the density results. SM-
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33

30:70 also had coarser grains, up to approximately 1 μ on average with a somewhat 

bimodal character. The coarser grains were explained by the reduction of pore drag 

associated with higher densities. The backscattered electron SEM image of the 

same sample is shown in Fig. 27b, with the brighter phases reflecting a higher 

atomic number. The second phase was reminiscent of an amorphous secondary 

phase. Many of the interfaces with Al2O3 grains were low-curvature/concave or 

high-curvature/convex, much like a pore-filling liquid phase.

Fig. 26 SEM images of sample MM using secondary electrons. A high degree of porosity can 

be seen in the region which was ion-polished.

Fig. 27 a) SEM images of sample SM-30:70 using secondary electrons, and b) back-scattered 

electrons. Regions of differing Z-contrast are very clear in b.

Overall, the microwave sintering parameters appeared to have a profound influence 

on the densification as well as migration and phase stability. Sintering in the singlemode microwave system with a 30%E:70%H mixed field produced samples with 
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34

significantly higher density (~97% of theoretical of alumina) than all of the other 

samples sintered at 1400 °C (and equivalent to the sample conventionally sintered 

at 1700 °C). This high density represented a significant improvement over the 

conventionally sintered (1400 °C) sample, which had a density approximately 70% 

of the theoretical density. This sample also contained the least amount of second 

phase, which indicated that more erbium formed a solid solution with Al2O3. The 

results also indicated that densification and erbium stability within the lattice 

improved with increasing magnetic field. These findings suggested that the 

magnetic component appeared to play a critical role in the processing of weakly 

magnetic materials such as Al2O3, and that the rare earth dopant played an 

important role in the material response to EM fields. 

6. Magnetic Field Processing of Rare-Earth-Doped Alumina

As detailed in Section 1.2, high-strength magnetic fields can be used to promote 

crystallographic texturing in materials by exploiting magnetic anisotropy 

susceptibility differences to exert a torque on the grains and align them along the 

easy magnetization axis.24–27,30,32,34 The superconductor literature also shows that 

magnetic anisotropy can be enhanced by up to a factor of 10 by incorporating low 

concentrations of rare-earth ions,60,61 which provided the motivation for developing 

a rare-earth-doped alumina material that could potentially be textured despite its

diamagnetic nature. Predictive DFT modeling and experimental testing methods 

were designed to explore magnetic field texturing of rare-earth-doped alumina, as 

discussed in the following sections.

6.1 DFT Modeling of Magnetic-Field Effects

DFT calculations were used to predict the effect of magnetic field on Ln-doped 

alumina. Properties of interest with respect to magnetic-field effects included the 

internal magnetic moment, magnetic anisotropy energy, and magnetic 

susceptibility. Spin-polarized calculations were performed using DFT as 

implemented in the Vienna ab initio simulation package (VASP 5.3)

62–64 with

generalized gradient approximation-Perdew-Burke-Ernzerhof (PBE) exchange 

correlation functional and projector augmented wave (PAW) pseudopotentials.

65,66

A plane-wave energy cutoff of 800 eV was used for the expansion of the electronic 

wave function. A 2 × 2 × 2 gamma-centered Monkhorst-Pack grid67 was used for 

both the α- and θ-Al2O3 120-atom supercells. The PBE-PAW pseudopotential core 

electron configurations were [He] for O, [Ne] for Al, and [Kr]-4d10 for all of the 

RE-elements such that f-electrons were considered to be valence electrons except 

for Yb, which had a full f-shell and was represented by [Kr]-4d10-5s2

-4f

14.
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The magnetic moments for each atom in the supercell were determined by the 

projection method within the VASP PAW scheme, in which the moments were 

calculated within the ion-centered spheres with Wigner-Seitz radii designated in 

the pseudopotential file. To accelerate the self-consistent convergence, an initial 

magnetic moment of 3 μb was assigned to each dopant. 

Noncollinear spin-orbit coupled (SOC) calculations were performed on the 

optimized Ln-doped supercells to determine the doping effect on cohesive energy, 

magnetocrystalline anisotropy energy 

MMMM [xxxxxx]: = EE[xxxxxx] − EE[uuuuuu], (5)

where EE[xxxxxx] is the total electronic energy of the crystal with spin-axes aligned 

along [ xx yy zz ] and EE[uuuuuu] is the minimum total electronic energy observed 

corresponding to spin-axes aligned along the [ uu vv ww ] direction, and the easy 

magnetic axis orientation. The nonself-consistent SOC calculations began from the 

corresponding converged collinear wave function and charge density and prevented 

spin reorientation to the easy axis during the calculation. The magnetocrystalline 

anisotropy energy (MAE) was defined as the change in energy resulting from spin 

axis reorientation, and was indicative of the magnetic anisotropy of the crystal.

The minimum energy direction was designated as the easy axis, and the hard axis 

corresponded to the maximum energy direction. To determine the MAE and easy 

and hard axes, the spin-axis orientation was manually defined along Cartesian 

vectors. Cartesian vectors were sampled over [ xx yy zz ] for xx ∈ Z(−5: 5) and yy, zz ∈

Z(0: 5) and transformed to crystallographic vectors. The remaining space not 

sampled (i.e., yy, zz ∈ Z(−5: 0)) was tested and determined to be symmetry 

equivalent to vectors from the sampled space. A 3-D representation of the MAE 

surface was determined using interpolation of the MAE.

Magnetic susceptibilities were computed via the linear response method, following 

literature,

68 as implemented in VASP 5.3 using the optimized RE-doped Al2O3

supercells. The effect of spin orbit coupling was included within the computation 

of the susceptibility. A 600 eV plane-wave energy cutoff was used for the 

expansion of the electronic wavefunction and a 2 × 2 × 2 gamma-centered 

Monkhorst-Pack k-point grid was used for both the α- and θ-Al2O3 120-atom 

supercells.

The intrinsic magnetic moment of Ln-Al2O3 was quantified based on the Ln-dopant 

moment and distribution of magnetic moment throughout the supercell. The total 

and local moments were calculated within the ion-centered spheres with WignerSeitz radii designated in the pseudopotential. Undoped Al2O3 had no net magnetic 

moment and the moment of Al and O atoms was zero for both α- and θ-Al2O3. The 
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36

magnetic moments of the Ln-doped supercells were independent of both the phase 

and dopant site, with a magnetic moment fluctuation of less than 0.2 μb for a given 

dopant. As expected, the net magnetic moment was correlated with the number of 

unpaired electrons of the dopant, as shown in Fig. 28a. Although Al2O3:Ln 

exhibited delocalization of the magnetic moments onto neighboring O-atoms, no 

magnetic moment was observed on the Al-atoms in any of the calculations. The 

heavier Ln-dopants (Er and Yb) induced a ferromagnetic moment on neighboring 

oxygen atoms, and also exhibited a higher magnetic moment within Al2O3

compared to their atomic ground state configuration. Conversely, the lighter Lnatoms (Pr and Nd) exhibited lower magnetic moment within Al2O3 than in their

atomic ground state configuration and had antiferromagnetic ordering with 

neighboring oxygen atoms. Only Gd had the same magnetic moment in its atomic 

ground state and as a dopant in Al2O3, indicating a strong localization of the 

magnetic moment around the Gd atom. Strong localization was observed for Pr, 

Nd, Gd, and Er, with the induced magnetic moment on the neighboring oxygen 

atoms accounting for approximately 2%, 2%, 0%, and 3%, respectively, of the total 

supercell moment. However, in the Yb-doped Al2O3, 83% of the magnetic moment 

was delocalized on O atoms in the supercell. The localization of the magnetic 

moment is depicted schematically in Fig. 28b and 28c for Al2O3:Gd and Al2O3:Yb, 

respectively, where the arrows illustrate the degree of delocalization of the 

magnetic moment and its asymmetric distribution. This variation in magnetic 

moment localization suggests that there may be a competing effect of global and 

local magnetic moment on the overall magnetic susceptibility, which may play a 

significant role in aligning alumina grains under magnetic fields during 

processing.

69,70

Fig. 28 DFT-calculated magnetic moment of Ln-doped Al2O3. a) Magnetic moment of Lndopant as a single atom in vacuum, the full α-Al2O3:Ln supercell, and localized on the Lndopant within the α-Al2O3:Ln supercell. b) 1/4 supercell of α-Al2O3:Gd, and c) 1/4 supercell of 

θ-Al2O3:Yb with arrows indicating the localization and magnitude of the magnetic moment 

for each atom, with atoms colored as O (red), Al (blue), Gd (green), and Yb (yellow).
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The magnetic moment was also found to localize on the Ln-dopant site, with the 

exception of Yb, which induced a magnetic moment on O2- ions throughout the 

supercell. This observation was independent of phase and dopant site. In general, it 

was found that increasing the number of unpaired valence electrons decreased the 

defect formation energy and also increased the local magnetic moment, suggesting 

that Ln-dopants may significantly affect the processing of Al2O3 under magnetic 

fields.

The inclusion of spin orbit coupling decreased the total energy of the rare-earthdoped alumina, but overall, it was found that the phase stability predicted by spinpolarized calculations was not affected. To determine the phase stability, the 

cohesive energy

Ecoh = E(Al47REO72) − [47 ∙ E(Al) + E(RE) + 72 ∙ E(O)], (6)

where E(Al47REO72), E(Al), E(Ln), and E(O) represent total energies of the rareearth-doped supercell, Al-atom, Ln-atom, and O-atom, respectively, was calculated 

as shown in Eq. 6 and compared among material phases. As shown in Table 3, the 

calculated Ecoh values show that the α-phase remains the most stable among the 3

phases studied. The θ-phase with octahedral dopant sites was the second most stable 

phase followed by the θ-phase with tetrahedral coordination for the dopant sites,

which was the least stable phase. 

Table 3 Cohesive energy (eV) of rare-earth-doped alumina with z-axis oriented spins from 

collinear and noncollinear spin orbit coupled calculations

Dopant location Al2O3 Pr:Al2O3 Nd:Al2O3 Gd:Al2O3 Er:Al2O3 Yb:Al2O3

Collinear [1]

α – octahedral –746.08 –743.76 –743.31 –745.26 –743.66 –740.77

θ – octahedral –744.28 –743.69 –743.16 –745.02 –743.34 –740.24

θ – tetrahedral –744.28 –743.16 –742.51 –744.29 –742.49 –739.41

Spin-orbit coupled: z-axis orientation

α – octahedral –746.09 –744.32 –743.77 –745.84 –744.91 –741.11

θ – octahedral –744.29 –744.21 –743.63 –745.60 –744.59 –740.55

θ – tetrahedral –744.29 –743.70 –742.99 –744.89 –743.76 –739.74

As a next step, the effect of spin-orbit coupling was included within the DFT 

simulations in VASP. Spin-orbit coupling was essential for accurate treatment of 

the effect of magnetic field on Ln-doped alumina. This phenomena was evaluated

for the cohesive energy, magnetocrystalline anisotropy energy, and magnetic 

susceptibility. The addition of spin-orbit coupling had the greatest influence over 
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the energetic contribution of the rare-earth dopant. The change in energy as a 

function of SOC for each alumina phase and dopant are given in Table 4. In general, 

it was the dopant type, rather than alumina phase, which had a much more 

significant effect on the energetic contribution to the SOC. Er-dopant had the 

largest energetic gain, which was double the next highest candidate dopant, Gd. For 

consistency, these results are also shown in Figs. 29–32.

Table 4 Energetic contribution (eV) of the rare-earth dopant spin-orbit coupling for z-axis 

oriented spins from nonself-consistent calculations

Dopant location Al2O3 Pr:Al2O3 Nd:Al2O3 Gd:Al2O3 Er:Al2O3 Yb:Al2O3

α – octahedral 0.00 –1.07 –0.90 –1.15 –2.26 –0.64

θ – octahedral 0.00 –1.04 –0.90 –1.14 –2.28 –0.59

θ – tetrahedral 0.00 –1.06 –0.93 –1.17 –2.30 –0.63

Fig. 29 Collinear vs. noncollinear spin-orbit coupled cohesive energy for α-phase RE-doped 

and undoped alumina
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Fig. 30 Collinear vs. noncollinear spin-orbit coupled cohesive energy for θ-phase 

(octahedral site) RE-doped alumina

Fig. 31 Collinear vs. noncollinear spin-orbit coupled cohesive energy for θ-phase 

(tetrahedral site) RE-doped and undoped alumina
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Fig. 32 Change in total energy as a result of the addition of spin-orbit coupling. Energy 

change is given in eV and shown for each RE-dopant and material phase.

By manually redefining and fixing the orientation of the spin axes, the 

magnetocrystalline anisotropy of the RE-doped alumina supercells was 

investigated. Understanding the MAE allowed for better understanding of the ease 

of magnetization along each selected axis. For each phase and dopant combination, 

a 3-D surface plot was generated to present a visual representation of the easy and 

hard magnetization axes. The 3-D surface plots for Er, Pr, and Gd dopants are 

shown Figs. 33–35.

Fig. 33 MAE interpolated surface plots for Pr-doped Al2O3
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Fig. 34 MAE interpolated surface plots for Er-doped Al2O3

Fig. 35 MAE interpolated surface plots for Gd-doped Al2O3

The MAE and easy axis were affected by the dopant site and phase as shown in 

Table 5, though the total magnetic moment remained consistent for a given dopant 

type. The largest anisotropy was generally observed for Er followed by Pr, with Gd 

having the smallest anisotropy despite having the largest magnetic moment. The 

Θ-Al2O3 was more magnetically anisotropic than α-Al2O3 and this effect was most 

pronounced for Pr-doped Al2O3, which had a 3-fold increase in MAE. Additionally, 

the easy axis was dependent on the dopant type. In α-Al2O3, both Gd and Yb 

maintained easy axes near to easy axis of undoped α-Al2O3, the c-axis. 

Table 5 DFT calculated easy magnetic axis and maximal MAE (meV) indicating degree of 

magnetic anisotropy in the Ln-doped supercell for Ln-dopants in the Al-octahedral site of αand θ-Al2O3

Yb:Al2O3 Er:Al2O3 Gd:Al2O3 Pr:Al2O3

α-Al2O3 < 3 2 10 > < 1 2 0 > < 0 0 1 > < 2 3 2 >

6.1 23.1 0.4 11.0

θ-Al2O3 < 3 0 1 > < –4 3 4 > < 1 0 20 > < 1 0 0 >

0.5 31.3 0.4 30.9
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Pr-doped Al2O3 MAE surface plots are shown in Fig. 33, including α-Al2O3 and θAl2O3, and both octahedral and tetrahedral doping sites for the θ-phase. From these 

plots, it was evident that throughout each of the material phases, the overall shape 

of the MAE remained ring-like, though there were some minor distinctive features 

within the α-phase. The consistent ring-like structure among the MAE surface plots 

suggested that a single preferential axis for alignment existed within this Pr-doped 

material. The MAE in the θ-phase exceeded the α-phase for both the octahedral and 

tetrahedral doping sites. 

Similar to the Pr-doped Al2O3 supercells, the Er-doped Al2O3 also had 

comparatively large MAE values. However, contrary to the ring shape associated 

with Pr doping, the Er doping seemed to have caused a more varied MAE landscape 

throughout the material phases and doping sites. The strong diversity between 

phases and dopant sites suggested that with Er doping there could be multiple sites 

and pathways available for orientation, as opposed to a single pathway. In addition, 

the largest overall anisotropy was found within the Er-doped θ-phase, octahedral 

site. This suggested that there was a diverse landscape for orientation within these 

material phases and dopant sites that could create a better chance for orientation 

and, thus, material processing. The MAE surface plots for Er-doped Al2O3 are 

shown in Fig. 34.

Contrary to what was found in the Er- and Pr-doped supercells, the Gd-doped cells 

were found to have the smallest anisotropy energy. The MAE surface plots for Gddoped cells are shown in Fig. 35. 

Material magnetic susceptibility (χ) was computed for RE-doped Al2O3, as shown 

in Fig. 36. Dopants included in the susceptibility calculation included Er, Gd, Nd, 

Pr, and Yb. Both alumina phases were considered, as well as both octahedral and 

tetrahedral dopant sites for the θ-phase. Magnetic susceptibility was important 

because it provided a qualitative understanding of the degree to which the alumina 

material could be aligned under the magnetic field. 
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Fig. 36 The magnetic susceptibility of α-phase and θ-phase (octahedral, tetrahedral) 

RE-doped alumina

Through this study, it was found that the dopant type, site, and phase had strong 

potential effects on the susceptibility. Among the doped samples, Er-, Gd-, and Nddoped alumina had the largest susceptibilities throughout each phase studied. Nddoped alumina, θ-phase (octahedral site) had the highest overall susceptibility but 

was closely followed in magnitude by both Gd and Er dopants. Conversely, Ybdoped alumina (α-phase) had the lowest overall magnetic susceptibility. Material 

phase also had a strong influence over the value of χ, where θ-phase shows a 

significant increase in magnitude as compared to α.

6.2 High-Temperature DSC Characterization under Applied 

Magnetic Field

Prior to experimental investigation of magnetic-field texturing, a continuation of 

the rare-earth-doped alumina phase formation characterization study was 

conducted under applied magnetic field. Experiments were conducted at Oak Ridge 

National Laboratory (ORNL), Oak Ridge, Tennessee, under the guidance of Drs

Gerry Ludtka and Orlando Rios. A superconducting magnet with a hightemperature induction furnace insert was used to collect DSC data of Er-doped 

alumina at 0 Tesla and 9 Tesla applied fields. The temperature was ramped from 

room temperature up to 1400 °C at 10 °C/min. Figure 37 shows DSC data from the 

same material batch of Er-doped AACH measured at ARL (black line) and ORNL 
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(blue line) under no applied magnetic field. The difference in sensitivity was 

apparent, as the ARL DSC was designed to go up to higher temperatures, and was 

more limited in sensitivity. The ORNL DSC was designed for enhanced sensitivity, 

but was not robust enough to withstand high temperatures for a sustained period of 

time or over extended numbers of cycles. The ORNL data clearly showed a sharp 

endotherm at approximately 250 °C where boehmite formed. Some minor 

exotherms were also identified at temperatures in which gamma and alpha alumina 

formed as well. The theta-alumina transformation was not easily detected in either 

DSC measurement, but was the common region of formation for this phase and is

highlighted in Fig. 37.

Fig. 37 DSC data comparison between ARL DSC data and ORNL DSC data, both data sets 

measured at a heating rate of 10 °C/min

Figure 38 shows the ORNL DSC data under the absence of magnetic field (0 T) 

and the presence of a high-magnetic field (9 T). There were no notable changes in 

the temperatures at which AACH decomposed or boehmite crystallized. However, 

there were some significant differences in transition temperature for both theta and 

alpha alumina. First, the crystallization of theta alumina occurred at approximately 

675 °C at 9 T, which was much lower than the approximately 850 °C without a 

magnetic field. The transformation temperature of alpha alumina also decreased to 

approximately 950 °C under the 9 T magnetic field.
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Fig. 38 DSC data collected at ORNL at both 0 T and 9 T magnetic field, both data sets 

measured at a heating rate of 10 °C/min

It was theorized that the magnetic moment residing in the erbium affected the local 

strain when the material was under the applied-magnetic field, which influenced 

the driving force for phase transformation. Generally, the magnetic field was 

satisfying the endothermic energy requirement for crystallization. It was possible 

that a similar behavior could occur in the other rare-earth dopants, but previous 

DFT modeling and characterization of Er-doped alumina indicated that erbium 

would have the strongest influence under the applied-magnetic field. The small but 

notable difference in transformation temperature that was observed upon rare-earth 

doping in Section 3 had been significantly enhanced under the influence of a highstrength 9 T magnetic field. 

6.3 Magnetic Field Texturing of Epoxy Samples

Experiments were set up to determine the effects of magnetic fields over 

crystallographic texturing of rare-earth-doped alumina materials. The critical 

parameters detailed in Section 1.2 were referenced during the design of 

experiments. One point of emphasis was that a low-viscosity casting system would 

be required to allow the grains to rotate in response to the magnetic field before 

stiffening or hardening to lock the textured condition in place.71 For this reason, 

epoxy was selected as a test matrix for running initial experiments before switching 

to a gel-casting process for final development of the rare-earth-doped samples. The 
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46

method used for quantifying the degree of texture was also considered, starting with 

the common Lotgering factor (LF) technique for initial samples, and evolving to 

the more accurate average facial angle method. Other considerations that were 

made before setting up the experiments included results from DFT modeling, which 

predicted that different crystalline phases of alumina would exhibit a different 

crystallographic easy axis, changing which plane was aligned with respect to the 

measurement direction. These computational findings generated interest in 

investigating the response of different phases of alumina cast under the same 

magnetic field. Furthermore, since DFT results predicted that dopants affected the 

choice of magnetization easy axis, the response of alumina phases containing 

different dopants was also of interest.

Two-part room-temperature curing epoxy (EP1112NC Clear, Resinlab, 

Germantown, WI), was used to suspend the rare-earth-doped alumina powder and 

lock it in place after alignment. First, alumina/methanol slurries were ball-milled to 

break up agglomerates generated from the calcination process. After ball milling, 

the alumina/methanol slurry was added to Part A of the epoxy and mixed using a 

wrist action shaker. Methanol was used as the solvent because it could be used to 

dilute the epoxy without changing the overall properties of the epoxy, allowing for 

thorough mixing of the alumina in the epoxy. Enough alumina/methanol slurry was 

added to Part A so that the final ratio of alumina to cured epoxy would yield 

20 wt%. Finally, the methanol was evaporated out of Part A in a hot water bath 

resulting in an alumina powder suspended in Part A epoxy. At the time of magnetic 

alignment, the alumina/Part A suspension was added to the calculated amount of 

Part B for curing. The parts were mixed well with a wooden stirrer, cast into 

lubricated, 1-inch cylindrical plastic potting cups, and set under no-field (control), 

1.8 T magnetic field (1.8 T electromagnet, Fig. 39), and 9 T magnetic field (9 T 

Horizontal Bore Superconducting Magnetic, American Magnetics Inc., Oak Ridge, 

TN). After sitting in field for at least 3 h, a heat gun was used to accelerate the 

epoxy curing process during the control and 1.8 T conditions. The samples cured 

at 9 T were allowed to cure at room temperature overnight.
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Fig. 39 Aligning epoxy and slurry casts within a 1.8 T magnetic field

After curing, the pucks were demolded, cut parallel to the field direction, and crosssectioned as shown in Fig. 40, for analysis with XRD using Cu-Κα radiation at 

30 KV, 15 mA (Rigaku MiniFlex II). XRD scans were performed over a 34–45 °2θ 

range, at a step angle of 0.01 °2θ, and a scan rate of 1 °2θ/min.

Fig. 40 Cutting and mounting pattern of epoxy pucks cured in magnetic field

The resulting scans were analyzed using Jade 8 software (MDI, Livermore, CA). 

For each scan, the background was automatically removed, peaks were identified, 

and pattern fitting was conducted to identify peak area and peak height values in 

addition to associated errors. The LF was calculated for each scan using the powder 

diffraction file no. 01-089-7717 (Synthetic Corundum, space group RR3�cc) and 

Eq. 7. The LF ranges from 0 to 1 with 0 indicating random alignment and 1 

indicating perfect alignment. 

LLLL = PPaaaaaaaaaaaaaaaaaa−PPrr rrrr

1−PPrr rrrr

(7)

where

PPaaaaaaaa aaaa = II(aaaaaaaaaaaa pp pp)

∑ II(aaaaaa)

(8)

and
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48

PPrr rrrr = II(aaaaaaaaaaaa pp pp),PPPPPP

∑ II(aaaaaa),PPPPPP

. (9)

According to Eq. 8, Palignment denotes the fraction of the summation of the peak 

intensities corresponding to the preferred orientation axis to that of the summation 

of all diffraction peaks in the particle-oriented materials. In Eq. 9, Prandom is simply 

the same as Palignment,, except it was calculated from the peak intensities in the 

powder diffraction file (random orientation). In addition to the LF, synchrotron 

X-ray powder diffraction and Rietveld refinements were used to calculate the 

amount of alpha- and theta-phase alumina in each material.

The (006) and (110) crystal planes were selected to calculate the LF due to their 

orientations with respect to one another. The 2 planes were perpendicular to each 

other, which helped gauge if there was alignment in the sample with respect to 2

different alignment directions. Figure 41 illustrates the (006) and (110) crystal 

planes in a rhombohedral unit cell, such as the unit cell of alumina. Additionally, 

the (006) crystal plane did not diffract with a large intensity, as it was only 0.6% of 

the highest intensity peak in alumina. This led to difficulties in data analysis, 

prompting the use of the (110) to study crystal alignment.

Fig. 41 Idealized rhombohedral unit cell illustrating the (006) and (110) crystal planes

To calculate the LF with respect to the (006) crystal plane, Eqs. 8 and 9 were

modified to Eqs. 10 and 11. Similarly, to calculate the LF with respect to the (110) 

crystal plane, Eqs. 8 and 9 were modified to Eqs. 12 and 13, as shown below:

PPaaaaaaaa aaaa ,(006) = II(006)

II(104)+II(006)+II(110)+II(113)

(10)
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PPrr rrrr ,(006) = II(006),PPPPPP

II(104),PPPPPP+II(006),PPPPPP+II(110),PPPPPP+II(113),PPPPPP

(11)

PPaaaaaaaa aaaa ,(110) = II(110)

II(104)+II(006)+II(110)+II(113)

(12)

PPrr rrrr ,(110) = II(110),PPPPPP

II(104),PPPPPP+II(006),PPPPPP+II(110),PPPPPP+II(113),PPPPPP

. (13)

The calculated LFs for each condition are listed in Table 6. Figure 42 compares 

alignment for each dopant series with increasing magnetic field by individual 

crystal-plane alignment. Figure 43 shows the XRD spectra obtained from the 

Yb:Al2O3 samples aligned at 0, 1.8, and 9 T. The (006) is not present in the 0 T 

pattern, but the (006) does appear as the particles align under an increasing 

magnetic field strength.

Table 6 LFs calculated from (006) and (110) planes for magnetically aligned ceramic 

composite samples

Composition

Lotgering factor (LF) (%)

0 T 1.8 T 9 T

(006) (110) (006) (110) (006) (110)

Gd: Al2O3 0.25 2.78 27.0 10.0 25.0 10.7

Yb: Al2O3 3.29 2.39 26.6 9.98 51.8 11.2

Pr: Al2O3 0.25 2.93 0.25 2.10 0.25 28.3

Er: Al2O3 10.1 2.65 31.0 12.3 . . . . . .

Undoped Al2O3 0.25 2.75 0.25 3.01 7.51 8.9

Fig. 42 a) LF as a function of field strength and dopant type with respect to the (006), LF(006)

and b) LF as a function of field strength and dopant type with respect to the (110), LF(110)

(a) (b)
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Fig. 43 XRD example spectra of Yb:Al2O3 samples with increasing magnetic field strength

The XRD data for LF(006) shows 3 compositions with significant alignment, 

Gd:Al2O3, Er:Al2O3, and Yb:Al2O3. The Pr:Al2O3 and undoped Al2O3 did not show 

significant (006) peak intensity to calculate the LF. However, after a 9 T field was 

applied to the undoped Al2O3, there was a large enough peak to calculate the LF. 

The XRD data for LF(110) shows essentially the opposite result, with Pr:Al2O3

showing the largest alignment along the (110) plane. The other compositions had 

comparable orientations, but all were higher than the samples cured without a 

magnetic field applied.

The alignment of the doped alumina may have been limited by several factors. First, 

the viscosity of the epoxy could have been increasing too quickly for significant 

particle alignment to occur. If that were the case, better alignment under 9 T field 

conditions would still be expected, since increasing the magnetic field would

decrease the amount of time necessary for alignment. However, not all the samples 

show increased magnetic alignment from 1.8 to 9 T. For example, the Gd-doped 

alumina specimen did not show improved orientation upon alignment under 9 T. 

This could have indicated that a maximum field strength existed for particle 

alignment in this system. Another potential explanation was that steric interactions 

were hindering particle rotation. This has been reported during other attempts to 

produce microtexture.

9 For example, when trying to magnetically align platelet 

alumina, they started to inhibit alignment by impinging on each other.

9 Since the 

powders used in these studies were derived from a chemical precipitation process, 

it was likely that the particles were not smooth and spherical, increasing the 

likelihood of strong interparticle interactions that could potentially inhibit 
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51

alignment. However, since the samples contained only 20 wt% solids, it was 

unlikely that steric hindrance had a large effect.

The overall agglomeration of alumina crystallites could have also led to the 

variation in data. Although no analysis had been done to quantify the degree of 

agglomeration, it was likely that some amount of agglomeration was present since 

no dispersant was used. If multiple crystallites were present in different orientations 

within the agglomerates, the torques applied to the agglomerate by the magnetic 

field would be in competition. It was unknown if these torques would be strong 

enough to break up hard agglomerates.

As can be seen in Fig. 42, alignment generally increases with magnetic field 

strength. Looking at the data, 2 points stood out. First, both the Gd-doped Al2O3

and the Yb-doped Al2O3 had similar alignment along the (110) plane despite Gddoped Al2O3 having a much stronger total magnetic moment. However, when 

considering the LF(006), the Yb:Al2O3 had a larger response. This may have been 

due, in part, to the localization of the magnetic moment. In the case of Gd:Al2O3, 

the magnetic moment was localized to the dopant position; whereas, for Yb-doped 

Al2O3 the magnetic moment was more globally distributed within the structure, 

possibly inducing higher torque along selected crystal planes at the same field 

strength. The second interesting result was that the undoped samples experienced a 

small degree of alignment when the field strength was high enough. Calculations 

indicated a field of approximately 10 T should be necessary for moderate amounts 

of alignment.27,30 However, Eqs. 1 and 2 indicated that alignment should be possible 

with a high enough magnetic field strength, no matter how small the magnetic 

susceptibility anisotropy was. 

The disproportionately weak response observed in the Pr-doped Al2O3 compared 

with the other dopants was due to the significant content of theta phase, as shown 

in Section 3. Table 7 shows the calculated amount of alpha and theta phases in each 

of the rare-earth-doped alumina materials, which were consistent with results from 

Fig. 15b. Due to the high theta-phase content, it was theorized that Pr-doped Al2O3

was preferentially aligned along the (110) plane.
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Table 7 Quantification of alumina polymorphs in the materials examined, determined by 

Rietveld refinement of synchrotron X-ray diffraction

Composition Polymorph

α θ η

Al2O3 . . . . . . 100

Gd:Al2O3 76 24 . . .

Yb:Al2O3 84.4 15.6 . . .

Pr:Al2O3 32.5 67.5 . . .

Er:Al2O3 62.6 37.4 . . .

The DFT results indicated that the magnetic anisotropy of alpha-phase Pr-doped 

Al2O3 was second only to Er-doped Al2O3. This anisotropy was greatly increased 

for praseodymium in θ-Al2O3 in comparison to the alpha phase. Additionally, 

earlier DFT results showed that increasing the dopant radii increased the relative 

stability of θ-Al2O3, potentially increasing the θ-Al2O3 content of the Pr-doped 

sample more than for the other dopants. This could have resulted in crystals 

aligning along different directions since the DFT results suggested that doped theta 

and alpha alumina had different magnetic anisotropies. DFT results also predicted 

that both erbium and praseodymium would shift the easy axis from the c-axis, the 

known easy axis for α-alumina, suggesting that the (006) peak was no longer the 

ideal plane to calculate LF. This was confirmed by calculating the LF of the (110) 

plane, which did show significant alignment in Pr-doped Al2O3.

In contrast to the LF method used to quantify microtexture, a technique based on 

percent alignment based of the average interfacial angle, as proposed by Asai,

71

was calculated for each scan using the powder diffraction file no. 01-089-7717 

(Synthetic Corundum, space group R3 ̅c) and Eqs. 14–16.

The facial angle, θF, is the angle between the magnetic easy-axis (the c-axis or [006]

plane specifically for alumina). A general formula based on elementary multivariate 

calculus can be used to find the angle between 2 vectors as described in Eq. 14. 

Since the vector denoted by v = (h k l) is perpendicular to the corresponding plane 

with those indices, Eq. 14 can be used to calculate the facial angle between 2 planes.

(θθhkk ) = ccccss−1 � (hkk ) · (hkk )aa

‖(hkk ) ‖‖(hkk )aa‖

� (14)

By taking the weighted average of the facial angles for each XRD spectra based on 

their individual peak intensities, which varies with increasing alignment, average 

facial angle for each specimen as described in Eq. 15 could be determined.

71 This 

average angle changed with respect to the degree of alignment present, and could 

be used to quantitatively track the amount of alignment achieved in a much more 

accurate manner.
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θθFF = ∑(IIh ) (θθh )

∑(IIh ) , (15)

where Ihkl denotes the intensity of the ith peak.

However, since the facial angle is in units of degrees and varies between 1 and 90, 

it is difficult to interpret. By adapting the Lotgering equation16,10 and comparing the 

observed average facial angle with that of the average facial angle of a perfectly 

random specimen (the PDF card), a percentage alignment for each specimen was 

calculated according to Eq. 16.

% aaaaaaaaaaaaaaaa = θθ rr−θθ

θθ rr

, (16)

where θFr denotes the average facial angle of the powder diffraction card with 

respect to the (006) peak. The percentage alignment values for each condition were 

averaged across the 3 repeats. Two-tailed, 2-sample t-tests were conducted to 

compare the alignment of the 1.8-T samples with the controls. An alpha value of α

= 0.05 was used.

Table 8 lists the average percent alignment value standard deviation for each 

condition while Fig. 44 compared the percent alignment across dopants. All of the 

magnetically aligned samples had higher statistically significant percent alignment 

values, as expected. As shown in Table 8 and Fig. 42, the Er-doped samples 

exhibited the highest degree of alignment, followed by Yb-doped and Gd-doped. 

This was in agreement with what was observed in the mixed-phase alumina epoxy 

samples when the data was recalculated using the average facial angle calculation 

(Table 8). Again, ytterbium exhibited a higher degree of alignment than 

gadolinium, despite having a much lower total magnetic moment. 

Table 8 Average percentage alignment values ± standard deviation for phase-pure αalumina epoxy samples. Third column also lists the percentage alignment values recalculated 

using the average facial angle method from the previous mixed-phase alumina epoxy 

alignment samples for comparison.

Dopant

Phase-pure α-alumina 

alignment 

(%)

Mixed-phase alumina 

alignment

(%)10

0 T 1.8 T 1.8 T

Gd 0.93 ± 0.86 6.49 ± 1.81 15.01 ± 9.65

Yb 2.22 ± 0.14 21.01 ± 0.64 20.50 ± 1.64

Er 2.20 ±0.41 26.43 ± 6.46 27.12 ± 0.56

Pr 2.18 ± 0.71 -2.37 ± 1.62 0.25 ± 6.11

Undoped 2.51 ± 0.58 5.86 ± 1.48 4.05 ± 0.48a

a

Indicates n = 2
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Fig. 44 Percentage alignment values for each dopant type

From previous work, it was found that the LF method was a less accurate 

representation of the degree of alignment at low alignment levels since it relied on 

detection of the (006) peak. Since the (006) peak was normally only 0.6 % of the 

maximum peak height in a randomly aligned sample (powder diffraction file no. 

01-089-7717, Synthetic Corundum, space group R3 ̅c), the LF typically showed no 

detectable alignment. Using a percent alignment value based on the average facial 

angle allowed the degree of peak deviation to be taken into account, which provided 

a much more accurate representation. For this reason, all of the previous results 

from the mixed-phase epoxy alignment study were recalculated using the facial 

angle method. Once that was completed, minimal discrepancy was found (Table 8).

Praseodymium showed a similar response, with a negative alignment value under 

a magnetic field due to the high theta phase content. This was consistent with the 

large negative response (–54.03 %) found in the 9 T mixed-phase alumina samples.

Table 9 lists the crystallographic alignment directions as calculated by DFT for 

each of the dopants tested. Since crystallographic directions were perpendicular to 

their corresponding crystallographic planes, calculating the dot product of the hkl 

indices of the XRD peak with the indices of the alignment direction identified 

which XRD peaks should be growing if alignment was achieved, since only XRD 

peaks that produced a dot product equal to zero were perpendicular to the alignment 

direction. The aligned peaks were identified for each of the dopants based on DFT 

calculations (Table 9). However, since some directions were perpendicular to peaks 
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55

that exhibited no XRD peak, it was not possible to track alignment using the 

previously described XRD method. This was true for both ytterbium and 

praseodymium dopants. 

Table 9 Alignment directions identified previously through DFT and their corresponding 

XRD alignment peak based on a dot product equal to zero. Some directions had no measurable 

XRD peaks.

Dopant Alignment direction Corresponding XRD alignment peak

Gd <0 0 1> (110)

Yb <3 2 10> . . .

Er <1 2 0> (006)

Pr <2 3 2> . . .

Undoped <1 2 0> (006)

Since Er-doped alumina was predicted to align to the same axis as undoped

alumina, there was no reason to recalculate the percentage alignment values. 

However, since gadolinium aligned to the (110) peak, a peak already within the 

angle range measured, the alignment value was recalculated. Average percentage 

alignment for Gd-doped samples was found to be –3.51 ± 1.08% and –0.20 ± 0.58% 

for the 1.8 T and 0 T conditions, respectively. 

Once the mixed-phase alignment values at 1.8 T were recalculated using the 

average facial angle alignment method, the phase–pure α-alumina sample trends 

were consistent with the mixed-phase alumina samples. Erbium again showed the 

highest response of approximately 26% alignment, followed by ytterbium and 

gadolinium (despite the much higher total magnetic moment).

6.4 Magnetic Field Texturing of Gel Cast Samples

For gel casting of green alumina parts under an applied magnetic field, commercial 

samples of a copolymer (1:1) of isobutylene and maleic anhydride (trade name 

ISOBAM) were obtained from Kuraray (Kuraray America, Elastomer BU, 

Houston, TX). ISOBAM no. 104 with an average molecular weight of 55–65 kDa. 

It was found that a slurry containing 70-wt% Er-doped Al2O3 and 0.3 powder wt% 

ISOBAM no. 104 provided acceptable gelling properties. The slurry was prepared 

by adding a premix to a glass beaker and stirring on a magnetic stir plate. The 

ISOBAM was dissolved in water before adding the maximum powder content that 

the slurry would allow while avoid seizing. After mixing for approximately 20 min, 

the slurry was added to a Nalgene mill jar 1/4-full of 1-cm alumina milling media. 

The jar was quickly sealed with parafilm and milled at medium speed for 24 h. 
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56

After milling, the slurry was cast and aligned using a 1.8 T magnetic field. Two 

1-inch-diameter potting cups were positioned for the alignment experiment. One

was placed in the center of the stable magnetic field, while one was placed on the 

bench outside of the field as a control. The mold was coated with a thin film of 

WD-40 (WD-40 Co., San Diego, CA) to prevent wall interaction stress that could

lead to cracks in the green body as it gelled and dried. The mill jar was removed 

from the mill rack and transported to the location of the electromagnet while 

rotating manually to prevent gelling, which was initiated when agitation was 

removed. Finally, the slurry was cast directly into the mold cups within the 

magnetic field (or control, respectively) and allowed to align and gel for 

approximately 4.5 h until a soft gel had developed to stabilize the slurry and prevent 

misalignment once the field was removed. After casting, the mill jar was resealed 

and transported back to the mill rack to continue milling until the first set of casts 

had gelled and another set could be cast. Since the slurry remained fluid and stable 

as long as agitation continued, the milling slurry could be kept and used to produce 

repeats (n = 3) in quick succession after the preceding experimental set had 

achieved an initial gel. Once initial gelling had been reached, the casts were 

removed and allowed to continue drying/gelling overnight. They were demolded 

and dried for approximately 48 h at 60 °C. Once the parts were dry, they were cut 

and measured using XRD. The XRD peak intensities were used to calculate the 

average facial angle, as described earlier.

Table 10 lists the calculated alignment values for each of the conditions tested, and 

Fig. 45 compares the alignment of precipitate Er-doped alumina powders and 

lower-purity precipitated undoped powders, both cast under a 1.8-T magnetic field. 

The rare-earth-doped samples showed much higher alignment than the undoped 

samples. However, the undoped samples also showed statistically significant 

alignment (α = 0.05). For the Er-doped powders, a higher degree of alignment was 

achieved for the gel cast samples as compared to the epoxy cast samples. This was 

attributed to better powder dispersion in the gel-cast slurry than in the epoxy slurry, 

as well as a lower viscosity, since the gel-cast slurries, once milled, were much 

more fluid than the epoxy suspensions.

Table 10 Average percentage alignment values ± standard deviation for phase-pure αalumina gel casting samples

Dopant

Phase-pure α-alumina gel-casting alignment (%) 

(green bodies)

Phase-pure α-alumina epoxy 

alignment 

(%)

0 T 1.8 T 1.8 T

Er 2.67 ± 0.24a 37.73 ± 7.72 26.43 ± 6.46

Undoped 1.07 ± 0.91 4.20 ± 1.43 5.86 ± 1.48 a

Indicates n = 2
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Fig. 45 Percent alignment values for each powder type of green gel-cast specimens

Figure 46 shows the XRD spectra change as a function of sintering. In a green body 

state, the sample exhibited 37.9% alignment. After sintering, the percent alignment 

value remained at 33.8%. This was unexpected, since it was hypothesized that the 

addition of thermal energy without a magnetic field would provide enough 

movement for the particles to become misaligned during the sintering process, 

resulting in reduced alignment values. This was not the case, indicating that a high 

degree of alignment achieved in the green-body state could potentially be 

maintained in the sintered body. The SEM cross-sectional image in Fig. 47 shows 

necking at the particle contact points, but no further densification. This indicated 

that the sintering profile was inadequate for densifying the nanopowders, and that 

further optimization was necessary.
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58

Fig. 46 XRD spectra of the unaligned green body, aligned green body, and sintered aligned 

body. As can be seen, the (006) peak at ~41.5 °2Θ increases with alignment.

Fig. 47 SEM image of a polished cross section from a sintered, aligned gel-cast part
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59

7. Conclusions

The addition of rare-earth dopants to diamagnetic Al2O3 was studied to determine 

the influence over structure, phase, and alignment under applied external fields.

The motivation for adding rare earths to Al2O3 was to enhance the magnetic 

susceptibility anisotropy and increase magnetic torque of the material system, 

thereby increasing the influence of magnetic field application on grain rotation and 

alignment. A coprecipitation synthesis method was developed to overcome ionic 

size mismatch between nano-Al2O3 particles and rare-earth dopants, leading to the 

successful fabrication of a number of rare-earth-doped alumina powders. The 

powders contained a maximum of 400 ppm of rare-earth dopant to avoid the 

formation of unwanted phases. Nine rare-earth dopants from the lanthanide 

(Ln)-series, including erbium (Er), neodymium (Nd), gadolinium (Gd), ytterbium 

(Yb), lanthanum (La), lutetium (Lu), praseodymium (Pr), dysprosium (Dy), and 

thulium (Tm) were used to fabricate rare-earth-doped Al2O3 powders.

Advanced characterization of the powders via SEM, TEM, HT-XRD, hightemperature DSC, ss-NMR, and MAS were conducted. It was determined that Ln 

dopants served as structural promoters to increase the phase-transformation 

temperature (θ →α) by a notable magnitude, which delayed the onset of alumina 

lattice phase transformation. Ln doping of alumina enabled control of the phase 

population, with no additional unwanted phases (i.e., LnAl2O3 or Ln2O3) observed. 

It was determined that the Ln dopants resided in the vacant octahedral locations 

within the alumina lattice. The formation of 100% α-phase was also observed in the 

case of Dy- and Lu-doped alumina.

Ln-doped alumina powders were subjected to microwave fields, which were found 

to affect rare-earth migration (phase formation) and enhance density at lower 

temperatures. Er-doped Al2O3 powders sintered in a single-mode microwave 

system with a 30%E:70%H mixed field produced samples with significantly higher 

density (~97% of theoretical density) compared to samples sintered conventionally 

at the same temperature of 1400 °C (~70% of theoretical density), representing a 

savings of 250 °C–300 °C for producing high-density samples. These samples also 

contained the lowest amount of second phase, which indicated that more Er formed 

a solid solution with Al2O3. The findings suggested that the magnetic component 

played a critical role in the processing of Al2O3 at microwave frequencies, and that 

the dopant material played an important role in material response to EM fields.

Ln-doped alumina powders exposed to magnetic fields were also evaluated in terms 

of phase development and crystallographic texturing. High-temperature DSC under 

applied magnetic fields indicated a significant change in phase formation of rareearth-doped alumina, as data collected under a 9 T field indicated crystallization of 
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60

α-Al2O3 at a temperature 300 °C lower than without the application of a magnetic 

field. This demonstrated that the application of a magnetic field could lead to 

crystallization of the ideal phase at reduced processing temperatures. Experiments 

showing overlapping transition temperatures between in-situ HT-XRD and hightemperature DSC data provided confirmation of the structural transitions.

Density functional theory was utilized, in conjunction with experimental efforts, to 

study the effects of rare-earth dopants on the structure, phase stability, magnetic 

properties, and magnetic field effects of α- and θ-Al2O3. Specific rare-earth dopants

(Er, Gd, Pr, Nd, Yb) were down-selected based on their potential to strongly 

influence material processing under magnetic fields. Initial study of the doped αand θ-phase Al2O3 found that dopant incorporation into the Al2O3 lattice resulted 

in an increase in the lattice parameters. The relative distortion was found to be 

proportional to the ionic radius of the selected dopant. As multiple material phases 

and dopant sites were investigated, the stability of the phases were determined 

through comparison of cohesive energies, which determined that the α-phase was 

the most stable overall. Initial work also investigated magnetic moment and 

localization in the crystal lattice. It was found that there was a strong localization 

of the magnetic moment on the rare-earth atom in all dopants except Yb, which 

showed delocalization of the magnetic moment throughout the supercell. As a 

natural progression, to investigate the effect of magnetic field on the doped 

alumina, the effect of spin-orbit coupling was introduced. Spin-orbit coupling 

decreased the total cohesive energy, but did not change the phase stability. Ease of 

magnetization was also probed through the computation of MAE. Dopant and 

material phase were found to have a strong effect on the MAE magnitude, with Er

and Pr dopants having the largest overall anisotropy energy. In addition, the 

magnetic susceptibility was evaluated to determine material responsivity with 

respect to exposure to magnetic field. It was found, similar to the MAE, that the 

susceptibility was strongly influenced by material phase and dopant, with the Er

dopant having the largest contribution. 

Ln-doped Al2O3 powders were added to epoxy during the application of a 1.8 Tesla 

magnetic field to study the effects of crystallographic orientation. XRD results 

showed that the (104) peak had the highest intensity for the “no field” condition, 

while the (110) peak had the highest intensity in a 1.8 T field, indicating crystallite 

alignment. When the (110)/(104) peak ratios were calculated and plotted for all of 

the Ln-doped Al2O3 powders to quantify texturing via the Lotgering factor, there 

was a consistent trend of improved particle orientation for all rare-earth additives, 

with the highest particle alignment evident for Er-doped Al2O3. These results were 

extremely encouraging, considering the relatively low 1.8-T magnetic field strength 

proved to be sufficient for affecting the crystallographic texturing of a rare-earth-
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61

doped diamagnetic material. Epoxy alignment experiments were expanded to 

include samples aligned under a 9 T magnetic field using undoped, Gd-doped, and 

Yb-doped Al2O3 powders, with an increase in alignment generally observed with 

increasing magnetic field strength. Results indicated that the Gd-doped and Ybdoped powders exhibited equivalent alignment, despite the latter having a weaker 

total magnetic moment. DFT modeling suggested that this may have been due to 

the global effect of the magnetic moment exhibited by Yb, despite its total magnetic 

moment being weaker than Gd. The data also supported the claim that undoped 

Al2O3 could be affected by a strong enough magnetic field. After identifying a more 

accurate method for quantifying texture, the average facial angle alignment method 

was used to recalculate texturing results. It was determined that the trends were the 

same, with erbium again showing the highest response, with approximately 26% 

alignment. The epoxy experiments demonstrated that dopant inclusion affected the 

responsiveness of alumina to a magnetic field, presumably by changing the 

magnetic anisotropy of the crystal. Both Gd and Yb were effective at increasing the 

grain alignment under lower magnetic field strengths as compared to undoped

alumina.

A gel casting system was also developed to enable casting under magnetic fields 

and sintering of aligned bodies to examine the effects of fields on texturing. 

Preliminary pressureless sintered gel cast samples were approximately 98% dense, 

indicating that gel casting could yield parts to achieve full densification under hot 

isostatic pressing. Formulas using both nanosized commercial Al2O3 powders were 

shown to set within 30 min while demonstrating moderate strength to allow easy 

transportation and sintering. For the Er-doped powders, a higher degree of 

alignment was achieved for the gel cast samples as compared to the epoxy cast 

samples. This was attributed to better powder dispersion in the gel-cast slurry than 

in the epoxy slurry, as well as a lower viscosity, since the gel cast slurries, once 

milled, were much more fluid than the epoxy suspensions. In a green-body state, 

the sample exhibited 37.9% alignment. After sintering, the percent alignment value 

remained at 33.8%, indicating that the high degree of alignment achieved in the 

green-body state could potentially be maintained in the sintered body.

The program produced a number of significant results for influencing the structure, 

phase formation, and crystallographic texturing of weakly magnetic alumina 

materials by doping with a small amount of Ln-series rare-earth materials and 

applying microwave and magnetic fields during processing. Transition of these 

results to future research is discussed in the following section.
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8. Transitions

The DSI program has been transitioned into a WMRD-MMSD 6.2 Mission 

program entitled, “Magnetic Field-Assisted Tailoring of Ceramic Materials for 

Unparalleled Properties”. The purpose of this new program is to enable new 

capabilities for gaining access to unique, nonequilibrium structures in ceramic 

materials through the use of magnetic fields, which will lead to new materials, 

functionalities, and property combinations. While rare-earth dopants were selected 

to enhance the responsiveness of alumina ceramics to applied fields during the DSI 

program, this decision was driven by compatibility with laser host applications. The 

selection of rare earths was not ideal, as the large ionic size mismatch with 

nanosized alumina led to significant doping challenges. The rare earths were also 

limited in their magnetic property values. Because the new 6.2 Mission program is 

not limited to laser host applications, transition metal dopants and ferromagnetic 

additives that have an ionic size that is more compatible with alumina (and therefore 

higher solubility in alumina) and higher magnetic properties should provide a much 

higher response to magnetic fields, which were shown to influence structure, phase 

formation, and texturing during the DSI. The 6.2 Mission program will seek to 

deliver the following:

• Novel synthesis methods for fabricating highly responsive ceramic powders 

containing transition metal dopants or ferromagnetic additives that can 

influence susceptibility, conductivity, and other key properties in the 

presence of magnetic fields.

• Advanced in-situ and ex-situ characterization methods for monitoring 

structure and property responses (conductivity, susceptibility, 

microstructural variations, etc.) during and after processing under magnetic 

fields. 

• Predictive models of materials properties (e.g., structure, mechanical 

response) from composition and processing conditions, in particular under 

magnetic fields, but also related to pressure, temperature, and so forth. 

Expected US Army impact related to the new applications will include the 

following:

• Improved Soldier and vehicle protection through higher ballistic efficiency 

ceramics with improved multihit capabilities.

• Improved lethality performance of munitions and/or gun barrels via 

magnetic field processing for improved reliability and wear resistance.
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63

• Lower manufacturing and design costs of high-performance ceramics 

through use of predictive, integrated modeling and simulation tools.

By taking lessons learned from the DSI program, the 6.2 Mission program should 

generate significant accomplishments in “Energy Coupled to Matter” research.
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10. Bibliography

Publications

1. Moorehead C, Blair V, Ku N, Brennan R. Magnetic alignment of erbium doped 

alpha alumina using a novel gel casting system. In preparation 2017.

2. Limmer K, Elward JM, Rinderspacher BC. Magnetic anisotropy in rare-earth 

doped alumina. In preparation 2017.

3. Patel K, Blair V, Douglas J, Dai Q, Liu Y, Ren S, Brennan R. Structural effects 

of lanthanide dopants on alumina. Nature: Scientific Reports. 2017;7. Article 

no. 39946.

4. Limmer KR, Neupane MR, Brennan RE, Chantawansri TL. Rare-earth dopant 

effects on the structural, energetic, and magnetic properties of alumina from 

first principles. J of the Amer Ceramic Soc. December 2016;99(12):4007–

4012.

5. Moorehead C, Kornecki M, Blair V, Brennan R. Sensitivity analysis and 

simulation of theoretical response of ceramics to strong magnetic field.

Adelphi (MD): Army Research Laboratory (US); 2016 Sep. Report No.: ARLTN-0774.

6. Moorehead C, Blair V, Brennan R, Adams J. Preferred orientation of rare-earth 

doped alumina crystallites by an applied magnetic field. ARL Technical 

Report, Adelphi (MD): Army Research Laboratory (US); 2016 Jun. Report 

No.: ARL-TR-7702.

7. Brennan R, Moorehead C, Blair V, Limmer K. Energy coupled to matter for 

magnetic alignment of rare earth-doped alumina. Materials and Manufacturing 

Processes. Published online 2016 Jun.

8. Moorehead C, Blair V, Adams J. Characterization of novel gel-casting system 

to make complex-shaped Al2O3 parts. ARL Technical Report, Adelphi (MD):

Army Research Laboratory (US); 2016 Mar. Report No.: ARL-TR-7620.

9. V Blair, J Marsico. Synthesis of Al2O3-coated Fe3O4 nanoparticles for 

thermomagnetic processing. Adelphi (MD): Army Research Laboratory (US);

2015 Dec. Report No.: ARL-TN-0720.

10. Pavlacka R, Brennan C, Blair V, Brennan R, Fountzoulas C, Cheng Agrawal 

JD. Single-mode microwave sintering of Er:Al2O3. Processing and Properties 

of Advanced Ceramics and Composites VII. John Wiley and Sons, Inc.; 2015

Oct;1–11.
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Presentations

1. Ku N, Blair V, Rahane A, Kumar V, Synowczynski-Dunn J, Moorehead C, 

Brennan R. Doping erbium into the lattice of aluminum oxide. 41st

International Conference on Advanced Ceramics and Composites; Optical 

Materials Session; 2017 Jan; Daytona Beach, FL.

2. Moorehead C, Sietins J, Blair V. MicroCT used to assess de-agglomeration 

and de-gassing methods for improvement of ISOBAM gel casting system for 

alumina poster. 41st International Conference on Advanced Ceramics and

Composites; Optical Materials Session; 2017 Jan; Daytona Beach, FL. 

3. Brennan R, McWilliams B, Blair V, Yu J, Ku N, Kornecki M. Energy coupled 

to matter for field-assisted sintering of materials. Invited talk; Materials 

Science and Technology Conference 2016; Sintering and Related Powder 

Processing Science and Technologies Session; 2016 Oct; Salt Lake City, UT.

4. Blair V, Moorehead C, Ku N, Limmer K, Brennan R. Magnetic alignment of 

rare earth doped alumina grains in an epoxy matrix – a proof of concept study.

Invited Talk; Materials Science and Technology Conference 2016; Processing 

and performance of materials using microwaves, electric and magnetic fields, 

ultrasound, lasers, and mechanical work – Rustum Roy Symposium; 2016 Oct;

Salt Lake City, UT.

5. Moorehead C, Blair V, Brennan R. Formation of micro-textured alumina 

bodies under applied magnetic field. Materials Science and Technology 

Conference 2016; Processing and performance of materials using microwaves, 

electric and magnetic fields, ultrasound, lasers, and mechanical work – Rustum 

Roy Symposium; 2016 Oct; Salt Lake City, UT.

6. Brennan R, Dowding R, Zabinski J. Energy coupled to matter research for

materials-by-design and advanced processing. Invited talk; 17th International 

Conference on Experimental Mechanics; 2016 Jul; Rhodes, Greece.

7. Brennan R, Dowding R, Zabinski J. Energy coupled to matter research for 

field-assisted processing. Invited talk; Engineering Conferences International 

Electric Field Assisted Sintering and Related Phenomena Far from 

Equilibrium; 2016 Mar; Tomar, Portugal.

8. Blair VL, Ku N, Lobur N, Brennan R, Rios O. High Temperature Phase 

Transformation of Alumina under Applied Magnetic Field and its Influences 

on Sintering. 40th International Conference on Advanced Ceramics and

Composites; Field Assisted Sintering and Related Phenomena at High 

Temperatures Session; 2016 Jan; Daytona Beach, FL.
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9. Moorehead C, Blair V, Brennan R. Formation of micro-textured alumina 

bodies under applied magnetic field using novel, water soluble polymer gelling 

system. 40th International Conference on Advanced Ceramics and

Composites; 5th Global Young Investigator Forum Session; 2016 Jan;

Daytona Beach, FL.

10. Blair VL, Pavlacka R, Lobur N, Brennan C, Brennan R. Synthesis and 

processing of nano-sized Er:Al2O3 transparent ceramics for laser applications.

Materials Science and Technology Conference; Innovative Processing and 

Synthesis of Ceramics, Glasses and Composites Session; 2015 Oct; Columbus, 

OH.

11. Brennan R, Brennan C, Pavlacka R, Fountzoulas C, Blair V. Multi and singlemode microwave sintering for field-enhanced texturing of alumina.

International Conference on Advanced Ceramics and Composites; 2015 Jan; 

Daytona Beach, FL.

12. Brennan R, Pavlacka R, Brennan C, Blair V, Fountzoulas C, Cheng J, Agrawal

D. Field-enhanced crystallographic texturing of transparent alumina. Materials 

Science and Technology 2014 Presentation; Rustum Roy Symposium on 

Processing and Performance of Materials using Microwaves, Electric and

Magnetic Fields, Ultrasound, Lasers, and Mechanical Work Session; 2014

October; Pittsburgh, PA.
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List of Symbols, Abbreviations, and Acronyms

2-D 2-dimensional

AACH ammonium aluminum hydroxycarbonate

ARL US Army Research Laboratory

BL baseline conventionally sintered

DFT density functional theory

DI deionized

DSC digital scanning calorimeter

Dy Dysprosium

EDS energy dispersive spectroscopy

EM electromagnetic

Er Erbium

Gd Gadolinium

HEL high-energy laser

HR-XRD high-resolution X-ray diffraction

HT-XRD high-temperature X-ray diffraction

La Lanthanum

LF Lotgering factor

Lu Lutetium

MAE magnetocrystalline anisotropy energy

MAS magic angle spinning

MM multimode microwave sintered

MQ-MAS multiple quantum magic angle spinning

Nd Neodymium

Nd:YAG neodymium-doped yttrium aluminum garnet

ORNL Oak Ridge National Laboratory

PAW projector augmented wave
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PBE Perdew-Burke-Ernzerhof

Pr Praseodymium

SEM scanning electron microscopy

SM single-mode microwave sintered

SOC spin-orbit coupled

ss-NMR solid-state nuclear magnetic resonance

TEM transmission electron microscopy

Tm Thulium

wt% weight-percent

XRD X-ray diffraction

Yb Ytterbium
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