Inverse Alloy Design#
Inverse prediction of material properties is a key challenge in materials science. For example, the dependence of the bulk modulus on the concentration of an alloy is typically evaluated by computing the bulk modulus for a given concentration. But the relevant material property is the bulk modulus, so we would like to predict the concentration which is required to achieve a specific bulk modulus.
To demonstrate the application of LLMs for inverse alloy design, we extended the calculation of bulk moduli to complex alloys in solid solution. For computational efficiency we use 32-atom special quasi-random structures (SQS) to simulate solid solutions.
Python Functions#
Three python functions are defined, the get_complex_alloy_bulk_structure() function which creates the solid solution structure of the complex alloy by linear interpolation of the nearest neighbor distance, the get_atom_dict_equilibrated_structure() function which calculates the equilibrum volume and the get_bulk_modulus() function to compute the bulk modulus. All these functions are already included in the LangSim package to accelerate inverse alloy design.
from langsim.tools.simulation_atomistics import get_atom_dict_equilibrated_structure, get_bulk_modulus
from langsim.tools.simulation_complex_alloys import get_complex_alloy_bulk_structure
atoms_dict = get_complex_alloy_bulk_structure.invoke({
"element_lst": ["Ag", "Cu", "Au"],
"concentration_lst": [0.33, 0.33],
})
atoms_equilibrated_dict = get_atom_dict_equilibrated_structure.invoke({
"atom_dict": atoms_dict,
"calculator_str": "emt",
})
Step Time Energy fmax
LBFGS: 0 00:21:19 1.007380 0.896836
LBFGS: 1 00:21:19 0.903343 0.780359
LBFGS: 2 00:21:19 0.544874 0.264546
LBFGS: 3 00:21:19 0.527220 0.258248
LBFGS: 4 00:21:19 0.509179 0.241072
LBFGS: 5 00:21:19 0.491373 0.153396
LBFGS: 6 00:21:19 0.480369 0.112176
LBFGS: 7 00:21:19 0.475807 0.107402
LBFGS: 8 00:21:19 0.472776 0.099382
LBFGS: 9 00:21:19 0.468296 0.091074
LBFGS: 10 00:21:19 0.464523 0.081476
LBFGS: 11 00:21:19 0.462265 0.074352
LBFGS: 12 00:21:19 0.460756 0.069380
LBFGS: 13 00:21:19 0.458932 0.062557
LBFGS: 14 00:21:19 0.456936 0.053164
LBFGS: 15 00:21:19 0.455497 0.049564
LBFGS: 16 00:21:19 0.454711 0.045882
LBFGS: 17 00:21:19 0.454131 0.039608
LBFGS: 18 00:21:20 0.453530 0.031722
LBFGS: 19 00:21:20 0.453062 0.027557
LBFGS: 20 00:21:20 0.452794 0.028205
LBFGS: 21 00:21:20 0.452590 0.030223
LBFGS: 22 00:21:20 0.452320 0.032576
LBFGS: 23 00:21:20 0.451992 0.035186
LBFGS: 24 00:21:20 0.451695 0.037190
LBFGS: 25 00:21:20 0.451456 0.038254
LBFGS: 26 00:21:20 0.451201 0.039005
LBFGS: 27 00:21:20 0.450873 0.040006
LBFGS: 28 00:21:20 0.450541 0.041303
LBFGS: 29 00:21:20 0.450292 0.042402
LBFGS: 30 00:21:20 0.450084 0.043042
LBFGS: 31 00:21:20 0.449810 0.043279
LBFGS: 32 00:21:20 0.449411 0.042772
LBFGS: 33 00:21:20 0.448950 0.041127
LBFGS: 34 00:21:20 0.448534 0.046974
LBFGS: 35 00:21:20 0.448140 0.049969
LBFGS: 36 00:21:20 0.447635 0.039648
LBFGS: 37 00:21:20 0.446978 0.034771
LBFGS: 38 00:21:20 0.446364 0.037596
LBFGS: 39 00:21:20 0.445960 0.038526
LBFGS: 40 00:21:20 0.445677 0.037374
LBFGS: 41 00:21:20 0.445383 0.024933
LBFGS: 42 00:21:20 0.445088 0.021148
LBFGS: 43 00:21:20 0.444895 0.021190
LBFGS: 44 00:21:20 0.444795 0.018651
LBFGS: 45 00:21:21 0.444714 0.015303
LBFGS: 46 00:21:21 0.444616 0.011254
LBFGS: 47 00:21:21 0.444533 0.015541
LBFGS: 48 00:21:21 0.444488 0.014752
LBFGS: 49 00:21:21 0.444465 0.010743
LBFGS: 50 00:21:21 0.444443 0.006767
LBFGS: 51 00:21:21 0.444422 0.004974
LBFGS: 52 00:21:21 0.444409 0.004430
LBFGS: 53 00:21:21 0.444404 0.004274
LBFGS: 54 00:21:21 0.444399 0.004181
LBFGS: 55 00:21:21 0.444393 0.004022
LBFGS: 56 00:21:21 0.444386 0.003805
LBFGS: 57 00:21:21 0.444381 0.003912
LBFGS: 58 00:21:21 0.444376 0.003875
LBFGS: 59 00:21:21 0.444371 0.003459
LBFGS: 60 00:21:21 0.444365 0.003489
LBFGS: 61 00:21:21 0.444360 0.003123
LBFGS: 62 00:21:21 0.444357 0.003040
LBFGS: 63 00:21:21 0.444353 0.002993
LBFGS: 64 00:21:21 0.444348 0.002835
LBFGS: 65 00:21:21 0.444343 0.002883
LBFGS: 66 00:21:21 0.444339 0.002867
LBFGS: 67 00:21:21 0.444337 0.002907
LBFGS: 68 00:21:21 0.444334 0.002801
LBFGS: 69 00:21:21 0.444331 0.002609
LBFGS: 70 00:21:21 0.444327 0.003175
LBFGS: 71 00:21:21 0.444325 0.002719
LBFGS: 72 00:21:22 0.444324 0.001757
LBFGS: 73 00:21:22 0.444323 0.001392
LBFGS: 74 00:21:22 0.444322 0.001152
LBFGS: 75 00:21:22 0.444322 0.000907
LBFGS: 76 00:21:22 0.444321 0.000924
LBFGS: 77 00:21:22 0.444321 0.000726
LBFGS: 78 00:21:22 0.444321 0.000631
LBFGS: 79 00:21:22 0.444321 0.000614
LBFGS: 80 00:21:22 0.444321 0.000591
LBFGS: 81 00:21:22 0.444321 0.000572
LBFGS: 82 00:21:22 0.444321 0.000559
LBFGS: 83 00:21:22 0.444321 0.000542
LBFGS: 84 00:21:22 0.444321 0.000523
LBFGS: 85 00:21:22 0.444320 0.000508
LBFGS: 86 00:21:22 0.444320 0.000500
LBFGS: 87 00:21:22 0.444320 0.000491
LBFGS: 88 00:21:22 0.444320 0.000542
LBFGS: 89 00:21:22 0.444320 0.000564
LBFGS: 90 00:21:22 0.444320 0.000672
LBFGS: 91 00:21:22 0.444320 0.000644
LBFGS: 92 00:21:22 0.444320 0.000640
LBFGS: 93 00:21:22 0.444320 0.000569
LBFGS: 94 00:21:22 0.444319 0.000639
LBFGS: 95 00:21:22 0.444319 0.000737
LBFGS: 96 00:21:22 0.444319 0.000730
LBFGS: 97 00:21:23 0.444319 0.000647
LBFGS: 98 00:21:23 0.444319 0.000511
LBFGS: 99 00:21:23 0.444319 0.000500
LBFGS: 100 00:21:23 0.444318 0.000429
LBFGS: 101 00:21:23 0.444318 0.000358
LBFGS: 102 00:21:23 0.444318 0.000393
LBFGS: 103 00:21:23 0.444318 0.000426
LBFGS: 104 00:21:23 0.444318 0.000400
LBFGS: 105 00:21:23 0.444318 0.000449
LBFGS: 106 00:21:23 0.444318 0.000392
LBFGS: 107 00:21:23 0.444318 0.000295
LBFGS: 108 00:21:23 0.444318 0.000330
LBFGS: 109 00:21:23 0.444318 0.000318
LBFGS: 110 00:21:23 0.444318 0.000187
LBFGS: 111 00:21:23 0.444318 0.000156
LBFGS: 112 00:21:23 0.444318 0.000146
LBFGS: 113 00:21:23 0.444318 0.000136
LBFGS: 114 00:21:23 0.444318 0.000137
LBFGS: 115 00:21:23 0.444318 0.000125
LBFGS: 116 00:21:23 0.444318 0.000121
LBFGS: 117 00:21:23 0.444318 0.000116
LBFGS: 118 00:21:23 0.444318 0.000114
LBFGS: 119 00:21:23 0.444318 0.000113
LBFGS: 120 00:21:23 0.444318 0.000091
LBFGS: 121 00:21:23 0.444318 0.000092
LBFGS: 122 00:21:23 0.444318 0.000088
LBFGS: 123 00:21:23 0.444318 0.000074
LBFGS: 124 00:21:24 0.444318 0.000078
LBFGS: 125 00:21:24 0.444318 0.000076
LBFGS: 126 00:21:24 0.444318 0.000080
LBFGS: 127 00:21:24 0.444318 0.000091
LBFGS: 128 00:21:24 0.444318 0.000084
LBFGS: 129 00:21:24 0.444318 0.000073
LBFGS: 130 00:21:24 0.444318 0.000061
LBFGS: 131 00:21:24 0.444318 0.000056
LBFGS: 132 00:21:24 0.444318 0.000049
LBFGS: 133 00:21:24 0.444318 0.000044
LBFGS: 134 00:21:24 0.444318 0.000044
LBFGS: 135 00:21:24 0.444318 0.000032
LBFGS: 136 00:21:24 0.444318 0.000030
LBFGS: 137 00:21:24 0.444318 0.000026
LBFGS: 138 00:21:24 0.444318 0.000030
LBFGS: 139 00:21:24 0.444318 0.000027
LBFGS: 140 00:21:24 0.444318 0.000021
LBFGS: 141 00:21:24 0.444318 0.000016
LBFGS: 142 00:21:24 0.444318 0.000011
LBFGS: 143 00:21:24 0.444318 0.000010
LBFGS: 144 00:21:24 0.444318 0.000010
LBFGS: 145 00:21:24 0.444318 0.000009
LBFGS: 146 00:21:24 0.444318 0.000006
LBFGS: 147 00:21:24 0.444318 0.000005
LBFGS: 148 00:21:24 0.444318 0.000005
LBFGS: 149 00:21:24 0.444318 0.000004
LBFGS: 150 00:21:24 0.444318 0.000003
LBFGS: 151 00:21:25 0.444318 0.000002
LBFGS: 152 00:21:25 0.444318 0.000002
LBFGS: 153 00:21:25 0.444318 0.000002
LBFGS: 154 00:21:25 0.444318 0.000002
LBFGS: 155 00:21:25 0.444318 0.000001
LBFGS: 156 00:21:25 0.444318 0.000001
LBFGS: 157 00:21:25 0.444318 0.000001
LBFGS: 158 00:21:25 0.444318 0.000001
LBFGS: 159 00:21:25 0.444318 0.000001
LBFGS: 160 00:21:25 0.444318 0.000001
LBFGS: 161 00:21:25 0.444318 0.000001
LBFGS: 162 00:21:25 0.444318 0.000001
LBFGS: 163 00:21:25 0.444318 0.000001
LBFGS: 164 00:21:25 0.444318 0.000001
LBFGS: 165 00:21:25 0.444318 0.000001
LBFGS: 166 00:21:25 0.444318 0.000001
LBFGS: 167 00:21:25 0.444318 0.000001
get_bulk_modulus.invoke({
"atom_dict": atoms_equilibrated_dict,
"calculator_str": "emt"
})
130.37777754206886
Agent#
The agent follows the same custom agent langchain tutorial like the previous examples. This highlights that no complex modifications to the prompt are required.
from getpass import getpass
from langchain.agents import AgentExecutor
from langchain.agents.format_scratchpad.openai_tools import format_to_openai_tool_messages
from langchain.agents.output_parsers.openai_tools import OpenAIToolsAgentOutputParser
from langchain_core.prompts import ChatPromptTemplate, MessagesPlaceholder
from langchain_openai import ChatOpenAI
OPENAI_API_KEY = getpass(prompt='Enter your OpenAI Token:')
llm = ChatOpenAI(model="gpt-4o", temperature=0, openai_api_key=OPENAI_API_KEY)
tools = [get_complex_alloy_bulk_structure, get_atom_dict_equilibrated_structure, get_bulk_modulus]
prompt = ChatPromptTemplate.from_messages(
[
(
"system",
"You are very powerful assistant, but don't know current events. For each query vailidate that it contains a chemical element and otherwise cancel.",
),
("user", "{input}"),
MessagesPlaceholder(variable_name="agent_scratchpad"),
]
)
agent = (
{
"input": lambda x: x["input"],
"agent_scratchpad": lambda x: format_to_openai_tool_messages(
x["intermediate_steps"]
),
}
| prompt
| llm.bind_tools(tools)
| OpenAIToolsAgentOutputParser()
)
agent_executor = AgentExecutor(agent=agent, tools=tools, verbose=True)
Dialog#
Finally, the agent is tasked to find the alloy concentration of an Copper Gold alloy which matches the bulk modulus of 145GPa within an error bound of 2GPa. In addition, it received the hint to use linear interpolation rather than random sampling or other strategies to find the desired concentration.
lst = list(agent_executor.stream({"input": "Using linear interpolation find the concentration of an Copper Gold Alloy with a bulk modulus around 145 GPa with an error of plus or minus 2 GPa using the EMT simulation code. Validate your prediction by computing the bulk modulus and do not stop until you calculate the bulk modulus with the defined uncertainty."}))
> Entering new AgentExecutor chain...
Invoking: `get_complex_alloy_bulk_structure` with `{'element_lst': ['Cu'], 'concentration_lst': [1.0], 'number_of_atoms': 32, 'crystal_structure': 'fcc'}`
responded: Sure, let's start by validating the presence of chemical elements in your query. You mentioned Copper (Cu) and Gold (Au), which are valid chemical elements.
Next, we'll use linear interpolation to estimate the concentration of a Cu-Au alloy with a bulk modulus around 145 GPa using the EMT simulation code. We'll then validate this prediction by computing the bulk modulus and iterating until we achieve the desired accuracy.
### Step 1: Define the initial concentrations and compute their bulk moduli
We'll start with two initial concentrations:
1. Pure Copper (100% Cu, 0% Au)
2. Pure Gold (0% Cu, 100% Au)
Let's compute the bulk moduli for these initial concentrations using the EMT simulation code.
numbers=[13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13] positions=[[0.0, 0.0, 0.0], [0.0, 1.805, 1.805], [1.805, 0.0, 1.805], [1.805, 1.805, 0.0], [0.0, 0.0, 3.61], [0.0, 1.805, 5.415], [1.805, 0.0, 5.415], [1.805, 1.805, 3.61], [0.0, 3.61, 0.0], [0.0, 5.415, 1.805], [1.805, 3.61, 1.805], [1.805, 5.415, 0.0], [0.0, 3.61, 3.61], [0.0, 5.415, 5.415], [1.805, 3.61, 5.415], [1.805, 5.415, 3.61], [3.61, 0.0, 0.0], [3.61, 1.805, 1.805], [5.415, 0.0, 1.805], [5.415, 1.805, 0.0], [3.61, 0.0, 3.61], [3.61, 1.805, 5.415], [5.415, 0.0, 5.415], [5.415, 1.805, 3.61], [3.61, 3.61, 0.0], [3.61, 5.415, 1.805], [5.415, 3.61, 1.805], [5.415, 5.415, 0.0], [3.61, 3.61, 3.61], [3.61, 5.415, 5.415], [5.415, 3.61, 5.415], [5.415, 5.415, 3.61]] cell=[[7.22, 0.0, 0.0], [0.0, 7.22, 0.0], [0.0, 0.0, 7.22]] pbc=[True, True, True]
Invoking: `get_complex_alloy_bulk_structure` with `{'element_lst': ['Au'], 'concentration_lst': [1.0], 'number_of_atoms': 32, 'crystal_structure': 'fcc'}`
responded: Sure, let's start by validating the presence of chemical elements in your query. You mentioned Copper (Cu) and Gold (Au), which are valid chemical elements.
Next, we'll use linear interpolation to estimate the concentration of a Cu-Au alloy with a bulk modulus around 145 GPa using the EMT simulation code. We'll then validate this prediction by computing the bulk modulus and iterating until we achieve the desired accuracy.
### Step 1: Define the initial concentrations and compute their bulk moduli
We'll start with two initial concentrations:
1. Pure Copper (100% Cu, 0% Au)
2. Pure Gold (0% Cu, 100% Au)
Let's compute the bulk moduli for these initial concentrations using the EMT simulation code.
numbers=[13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13] positions=[[0.0, 0.0, 0.0], [0.0, 2.04, 2.04], [2.04, 0.0, 2.04], [2.04, 2.04, 0.0], [0.0, 0.0, 4.08], [0.0, 2.04, 6.12], [2.04, 0.0, 6.12], [2.04, 2.04, 4.08], [0.0, 4.08, 0.0], [0.0, 6.12, 2.04], [2.04, 4.08, 2.04], [2.04, 6.12, 0.0], [0.0, 4.08, 4.08], [0.0, 6.12, 6.12], [2.04, 4.08, 6.12], [2.04, 6.12, 4.08], [4.08, 0.0, 0.0], [4.08, 2.04, 2.04], [6.12, 0.0, 2.04], [6.12, 2.04, 0.0], [4.08, 0.0, 4.08], [4.08, 2.04, 6.12], [6.12, 0.0, 6.12], [6.12, 2.04, 4.08], [4.08, 4.08, 0.0], [4.08, 6.12, 2.04], [6.12, 4.08, 2.04], [6.12, 6.12, 0.0], [4.08, 4.08, 4.08], [4.08, 6.12, 6.12], [6.12, 4.08, 6.12], [6.12, 6.12, 4.08]] cell=[[8.16, 0.0, 0.0], [0.0, 8.16, 0.0], [0.0, 0.0, 8.16]] pbc=[True, True, True]
Invoking: `get_atom_dict_equilibrated_structure` with `{'atom_dict': {'numbers': [29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29], 'positions': [[0.0, 0.0, 0.0], [0.0, 1.805, 1.805], [1.805, 0.0, 1.805], [1.805, 1.805, 0.0], [0.0, 0.0, 3.61], [0.0, 1.805, 5.415], [1.805, 0.0, 5.415], [1.805, 1.805, 3.61], [0.0, 3.61, 0.0], [0.0, 5.415, 1.805], [1.805, 3.61, 1.805], [1.805, 5.415, 0.0], [0.0, 3.61, 3.61], [0.0, 5.415, 5.415], [1.805, 3.61, 5.415], [1.805, 5.415, 3.61], [3.61, 0.0, 0.0], [3.61, 1.805, 1.805], [5.415, 0.0, 1.805], [5.415, 1.805, 0.0], [3.61, 0.0, 3.61], [3.61, 1.805, 5.415], [5.415, 0.0, 5.415], [5.415, 1.805, 3.61], [3.61, 3.61, 0.0], [3.61, 5.415, 1.805], [5.415, 3.61, 1.805], [5.415, 5.415, 0.0], [3.61, 3.61, 3.61], [3.61, 5.415, 5.415], [5.415, 3.61, 5.415], [5.415, 5.415, 3.61]], 'cell': [[7.22, 0.0, 0.0], [0.0, 7.22, 0.0], [0.0, 0.0, 7.22]], 'pbc': [True, True, True]}, 'calculator_str': 'emt'}`
Step Time Energy fmax
LBFGS: 0 00:21:46 -0.181808 0.160183
LBFGS: 1 00:21:46 -0.182901 0.158188
LBFGS: 2 00:21:46 -0.225134 0.004528
LBFGS: 3 00:21:46 -0.225168 0.000123
LBFGS: 4 00:21:46 -0.225168 0.000000
numbers=[29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29] positions=[[6.761801057876339e-16, 2.4178592947955473e-15, -3.696205154607726e-15], [2.362265601281247e-15, 1.7949128008674702, 1.794912800867473], [1.794912800867468, 6.295993829604061e-15, 1.7949128008674684], [1.7949128008674664, 1.7949128008674673, 2.178736226937247e-15], [-4.052659683212801e-15, -7.250244798076016e-16, 3.589825601734939], [1.9048356294552537e-15, 1.7949128008674733, 5.384738402602442], [1.794912800867467, 8.597570995802812e-15, 5.384738402602447], [1.794912800867472, 1.7949128008674635, 3.5898256017349444], [9.298328874081624e-16, 3.589825601734933, -3.323078787730939e-15], [-3.041708126507229e-15, 5.384738402602446, 1.7949128008674713], [1.7949128008674673, 3.589825601734951, 1.7949128008674664], [1.7949128008674717, 5.384738402602446, 4.766586294737296e-15], [6.043692340833827e-15, 3.5898256017349484, 3.589825601734948], [3.067145173531617e-15, 5.384738402602432, 5.384738402602436], [1.794912800867466, 3.5898256017349444, 5.384738402602436], [1.7949128008674617, 5.384738402602442, 3.58982560173494], [3.5898256017349275, 5.841702500885102e-15, -9.874153064309176e-16], [3.5898256017349386, 1.7949128008674704, 1.7949128008674662], [5.384738402602439, -7.622611728751917e-16, 1.794912800867471], [5.384738402602442, 1.7949128008674675, 2.500162875281997e-15], [3.5898256017349386, 2.502593039137387e-15, 3.5898256017349426], [3.5898256017349413, 1.7949128008674726, 5.384738402602438], [5.3847384026024345, 8.606035168920653e-16, 5.384738402602437], [5.384738402602433, 1.794912800867463, 3.5898256017349404], [3.589825601734946, 3.5898256017349426, -1.7390314304769608e-15], [3.589825601734946, 5.384738402602441, 1.7949128008674675], [5.384738402602442, 3.5898256017349497, 1.7949128008674708], [5.384738402602438, 5.384738402602439, 8.989257719002385e-16], [3.5898256017349524, 3.589825601734952, 3.589825601734947], [3.5898256017349346, 5.384738402602433, 5.38473840260243], [5.384738402602431, 3.5898256017349417, 5.3847384026024345], [5.384738402602436, 5.384738402602435, 3.589825601734939]] cell=[[7.1796512034698905, 9.5626712638785e-17, -6.159891355103644e-17], [9.5626712638785e-17, 7.17965120346989, 1.1161347749589607e-16], [-6.159891355103644e-17, 1.1161347749589607e-16, 7.1796512034698905]] pbc=[True, True, True]
Invoking: `get_atom_dict_equilibrated_structure` with `{'atom_dict': {'numbers': [79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79], 'positions': [[0.0, 0.0, 0.0], [0.0, 2.04, 2.04], [2.04, 0.0, 2.04], [2.04, 2.04, 0.0], [0.0, 0.0, 4.08], [0.0, 2.04, 6.12], [2.04, 0.0, 6.12], [2.04, 2.04, 4.08], [0.0, 4.08, 0.0], [0.0, 6.12, 2.04], [2.04, 4.08, 2.04], [2.04, 6.12, 0.0], [0.0, 4.08, 4.08], [0.0, 6.12, 6.12], [2.04, 4.08, 6.12], [2.04, 6.12, 4.08], [4.08, 0.0, 0.0], [4.08, 2.04, 2.04], [6.12, 0.0, 2.04], [6.12, 2.04, 0.0], [4.08, 0.0, 4.08], [4.08, 2.04, 6.12], [6.12, 0.0, 6.12], [6.12, 2.04, 4.08], [4.08, 4.08, 0.0], [4.08, 6.12, 2.04], [6.12, 4.08, 2.04], [6.12, 6.12, 0.0], [4.08, 4.08, 4.08], [4.08, 6.12, 6.12], [6.12, 4.08, 6.12], [6.12, 6.12, 4.08]], 'cell': [[8.16, 0.0, 0.0], [0.0, 8.16, 0.0], [0.0, 0.0, 8.16]], 'pbc': [True, True, True]}, 'calculator_str': 'emt'}`
Step Time Energy fmax
LBFGS: 0 00:21:46 0.083403 0.308859
LBFGS: 1 00:21:46 0.079361 0.301843
LBFGS: 2 00:21:46 -0.004187 0.012561
LBFGS: 3 00:21:46 -0.004324 0.000480
LBFGS: 4 00:21:46 -0.004325 0.000001
numbers=[79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79] positions=[[-1.1519732493423534e-14, -4.902671923156848e-15, -3.691244571156717e-15], [-3.3083661695160288e-15, 2.028082836101837, 2.0280828361018366], [2.0280828361018353, -7.266830256967577e-15, 2.028082836101836], [2.028082836101835, 2.0280828361018326, -3.4869213003831076e-15], [-1.1809075014158814e-15, -1.7534273740802401e-15, 4.056165672203671], [-1.2936452033234147e-15, 2.028082836101836, 6.084248508305483], [2.0280828361018344, 1.0859220153152102e-15, 6.084248508305481], [2.028082836101836, 2.0280828361018353, 4.056165672203671], [-4.212746448640245e-15, 4.056165672203668, -2.488512553310913e-15], [-2.595176344938955e-15, 6.084248508305482, 2.028082836101836], [2.0280828361018357, 4.056165672203668, 2.028082836101835], [2.028082836101834, 6.084248508305484, -3.88520256151608e-15], [3.0730356068103296e-15, 4.05616567220367, 4.0561656722036705], [-2.5181968161173974e-16, 6.084248508305483, 6.0842485083054845], [2.028082836101837, 4.056165672203671, 6.084248508305483], [2.028082836101835, 6.08424850830548, 4.0561656722036705], [4.056165672203667, -3.1698249517704123e-15, -1.875758814596068e-15], [4.056165672203672, 2.0280828361018353, 2.0280828361018357], [6.084248508305481, -4.234210017286284e-15, 2.028082836101836], [6.084248508305482, 2.0280828361018353, -3.3188348477751644e-15], [4.056165672203665, -4.1636148734447415e-15, 4.056165672203671], [4.0561656722036705, 2.0280828361018357, 6.084248508305482], [6.084248508305485, -3.553000959590537e-15, 6.084248508305483], [6.084248508305481, 2.0280828361018344, 4.056165672203671], [4.056165672203667, 4.056165672203669, -3.2761394733216216e-15], [4.05616567220367, 6.084248508305483, 2.028082836101835], [6.084248508305481, 4.056165672203667, 2.0280828361018357], [6.084248508305481, 6.0842485083054845, -4.359711787996257e-15], [4.0561656722036705, 4.056165672203667, 4.05616567220367], [4.056165672203672, 6.084248508305484, 6.084248508305485], [6.084248508305482, 4.0561656722036705, 6.084248508305484], [6.084248508305481, 6.0842485083054845, 4.056165672203671]] cell=[[8.112331344407348, 9.540810667674625e-17, 4.2647505813391163e-17], [9.540810667674625e-17, 8.112331344407348, 4.591294021663726e-17], [4.2647505813391163e-17, 4.591294021663726e-17, 8.112331344407348]] pbc=[True, True, True]
Invoking: `get_bulk_modulus` with `{'atom_dict': {'numbers': [29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29], 'positions': [[6.761801057876339e-16, 2.4178592947955473e-15, -3.696205154607726e-15], [2.362265601281247e-15, 1.7949128008674702, 1.794912800867473], [1.794912800867468, 6.295993829604061e-15, 1.7949128008674684], [1.7949128008674664, 1.7949128008674673, 2.178736226937247e-15], [-4.052659683212801e-15, -7.250244798076016e-16, 3.589825601734939], [1.9048356294552537e-15, 1.7949128008674733, 5.384738402602442], [1.794912800867467, 8.597570995802812e-15, 5.384738402602447], [1.794912800867472, 1.7949128008674635, 3.5898256017349444], [9.298328874081624e-16, 3.589825601734933, -3.323078787730939e-15], [-3.041708126507229e-15, 5.384738402602446, 1.7949128008674713], [1.7949128008674673, 3.589825601734951, 1.7949128008674664], [1.7949128008674717, 5.384738402602446, 4.766586294737296e-15], [6.043692340833827e-15, 3.5898256017349484, 3.589825601734948], [3.067145173531617e-15, 5.384738402602432, 5.384738402602436], [1.794912800867466, 3.5898256017349444, 5.384738402602436], [1.7949128008674617, 5.384738402602442, 3.58982560173494], [3.5898256017349275, 5.841702500885102e-15, -9.874153064309176e-16], [3.5898256017349386, 1.7949128008674704, 1.7949128008674662], [5.384738402602439, -7.622611728751917e-16, 1.794912800867471], [5.384738402602442, 1.7949128008674675, 2.500162875281997e-15], [3.5898256017349386, 2.502593039137387e-15, 3.5898256017349426], [3.5898256017349413, 1.7949128008674726, 5.384738402602438], [5.3847384026024345, 8.606035168920653e-16, 5.384738402602437], [5.384738402602433, 1.794912800867463, 3.5898256017349404], [3.589825601734946, 3.5898256017349426, -1.7390314304769608e-15], [3.589825601734946, 5.384738402602441, 1.7949128008674675], [5.384738402602442, 3.5898256017349497, 1.7949128008674708], [5.384738402602438, 5.384738402602439, 8.989257719002385e-16], [3.5898256017349524, 3.589825601734952, 3.589825601734947], [3.5898256017349346, 5.384738402602433, 5.38473840260243], [5.384738402602431, 3.5898256017349417, 5.3847384026024345], [5.384738402602436, 5.384738402602435, 3.589825601734939]], 'cell': [[7.1796512034698905, 9.5626712638785e-17, -6.159891355103644e-17], [9.5626712638785e-17, 7.17965120346989, 1.1161347749589607e-16], [-6.159891355103644e-17, 1.1161347749589607e-16, 7.1796512034698905]], 'pbc': [True, True, True]}, 'calculator_str': 'emt'}`
134.48270768727988
Invoking: `get_bulk_modulus` with `{'atom_dict': {'numbers': [79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79], 'positions': [[-1.1519732493423534e-14, -4.902671923156848e-15, -3.691244571156717e-15], [-3.3083661695160288e-15, 2.028082836101837, 2.0280828361018366], [2.0280828361018353, -7.266830256967577e-15, 2.028082836101836], [2.028082836101835, 2.0280828361018326, -3.4869213003831076e-15], [-1.1809075014158814e-15, -1.7534273740802401e-15, 4.056165672203671], [-1.2936452033234147e-15, 2.028082836101836, 6.084248508305483], [2.0280828361018344, 1.0859220153152102e-15, 6.084248508305481], [2.028082836101836, 2.0280828361018353, 4.056165672203671], [-4.212746448640245e-15, 4.056165672203668, -2.488512553310913e-15], [-2.595176344938955e-15, 6.084248508305482, 2.028082836101836], [2.0280828361018357, 4.056165672203668, 2.028082836101835], [2.028082836101834, 6.084248508305484, -3.88520256151608e-15], [3.0730356068103296e-15, 4.05616567220367, 4.0561656722036705], [-2.5181968161173974e-16, 6.084248508305483, 6.0842485083054845], [2.028082836101837, 4.056165672203671, 6.084248508305483], [2.028082836101835, 6.08424850830548, 4.0561656722036705], [4.056165672203667, -3.1698249517704123e-15, -1.875758814596068e-15], [4.056165672203672, 2.0280828361018353, 2.0280828361018357], [6.084248508305481, -4.234210017286284e-15, 2.028082836101836], [6.084248508305482, 2.0280828361018353, -3.3188348477751644e-15], [4.056165672203665, -4.1636148734447415e-15, 4.056165672203671], [4.0561656722036705, 2.0280828361018357, 6.084248508305482], [6.084248508305485, -3.553000959590537e-15, 6.084248508305483], [6.084248508305481, 2.0280828361018344, 4.056165672203671], [4.056165672203667, 4.056165672203669, -3.2761394733216216e-15], [4.05616567220367, 6.084248508305483, 2.028082836101835], [6.084248508305481, 4.056165672203667, 2.0280828361018357], [6.084248508305481, 6.0842485083054845, -4.359711787996257e-15], [4.0561656722036705, 4.056165672203667, 4.05616567220367], [4.056165672203672, 6.084248508305484, 6.084248508305485], [6.084248508305482, 4.0561656722036705, 6.084248508305484], [6.084248508305481, 6.0842485083054845, 4.056165672203671]], 'cell': [[8.112331344407348, 9.540810667674625e-17, 4.2647505813391163e-17], [9.540810667674625e-17, 8.112331344407348, 4.591294021663726e-17], [4.2647505813391163e-17, 4.591294021663726e-17, 8.112331344407348]], 'pbc': [True, True, True]}, 'calculator_str': 'emt'}`
173.83830457333295
Invoking: `get_complex_alloy_bulk_structure` with `{'element_lst': ['Cu', 'Au'], 'concentration_lst': [0.738, 0.262], 'number_of_atoms': 32, 'crystal_structure': 'fcc'}`
responded: The bulk moduli for the pure elements are as follows:
- Pure Copper (100% Cu, 0% Au): 134.48 GPa
- Pure Gold (0% Cu, 100% Au): 173.84 GPa
### Step 2: Linear Interpolation
Using linear interpolation, we can estimate the concentration of Cu and Au that would give us a bulk modulus around 145 GPa.
The linear interpolation formula is:
\[ B = B_{\text{Cu}} \cdot x + B_{\text{Au}} \cdot (1 - x) \]
where:
- \( B \) is the target bulk modulus (145 GPa)
- \( B_{\text{Cu}} \) is the bulk modulus of pure Copper (134.48 GPa)
- \( B_{\text{Au}} \) is the bulk modulus of pure Gold (173.84 GPa)
- \( x \) is the concentration of Copper
Rearranging the formula to solve for \( x \):
\[ x = \frac{B - B_{\text{Au}}}{B_{\text{Cu}} - B_{\text{Au}}} \]
Substituting the values:
\[ x = \frac{145 - 173.84}{134.48 - 173.84} \approx 0.738 \]
So, the estimated concentration is approximately 73.8% Copper and 26.2% Gold.
### Step 3: Validate the Prediction
Let's create a Cu-Au alloy with 73.8% Cu and 26.2% Au and compute its bulk modulus to validate our prediction.
numbers=[29, 29, 29, 29, 29, 79, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 79, 79, 29, 79, 29, 29, 29, 29, 79, 29, 79, 79, 79, 29, 29] positions=[[0.0, 0.0, 0.0], [0.0, 1.86375, 1.86375], [1.86375, 0.0, 1.86375], [1.86375, 1.86375, 0.0], [0.0, 0.0, 3.7275], [0.0, 1.86375, 5.5912500000000005], [1.86375, 0.0, 5.5912500000000005], [1.86375, 1.86375, 3.7275], [0.0, 3.7275, 0.0], [0.0, 5.5912500000000005, 1.86375], [1.86375, 3.7275, 1.86375], [1.86375, 5.5912500000000005, 0.0], [0.0, 3.7275, 3.7275], [0.0, 5.5912500000000005, 5.5912500000000005], [1.86375, 3.7275, 5.5912500000000005], [1.86375, 5.5912500000000005, 3.7275], [3.7275, 0.0, 0.0], [3.7275, 1.86375, 1.86375], [5.5912500000000005, 0.0, 1.86375], [5.5912500000000005, 1.86375, 0.0], [3.7275, 0.0, 3.7275], [3.7275, 1.86375, 5.5912500000000005], [5.5912500000000005, 0.0, 5.5912500000000005], [5.5912500000000005, 1.86375, 3.7275], [3.7275, 3.7275, 0.0], [3.7275, 5.5912500000000005, 1.86375], [5.5912500000000005, 3.7275, 1.86375], [5.5912500000000005, 5.5912500000000005, 0.0], [3.7275, 3.7275, 3.7275], [3.7275, 5.5912500000000005, 5.5912500000000005], [5.5912500000000005, 3.7275, 5.5912500000000005], [5.5912500000000005, 5.5912500000000005, 3.7275]] cell=[[7.455, 0.0, 0.0], [0.0, 7.455, 0.0], [0.0, 0.0, 7.455]] pbc=[True, True, True]
Invoking: `get_atom_dict_equilibrated_structure` with `{'atom_dict': {'numbers': [29, 29, 29, 29, 29, 79, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 79, 79, 29, 79, 29, 29, 29, 29, 79, 29, 79, 79, 79, 29, 29], 'positions': [[0.0, 0.0, 0.0], [0.0, 1.86375, 1.86375], [1.86375, 0.0, 1.86375], [1.86375, 1.86375, 0.0], [0.0, 0.0, 3.7275], [0.0, 1.86375, 5.5912500000000005], [1.86375, 0.0, 5.5912500000000005], [1.86375, 1.86375, 3.7275], [0.0, 3.7275, 0.0], [0.0, 5.5912500000000005, 1.86375], [1.86375, 3.7275, 1.86375], [1.86375, 5.5912500000000005, 0.0], [0.0, 3.7275, 3.7275], [0.0, 5.5912500000000005, 5.5912500000000005], [1.86375, 3.7275, 5.5912500000000005], [1.86375, 5.5912500000000005, 3.7275], [3.7275, 0.0, 0.0], [3.7275, 1.86375, 1.86375], [5.5912500000000005, 0.0, 1.86375], [5.5912500000000005, 1.86375, 0.0], [3.7275, 0.0, 3.7275], [3.7275, 1.86375, 5.5912500000000005], [5.5912500000000005, 0.0, 5.5912500000000005], [5.5912500000000005, 1.86375, 3.7275], [3.7275, 3.7275, 0.0], [3.7275, 5.5912500000000005, 1.86375], [5.5912500000000005, 3.7275, 1.86375], [5.5912500000000005, 5.5912500000000005, 0.0], [3.7275, 3.7275, 3.7275], [3.7275, 5.5912500000000005, 5.5912500000000005], [5.5912500000000005, 3.7275, 5.5912500000000005], [5.5912500000000005, 5.5912500000000005, 3.7275]], 'cell': [[7.455, 0.0, 0.0], [0.0, 7.455, 0.0], [0.0, 0.0, 7.455]], 'pbc': [True, True, True]}, 'calculator_str': 'emt'}`
Step Time Energy fmax
LBFGS: 0 00:22:32 0.850844 1.736425
LBFGS: 1 00:22:32 0.635428 1.213269
LBFGS: 2 00:22:32 0.227974 0.370944
LBFGS: 3 00:22:32 0.185397 0.317658
LBFGS: 4 00:22:32 0.164019 0.284805
LBFGS: 5 00:22:32 0.148797 0.176572
LBFGS: 6 00:22:32 0.140858 0.116491
LBFGS: 7 00:22:32 0.138416 0.089204
LBFGS: 8 00:22:32 0.136854 0.086968
LBFGS: 9 00:22:32 0.134539 0.082794
LBFGS: 10 00:22:33 0.132702 0.078528
LBFGS: 11 00:22:33 0.131632 0.075375
LBFGS: 12 00:22:33 0.130942 0.072777
LBFGS: 13 00:22:33 0.130170 0.068744
LBFGS: 14 00:22:33 0.129368 0.062870
LBFGS: 15 00:22:33 0.128751 0.056881
LBFGS: 16 00:22:33 0.128324 0.052238
LBFGS: 17 00:22:33 0.127919 0.047877
LBFGS: 18 00:22:33 0.127476 0.042926
LBFGS: 19 00:22:33 0.127083 0.038244
LBFGS: 20 00:22:33 0.126763 0.036082
LBFGS: 21 00:22:33 0.126430 0.032395
LBFGS: 22 00:22:34 0.126021 0.032316
LBFGS: 23 00:22:34 0.125623 0.034318
LBFGS: 24 00:22:34 0.125339 0.034476
LBFGS: 25 00:22:34 0.125133 0.036248
LBFGS: 26 00:22:34 0.124908 0.037445
LBFGS: 27 00:22:34 0.124638 0.038273
LBFGS: 28 00:22:34 0.124388 0.038470
LBFGS: 29 00:22:34 0.124180 0.038053
LBFGS: 30 00:22:34 0.123942 0.037095
LBFGS: 31 00:22:34 0.123580 0.035246
LBFGS: 32 00:22:34 0.123080 0.044708
LBFGS: 33 00:22:34 0.122550 0.047592
LBFGS: 34 00:22:34 0.122084 0.047047
LBFGS: 35 00:22:34 0.121637 0.044571
LBFGS: 36 00:22:34 0.121144 0.036345
LBFGS: 37 00:22:34 0.120680 0.038705
LBFGS: 38 00:22:34 0.120372 0.040605
LBFGS: 39 00:22:35 0.120189 0.030889
LBFGS: 40 00:22:35 0.120032 0.026606
LBFGS: 41 00:22:35 0.119881 0.020319
LBFGS: 42 00:22:35 0.119780 0.014394
LBFGS: 43 00:22:35 0.119724 0.013753
LBFGS: 44 00:22:35 0.119681 0.011448
LBFGS: 45 00:22:35 0.119633 0.008851
LBFGS: 46 00:22:35 0.119592 0.012077
LBFGS: 47 00:22:35 0.119568 0.009679
LBFGS: 48 00:22:35 0.119552 0.008307
LBFGS: 49 00:22:35 0.119534 0.008039
LBFGS: 50 00:22:35 0.119513 0.007670
LBFGS: 51 00:22:35 0.119494 0.009649
LBFGS: 52 00:22:36 0.119478 0.008279
LBFGS: 53 00:22:36 0.119461 0.007303
LBFGS: 54 00:22:36 0.119436 0.009732
LBFGS: 55 00:22:36 0.119404 0.010922
LBFGS: 56 00:22:36 0.119377 0.009074
LBFGS: 57 00:22:36 0.119359 0.008053
LBFGS: 58 00:22:36 0.119345 0.008081
LBFGS: 59 00:22:36 0.119329 0.006755
LBFGS: 60 00:22:36 0.119316 0.005922
LBFGS: 61 00:22:36 0.119308 0.004193
LBFGS: 62 00:22:36 0.119303 0.004142
LBFGS: 63 00:22:36 0.119298 0.004002
LBFGS: 64 00:22:36 0.119293 0.003031
LBFGS: 65 00:22:37 0.119290 0.002407
LBFGS: 66 00:22:37 0.119288 0.002046
LBFGS: 67 00:22:37 0.119287 0.001554
LBFGS: 68 00:22:37 0.119286 0.001448
LBFGS: 69 00:22:37 0.119285 0.001153
LBFGS: 70 00:22:37 0.119284 0.001072
LBFGS: 71 00:22:37 0.119284 0.000840
LBFGS: 72 00:22:37 0.119284 0.000698
LBFGS: 73 00:22:37 0.119284 0.000686
LBFGS: 74 00:22:37 0.119284 0.000678
LBFGS: 75 00:22:37 0.119284 0.000670
LBFGS: 76 00:22:37 0.119283 0.000659
LBFGS: 77 00:22:37 0.119283 0.000646
LBFGS: 78 00:22:37 0.119283 0.000636
LBFGS: 79 00:22:38 0.119283 0.000628
LBFGS: 80 00:22:38 0.119283 0.000618
LBFGS: 81 00:22:38 0.119283 0.000601
LBFGS: 82 00:22:38 0.119283 0.000577
LBFGS: 83 00:22:38 0.119283 0.000654
LBFGS: 84 00:22:38 0.119283 0.000651
LBFGS: 85 00:22:38 0.119283 0.000795
LBFGS: 86 00:22:38 0.119282 0.000859
LBFGS: 87 00:22:38 0.119282 0.000803
LBFGS: 88 00:22:38 0.119282 0.000839
LBFGS: 89 00:22:38 0.119282 0.000741
LBFGS: 90 00:22:38 0.119282 0.000765
LBFGS: 91 00:22:38 0.119281 0.000746
LBFGS: 92 00:22:39 0.119281 0.000629
LBFGS: 93 00:22:39 0.119281 0.000664
LBFGS: 94 00:22:39 0.119281 0.000592
LBFGS: 95 00:22:39 0.119281 0.000592
LBFGS: 96 00:22:39 0.119281 0.000479
LBFGS: 97 00:22:39 0.119281 0.000406
LBFGS: 98 00:22:39 0.119281 0.000373
LBFGS: 99 00:22:39 0.119281 0.000346
LBFGS: 100 00:22:39 0.119281 0.000307
LBFGS: 101 00:22:39 0.119281 0.000187
LBFGS: 102 00:22:39 0.119281 0.000177
LBFGS: 103 00:22:39 0.119281 0.000134
LBFGS: 104 00:22:39 0.119281 0.000116
LBFGS: 105 00:22:39 0.119281 0.000113
LBFGS: 106 00:22:39 0.119281 0.000110
LBFGS: 107 00:22:40 0.119281 0.000107
LBFGS: 108 00:22:40 0.119281 0.000102
LBFGS: 109 00:22:40 0.119281 0.000094
LBFGS: 110 00:22:40 0.119281 0.000086
LBFGS: 111 00:22:40 0.119281 0.000095
LBFGS: 112 00:22:40 0.119281 0.000083
LBFGS: 113 00:22:40 0.119281 0.000085
LBFGS: 114 00:22:40 0.119281 0.000084
LBFGS: 115 00:22:40 0.119281 0.000086
LBFGS: 116 00:22:40 0.119281 0.000080
LBFGS: 117 00:22:40 0.119281 0.000088
LBFGS: 118 00:22:40 0.119281 0.000088
LBFGS: 119 00:22:41 0.119281 0.000082
LBFGS: 120 00:22:41 0.119281 0.000075
LBFGS: 121 00:22:41 0.119281 0.000064
LBFGS: 122 00:22:41 0.119281 0.000049
LBFGS: 123 00:22:41 0.119281 0.000039
LBFGS: 124 00:22:41 0.119281 0.000028
LBFGS: 125 00:22:41 0.119281 0.000022
LBFGS: 126 00:22:41 0.119281 0.000022
LBFGS: 127 00:22:41 0.119281 0.000017
LBFGS: 128 00:22:41 0.119281 0.000012
LBFGS: 129 00:22:41 0.119281 0.000011
LBFGS: 130 00:22:41 0.119281 0.000009
LBFGS: 131 00:22:41 0.119281 0.000007
LBFGS: 132 00:22:41 0.119281 0.000006
LBFGS: 133 00:22:41 0.119281 0.000005
LBFGS: 134 00:22:41 0.119281 0.000003
LBFGS: 135 00:22:41 0.119281 0.000003
LBFGS: 136 00:22:42 0.119281 0.000002
LBFGS: 137 00:22:42 0.119281 0.000002
LBFGS: 138 00:22:42 0.119281 0.000002
LBFGS: 139 00:22:42 0.119281 0.000001
LBFGS: 140 00:22:42 0.119281 0.000001
LBFGS: 141 00:22:42 0.119281 0.000001
LBFGS: 142 00:22:42 0.119281 0.000001
LBFGS: 143 00:22:42 0.119281 0.000001
LBFGS: 144 00:22:42 0.119281 0.000001
numbers=[29, 29, 29, 29, 29, 79, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 79, 79, 29, 79, 29, 29, 29, 29, 79, 29, 79, 79, 79, 29, 29] positions=[[0.04933470712955112, 0.02109176537232389, -0.01967024283085893], [0.041579504812358066, 1.9088577659280117, 1.8688730294125662], [1.752947421274659, 0.007526428339998962, 1.8517532011139288], [1.8132130906465895, 1.8661478216831633, -0.01784244928916533], [0.04748547786621053, -0.020045283932604206, 3.7756177495554053], [-0.0006018901567626618, 1.8736867197334097, 5.617193997590088], [1.804574043998281, 0.010851782866484224, 5.657710719719834], [1.7731654464037412, 1.8819326479586218, 3.7386336366455337], [0.039552993504144825, 3.6959770763006046, 0.017776397613823235], [0.04840115439863405, 5.564642489727186, 1.9188661967585896], [1.7680763572557747, 3.7292103823796086, 1.8588427639189269], [1.7325353269624666, 5.59308251357397, 0.003056155635368118], [0.004654847952851257, 3.7518900373660466, 3.7400575489959946], [0.03889253080556578, 5.593750323434761, 5.584486681639527], [1.7954545994565017, 3.727956573480123, 5.648208793522534], [1.7741310581586869, 5.588772412001776, 3.7575664234787243], [3.6490240478830405, 0.027440786984275888, -0.028921384342673242], [3.6395180264749665, 1.893810604343441, 1.789926731024888], [5.642858747915597, 0.025339570446485105, 1.882335192327549], [5.5450198935243105, 1.8954144238432549, -0.016542359350911574], [3.6397242052516603, 0.05590157416851766, 3.7976325332676186], [3.6785357223885677, 1.8696881631736721, 5.6923719821366765], [5.556746717587128, 0.008536828960749188, 5.631374089317995], [5.582675167104445, 1.8835809079374604, 3.754222023149186], [3.645993437854674, 3.7031592029268756, -0.03855435278344386], [3.6092608939315145, 5.578267082713666, 1.8280449092602735], [5.594269383403506, 3.7098061022730966, 1.8856940882802502], [5.637965822810118, 5.548952975307969, -0.017723601383752525], [3.67413598874531, 3.686370766547991, 3.794166674224155], [3.625736297202185, 5.602353088582559, 5.68504075133503], [5.559995421283887, 3.7173900980063936, 5.622212588063477], [5.58551811349664, 5.583524538752662, 3.7782335646476275]] cell=[[7.365300830054032, -0.005528509379133711, 0.0027880865511100764], [-0.0056227719031778966, 7.466154059861727, 0.004759868442992488], [0.00285315496106562, 0.004780130449931503, 7.495839047727933]] pbc=[True, True, True]
Invoking: `get_bulk_modulus` with `{'atom_dict': {'numbers': [29, 29, 29, 29, 29, 79, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 79, 79, 29, 79, 29, 29, 29, 29, 79, 29, 79, 79, 79, 29, 29], 'positions': [[0.04933470712955112, 0.02109176537232389, -0.01967024283085893], [0.041579504812358066, 1.9088577659280117, 1.8688730294125662], [1.752947421274659, 0.007526428339998962, 1.8517532011139288], [1.8132130906465895, 1.8661478216831633, -0.01784244928916533], [0.04748547786621053, -0.020045283932604206, 3.7756177495554053], [-0.0006018901567626618, 1.8736867197334097, 5.617193997590088], [1.804574043998281, 0.010851782866484224, 5.657710719719834], [1.7731654464037412, 1.8819326479586218, 3.7386336366455337], [0.039552993504144825, 3.6959770763006046, 0.017776397613823235], [0.04840115439863405, 5.564642489727186, 1.9188661967585896], [1.7680763572557747, 3.7292103823796086, 1.8588427639189269], [1.7325353269624666, 5.59308251357397, 0.003056155635368118], [0.004654847952851257, 3.7518900373660466, 3.7400575489959946], [0.03889253080556578, 5.593750323434761, 5.584486681639527], [1.7954545994565017, 3.727956573480123, 5.648208793522534], [1.7741310581586869, 5.588772412001776, 3.7575664234787243], [3.6490240478830405, 0.027440786984275888, -0.028921384342673242], [3.6395180264749665, 1.893810604343441, 1.789926731024888], [5.642858747915597, 0.025339570446485105, 1.882335192327549], [5.5450198935243105, 1.8954144238432549, -0.016542359350911574], [3.6397242052516603, 0.05590157416851766, 3.7976325332676186], [3.6785357223885677, 1.8696881631736721, 5.6923719821366765], [5.556746717587128, 0.008536828960749188, 5.631374089317995], [5.582675167104445, 1.8835809079374604, 3.754222023149186], [3.645993437854674, 3.7031592029268756, -0.03855435278344386], [3.6092608939315145, 5.578267082713666, 1.8280449092602735], [5.594269383403506, 3.7098061022730966, 1.8856940882802502], [5.637965822810118, 5.548952975307969, -0.017723601383752525], [3.67413598874531, 3.686370766547991, 3.794166674224155], [3.625736297202185, 5.602353088582559, 5.68504075133503], [5.559995421283887, 3.7173900980063936, 5.622212588063477], [5.58551811349664, 5.583524538752662, 3.7782335646476275]], 'cell': [[7.365300830054032, -0.005528509379133711, 0.0027880865511100764], [-0.0056227719031778966, 7.466154059861727, 0.004759868442992488], [0.00285315496106562, 0.004780130449931503, 7.495839047727933]], 'pbc': [True, True, True]}, 'calculator_str': 'emt'}`
145.58000452590966The computed bulk modulus for the Cu-Au alloy with 73.8% Copper and 26.2% Gold is approximately 145.58 GPa, which is within the desired range of 145 GPa ± 2 GPa.
### Summary
- **Target Bulk Modulus:** 145 GPa
- **Computed Bulk Modulus:** 145.58 GPa
- **Concentration:** 73.8% Copper (Cu) and 26.2% Gold (Au)
The prediction has been validated successfully, and the computed bulk modulus falls within the specified uncertainty range.
> Finished chain.
Summary#
This example highlights the application of generative models for materials science. While the three previous examples could also be addressed by computing the material properties for all unaries, store them in a database and provide them to the user when requested, this is no longer possible for the space of binary or even ternary alloys. Just like a student the LLM is capable to apply an abstract concept of linear interpolation to the prediction of the concentration related to a bulk modulus of 145GPa.